NTA JEE Main 2004

NTA JEE Main 2004 - Question 1

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If $$\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$$, then the angle between $$A$$ and $$B$$ is

A

$$\pi$$

B

$$\pi/3$$

C

$$\pi/2$$

D

$$\pi/4$$

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NTA JEE Main 2004 - Question 2

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Which one of the following represents the correct dimensions of the coefficient of viscosity?

A

$$ML^{-1}T^{-2}$$

B

$$MLT^{-1}$$

C

$$ML^{-1}T^{-1}$$

D

$$ML^{-2}T^{-2}$$

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NTA JEE Main 2004 - Question 3

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A ball is released from the top of a tower of height $$h$$ metres. It takes $$T$$ seconds to reach the ground. What is the position of the ball in $$T/3$$ seconds?

A

$$h/9$$ metres from the ground

B

$$7h/9$$ metres from the ground

C

$$8h/9$$ metres from the ground

D

$$17h/18$$ metres from the ground

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NTA JEE Main 2004 - Question 4

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An automobile travelling with speed of $$60$$ km/h, can brake to stop within a distance of $$20$$ m. If the car is going twice as fast, i.e $$120$$ km/h, the stopping distance will be

A

$$20$$ m

B

$$40$$ m

C

$$60$$ m

D

$$80$$ m

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NTA JEE Main 2004 - Question 5

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A ball is thrown from a point with a speed $$v_0$$ at an angle of projection $$\theta$$. From the same point and at the same instant person starts running with a constant speed $$v_0/2$$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

A

yes, $$60^\circ$$

B

yes, $$30^\circ$$

C

no

D

yes, $$45^\circ$$

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NTA JEE Main 2004 - Question 6

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A projectile can have the same range $$R$$ for two angles of projection. If $$T_1$$ and $$T_2$$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

A

$$1/R^2$$

B

$$1/R$$

C

$$R$$

D

$$R^2$$

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NTA JEE Main 2004 - Question 7

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If $$t_1$$ and $$t_2$$ are the times of flight of two particles having the same initial velocity $$u$$ and range $$R$$ on the horizontal, then $$t_1^2 + t_2^2$$ is equal to

A

$$\frac{u^2}{g}$$

B

$$\frac{4u^2}{g^2}$$

C

$$\frac{u^2}{2g}$$

D

$$1$$

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NTA JEE Main 2004 - Question 8

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A machine gun fires a bullet of mass $$40$$ g with a velocity $$1200 \text{ ms}^{-1}$$. The man holding it can exert a maximum force of $$144$$ N on the gun. How many bullets can he fire per second at the most?

A

one

B

four

C

two

D

three

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NTA JEE Main 2004 - Question 9

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Two masses $$m_1 = 5$$ kg and $$m_2 = 4.8$$ kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move $$(g = 9.8 \text{ m/s}^2)$$?

A

$$0.2 \text{ m/s}^2$$

B

$$9.8 \text{ m/s}^2$$

C

$$5 \text{ m/s}^2$$

D

$$4.8 \text{ m/s}^2$$

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NTA JEE Main 2004 - Question 10

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A block rests on a rough inclined plane making an angle of $$30^\circ$$ with the horizontal. The coefficient of static friction between the block and the plane is $$0.8$$. If the frictional force on the block is $$10$$ N, the mass of the block (in kg) is (take $$g = 10 \text{ m/s}^2$$)

A

$$2.0$$

B

$$4.0$$

C

$$1.6$$

D

$$2.5$$

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NTA JEE Main 2004 - Question 11

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A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $$x$$ is proportional to

A

$$x^3$$

B

$$e^x$$

C

$$x$$

D

$$\log_e x$$

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NTA JEE Main 2004 - Question 12

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Which of the following statements is false for a particle moving in a circle with a constant angular speed?

A

The velocity vector is tangent to the circle.

B

The acceleration vector is tangent to the circle.

C

The acceleration vector points to the centre of the circle.

D

The velocity and acceleration vectors are perpendicular to each other.

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NTA JEE Main 2004 - Question 13

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A uniform chain of length $$2$$ m is kept on a table such that a length of $$60$$ cm hangs freely from the edge of the table. The total mass of the chain is $$4$$ kg. What is the work done in pulling the entire chain on the table?

A

$$7.2$$ J

B

$$3.6$$ J

C

$$120$$ J

D

$$1200$$ J

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NTA JEE Main 2004 - Question 14

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A force $$\vec{F} = (5\hat{i} + 3\hat{j} + 2\hat{k})N$$ is applied over a particle which displaces it from origin to the point $$\vec{r} = (2\hat{i} - \hat{j})$$ m. The work done on the particle in joules is

A

$$-7$$

B

$$+7$$

C

$$+10$$

D

$$+13$$

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NTA JEE Main 2004 - Question 15

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A body of mass $$m$$, accelerates uniformly from rest to $$v_1$$ in time $$t_1$$. The instantaneous power delivered to the body as a function of time $$t$$ is

A

$$\frac{mv_1 t}{t_1}$$

B

$$\frac{mv_1^2 t}{t_1^2}$$

C

$$\frac{mv_1 t^2}{t_1}$$

D

$$\frac{mv_1^2 t}{t_1}$$

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NTA JEE Main 2004 - Question 16

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A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

A

its velocity is constant

B

its acceleration is constant

C

its kinetic energy is constant

D

it moves in a straight line.

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NTA JEE Main 2004 - Question 17

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A wire fixed at the upper end stretches by length $$\ell$$ by applying a force $$F$$. The work done in stretching is

A

$$F/2\ell$$

B

$$F\ell$$

C

$$2F\ell$$

D

$$F\ell/2$$

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NTA JEE Main 2004 - Question 18

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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

A

moment of inertia

B

angular momentum

C

angular velocity

D

rotational kinetic energy

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NTA JEE Main 2004 - Question 19

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One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $$I_A$$ and $$I_B$$ such that

A

$$I_A = I_B$$

B

$$I_A > I_B$$

C

$$I_A < I_B$$

D

$$I_A/I_B = d_A/d_B$$ where $$d_A$$ and $$d_B$$ are their densities.

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NTA JEE Main 2004 - Question 20

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A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

A

$$gx$$

B

$$\frac{gR}{R-x}$$

C

$$\frac{g^2}{R+x}$$

D

$$\left(\frac{gR^2}{R+x}\right)^{1/2}$$

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NTA JEE Main 2004 - Question 21

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The time period of an earth satellite in circular orbit is independent of

A

the mass of the satellite

B

radius of its orbit

C

both the mass and radius of the orbit

D

neither the mass of the satellite nor the radius of its orbit

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NTA JEE Main 2004 - Question 22

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If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth is

A

$$2mgR$$

B

$$\frac{1}{2}mgR$$

C

$$\frac{1}{4}mgR$$

D

$$mgR$$

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NTA JEE Main 2004 - Question 23

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Suppose the gravitational force varies inversely as the $$n$$th power of distance. Then the time period planet in circular orbit of radius $$R$$ around the sun will be proportional to

A

$$R^{\left(\frac{n+1}{2}\right)}$$

B

$$R^{\left(\frac{n-1}{2}\right)}$$

C

$$R^n$$

D

$$R^{\left(\frac{n-2}{2}\right)}$$

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NTA JEE Main 2004 - Question 24

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Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta$$ with a velocity $$v$$. The retarding viscous force acting on the spherical ball is

A

directly proportional to $$R$$ but inversely proportional to $$v$$.

B

directly proportional to both radius $$R$$ and velocity $$v$$.

C

inversely proportional to both radius $$R$$ and velocity $$v$$.

D

inversely proportional to $$R$$ but directly proportional to velocity $$v$$.

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NTA JEE Main 2004 - Question 25

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If two soap bubbles of different radii are connected by a tube,

A

air flows from the bigger bubble to the smaller bubble till the sizes are interchanged.

B

air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C

air flows from the smaller bubble to the bigger.

D

there is no flow of air.

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NTA JEE Main 2004 - Question 26

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If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

A

$$4$$

B

$$16$$

C

$$32$$

D

$$64$$

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NTA JEE Main 2004 - Question 27

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The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$$ and thickness $$x$$ and $$4x$$, respectively are $$T_2$$ and $$T_1$$ $$(T_2 > T_1)$$. The rate of heat transfer through the slab, in a steady state is $$\left(\frac{A(T_2 - T_1)K}{x}\right)f$$, with $$f$$ equal to

A

$$1$$

B

$$1/2$$

C

$$2/3$$

D

$$1/3$$

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NTA JEE Main 2004 - Question 28

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The thermistors are usually made of

A

metals with low temperature coefficient of resistivity

B

metals with high temperature coefficient of resistivity

C

metal oxides with high temperature coefficient of resistivity

D

semiconducting materials having low temperature coefficient of resistivity.

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NTA JEE Main 2004 - Question 29

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Time taken by a $$836$$ W heater to heat one litre of water from $$10^\circ$$C to $$40^\circ$$C is

A

$$50$$ s

B

$$100$$ s

C

$$150$$ s

D

$$200$$ s

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NTA JEE Main 2004 - Question 30

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The thermo emf of a thermocouple varies with the temperature $$\theta$$ of the hot junction as $$E = a\theta + b\theta^2$$ in volts where the ratio $$a/b$$ is $$700^\circ$$C. If the cold junction is kept at $$0^\circ$$C, then the neutral temperature is

A

$$700^\circ$$C

B

$$350^\circ$$C

C

$$1400^\circ$$C

D

no neutral temperature is possible for this thermocouple.

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NTA JEE Main 2004 - Question 31

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Which of the following statements is correct for any thermodynamic system?

A

The internal energy changes in all processes.

B

Internal energy and entropy are state functions.

C

The change in entropy can never be zero.

D

The work done in an adiabatic process is always zero.

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NTA JEE Main 2004 - Question 32

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One mole of ideal monoatomic gas $$(\gamma = 5/3)$$ is mixed with one mole of diatomic gas $$(\gamma = 7/5)$$. What is $$\gamma$$ for the mixture? $$\gamma$$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

A

$$3/2$$

B

$$23/15$$

C

$$35/23$$

D

$$4/3$$

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NTA JEE Main 2004 - Question 33

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Two thermally insulated vessels 1 and 2 are filled with air at temperatures $$(T_1, T_2)$$, volume $$(V_1, V_2)$$ and pressure $$(P_1, P_2)$$ respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be

A

$$T_1 + T_2$$

B

$$(T_1 + T_2)/2$$

C

$$\frac{T_1 T_2 (P_1 V_1 + P_2 V_2)}{P_1 V_1 T_2 + P_2 V_2 T_1}$$

D

$$\frac{T_1 T_2 (P_1 V_1 + P_2 V_2)}{P_1 V_1 T_1 + P_2 V_2 T_2}$$

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NTA JEE Main 2004 - Question 34

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The bob of a simple pendulum executes simple harmonic motion in water with a period $$t$$, while the period of oscillation of the bob is $$t_0$$ in air. Neglecting frictional force of water and given that the density of the bob is $$\left(\frac{4}{3}\right) \times 1000 \text{ kg/m}^3$$. What relationship between $$t$$ and $$t_0$$ is true?

A

$$t = t_0$$

B

$$t = t_0/2$$

C

$$t = 2t_0$$

D

$$t = 4t_0$$

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NTA JEE Main 2004 - Question 35

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A particle at the end of a spring executes simple harmonic motion with a period $$t_1$$, while the corresponding period for another spring is $$t_2$$. If the period of oscillation with the two springs in series is $$t$$, then

A

$$T = t_1 + t_2$$

B

$$T^2 = t_1^2 + t_2^2$$

C

$$T^{-1} = t_1^{-1} + t_2^{-1}$$

D

$$T^{-2} = t_1^{-2} + t_2^{-2}$$

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NTA JEE Main 2004 - Question 36

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The total energy of particle, executing simple harmonic motion is

A

$$\propto x$$

B

$$\propto x^2$$

C

independent of $$x$$

D

$$\propto x^{1/2}$$

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NTA JEE Main 2004 - Question 37

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A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $$\omega_0$$. An external force $$F(t)$$ proportional to $$\cos\omega t$$ $$(\omega \neq \omega_0)$$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

A

$$\frac{m}{\omega_0^2 - \omega^2}$$

B

$$\frac{1}{m(\omega_0^2 - \omega^2)}$$

C

$$\frac{1}{m(\omega_0^2 + \omega^2)}$$

D

$$\frac{m}{\omega_0^2 + \omega^2}$$

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NTA JEE Main 2004 - Question 38

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In forced oscillation of a particle the amplitude is maximum for a frequency $$\omega_1$$ of the force, while the energy is maximum for a frequency $$\omega_2$$ of the force, then

A

$$\omega_1 = \omega_2$$

B

$$\omega_1 > \omega_2$$

C

$$\omega_1 < \omega_2$$ when damping is small and $$\omega_1 > \omega_2$$ when damping is large

D

$$\omega_1 < \omega_2$$

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NTA JEE Main 2004 - Question 39

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The displacement $$y$$ of a particle in a medium can be expressed as $$y = 10^{-6} \sin(110t + 20x + \pi/4)$$ m, where $$t$$ is in seconds and $$x$$ in meter. The speed of the wave is

A

$$2000$$ m/s

B

$$5$$ m/s

C

$$20$$ m/s

D

$$5\pi$$ m/s

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NTA JEE Main 2004 - Question 40

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Two spherical conductor $$B$$ and $$C$$ having equal radii and carrying equal charges in them repel each other with a force $$F$$ when kept apart at some distance. A third spherical conductor having same radius as that of $$B$$ but uncharged brought in contact with $$B$$, then brought in contact with $$C$$ and finally removed away from both. The new force of repulsion, between $$B$$ and $$C$$ is

A

$$F/4$$

B

$$3F/4$$

C

$$F/8$$

D

$$3F/8$$

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NTA JEE Main 2004 - Question 41

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A charged particle $$q$$ is shot towards another charged particle $$Q$$ which is fixed, with a speed $$v$$ it approaches $$Q$$ upto a closest distance $$r$$ and then returns. If $$q$$ were given a speed $$2v$$, the closest distances of approach would be

A

$$r$$

B

$$2r$$

C

$$r/2$$

D

$$r/4$$

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NTA JEE Main 2004 - Question 42

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Four charges equal to $$-Q$$ are placed at the four corners of a square and a charge $$q$$ is at its centre. If the system is in equilibrium the value of $$q$$ is

A

$$-\frac{Q}{4}(1 + 2\sqrt{2})$$

B

$$-\frac{Q}{2}(1 + 2\sqrt{2})$$

C

$$\frac{Q}{4}(1 + 2\sqrt{2})$$

D

$$\frac{Q}{2}(1 + 2\sqrt{2})$$

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NTA JEE Main 2004 - Question 43

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A charged oil drop is suspended in a uniform field of $$3 \times 10^4$$ V/m so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge $$= 9.9 \times 10^{-15}$$ kg and $$g = 10 \text{ m/s}^2$$)

A

$$3.3 \times 10^{-18}$$ C

B

$$3.2 \times 10^{-18}$$ C

C

$$1.6 \times 10^{-18}$$ C

D

$$4.8 \times 10^{-18}$$ C

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NTA JEE Main 2004 - Question 44

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An $$\alpha$$-particle of energy $$5$$ MeV is scattered through $$180^\circ$$ by a fixed uranium nucleus. The distance of the closest approach is of the order of

A

$$1$$ Å

B

$$10^{-10}$$ cm

C

$$10^{-12}$$ cm

D

$$10^{-15}$$ cm

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NTA JEE Main 2004 - Question 45

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The total current supplied to the circuit by the battery is

A

$$1$$ A

B

$$2$$ A

C

$$4$$ A

D

$$6$$ A

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NTA JEE Main 2004 - Question 46

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The resistance of the series combination of two resistances is $$S$$. When they are joined in parallel through total resistance is $$P$$. If $$S = nP$$, then the minimum possible value of $$n$$ is

A

$$4$$

B

$$3$$

C

$$2$$

D

$$1$$

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NTA JEE Main 2004 - Question 47

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An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of $$4/3$$ and $$2/3$$, then the ratio of the currents passing through the wire will be

A

$$3$$

B

$$1/3$$

C

$$8/9$$

D

$$2$$

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NTA JEE Main 2004 - Question 48

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In a metre bridge experiment null point is obtained at $$20$$ cm from one end of the wire when resistance $$X$$ is balanced against another resistance $$Y$$. If $$X < Y$$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $$4X$$ against $$Y$$?

A

$$50$$ cm

B

$$80$$ cm

C

$$40$$ cm

D

$$70$$ cm

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NTA JEE Main 2004 - Question 49

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The electrochemical equivalent of a metal is $$3.3 \times 10^{-7}$$ kg per coulomb. The mass of the metal liberated at the cathode when a $$3$$ A current is passed for $$2$$ seconds will be

A

$$19.8 \times 10^{-7}$$ kg

B

$$9.9 \times 10^{-7}$$ kg

C

$$6.6 \times 10^{-7}$$ kg

D

$$1.1 \times 10^{-7}$$ kg

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NTA JEE Main 2004 - Question 50

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A piece of copper and another of germanium are cooled from room temperature to $$77$$ K, the resistance of

A

each of them increases

B

each of them decreases

C

copper decreases and germanium increases

D

copper increases and germanium decreases

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NTA JEE Main 2004 - Question 51

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The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $$2$$ s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be

A

$$2$$ s

B

$$2/3$$ s

C

$$2\sqrt{3}$$ s

D

$$2/\sqrt{3}$$ s

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NTA JEE Main 2004 - Question 52

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The materials suitable for making electromagnets should have

A

high retentivity and high coercivity

B

low retentivity and low coercivity

C

high retentivity and low coercivity

D

low retentivity and high coercivity

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NTA JEE Main 2004 - Question 53

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A current $$I$$ ampere flows along an infinitely long straight thin-walled tube, then the magnetic induction at any point inside the tube is

A

infinite

B

zero

C

$$\frac{\mu_0}{4\pi} \cdot \frac{2I}{r}$$ tesla

D

$$2n^2 B$$

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NTA JEE Main 2004 - Question 54

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A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $$B$$. It is then bent into a circular loop of $$n$$ turns. The magnetic field at the centre of the coil will be

A

$$nB$$

B

$$n^2 B$$

C

$$2nB$$

D

$$2n^2 B$$

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NTA JEE Main 2004 - Question 55

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The magnetic field due to a current carrying circular loop of radius $$3$$ cm at a point on the axis at a distance of $$4$$ cm from the centre is $$54\mu$$T. What will be its value at the centre of the Loop?

A

$$250\mu$$T

B

$$150\mu$$T

C

$$125\mu$$T

D

$$75\mu$$T

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NTA JEE Main 2004 - Question 56

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Two long conductors, separated by a distance $$d$$ carry current $$I_1$$ and $$I_2$$ in the same direction. They exert a force $$F$$ on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to $$3d$$. The new value of the force between them is

A

$$-2F$$

B

$$F/3$$

C

$$-2F/3$$

D

$$-F/3$$

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NTA JEE Main 2004 - Question 57

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A coil having $$n$$ turns and resistance $$4R\Omega$$. This combination is moved in time $$t$$ seconds from a magnetic field $$W_1$$ weber to $$W_2$$ weber. The induced current in the circuit is

A

$$-\frac{W_2 - W_1}{5Rnt}$$

B

$$-\frac{n(W_2 - W_1)}{5Rt}$$

C

$$-\frac{W_2 - W_1}{Rnt}$$

D

$$-\frac{n(W_2 - W_1)}{Rt}$$

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NTA JEE Main 2004 - Question 58

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In a uniform magnetic field of induction $$B$$ a wire in the form of semicircle of radius $$r$$ rotates about the diameter of the circle with angular frequency $$\omega$$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $$R$$ the mean power generated per period of rotation is

A

$$\frac{B\pi r^2 \omega}{2R}$$

B

$$\frac{(B\pi r^2 \omega)^2}{2R}$$

C

$$\frac{(B\pi r \omega)^2}{2R}$$

D

$$\frac{(B\pi r \omega^2)^2}{8R}$$

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NTA JEE Main 2004 - Question 59

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A metal conductor of length $$1$$ m rotates vertically about one of its ends at angular velocity $$5$$ radians per second. If the horizontal component of earth's magnetic field is $$0.3 \times 10^{-4}$$ T, then the e.m.f. developed between the two ends of the conductor is

A

$$5 \times 10^{-9}$$ V

B

$$5 \times 10^{-5}$$ V

C

$$50\mu$$V

D

$$5\mu$$V

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NTA JEE Main 2004 - Question 60

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Alternating current can not be measured by D.C. ammeter because

A

A.C. cannot pass through D.C.

B

A.C. changes direction

C

average value of current for complete cycle is zero

D

D.C. ammeter will get damaged.

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NTA JEE Main 2004 - Question 61

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In an LCR series a.c. circuit, the voltage across each of the components, $$L, C$$ and $$R$$ is $$50$$ V. The voltage across the LC combination will be

A

$$50$$ V

B

$$50\sqrt{2}$$ V

C

$$100$$ V

D

$$0$$ V (zero)

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NTA JEE Main 2004 - Question 62

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In a LCR circuit capacitance is changed from $$C$$ to $$2C$$. For the resonant frequency to remain unchanged, the inductance should be changed from $$L$$ to

A

$$4L$$

B

$$2L$$

C

$$L/2$$

D

$$L/4$$

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NTA JEE Main 2004 - Question 63

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An electromagnetic wave of frequency $$v = 3.0$$ MHz passes from vacuum into a dielectric medium with permittivity $$\varepsilon = 4.0$$. Then

A

wavelength is doubled and the frequency remains unchanged

B

wavelength is doubled and frequency becomes half

C

wavelength is halved and frequency remains unchanged

D

wavelength and frequency both remain unchanged

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NTA JEE Main 2004 - Question 64

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A light ray is incident perpendicular to one face of a $$90^\circ$$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $$45^\circ$$, we conclude that the refractive index $$n$$

A

$$n < \frac{1}{2}$$

B

$$n > \sqrt{2}$$

C

$$n > \frac{1}{\sqrt{2}}$$

D

$$n < \sqrt{2}$$

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NTA JEE Main 2004 - Question 65

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A plane convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?

A

$$20$$ cm

B

$$30$$ cm

C

$$60$$ cm

D

$$80$$ cm

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NTA JEE Main 2004 - Question 66

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The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index $$n$$), is

A

$$\sin^{-1}(n)$$

B

$$\sin^{-1}(1/n)$$

C

$$\tan^{-1}(1/n)$$

D

$$\tan^{-1}(n)$$

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NTA JEE Main 2004 - Question 67

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The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment is

A

infinite

B

five

C

three

D

zero

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NTA JEE Main 2004 - Question 68

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A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

A

$$E/c$$

B

$$2E/c$$

C

$$Ec$$

D

$$E/c^2$$

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NTA JEE Main 2004 - Question 69

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According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal $$V_s$$ the frequency, of the incident radiation gives straight line whose slope

A

depends on the nature of the metal used

B

depends on the intensity of the radiation

C

depends both on the intensity of the radiation and the metal used

D

is the same for all metals and independent of the intensity of the radiation.

View Solution

NTA JEE Main 2004 - Question 70

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The work function of a substance is $$4.0$$ eV. Then longest wavelength of light that can cause photoelectron emission from this substance approximately

A

$$540$$ nm

B

$$400$$ nm

C

$$310$$ nm

D

$$220$$ nm

View Solution

NTA JEE Main 2004 - Question 71

Report

The manifestation of band structure in solids is due to

A

Heisenberg's uncertainty principle

B

Pauli's exclusion principle

C

Bohr's correspondence principle

D

Boltzmann's law

View Solution

NTA JEE Main 2004 - Question 72

Report

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $$2 : 1$$. The ratio of their nuclear sizes will be

A

$$2^{1/3} : 1$$

B

$$1 : 3^{1/2}$$

C

$$3^{1/2} : 1$$

D

$$1 : 2^{1/3}$$

View Solution

NTA JEE Main 2004 - Question 73

Report

The binding energy per nucleon of deuteron $$\binom{2}{1}H$$ and helium nucleus $$\binom{4}{2}He$$ is $$1.1$$ MeV and $$7$$ MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

A

$$13.9$$ MeV

B

$$26.9$$ MeV

C

$$23.6$$ MeV

D

$$19.2$$ MeV

View Solution

NTA JEE Main 2004 - Question 74

Report

When npn transistor is used as amplifier

A

electrons move from base to collector

B

holes move from emitter to base

C

electrons move from collector to base

D

holes move from base to emitter

View Solution

NTA JEE Main 2004 - Question 75

Report

For a transistor amplifier in common emitter configuration having load impedance of $$1$$ k$$\Omega$$ ($$h_{fe} = 50$$ and $$h_{oe} = 25$$) the current gain is

A

$$-5.2$$

B

$$-15.7$$

C

$$-24.8$$

D

$$-48.78$$

View Solution

NTA JEE Main 2004 - Question 76

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When p-n junction diode is forward biased

A

the depletion region is reduced and barrier height is increased

B

the depletion region is widened and barrier height is reduced

C

both the depletion region and barrier height reduced

D

both the depletion region and barrier height increased

View Solution

NTA JEE Main 2004 - Question 77

Report

$$6.02 \times 10^{20}$$ molecules of urea are present in $$100$$ mL of its solution. The concentration of urea solution is

A

$$0.001$$ M

B

$$0.1$$ M

C

$$0.02$$ M

D

$$0.01$$ M

View Solution

NTA JEE Main 2004 - Question 78

Report

To neutralize completely $$20$$ mL of $$0.1$$ M aqueous solution of phosphorous acid $$(H_3PO_3)$$, the volume of $$0.1$$ M aqueous KOH solution required is

A

$$10$$ mL

B

$$60$$ mL

C

$$40$$ mL

D

$$20$$ mL

View Solution

NTA JEE Main 2004 - Question 79

Report

Which of the following sets of quantum numbers is correct for an electron in $$4f$$ orbital?

A

$$n = 4, l = 3, m = +4, s = +\frac{1}{2}$$

B

$$n = 3, l = 2, m = -2, s = +\frac{1}{2}$$

C

$$n = 4, l = 3, m = +1, s = +\frac{1}{2}$$

D

$$n = 4, l = 4, m = -4, s = -\frac{1}{2}$$

View Solution

NTA JEE Main 2004 - Question 80

Report

Consider the ground state of Cr atom $$(Z = 24)$$. The number of electrons with the azimuthal quantum numbers $$l = 1$$ and $$2$$ are respectively

A

$$12$$ and $$4$$

B

$$16$$ and $$5$$

C

$$16$$ and $$4$$

D

$$12$$ and $$5$$

View Solution

NTA JEE Main 2004 - Question 81

Report

The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state $$1$$, would be (Rydberg constant $$= 1.097 \times 10^7$$ m$$^{-1}$$)

A

$$91$$ nm

B

$$9.1 \times 10^{-8}$$ nm

C

$$406$$ nm

D

$$192$$ nm

View Solution

NTA JEE Main 2004 - Question 82

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Which one the following sets of ions represents the collection of isoelectronic species?

A

$$K^+, Ca^{2+}, Sc^{3+}, Cl^-$$

B

$$Na^+, Mg^{2+}, Al^{3+}, Cl^-$$

C

$$K^+, Cl^-, Mg^{2+}, Sc^{3+}$$

D

$$Na^+, Ca^{2+}, Sc^{3+}, F^-$$

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NTA JEE Main 2004 - Question 83

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Which one the following ions has the highest value of ionic radius?

A

$$Li^+$$

B

$$F^-$$

C

$$O^{2-}$$

D

$$B^{3+}$$

View Solution Video Solution

NTA JEE Main 2004 - Question 84

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Consider the following nuclear reactions $$_{92}^{238}M \rightarrow {}_y^x N + {}_2^4 He$$; $$_y^N N \rightarrow {}_B^{A} L + 2\beta^+$$. The number of neutrons in the element $$L$$ is

A

$$142$$

B

$$146$$

C

$$140$$

D

$$144$$

View Solution

NTA JEE Main 2004 - Question 85

Report

The correct order of bond angles (smallest first) in $$H_2S, NH_3, BF_3$$ and $$SiH_4$$ is

A

$$H_2S < SiH_4 < NH_3 < BF_3$$

B

$$H_2S < NH_3 < BF_3 < SiH_4$$

C

$$H_2S < NH_3 < SiH_4 < BF_3$$

D

$$NH_3 < H_2S < SiH_4 < BF_3$$

View Solution

NTA JEE Main 2004 - Question 86

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The bond order in NO is $$2.5$$ while that in $$NO^+$$ is $$3$$. Which of the following statements is true for these two species?

A

Bond length in $$NO^+$$ is greater than in NO

B

Bond length is unpredictable

C

Bond length in $$NO^+$$ in equal to that in NO

D

Bond length in NO is greater than in $$NO^+$$

View Solution

NTA JEE Main 2004 - Question 87

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The states of hybridization of boron and oxygen atoms in boric acid $$(H_3BO_3)$$ are respectively

A

$$sp^2$$ and $$sp^2$$

B

$$sp^3$$ and $$sp^3$$

C

$$sp^3$$ and $$sp^2$$

D

$$sp^2$$ and $$sp^3$$

View Solution

NTA JEE Main 2004 - Question 88

Report

Which one of the following has the regular tetrahedral structure?

A

$$XeF_4$$

B

$$[Ni(CN)_4]^{2-}$$

C

$$BF_4^{-}$$

D

$$SF_4$$

View Solution

NTA JEE Main 2004 - Question 89

Report

The maximum number of $$90^\circ$$ angles between bond pair of electrons is observed in

A

$$dsp^3$$ hybridization

B

$$sp^3 d^2$$ hybridization

C

$$dsp^2$$ hybridization

D

$$sp^3 d$$ hybridization

View Solution

NTA JEE Main 2004 - Question 90

Report

Which one of the following aqueous solutions will exhibit highest boiling point?

A

$$0.01$$ M $$Na_2SO_4$$

B

$$0.015$$ M glucose

C

$$0.015$$ M urea

D

$$0.01$$ M $$KNO_3$$

View Solution

NTA JEE Main 2004 - Question 91

Report

Which one the following does not have $$sp^2$$ hybridized carbon?

A

Acetone

B

Acetamide

C

Acetonitrile

D

Acetic acid

View Solution

NTA JEE Main 2004 - Question 92

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As the temperature is raised from $$20^\circ$$C to $$40^\circ$$C, the average kinetic energy of neon atoms changes by a factor of which of the following?

A

$$1/2$$

B

$$2$$

C

$$\frac{313}{293}$$

D

$$\sqrt{\frac{313}{293}}$$

View Solution

NTA JEE Main 2004 - Question 93

Report

In Vander Waals equation of state of the gas law, the constant '$$b$$' is a measure of

A

intermolecular repulsions

B

intermolecular collisions per unit volume

C

Volume occupied by the molecules

D

intermolecular attraction

View Solution

NTA JEE Main 2004 - Question 94

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The formation of the oxide ion $$O^{2-}(g)$$ requires first an exothermic and then an endothermic step as shown below: $$O(g) + e^- \rightarrow O^-(g)$$, $$\Delta H^\circ = -142$$ kJ mol$$^{-1}$$; $$O^-(g) + e^- \rightarrow O^{2-}(g)$$, $$\Delta H^\circ = 844$$ kJ mol$$^{-1}$$. This is because

A

Oxygen is more electronegative

B

$$O^-$$ ion has comparatively larger size than oxygen atom

C

$$O^-$$ ion will tend to resist the addition of another electron

D

Oxygen has high electron affinity

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NTA JEE Main 2004 - Question 95

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An ideal gas expands in volume from $$1 \times 10^{-3}$$ m$$^3$$ to $$1 \times 10^{-2}$$ m$$^3$$ at $$300$$ K against a constant pressure of $$1 \times 10^5$$ N m$$^{-2}$$. The work done is

A

$$-900$$ J

B

$$900$$ kJ

C

$$2780$$ kJ

D

$$-900$$ kJ

View Solution

NTA JEE Main 2004 - Question 96

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The enthalpies of combustion of carbon and carbon monoxide are $$-393.5$$ and $$-283$$ kJ mol$$^{-1}$$ respectively. The enthalpy of formation of carbon monoxide per mole is

A

$$110.5$$ kJ

B

$$-110.5$$ kJ

C

$$-676.5$$ kJ

D

$$676.5$$ kJ

View Solution

NTA JEE Main 2004 - Question 97

Report

What is the equilibrium expression for the reaction $$P_{4(s)} + 5O_{2(g)} \rightleftharpoons P_4O_{10(s)}$$?

A

$$K_c = [P_4O_{10}]/[P_4][O_2]^5$$

B

$$K_c = 1/[O_2]^5$$

C

$$K_c = [O_2]^5$$

D

$$K_c = [P_4O_{10}]/5[P_4][O_2]$$

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NTA JEE Main 2004 - Question 98

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For the reaction, $$CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g)$$ the $$\frac{K_p}{K_c}$$ is equal to

A

$$\frac{1}{RT}$$

B

$$1.0$$

C

$$\sqrt{RT}$$

D

$$RT$$

View Solution Video Solution

NTA JEE Main 2004 - Question 99

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The equilibrium constant for the reaction $$N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$$ at temperature $$T$$ is $$4 \times 10^{-4}$$. The value of $$K_c$$ for the reaction $$NO(g) \rightleftharpoons \frac{1}{2}N_2(g) + \frac{1}{2}O_2(g)$$ at the same temperature is

A

$$2.5 \times 10^2$$

B

$$0.02$$

C

$$4 \times 10^{-4}$$

D

$$50$$

View Solution Video Solution

NTA JEE Main 2004 - Question 100

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Among $$Al_2O_3, SiO_2, P_2O_3$$ and $$SO_2$$ the correct order of acid strength is

A

$$SO_2 < P_2O_3 < SiO_2 < Al_2O_3$$

B

$$Al_2O_3 < SiO_2 < P_2O_3 < SO_2$$

C

$$Al_2O_3 < SiO_2 < SO_2 < P_2O_3$$

D

$$SiO_2 < SO_2 < Al_2O_3 < P_2O_3$$

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NTA JEE Main 2004 - Question 101

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The conjugate base of $$H_2PO_4^-$$ is

A

$$PO_4^{3-}$$

B

$$HPO_4^{2-}$$

C

$$H_3PO_4$$

D

$$P_2O_5$$

View Solution

NTA JEE Main 2004 - Question 102

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The molar solubility product is $$K_{sp}$$. '$$s$$' is given in terms of $$K_{sp}$$ by the relation

A

$$s = (K_{sp}/128)^{1/4}$$

B

$$s = (K_{sp}/256)^{1/5}$$

C

$$S = (256 K_{sp})^{1/5}$$

D

$$s = (128 K_{sp})^{1/4}$$

View Solution

NTA JEE Main 2004 - Question 103

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Excess of KI reacts with $$CuSO_4$$ solution and then $$Na_2S_2O_3$$ solution is added to it. Which of the statements is incorrect for this reaction?

A

$$Cu_2I_2$$ is reduced

B

Evolved $$I_2$$ is reduced

C

$$Na_2S_2O_3$$ is oxidized

D

$$CuI_2$$ is formed

View Solution

NTA JEE Main 2004 - Question 104

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Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by $$CN^-$$ ion towards metal species is

A

$$a, b, c$$

B

$$a, b$$

C

$$c, a$$

D

$$b, c$$

View Solution

NTA JEE Main 2004 - Question 105

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Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in

A

exhibiting maximum covalency in compound

B

exhibiting amphoteric nature in their oxides

C

forming covalent halides

D

forming polymeric hydrides

View Solution Video Solution

NTA JEE Main 2004 - Question 106

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Aluminium chloride exists as dimer, $$Al_2Cl_6$$ in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives

A

$$Al^{3+} + 3Cl^-$$

B

$$Al_2O_3 + 6HCl$$

C

$$[Al(OH)_6]^{3-}$$

D

$$[Al(H_2O)_6]^{3+} + 3Cl^-$$

View Solution Video Solution

NTA JEE Main 2004 - Question 107

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The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to

A

an interaction with nitrogen of the air at very low temperatures

B

an interaction with water vapour contained in the humid air

C

a change in the partial pressure of oxygen in the air

D

a change in the crystalline structure of tin

View Solution Video Solution

NTA JEE Main 2004 - Question 108

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For which of the following parameters the structural isomers $$C_2H_5OH$$ and $$CH_3OCH_3$$ would be expected to have the same values? (Assume ideal behaviour)

A

Heat of vaporization

B

Gaseous densities at the same temperature and pressure

C

Boiling points

D

Vapour pressure at the same temperature

View Solution

NTA JEE Main 2004 - Question 109

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The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is

A

$$Fe_4[Fe(CN)_6]_3$$

B

$$Na_4[Fe(CN)_5 NOS]$$

C

$$Fe(CN)_3$$

D

$$Na_3[Fe(CN)_6]$$

View Solution

NTA JEE Main 2004 - Question 110

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The ammonia evolved from the treatment of $$0.30$$ g of an organic compound for the estimation of nitrogen was passed in $$100$$ mL of $$0.1$$ M sulphuric acid. The excess of acid required $$20$$ mL of $$0.5$$ M sodium hydroxide solution for complete neutralization. The organic compound is

A

acetamide

B

thiourea

C

urea

D

benzamide

View Solution Video Solution

NTA JEE Main 2004 - Question 111

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The IUPAC name of the compound

A

3,3-dimethyl-1-hydroxy cyclohexane

B

1,1-dimethyl-3-cyclohexanol

C

3,3-dimethyl-1-cyclohexanol

D

1,1-dimethyl-3-hydroxy cyclohexane

View Solution Video Solution

NTA JEE Main 2004 - Question 112

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Which of the following will have meso-isomer also?

A

2-chlorobutane

B

2-hydroxypropanoic acid

C

2,3-dichloropentane

D

2,3-dichlorobutane

View Solution

NTA JEE Main 2004 - Question 113

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Rate of the reaction

is fastest when Z is

A

Cl

B

$$OCOCH_3$$

C

$$OC_2H_5$$

D

$$NH_2$$

View Solution

NTA JEE Main 2004 - Question 114

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Amongst the following compounds, the optically active alkane having lowest molecular mass is

A

B

C

D

View Solution

NTA JEE Main 2004 - Question 115

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Which of the following compound is not chiral?

A

1-chloropentane

B

3-chloro-2-methyl pentane

C

1-chloro-2-methyl pentane

D

2-chloropentane

View Solution

NTA JEE Main 2004 - Question 116

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Which one of the following has the minimum boiling point?

A

n-butane

B

isobutane

C

1-butene

D

1-butyne

View Solution

NTA JEE Main 2004 - Question 117

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The smog is essentially caused by the presence of

A

$$O_2$$ and $$O_3$$

B

$$O_3$$ and $$N_2$$

C

Oxides of sulphur and nitrogen

D

$$O_2$$ and $$N_2$$

View Solution

NTA JEE Main 2004 - Question 118

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What type of crystal defect is indicated in the diagram below? Na$$^+$$ Cl$$^-$$ Na$$^+$$ Cl$$^-$$ Na$$^+$$ Cl$$^-$$ Cl$$^-$$ $$\square$$ Cl$$^-$$ $$\square$$ Na$$^+$$ $$\square$$ Na$$^+$$ Na$$^+$$ Cl$$^-$$ $$\square$$ Cl$$^-$$ Na$$^+$$ Cl$$^-$$ Cl$$^-$$ Na$$^+$$ Cl$$^-$$ Na$$^+$$ $$\square$$ Na$$^+$$

A

Frenkel defect

B

Frenkel and Schottky defects

C

Interstitial defect

D

Schottky defect

View Solution

NTA JEE Main 2004 - Question 119

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Which of the following liquid pairs shows a positive deviation from Raoult's law?

A

Water - hydrochloric acid

B

Acetone - chloroform

C

Water - nitric acid

D

Benzene - methanol

View Solution

NTA JEE Main 2004 - Question 120

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In hydrogen-oxygen fuel cell, combustion of hydrogen occurs to

A

generate heat

B

remove adsorbed oxygen from electrode surfaces

C

produce high purity water

D

create potential difference between the two electrodes

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NTA JEE Main 2004 - Question 121

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Consider the following $$E^\circ$$ values: $$E^\circ_{Fe^{3+}/Fe^{2+}} = 0.77$$ V; $$E^\circ_{Sn^{2+}/Sn} = -0.14$$ V. Under standard conditions the potential for the reaction $$Sn(s) + 2Fe^{3+}(aq) \rightarrow 2Fe^{2+}(aq) + Sn^{2+}(aq)$$ is

A

$$1.68$$ V

B

$$0.63$$ V

C

$$0.91$$ V

D

$$1.40$$ V

View Solution Video Solution

NTA JEE Main 2004 - Question 122

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The standard e.m.f of a cell, involving one electron change is found to be $$0.591$$ V at $$25^\circ$$C. The equilibrium constant of the reaction is ($$F = 96{,}500$$ C mol$$^{-1}$$; $$R = 8.314$$ J K$$^{-1}$$ mol$$^{-1}$$)

A

$$1.0 \times 10^1$$

B

$$1.0 \times 10^{30}$$

C

$$1.0 \times 10^{10}$$

D

$$1.0 \times 10^5$$

View Solution Video Solution

NTA JEE Main 2004 - Question 123

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The limiting molar conductivities $$\Lambda^\circ$$ for NaCl, KBr and KCl are $$126, 152$$ and $$150$$ S cm$$^2$$ mol$$^{-1}$$ respectively. The $$\Lambda^\circ$$ for NaBr is

A

$$128$$ S cm$$^2$$ mol$$^{-1}$$

B

$$302$$ S cm$$^2$$ mol$$^{-1}$$

C

$$278$$ S cm$$^2$$ mol$$^{-1}$$

D

$$176$$ S cm$$^2$$ mol$$^{-1}$$

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NTA JEE Main 2004 - Question 124

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In a cell that utilises the reaction $$Zn(s) + 2H^+(aq) \rightarrow Zn^{2+}(aq) + H_2(g)$$ addition of $$H_2SO_4$$ to cathode compartment, will

A

lower the $$E$$ and shift equilibrium to the left

B

increases the $$E$$ and shift equilibrium to the left

C

increase the $$E$$ and shift equilibrium to the right

D

Lower the $$E$$ and shift equilibrium to the right

View Solution

NTA JEE Main 2004 - Question 125

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The $$E^\circ_{M^{3+}/M^{2+}}$$ values for Cr, Mn, Fe and Co are $$-0.41, +1.57, +0.77$$ and $$+1.97$$ V respectively. For which one of these metals the change in oxidation state form $$+2$$ to $$+3$$ is easiest?

A

Cr

B

Co

C

Fe

D

Mn

View Solution Video Solution

NTA JEE Main 2004 - Question 126

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In first order reaction, the concentration of the reactant decreases from $$0.8$$ M to $$0.4$$ M in $$15$$ minutes. The time taken for the concentration to change from $$0.1$$ M to $$0.025$$ M is

A

$$30$$ minutes

B

$$60$$ minutes

C

$$7.5$$ minutes

D

$$15$$ minutes

View Solution

NTA JEE Main 2004 - Question 127

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The rate equation for the reaction $$2A + B \rightarrow C$$ is found to be: rate $$= k[A][B]$$. The correct statement in relation to this reaction is that the

A

unit of $$k$$ must be s$$^{-1}$$

B

values of $$k$$ is independent of the initial concentration of $$A$$ and $$B$$

C

rate of formation of $$C$$ is twice the rate of disappearance of $$A$$

D

$$t_{1/2}$$ is a constant

View Solution

NTA JEE Main 2004 - Question 128

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The half-life of a radioisotope is four hours. If the initial mass of the isotope was $$200$$ g, the mass remaining after $$24$$ hours undecayed is

A

$$1.042$$ g

B

$$4.167$$ g

C

$$3.125$$ g

D

$$2.084$$ g

View Solution

NTA JEE Main 2004 - Question 129

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Which one of the following ores is best concentrated by froth-flotation method?

A

Magnetite

B

Malachite

C

Galena

D

Cassiterite

View Solution

NTA JEE Main 2004 - Question 130

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Which among the following factors is the most important in making fluorine the strongest oxidizing halogen?

A

Electron affinity

B

Bond dissociation energy

C

Hydration enthalpy

D

Ionization enthalpy

View Solution

NTA JEE Main 2004 - Question 131

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Which one the following statement regarding helium is incorrect?

A

It is used to fill gas balloons instead of hydrogen because it is lighter and non inflammable

B

It is used in gas-cooled nuclear reactors

C

It is used to produce and sustain powerful superconducting reagents

D

It is used as cryogenic agent for carrying out experiments at low temperatures

View Solution Video Solution

NTA JEE Main 2004 - Question 132

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One mole of magnesium nitride on the reaction with an excess of water gives

A

one mole of ammonia

B

two moles of nitric acid

C

two moles of ammonia

D

one mole of nitric acid

View Solution

NTA JEE Main 2004 - Question 133

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Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

A

$$(n-1)d^8 ns^2$$

B

$$(n-1)d^5 ns^2$$

C

$$(n-1)d^3 ns^2$$

D

$$(n-1)d^5 ns^1$$

View Solution Video Solution

NTA JEE Main 2004 - Question 134

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Cerium $$(Z = 58)$$ is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?

A

The common oxidation states of cerium are $$+3$$ and $$+4$$

B

Cerium (IV) acts as an oxidizing agent

C

The $$+4$$ oxidation state of cerium is not known in solutions

D

The $$+3$$ oxidation state of cerium is more stable than the $$+4$$ oxidation state

View Solution Video Solution

NTA JEE Main 2004 - Question 135

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The coordination number of central metal atom in a complex is determined by

A

the number of ligands around a metal ion bonded by sigma bonds

B

the number of only anionic ligands bonded to the metal ion

C

the number of ligands around a metal ion bonded by sigma and pi-bonds both

D

the number of ligands around a metal ion bonded by pi-bonds

View Solution

NTA JEE Main 2004 - Question 136

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Which one of the following complexes in an outer orbital complex?

A

$$[Fe(CN)_6]^{4-}$$

B

$$[Ni(NH_3)_6]^{2+}$$

C

$$[Co(NH_3)_6]^{3+}$$

D

$$[Mn(CN)_6]^{4-}$$

View Solution

NTA JEE Main 2004 - Question 137

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Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect?

A

Chlorophylls are green pigments in plants and contains calcium

B

Carboxypeptidase-A is an enzyme and contains zinc

C

Cyanocobalamin is $$B_{12}$$ and contains cobalt

D

Haemoglobin is the red pigment of blood and contains iron

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NTA JEE Main 2004 - Question 138

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Which one the following has largest number of isomers?

A

$$[Ru(NH_3)_4 Cl_2]^+$$

B

$$[Co(en)_2 Cl_2]^+$$

C

$$[Ir(PR_3)_2 H(CO)]^{2+}$$

D

$$[Co(NH_3)_5 Cl]^{2+}$$ (R = alkyl group, en = ethylenediamine)

View Solution

NTA JEE Main 2004 - Question 139

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The correct order of magnetic moments (spin only values in B.M.) among is (Atomic numbers: Mn = 25, Fe = 26, Co = 27)

A

$$[MnCl_4]^{2-} > [CoCl_4]^{2-} > [Fe(CN)_6]^{4-}$$

B

$$[Fe(CN)_6]^{4-} > [CoCl_4]^{2-} > [MnCl_4]^{2-}$$

C

$$[Fe(CN)_6]^{4-} > [MnCl_4]^{2-} > [CoCl_4]^{2-}$$

D

$$[MnCl_4]^{2-} > [Fe(CN)_6]^{4-} > [CoCl_4]^{2-}$$

View Solution

NTA JEE Main 2004 - Question 140

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The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is

A

gammexene

B

hexachloroethane

C

Freon

D

DDT

View Solution

NTA JEE Main 2004 - Question 141

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Acetyl bromide reacts with excess of $$CH_3MgI$$ followed by treatment with a saturated solution of $$NH_4Cl$$ given

A

acetone

B

acetyl iodide

C

2-methyl-2-propanol

D

acetamide

View Solution

NTA JEE Main 2004 - Question 142

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Among the following compound which can be dehydrated very easily is

A

Pentan-1-ol

B

2-pentanol

C

2-butanol

D

2-heptanol

View Solution

NTA JEE Main 2004 - Question 143

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Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?

A

Ethyl acetate

B

Butan-2-one

C

Acetamide

D

Acetic acid

View Solution

NTA JEE Main 2004 - Question 144

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Consider the acidity of the carboxylic acids:

A

PhCOOH

B

$$o-NO_2 C_6 H_4 COOH$$

C

$$p-NO_2 C_6 H_4 COOH$$

D

$$m-NO_2 C_6 H_4 COOH$$

View Solution

NTA JEE Main 2004 - Question 145

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On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is

A

$$CH_3 COOC_2 H_5 + NaCl$$

B

$$CH_3 Cl + C_2 H_5 COONa$$

C

$$CH_3 COCl + C_2 H_5 OH + NaOH$$

D

$$CH_3 COONa + C_2 H_5 OH$$

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NTA JEE Main 2004 - Question 146

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Which of the following undergoes reaction with $$50\%$$ sodium hydroxide solution to give the corresponding alcohol and acid?

A

Phenol

B

Benzoic acid

C

Butanal

D

Benzaldehyde

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NTA JEE Main 2004 - Question 147

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Which of the following is the strongest base?

A

<smiles>Nc1ccccc1</smiles>

B

<smiles>NCc1ccccc1</smiles>

C

<smiles>Cc1ccccc1N</smiles>

D

<smiles>CNc1ccccc1</smiles>

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NTA JEE Main 2004 - Question 148

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Identify the correct statements regarding enzymes

A

Enzymes are specific biological catalysts that can normally function at very high temperature $$(T \sim 1000$$ K)

B

Enzymes are specific biological catalysts that posses well-defined active sites

C

Enzymes are specific biological catalysts that can not be poisoned

D

Enzymes are normally heterogeneous catalysts that are very specific in their action

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NTA JEE Main 2004 - Question 149

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Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?

A

A co-enzyme

B

An antibiotic

C

An enzyme

D

A hormone

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NTA JEE Main 2004 - Question 150

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Which one of the following statements is false?

A

Raoult's law states that the vapour pressure of a components over a solution is proportional to its mole fraction

B

Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression

C

The correct order of osmotic pressure for $$0.01$$ M aqueous solution of each compound is $$BaCl_2 > KCl > CH_3 COOH > $$ sucrose

D

The osmotic pressure $$(\pi) = MRT$$, where $$M$$ is the molarity of the solution

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NTA JEE Main 2004 - Question 151

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Which base is present in RNA but not in DNA?

A

Uracil

B

Thymine

C

Guanine

D

Cytosine

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NTA JEE Main 2004 - Question 152

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Let two numbers have arithmetic mean $$9$$ and geometric mean $$4$$. Then these numbers are the roots of the quadratic equation

A

$$x^2 + 18x + 16 = 0$$

B

$$x^2 - 18x - 16 = 0$$

C

$$x^2 + 18x - 16 = 0$$

D

$$x^2 - 18x + 16 = 0$$

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NTA JEE Main 2004 - Question 153

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If $$(1 - p)$$ is a root of quadratic equation $$x^2 + px + (1 - p) = 0$$, then its roots are

A

$$0, 1$$

B

$$-1, 2$$

C

$$0, -1$$

D

$$-1, 1$$

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NTA JEE Main 2004 - Question 154

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If one root of the equation $$x^2 + px + 12 = 0$$ is $$4$$, while the equation $$x^2 + px + q = 0$$ has equal roots, then the value of '$$q$$' is

A

$$\frac{49}{4}$$

B

$$4$$

C

$$3$$

D

$$12$$

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NTA JEE Main 2004 - Question 155

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Let $$z, w$$ be complex numbers such that $$\bar{z} + i\bar{w} = 0$$ and $$\arg zw = \pi$$. Then $$\arg z$$ equals

A

$$\frac{\pi}{4}$$

B

$$\frac{5\pi}{4}$$

C

$$\frac{3\pi}{4}$$

D

$$\frac{\pi}{2}$$

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NTA JEE Main 2004 - Question 156

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If $$z = x - iy$$ and $$z^{1/3} = p + iq$$, then $$\frac{\left(\frac{x}{p} + \frac{y}{q}\right)}{(p^2 + q^2)}$$ is equal to

A

$$1$$

B

$$-2$$

C

$$2$$

D

$$-1$$

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NTA JEE Main 2004 - Question 157

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If $$|z^2 - 1| = |z|^2 + 1$$, then $$z$$ lies on

A

the real axis

B

an ellipse

C

a circle

D

the imaginary axis

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NTA JEE Main 2004 - Question 158

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How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

A

$$120$$

B

$$480$$

C

$$360$$

D

$$240$$

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NTA JEE Main 2004 - Question 159

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The number of ways of distributing $$8$$ identical balls in $$3$$ distinct boxes so that none of the boxes is empty is

A

$$5$$

B

$${}^8 C_3$$

C

$$3^8$$

D

$$21$$

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NTA JEE Main 2004 - Question 160

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Let $$T_r$$ be the $$r$$th term of an A.P. whose first term is $$a$$ and common difference is $$d$$. If for some positive integers $$m, n, m \neq n, T_m = \frac{1}{n}$$ and $$T_n = \frac{1}{m}$$, then $$a - d$$ equals

A

$$0$$

B

$$1$$

C

$$\frac{1}{mn}$$

D

$$\frac{1}{m} + \frac{1}{n}$$

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NTA JEE Main 2004 - Question 161

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The sum of the first $$n$$ terms of the series $$1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \ldots$$ is $$\frac{n(n+1)^2}{2}$$ when $$n$$ is even. When $$n$$ is odd the sum is

A

$$\frac{3n(n+1)}{2}$$

B

$$\frac{n^2(n+1)}{2}$$

C

$$\frac{n(n+1)^2}{4}$$

D

$$\left[\frac{n(n+1)}{2}\right]^2$$

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NTA JEE Main 2004 - Question 162

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The sum of series $$\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \ldots$$ is

A

$$\frac{(e^2 - 1)}{2}$$

B

$$\frac{(e-1)^2}{2e}$$

C

$$\frac{(e^2 - 1)}{2e}$$

D

$$\frac{(e^2 - 2)}{e}$$

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NTA JEE Main 2004 - Question 163

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If $$u = \sqrt{a^2 \cos^2 \theta + b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta + b^2 \cos^2 \theta}$$, then the difference between the maximum and minimum values of $$u^2$$ is given by

A

$$2(a^2 + b^2)$$

B

$$2\sqrt{a^2 + b^2}$$

C

$$(a + b)^2$$

D

$$(a - b)^2$$

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NTA JEE Main 2004 - Question 164

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Let $$S(K) = 1 + 3 + 5 + \ldots + (2K - 1) = 3 + K^2$$. Then which of the following is true?

A

$$S(1)$$ is correct

B

Principle of mathematical induction can be used to prove the formula

C

$$S(K) \neq S(K + 1)$$

D

$$S(K) \Rightarrow S(K + 1)$$

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NTA JEE Main 2004 - Question 165

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The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $$(1 + \alpha x)^4$$ and of $$(1 - \alpha x)^6$$ is the same if $$\alpha$$ equals

A

$$-\frac{5}{3}$$

B

$$\frac{3}{5}$$

C

$$\frac{-3}{10}$$

D

$$\frac{10}{3}$$

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NTA JEE Main 2004 - Question 166

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The coefficient of $$x^n$$ in expansion of $$(1 + x)(1 - x)^n$$ is

A

$$(n - 1)$$

B

$$(-1)^n (1 - n)$$

C

$$(-1)^{n-1}(n - 1)^2$$

D

$$(-1)^{n-1} n$$

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NTA JEE Main 2004 - Question 167

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If $$S_n = \sum_{r=0}^n \frac{1}{{}^n C_r}$$ and $$t_n = \sum_{r=0}^n \frac{r}{{}^n C_r}$$, then $$\frac{t_n}{S_n}$$ is equal to

A

$$\frac{1}{2}n$$

B

$$\frac{1}{2}n - 1$$

C

$$n - 1$$

D

$$\frac{2n - 1}{2}$$

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NTA JEE Main 2004 - Question 168

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Let $$\alpha, \beta$$ be such that $$\pi < \alpha - \beta < 3\pi$$. If $$\sin\alpha + \sin\beta = -\frac{21}{65}$$ and $$\cos\alpha + \cos\beta = -\frac{27}{65}$$, then the value of $$\cos\frac{\alpha - \beta}{2}$$ is

A

$$-\frac{3}{\sqrt{130}}$$

B

$$\frac{3}{\sqrt{130}}$$

C

$$\frac{6}{65}$$

D

$$-\frac{6}{65}$$

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NTA JEE Main 2004 - Question 169

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Let $$A(2, -3)$$ and $$B(-2, 1)$$ be vertices of a triangle $$ABC$$. If the centroid of this triangle moves on the line $$2x + 3y = 1$$, then the locus of the vertex $$C$$ is the line

A

$$2x + 3y = 9$$

B

$$2x - 3y = 7$$

C

$$3x + 2y = 5$$

D

$$3x - 2y = 3$$

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NTA JEE Main 2004 - Question 170

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The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes whose sum is $$-1$$ is

A

$$\frac{x}{2} + \frac{y}{3} = -1$$ and $$\frac{x}{-2} + \frac{y}{1} = -1$$

B

$$\frac{x}{2} - \frac{y}{3} = -1$$ and $$\frac{x}{-2} + \frac{y}{1} = -1$$

C

$$\frac{x}{2} + \frac{y}{3} = 1$$ and $$\frac{x}{-2} + \frac{y}{1} = 1$$

D

$$\frac{x}{2} - \frac{y}{3} = 1$$ and $$\frac{x}{-2} + \frac{y}{1} = 1$$

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NTA JEE Main 2004 - Question 171

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If one of the lines given by $$6x^2 - xy + 4cy^2 = 0$$ is $$3x + 4y = 0$$, then $$c$$ equals

A

$$1$$

B

$$-1$$

C

$$3$$

D

$$-3$$

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NTA JEE Main 2004 - Question 172

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A line makes the same angle $$\theta$$, with each of the $$x$$ and $$z$$ axis. If the angle $$\beta$$, which it makes with $$y$$-axis, is such that $$\sin^2 \beta = 3 \sin^2 \theta$$, then $$\cos^2 \theta$$ equals

A

$$\frac{2}{3}$$

B

$$\frac{1}{5}$$

C

$$\frac{3}{5}$$

D

$$\frac{2}{5}$$

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NTA JEE Main 2004 - Question 173

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If a circle passes through the point $$(a, b)$$ and cuts the circle $$x^2 + y^2 = 4$$ orthogonally, then the locus of its centre is

A

$$2ax + 2by + (a^2 + b^2 + 4) = 0$$

B

$$2ax + 2by - (a^2 + b^2 + 4) = 0$$

C

$$2ax - 2by + (a^2 + b^2 + 4) = 0$$

D

$$2ax - 2by - (a^2 + b^2 + 4) = 0$$

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NTA JEE Main 2004 - Question 174

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If the lines $$2x + 3y + 1 = 0$$ and $$3x - y - 4 = 0$$ lie along diameters of a circle of circumference $$10\pi$$, then the equation of the circle is

A

$$x^2 + y^2 - 2x + 2y - 23 = 0$$

B

$$x^2 + y^2 - 2x - 2y - 23 = 0$$

C

$$x^2 + y^2 + 2x + 2y - 23 = 0$$

D

$$x^2 + y^2 + 2x - 2y - 23 = 0$$

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NTA JEE Main 2004 - Question 175

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The intercept on the line $$y = x$$ by the circle $$x^2 + y^2 - 2x = 0$$ is $$AB$$. Equation of the circle on $$AB$$ as a diameter is

A

$$x^2 + y^2 - x - y = 0$$

B

$$x^2 + y^2 - x + y = 0$$

C

$$x^2 + y^2 + x + y = 0$$

D

$$x^2 + y^2 + x - y = 0$$

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NTA JEE Main 2004 - Question 176

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A variable circle passes through the fixed point $$A(p, q)$$ and touches $$x$$-axis. The locus of the other end of the diameter through $$A$$ is

A

$$(x - p)^2 = 4qy$$

B

$$(x - q)^2 = 4py$$

C

$$(y - p)^2 = 4qx$$

D

$$(y - q)^2 = 4px$$

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NTA JEE Main 2004 - Question 177

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If $$a \neq 0$$ and the line $$2bx + 3cy + 4d = 0$$ passes through the points of intersection of the parabolas $$y^2 = 4ax$$ and $$x^2 = 4ay$$, then

A

$$d^2 + (2b + 3c)^2 = 0$$

B

$$d^2 + (3b + 2c)^2 = 0$$

C

$$d^2 + (2b - 3c)^2 = 0$$

D

$$d^2 + (3b - 2c)^2 = 0$$

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NTA JEE Main 2004 - Question 178

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The eccentricity of an ellipse, with its centre at the origin, is $$\frac{1}{2}$$. If one of the directrices is $$x = 4$$, then the equation of the ellipse is

A

$$3x^2 + 4y^2 = 1$$

B

$$3x^2 + 4y^2 = 12$$

C

$$4x^2 + 3y^2 = 12$$

D

$$4x^2 + 3y^2 = 1$$

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NTA JEE Main 2004 - Question 179

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If $$\lim_{x \to \infty}\left(1 + \frac{a}{x} + \frac{b}{x^2}\right)^{2x} = e^2$$, then the values of $$a$$ and $$b$$, are

A

$$a \in R, b \in R$$

B

$$a = 1, b \in R$$

C

$$a \in R, b = 2$$

D

$$a = 1$$ and $$b = 2$$

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NTA JEE Main 2004 - Question 180

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Let $$f(x) = \frac{1 - \tan x}{4x - \pi}, x \neq \frac{\pi}{4}, x \in \left[0, \frac{\pi}{2}\right]$$. If $$f(x)$$ is continuous in $$\left[0, \frac{\pi}{2}\right]$$, then $$f\left(\frac{\pi}{4}\right)$$ is

A

$$1$$

B

$$\frac{1}{2}$$

C

$$-\frac{1}{2}$$

D

$$-1$$

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NTA JEE Main 2004 - Question 181

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$$\lim_{n \to \infty} \sum_{r=1}^n \frac{1}{n} e^{r/n}$$ is

A

$$e$$

B

$$e - 1$$

C

$$1 - e$$

D

$$e + 1$$

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NTA JEE Main 2004 - Question 182

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Consider the following statements: 

(a) Mode can be computed from histogram.

(b) Median is not independent of change of scale.

(c) Variance is independent of change of origin and scale.

A

only (a)

B

only (b)

C

only (a) and (b)

D

(a), (b) and (c)

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NTA JEE Main 2004 - Question 183

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In a series of $$2n$$ observations, half of them equal $$a$$ and remaining half equal $$-a$$. If the standard deviation of the observations is $$2$$, then $$|a|$$ equals

A

$$\frac{1}{n}$$

B

$$\sqrt{2}$$

C

$$2$$

D

$$\frac{\sqrt{2}}{n}$$

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NTA JEE Main 2004 - Question 184

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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $$60^\circ$$ and when he retires $$40$$ meter away from the tree the angle of elevation becomes $$30^\circ$$. The breadth of the river is

A

$$20$$ m

B

$$30$$ m

C

$$40$$ m

D

$$60$$ m

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NTA JEE Main 2004 - Question 185

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A particle moves towards east from a point $$A$$ to a point $$B$$ at the rate of $$4$$ km/h and then towards north from $$B$$ to $$C$$ at the rate of $$5$$ km/h. If $$AB = 12$$ km and $$BC = 5$$ km, then its average speed for its journey from $$A$$ to $$C$$ and resultant average velocity direct from $$A$$ to $$C$$ are respectively

A

$$\frac{17}{4}$$ km/h and $$\frac{13}{4}$$ km/h

B

$$\frac{13}{4}$$ km/h and $$\frac{17}{4}$$ km/h

C

$$\frac{17}{9}$$ km/h and $$\frac{13}{9}$$ km/h

D

$$\frac{13}{9}$$ km/h and $$\frac{17}{9}$$ km/h

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NTA JEE Main 2004 - Question 186

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The sides of a triangle are $$\sin\alpha, \cos\alpha$$ and $$\sqrt{1 + \sin\alpha \cos\alpha}$$ for some $$0 < \alpha < \frac{\pi}{2}$$. Then the greatest angle of the triangle is

A

$$60^\circ$$

B

$$90^\circ$$

C

$$120^\circ$$

D

$$150^\circ$$

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NTA JEE Main 2004 - Question 187

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Let $$R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$$ be a relation on the set $$A = \{1, 2, 3, 4\}$$. The relation $$R$$ is

A

a function

B

reflexive

C

not symmetric

D

transitive

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NTA JEE Main 2004 - Question 188

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Let $$A = \begin{pmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{pmatrix}$$. The only correct statement about the matrix $$A$$ is

A

$$A$$ is a zero matrix

B

$$A^2 = I$$

C

$$A^{-1}$$ does not exist

D

$$A = (-1)I$$, where $$I$$ is a unit matrix

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NTA JEE Main 2004 - Question 189

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Let $$A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}$$ and $$10 B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix}$$. If $$B$$ is the inverse of matrix $$A$$, then $$\alpha$$ is

A

$$-2$$

B

$$5$$

C

$$2$$

D

$$-1$$

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NTA JEE Main 2004 - Question 190

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If $$a_1, a_2, a_3, \ldots, a_n, \ldots$$ are in G.P., then the value of the determinant $$\begin{vmatrix} \log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8} \end{vmatrix}$$ is

A

$$0$$

B

$$-2$$

C

$$2$$

D

$$1$$

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NTA JEE Main 2004 - Question 191

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The range of the function $$f(x) = {}^{7-x} P_{x-3}$$ is

A

$$\{1, 2, 3\}$$

B

$$\{1, 2, 3, 4, 5\}$$

C

$$\{1, 2, 3, 4\}$$

D

$$\{1, 2, 3, 4, 5, 6\}$$

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NTA JEE Main 2004 - Question 192

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If $$f: R \to S$$, defined by $$f(x) = \sin x - \sqrt{3}\cos x + 1$$, is onto, then the interval of $$S$$ is

A

$$[0, 3]$$

B

$$[-1, 1]$$

C

$$[0, 1]$$

D

$$[-1, 3]$$

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NTA JEE Main 2004 - Question 193

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The graph of the function $$y = f(x)$$ is symmetrical about the line $$x = 2$$, then

A

$$f(x + 2) = f(x - 2)$$

B

$$f(2 + x) = f(2 - x)$$

C

$$f(x) = f(-x)$$

D

$$f(x) = -f(-x)$$

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NTA JEE Main 2004 - Question 194

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The domain of the function $$f(x) = \frac{\sin^{-1}(x - 3)}{\sqrt{9 - x^2}}$$ is

A

$$[2, 3]$$

B

$$[2, 3)$$

C

$$[1, 2]$$

D

$$[1, 2)$$

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NTA JEE Main 2004 - Question 195

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If $$x = e^{y + e^{y + \ldots \infty}}, x > 0$$, then $$\frac{dy}{dx}$$ is

A

$$\frac{x}{1 + x}$$

B

$$\frac{1}{x}$$

C

$$\frac{1 - x}{x}$$

D

$$\frac{1 + x}{x}$$

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NTA JEE Main 2004 - Question 196

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A point on the parabola $$y^2 = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

A

$$(2, 4)$$

B

$$(2, -4)$$

C

$$\left(\frac{-9}{8}, \frac{9}{2}\right)$$

D

$$\left(\frac{9}{8}, \frac{9}{2}\right)$$

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NTA JEE Main 2004 - Question 197

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A function $$y = f(x)$$ has a second order derivative $$f''(x) = 6(x - 1)$$. If its graph passes through the point $$(2, 1)$$ and at that point the tangent to the graph is $$y = 3x - 5$$, then the function is

A

$$(x - 1)^2$$

B

$$(x - 1)^3$$

C

$$(x + 1)^3$$

D

$$(x + 1)^2$$

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NTA JEE Main 2004 - Question 198

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The normal to the curve $$x = a(1 + \cos\theta), y = a\sin\theta$$ at '$$\theta$$' always passes through the fixed point

A

$$(a, 0)$$

B

$$(0, a)$$

C

$$(0, 0)$$

D

$$(a, a)$$

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NTA JEE Main 2004 - Question 199

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If $$2a + 3b + 6c = 0$$, then at least one root of the equation $$ax^2 + bx + c = 0$$ lies in the interval

A

$$(0, 1)$$

B

$$(1, 2)$$

C

$$(2, 3)$$

D

$$(1, 3)$$

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NTA JEE Main 2004 - Question 200

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If the sum of the slopes of the lines given by $$x^2 - 2cxy - 7y^2 = 0$$ is four times their product, then $$c$$ has the value

A

$$1$$

B

$$-1$$

C

$$2$$

D

$$-2$$

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NTA JEE Main 2004 - Question 201

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If $$\int \frac{\sin x}{\sin(x - \alpha)} dx = Ax + B \log \sin(x - \alpha) + C$$, then value of $$(A, B)$$ is

A

$$(\sin\alpha, \cos\alpha)$$

B

$$(\cos\alpha, \sin\alpha)$$

C

$$(-\sin\alpha, \cos\alpha)$$

D

$$(-\cos\alpha, \sin\alpha)$$

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NTA JEE Main 2004 - Question 202

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$$\int \frac{dx}{\cos x - \sin x}$$ is equal to

A

$$\frac{1}{\sqrt{2}} \log \left|\tan\left(\frac{x}{2} - \frac{\pi}{8}\right)\right| + C$$

B

$$\frac{1}{\sqrt{2}} \log \left|\cot\left(\frac{x}{2}\right)\right| + C$$

C

$$\frac{1}{\sqrt{2}} \log \left|\tan\left(\frac{x}{2} - \frac{3\pi}{8}\right)\right| + C$$

D

$$\frac{1}{\sqrt{2}} \log \left|\tan\left(\frac{x}{2} + \frac{3\pi}{8}\right)\right| + C$$

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NTA JEE Main 2004 - Question 203

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The value of $$\int_{-2}^3 |1 - x^2| dx$$ is

A

$$\frac{28}{3}$$

B

$$\frac{14}{3}$$

C

$$\frac{7}{3}$$

D

$$\frac{1}{3}$$

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NTA JEE Main 2004 - Question 204

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The value of $$I = \int_0^{\pi/2} \frac{(\sin x + \cos x)^2}{\sqrt{1 + \sin 2x}} dx$$ is

A

$$0$$

B

$$1$$

C

$$2$$

D

$$3$$

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NTA JEE Main 2004 - Question 205

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If $$\int_0^\pi x f(\sin x) dx = A \int_0^{\pi/2} f(\sin x) dx$$, then $$A$$ is

A

$$0$$

B

$$\pi$$

C

$$\frac{\pi}{4}$$

D

$$2\pi$$

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NTA JEE Main 2004 - Question 206

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If $$f(x) = \frac{e^x}{1 + e^x}$$, $$I_1 = \int_{f(-a)}^{f(a)} xg\{x(1 - x)\} dx$$ and $$I_2 = \int_{f(-a)}^{f(a)} g\{x(1 - x)\} dx$$, then the value of $$\frac{I_2}{I_1}$$ is

A

$$2$$

B

$$-3$$

C

$$-1$$

D

$$1$$

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NTA JEE Main 2004 - Question 207

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The area of the region bounded by the curves $$y = |x - 2|, x = 1, x = 3$$ and the $$x$$-axis is

A

$$1$$

B

$$2$$

C

$$3$$

D

$$4$$

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NTA JEE Main 2004 - Question 208

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The differential equation for the family of curves $$x^2 + y^2 - 2ay = 0$$, where $$a$$ is an arbitrary constant is

A

$$2(x^2 - y^2)y' = xy$$

B

$$2(x^2 + y^2)y' = xy$$

C

$$(x^2 - y^2)y' = 2xy$$

D

$$(x^2 + y^2)y' = 2xy$$

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NTA JEE Main 2004 - Question 209

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The solution of the differential equation $$y \, dx + (x + x^2 y) dy = 0$$ is

A

$$-\frac{1}{xy} = C$$

B

$$-\frac{1}{xy} + \log y = C$$

C

$$\frac{1}{xy} + \log y = C$$

D

$$\log y = Cx$$

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NTA JEE Main 2004 - Question 210

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If the straight lines $$x = 1 + s, y = -3 - \lambda s, z = 1 + \lambda s$$ and $$x = \frac{t}{2}, y = 1 + t, z = 2 - t$$ with parameters $$s$$ and $$t$$ respectively, are co-planar then $$\lambda$$ equals

A

$$-2$$

B

$$-1$$

C

$$-\frac{1}{2}$$

D

$$0$$

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NTA JEE Main 2004 - Question 211

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Let $$\vec{a}, \vec{b}$$ and $$\vec{c}$$ be three non-zero vectors such that no two of these are collinear. If the vector $$\vec{a} + 2\vec{b}$$ is collinear with $$\vec{c}$$ and $$\vec{b} + 3\vec{c}$$ is collinear with $$\vec{a}$$ ($$\lambda$$ being some non-zero scalar) then $$\vec{a} + 2\vec{b} + 6\vec{c}$$ equals

A

$$\lambda \vec{a}$$

B

$$\lambda \vec{b}$$

C

$$\lambda \vec{c}$$

D

$$\vec{0}$$

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NTA JEE Main 2004 - Question 212

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A particle is acted upon by constant forces $$4\hat{i} + \hat{j} - 3\hat{k}$$ and $$3\hat{i} + \hat{j} - \hat{k}$$ which displace it from a point $$\hat{i} + 2\hat{j} + 3\hat{k}$$ to the point $$5\hat{i} + 4\hat{j} + \hat{k}$$. The work done in standard units by the forces is given by

A

$$40$$

B

$$30$$

C

$$25$$

D

$$15$$

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NTA JEE Main 2004 - Question 213

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If $$\vec{a}, \vec{b}, \vec{c}$$ are non-coplanar vectors and $$\lambda$$ is a real number, then the vectors $$\vec{a} + 2\vec{b} + 3\vec{c}, \lambda \vec{b} + 4\vec{c}$$ and $$(2\lambda - 1)\vec{c}$$ are non-coplanar for

A

all values of $$\lambda$$

B

all except one value of $$\lambda$$

C

all except two values of $$\lambda$$

D

no value of $$\lambda$$

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NTA JEE Main 2004 - Question 214

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Let $$\vec{a}, \vec{b}$$ and $$\vec{c}$$ be non-zero vectors such that $$(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$$. If $$\theta$$ is the acute angle between the vectors $$\vec{b}$$ and $$\vec{c}$$, then $$\sin\theta$$ equals

A

$$\frac{1}{3}$$

B

$$\frac{\sqrt{2}}{3}$$

C

$$\frac{2}{3}$$

D

$$\frac{2\sqrt{2}}{3}$$

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NTA JEE Main 2004 - Question 215

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With two forces acting at a point, the maximum effect is obtained when their resultant is $$4$$ N. If they act at right angles, then their resultant is $$3$$ N. Then the forces are

A

$$(2 + \sqrt{2})$$ N and $$(2 - \sqrt{2})$$ N

B

$$(2 + \sqrt{3})$$ N and $$(2 - \sqrt{3})$$ N

C

$$\left(2 + \frac{1}{2}\sqrt{2}\right)$$ N and $$\left(2 - \frac{1}{2}\sqrt{2}\right)$$ N

D

$$\left(2 + \frac{1}{2}\sqrt{3}\right)$$ N and $$\left(2 - \frac{1}{2}\sqrt{3}\right)$$ N

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NTA JEE Main 2004 - Question 216

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In a right angle $$\triangle ABC, \angle A = 90^\circ$$ and sides $$a, b, c$$ are respectively, $$5$$ cm, $$4$$ cm and $$3$$ cm. If a force $$\vec{F}$$ has moments $$0, 9$$ and $$16$$ in N cm. units respectively about vertices $$A, B$$ and $$C$$, then magnitude of $$\vec{F}$$ is

A

$$3$$

B

$$4$$

C

$$5$$

D

$$9$$

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NTA JEE Main 2004 - Question 217

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Three forces $$\vec{P}, \vec{Q}$$ and $$\vec{R}$$ acting along $$IA, IB$$ and $$IC$$, where $$I$$ is the incentre of a $$\triangle ABC$$, are in equilibrium. Then $$\vec{P} : \vec{Q} : \vec{R}$$ is

A

$$\cos\frac{A}{2} : \cos\frac{B}{2} : \cos\frac{C}{2}$$

B

$$\sin\frac{A}{2} : \sin\frac{B}{2} : \sin\frac{C}{2}$$

C

$$\sec\frac{A}{2} : \sec\frac{B}{2} : \sec\frac{C}{2}$$

D

$$\csc\frac{A}{2} : \csc\frac{B}{2} : \csc\frac{C}{2}$$

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NTA JEE Main 2004 - Question 218

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A velocity $$\frac{1}{4}$$ m/s is resolved into two components along $$OA$$ and $$OB$$ making angles $$30^\circ$$ and $$45^\circ$$ respectively with the given velocity. Then the component along $$OB$$ is

A

$$\frac{1}{8}$$ m/s

B

$$\frac{1}{4}(\sqrt{3} - 1)$$ m/s

C

$$\frac{1}{4}$$ m/s

D

$$\frac{1}{8}(\sqrt{6} - \sqrt{2})$$ m/s

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NTA JEE Main 2004 - Question 219

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Distance between two parallel planes $$2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is

A

$$\frac{3}{2}$$

B

$$\frac{5}{2}$$

C

$$\frac{7}{2}$$

D

$$\frac{9}{2}$$

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NTA JEE Main 2004 - Question 220

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A line with direction cosines proportional to $$2, 1, 2$$ meets each of the lines $$x = y + a = z$$ and $$x + a = 2y = 2z$$. The co-ordinates of each of the point of intersection are given by

A

$$(3a, 3a, 3a), (a, a, a)$$

B

$$(3a, 2a, 3a), (a, a, a)$$

C

$$(3a, 2a, 3a), (a, a, 2a)$$

D

$$(2a, 3a, 3a), (2a, a, a)$$

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NTA JEE Main 2004 - Question 221

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The intersection of the spheres $$x^2 + y^2 + z^2 + 7x - 2y - z = 13$$ and $$x^2 + y^2 + z^2 - 3x + 3y + 4z = 8$$ is the same as the intersection of one of the sphere and the plane

A

$$x - y - z = 1$$

B

$$x - 2y - z = 1$$

C

$$x - y - 2z = 1$$

D

$$2x - y - z = 1$$

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NTA JEE Main 2004 - Question 222

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Let $$\vec{u}, \vec{v}, \vec{w}$$ be such that $$|\vec{u}| = 1, |\vec{v}| = 2, |\vec{w}| = 3$$. If the projection $$\vec{v}$$ along $$\vec{u}$$ is equal to that of $$\vec{w}$$ along $$\vec{u}$$ and $$\vec{v}, \vec{w}$$ are perpendicular to each other then $$|\vec{u} - \vec{v} + \vec{w}|$$ equals

A

$$2$$

B

$$\sqrt{7}$$

C

$$\sqrt{14}$$

D

$$14$$

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NTA JEE Main 2004 - Question 223

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The probability that $$A$$ speaks truth is $$\frac{4}{5}$$, while this probability for $$B$$ is $$\frac{3}{4}$$. The probability that they contradict each other when asked to speak on a fact is

A

$$\frac{3}{20}$$

B

$$\frac{1}{5}$$

C

$$\frac{7}{20}$$

D

$$\frac{4}{5}$$

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NTA JEE Main 2004 - Question 224

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A random variable $$X$$ has the probability distribution: $$X: 1, 2, 3, 4, 5, 6, 7, 8$$; $$p(X): 0.15, 0.23, 0.12, 0.10, 0.20, 0.08, 0.07, 0.05$$. For the events $$E = \{X$$ is a prime number$$\}$$ and $$F = \{X < 4\}$$, the probability $$P(E \cup F)$$ is

A

$$0.87$$

B

$$0.77$$

C

$$0.35$$

D

$$0.50$$

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NTA JEE Main 2004 - Question 225

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The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ successes is

A

$$\frac{37}{256}$$

B

$$\frac{219}{256}$$

C

$$\frac{128}{256}$$

D

$$\frac{28}{256}$$

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