NTA JEE Main 8th April 2019 Shift 2

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NTA JEE Main 8th April 2019 Shift 2 - Question 2

In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of the pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to:

NTA JEE Main 8th April 2019 Shift 2 - Question 3

If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

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NTA JEE Main 8th April 2019 Shift 2 - Question 4

A particle starts from origin O from rest and moves with a uniform acceleration along the positive $$x$$-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

NTA JEE Main 8th April 2019 Shift 2 - Question 5

A uniform rectangular thin sheet $$ABCD$$ of mass $$M$$ has length $$a$$ and breadth $$b$$, as shown in the figure. If the shaded portion $$HBGO$$ is cut-off, the coordinates of the centre of mass of the remaining portion will be:

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NTA JEE Main 8th April 2019 Shift 2 - Question 6

A body of mass $$m_1$$ moving with an unknown velocity of $$v_1 \hat{i}$$, undergoes a collinear collision with a body of mass $$m_2$$ moving with a velocity $$v_2 \hat{i}$$. After the collision, $$m_1$$ and $$m_2$$ move with velocities of $$v_3 \hat{i}$$ and $$v_4 \hat{i}$$, respectively. If $$m_2 = 0.5 m_1$$ and $$v_3 = 0.5 v_1$$, then $$v_1$$ is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 7

A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m. When released, it slips off the table in a very short time $$\tau = 0.01$$ s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

NTA JEE Main 8th April 2019 Shift 2 - Question 8

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $$h_{sph}$$ and $$h_{cyl}$$ on the incline. The ratio $$\frac{h_{sph}}{h_{cyl}}$$ is given by:

NTA JEE Main 8th April 2019 Shift 2 - Question 9

A rocket has to be launched from earth in such a way that it never returns. If $$E$$ is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon.

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NTA JEE Main 8th April 2019 Shift 2 - Question 10

Young's moduli of two wires A and B are in the ratio 7:4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, the value of R is close to:

NTA JEE Main 8th April 2019 Shift 2 - Question 12

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to:
[Boltzmann Constant $$k_B = 1.38 \times 10^{-23}$$ J/K, Avogadro number $$N_A = 6.02 \times 10^{26}$$/kg, Radius of Earth: $$6.4 \times 10^{6}$$ m, Gravitational acceleration on Earth = 10 ms$$^{-2}$$]

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NTA JEE Main 8th April 2019 Shift 2 - Question 13

A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to $$\frac{1}{1000}$$ of the original amplitude is close to:

NTA JEE Main 8th April 2019 Shift 2 - Question 14

A positive point charge is released from rest at a distance $$r_0$$ from a positive line charge with uniform charge density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to:

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NTA JEE Main 8th April 2019 Shift 2 - Question 15

An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $$\omega$$ is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 16

The electric field in a region is given by $$\vec{E} = (Ax + B)\hat{i}$$, where E is in NC$$^{-1}$$ and $$x$$ is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at $$x = 1$$ is $$V_1$$ and that at $$x = -5$$ is $$V_2$$, then $$V_1 - V_2$$ is:

NTA JEE Main 8th April 2019 Shift 2 - Question 18

In the circuit shown, a four-wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r = 0.01 $$\Omega$$/cm. If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be:

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NTA JEE Main 8th April 2019 Shift 2 - Question 20

In the figure shown, what is the current (in Ampere) drawn from the battery? You are given: $$R_1 = 15 \; \Omega$$, $$R_2 = 10 \; \Omega$$, $$R_3 = 20 \; \Omega$$, $$R_4 = 5 \; \Omega$$, $$R_5 = 25 \; \Omega$$, $$R_6 = 30 \; \Omega$$, $$E = 15$$ V

NTA JEE Main 8th April 2019 Shift 2 - Question 21

Two very long, straight, and insulated wires are kept at 90° angle from each other in xy-plane as shown in figure. These wires carry currents of equal magnitude I, whose direction are shown in the figure. The net magnetic field at point P will be:

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NTA JEE Main 8th April 2019 Shift 2 - Question 22

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing through their mid-point P, at angle $$\theta = 45°$$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimension of the dipole)

NTA JEE Main 8th April 2019 Shift 2 - Question 23

A circuit connected to an ac source of emf $$e = e_0 \sin(100t)$$ with t in seconds, gives a phase difference of $$\frac{\pi}{4}$$ between the emf $$e$$ and current $$i$$. Which of the following circuits will exhibit this?

NTA JEE Main 8th April 2019 Shift 2 - Question 24

The magnetic field of an electromagnetic wave is given by:
$$\vec{B} = 1.6 \times 10^{-6} \cos(2 \times 10^{7}z + 6 \times 10^{15}t)(2\hat{i} + \hat{j}) \frac{Wb}{m^2}$$
The associated electric field will be:

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NTA JEE Main 8th April 2019 Shift 2 - Question 25

Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star.

NTA JEE Main 8th April 2019 Shift 2 - Question 26

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be:

NTA JEE Main 8th April 2019 Shift 2 - Question 27

A nucleus A, with a finite de-broglie wavelength $$\lambda_A$$, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths $$\lambda_B$$ and $$\lambda_C$$ of B and C are respectively:

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NTA JEE Main 8th April 2019 Shift 2 - Question 29

A common emitter amplifier circuit, built using an NPN transistor, is shown in the figure. Its dc current gain is 250, $$R_C = 1$$ k$$\Omega$$ and $$V_{CC} = 10$$ V. The minimum base current for $$V_{CE}$$ to reach saturation is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 30

In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be: (Radius of the Earth = $$6.4 \times 10^{6}$$ m)

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NTA JEE Main 8th April 2019 Shift 2 - Question 32

0.27 g of a long chain fatty acid was dissolved in 100 cm$$^3$$ of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer?
[Density of fatty acid = 0.9 g cm$$^{-3}$$; $$\pi = 3$$]

NTA JEE Main 8th April 2019 Shift 2 - Question 33

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $$\lambda$$, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be: (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

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NTA JEE Main 8th April 2019 Shift 2 - Question 36

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If $$C_V = 28$$ J K$$^{-1}$$, calculate $$\Delta U$$ and $$\Delta pV$$ for the process. (R = 8.0 J K$$^{-1}$$ mol$$^{-1}$$)

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NTA JEE Main 8th April 2019 Shift 2 - Question 37

For the following reaction, equilibrium constants are given:
$$S(s) + O_2(g) \rightleftharpoons SO_2(g); \quad K_1 = 10^{52}$$
$$2S(s) + 3O_2(g) \rightleftharpoons 2SO_3(g); \quad K_2 = 10^{129}$$
The equilibrium constant for the reaction, $$2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$$ is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 40

Which of the following compounds will show the maximum 'enol' content?

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NTA JEE Main 8th April 2019 Shift 2 - Question 44

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

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NTA JEE Main 8th April 2019 Shift 2 - Question 46

Calculate the standard cell potential (in V) of the cell in which the following reaction takes place:
Fe$$^{2+}$$(aq) + Ag$$^+$$(aq) $$\rightarrow$$ Fe$$^{3+}$$(aq) + Ag(s)
Given that $$E^{0}_{Ag^+/Ag} = x$$ V, $$E^{0}_{Fe^{2+}/Fe} = y$$ V, $$E^{0}_{Fe^{3+}/Fe} = z$$ V

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NTA JEE Main 8th April 2019 Shift 2 - Question 50

The correct statement about ICl$$_5$$ and ICl$$_4^{-}$$ is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 61

If three distinct numbers $$a$$, $$b$$, $$c$$ are in G.P. and the equations $$ax^{2} + 2bx + c = 0$$ and $$dx^{2} + 2ex + f = 0$$ have a common root, then which one of the following statements is correct?

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NTA JEE Main 8th April 2019 Shift 2 - Question 67

Suppose that the points $$(h, k)$$, $$(1, 2)$$ and $$(-3, 4)$$ lie on the line $$L_1$$. If a line $$L_2$$ passing through the points $$h, k$$ and $$(4, 3)$$ is perpendicular to $$L_1$$, then $$\frac{k}{h}$$ equals:

NTA JEE Main 8th April 2019 Shift 2 - Question 68

The tangent and the normal lines at the point $$(\sqrt{3}, 1)$$ to the circle $$x^{2} + y^{2} = 4$$ and the x-axis form a triangle. The area of this triangle (in square units) is:

NTA JEE Main 8th April 2019 Shift 2 - Question 69

The tangent to the parabola $$y^{2} = 4x$$ at the point where it intersects the circle $$x^{2} + y^{2} = 5$$ in the first quadrant, passes through the point:

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NTA JEE Main 8th April 2019 Shift 2 - Question 72

Let $$f: R \rightarrow R$$ be a differentiable function satisfying $$f'(3) + f'(2) = 0$$. Then $$\lim_{x \to 0} \frac{1 + f(3 + x) - f(3)}{1 + f(2 - x) - f(2)}^{\frac{1}{x}}$$ is equal to:

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NTA JEE Main 8th April 2019 Shift 2 - Question 74

A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

NTA JEE Main 8th April 2019 Shift 2 - Question 75

Two vertical poles of height, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 77

Let the numbers 2, b, c be in an A.P. and $$A = \begin{pmatrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^{2} & c^{2} \end{pmatrix}$$. If $$\det(A) \in [2, 16]$$, then $$c$$ lies in the interval:

NTA JEE Main 8th April 2019 Shift 2 - Question 78

If the system of linear equations
$$x - 2y + kz = 1$$
$$2x + y + z = 2$$
$$3x - y - kz = 3$$
has a solution $$(x, y, z), z \neq 0$$, then $$(x, y)$$ lies on the straight line whose equation is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 79

Let $$f(x) = a^x$$ ($$a > 0$$) be written as $$f(x) = f_1(x) + f_2(x)$$, where $$f_1(x)$$ is an even function and $$f_2(x)$$ is an odd function. Then $$f_1(x + y) + f_1(x - y)$$ equals:

NTA JEE Main 8th April 2019 Shift 2 - Question 80

Let $$f: [-1, 3] \rightarrow R$$ be defined as
$$f(x) = \begin{cases} x + x, & -1 \le x < 1 \\ x + x, & 1 \le x < 2 \\ x + x, & 2 \le x \le 3 \end{cases}$$
where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at:

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NTA JEE Main 8th April 2019 Shift 2 - Question 83

Given that the slope of the tangent to a curve $$y = y(x)$$ at any point $$(x, y)$$ is $$\frac{2y}{x^{2}}$$. If the curve passes through the centre of the circle $$x^{2} + y^{2} - 2x - 2y = 0$$, then its equation is:

NTA JEE Main 8th April 2019 Shift 2 - Question 84

If $$\int \frac{dx}{x^3(1 + x^6)^{2/3}} = xf(x)(1 + x^6)^{1/3} + C$$, where C is a constant of integration, then the function $$f(x)$$ is equal to:

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NTA JEE Main 8th April 2019 Shift 2 - Question 85

Let $$f(x) = \int_0^x g(t) \, dt$$, where $$g$$ is a non-zero even function. If $$f(x + 5) = g(x)$$, then $$\int_0^x f(t) \, dt$$ equals:

NTA JEE Main 8th April 2019 Shift 2 - Question 86

Let $$S(\alpha) = \{(x, y): y^{2} \le x, 0 \le x \le \alpha\}$$ and $$A(\alpha)$$ is area of the region $$S(\alpha)$$. If for a $$\lambda$$, $$0 < \lambda < 4$$, $$A(\lambda):A(4) = 2:5$$, then $$\lambda$$ equals:

NTA JEE Main 8th April 2019 Shift 2 - Question 87

Let $$\vec{a} = 3\hat{i} + 2\hat{j} + x\hat{k}$$ and $$\vec{b} = \hat{i} - \hat{j} + \hat{k}$$, for some real $$x$$. Then the condition for $$\vec{a} \times \vec{b} = r$$ to follow is:

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NTA JEE Main 8th April 2019 Shift 2 - Question 88

The vector equation of the plane through the line of intersection of the planes $$x + y + z = 1$$ and $$2x + 3y + 4z = 5$$ which is perpendicular to the plane $$x - y + z = 0$$ is:

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