NTA JEE Main 9th January 2019 Shift 1

NTA JEE Main 9th January 2019 Shift 1 - Question 1

Report

A particle is moving with a velocity $$\vec{v} = K(y\hat{i} + x\hat{j})$$, where $$K$$ is a constant. The general equation for its path is:

A

$$y^2 = x$$ + constant

B

$$xy$$ = constant

C

$$y = x^2$$ + constant

D

$$y^2 = x^2$$ + constant

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 2

Report

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:

A

2.5%

B

1.0%

C

2.0%

D

0.5%

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 3

Report

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take $$g = 10 \; ms^{-2}$$)

A

23 N

B

25 N

C

18 N

D

32 N

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 4

Report

A block of mass $$m$$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $$k$$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $$F$$, the maximum speed of the block is:

A

$$\frac{F}{\sqrt{mk}}$$

B

$$\frac{2F}{\sqrt{mk}}$$

C

$$\frac{\pi F}{\sqrt{mk}}$$

D

$$\frac{F}{\pi\sqrt{mk}}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 5

Report

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, $$m$$ while C has mass $$M$$. Block A is given an initial speed $$v$$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically. $$\frac{5}{6}$$th of the initial kinetic energy is lost in the whole process. What is the value of $$M/m$$?

A

3

B

4

C

5

D

2

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 6

Report

Two masses $$m$$ and $$\frac{m}{2}$$ are connected at the two ends of a massless rigid rod of length $$l$$. The rod is suspended by a thin wire of torsional constant $$k$$ at the centre of mass of the rod-mass system (see figure). Because of torsional constant $$k$$, the restoring torque is $$\tau = k\theta$$ for angular displacement $$\theta$$. If the rod is rotated by $$\theta_0$$ and released, the tension in it when it passes through its mean position will be:

A

$$k\theta_0^2$$

B

$$\frac{3k\theta_0^2}{l}$$

C

$$\frac{2k\theta_0^2}{l}$$

D

$$\frac{k\theta_0^2}{l}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 7

Report

An $$L$$-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If $$AB = BC$$, and the angle made by $$AB$$ with downward vertical is $$\theta$$, then:

A

$$\tan\theta = \frac{2}{\sqrt{3}}$$

B

$$\tan\theta = \frac{1}{3}$$

C

$$\tan\theta = \frac{1}{2}$$

D

$$\tan\theta = \frac{1}{2\sqrt{3}}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 8

Report

If the angular momentum of a planet of mass $$m$$, moving around the Sun in a circular orbit is $$L$$, about the center of the Sun, its areal velocity is:

A

$$\frac{L}{m}$$

B

$$\frac{4L}{m}$$

C

$$\frac{L}{2m}$$

D

$$\frac{2L}{m}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 9

Report

A heavy ball of mass $$M$$ is suspended from the ceiling of a car by a light string of mass $$m$$ ($$m \ll M$$). When the car is at rest, the speed of transverse waves in the string is 60 ms$$^{-1}$$. When the car has acceleration $$a$$, the wave-speed increases to 60.5 ms$$^{-1}$$. The value of $$a$$, in terms of gravitational acceleration $$g$$, is closest to:

A

$$\frac{g}{10}$$

B

$$\frac{g}{20}$$

C

$$\frac{g}{5}$$

D

$$\frac{g}{30}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 10

Report

A rod, of length $$L$$ at room temperature and uniform area of cross section $$A$$, is made of a metal having coefficient of linear expansion $$\alpha$$ /$$^{\circ}$$C. It is observed that an external compressive force $$F$$ is applied on each of its ends, prevents any change in the length of the rod when its temperature rises by $$\Delta T$$ K. Young's modulus, $$Y$$ for this metal is:

A

$$\frac{F}{A\alpha \Delta T - 273}$$

B

$$\frac{2F}{A\alpha \Delta T}$$

C

$$\frac{F}{A\alpha \Delta T}$$

D

$$\frac{F}{2A\alpha \Delta T}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 11

Report

Temperature difference of 120$$^{\circ}$$C is maintained between two ends of a uniform rod $$AB$$ of length $$2L$$. Another bent rod $$PQ$$, of same cross-section as $$AB$$ and length $$\frac{3L}{2}$$, is connected across $$AB$$ (See figure). In steady state, temperature difference between $$P$$ and $$Q$$ will be close to:

A

45$$^{\circ}$$C

B

35$$^{\circ}$$C

C

60$$^{\circ}$$C

D

75$$^{\circ}$$C

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 12

Report

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If the path ADB is used then work done by the system is 10 J, the heat flows into the system in the path ADB is:

A

100 J

B

20 J

C

40 J

D

80 J

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 13

Report

A mixture of 2 moles of helium gas (atomic mass = 4u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\frac{v_{rms}(helium)}{v_{rms}(argon)}$$, is close to:

A

0.45

B

2.24

C

0.32

D

3.16

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 14

Report

Three charges $$+Q$$, $$q$$, $$+Q$$ are placed respectively, at distance, $$0$$, $$d/2$$ and $$d$$ from the origin, on the $$x$$-axis. If the net force experienced by $$+Q$$, placed at $$x = 0$$, is zero, then value of $$q$$ is:

A

$$+Q/2$$

B

$$+Q/4$$

C

$$-Q/4$$

D

$$-Q/2$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 15

Report

For a uniformly charged ring of radius $$R$$, the electric field on its axis has the largest magnitude at a distance $$h$$ from its centre. Then value of $$h$$ is:

A

$$\frac{R}{\sqrt{2}}$$

B

$$\frac{R}{\sqrt{5}}$$

C

$$R\sqrt{2}$$

D

$$R$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 16

Report

A parallel plate capacitor is made of two square plates of side $$a$$, separated by a distance $$d$$ ($$d \ll a$$). The lower triangular portion filled with a dielectric of dielectric constant $$K$$, as shown in the figure. Capacitance of this capacitor is:

A

$$\frac{K\varepsilon_0 a^2}{d(K+1)} \ln K$$

B

$$\frac{K\varepsilon_0 a^2}{d(K-1)} \ln K$$

C

$$\frac{K\varepsilon_0 a^2}{d} \ln K$$

D

$$\frac{1}{2} \frac{K\varepsilon_0 a^2}{d}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 17

Report

When the switch $$S$$, in the circuit shown, is closed, then the value of current $$i$$ will be:

A

2 A

B

5 A

C

3 A

D

4 A

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 18

Report

Drift speed of electrons, when 1.5 A current flows in a copper wire of cross section 5 mm$$^2$$ is $$v_d$$. If the electron density in copper is $$9 \times 10^{28}$$ m$$^{-3}$$, the value of $$v_d$$ in mm s$$^{-1}$$ is close to (Take charge of an electron to be $$= 1.6 \times 10^{-19}$$ C)

A

0.2

B

3

C

2

D

0.02

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 19

Report

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an N-type semiconductor, the density of electrons is $$10^{19}$$ m$$^{-3}$$ and their mobility is 1.6 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$, then the resistivity of the semiconductor (since it is an N-type semiconductor contribution of holes is ignored) is close to:

A

0.2 $$\Omega$$ m

B

4 $$\Omega$$ m

C

2 $$\Omega$$ m

D

0.4 $$\Omega$$ m

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 20

Report

A resistance is shown in the figure. Its value and tolerance are given respectively by:

A

27 k$$\Omega$$, 10%

B

270 $$\Omega$$, 5%

C

270 $$\Omega$$, 10%

D

27 k$$\Omega$$, 20%

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 21

Report

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is:

A

285 A/m

B

2600 A/m

C

520 A/m

D

1200 A/m

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 22

Report

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

A

$$1.5 \times 10^{-7}$$ T

B

$$1.0 \times 10^{-7}$$ T

C

$$1.5 \times 10^{-5}$$ T

D

$$1.0 \times 10^{-5}$$ T

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 23

Report

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is $$a$$ and distance of its centre from the wire is $$d$$ ($$d \gg a$$). If the loop applies a force $$F$$ on the wire then:

A

$$F \propto \frac{a^2}{d^2}$$

B

$$F = 0$$

C

$$F \propto \frac{a^2}{d^3}$$

D

$$F \propto \frac{a}{d}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 24

Report

A conducting circular loop made of a thin wire has area $$3.5 \times 10^{-2}$$ m$$^2$$ and resistance 10 $$\Omega$$. It is placed perpendicular to a time-dependent magnetic field $$B(t) = 0.4 \; T \sin 50\pi t$$. The field is uniform in space. Then the net charge flowing through the loop during $$t = 0$$ s and $$t = 10$$ ms is close to:

A

1.4 mC

B

7 mC

C

21 mC

D

6 mC

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 25

Report

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive $$x$$-direction. At a particular point in space and time, $$\vec{E} = 6.3 \hat{j}$$ V/m. The corresponding magnetic field $$\vec{B}$$, at that point will be:

A

$$2.1 \times 10^{-8} \hat{k}$$ T

B

$$18.9 \times 10^{8} \hat{k}$$ T

C

$$18.9 \times 10^{-8} \hat{k}$$ T

D

$$6.3 \times 10^{-8} \hat{k}$$ T

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 26

Report

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in between the light source and the lens. To get the sharp image again, the screen is shifted by a distance $$d$$. Then $$d$$ is:

A

0

B

0.55 cm away from the lens

C

0.55 cm towards the lens

D

1.1 cm away from the lens

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 27

Report

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

A

25 : 9

B

16 : 9

C

5 : 3

D

4 : 1

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 28

Report

Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $$\mu$$. A student finds that, irrespective of what the incident angle $$i$$ (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $$\mu$$ is:

A

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

B

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

C

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

D

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

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 29

Report

The surface of certain metal is first illuminated with light of wavelength $$\lambda_1 = 350$$ nm and then, by a light of wavelength $$\lambda_2 = 540$$ nm. It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to (Energy of photon $$= \frac{1240}{\lambda \; in \; nm}$$ eV)

A

2.5

B

1.8

C

5.6

D

1.4

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 30

Report

A Sample of radioactive material A, that has an activity of 10 mCi (1 Ci $$= 3.7 \times 10^{10}$$ decays s$$^{-1}$$), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be, respectively:

A

5 days and 10 days

B

10 days and 40 days

C

20 days and 10 days

D

20 days and 5 days

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 31

Report

For emission line of atomic hydrogen from $$n_i = 8$$ to $$n_f = n$$, the plot of wave number $$\bar{\nu}$$ against $$\frac{1}{n^2}$$ will be: (The Rydberg constant, $$R_H$$ is in wave number unit)

A

Linear with slope $$-R_H$$

B

Non linear

C

Linear with slope $$R_H$$

D

Linear with intercept $$-R_H$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 32

Report

In general, the properties that decrease and increase down a group in the periodic table, respectively, are:

A

Atomic radius and electronegativity

B

Electronegativity and atomic radius

C

Electronegativity and electron gain enthalpy

D

Electron gain enthalpy and electronegativity

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 33

Report

Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3 oxidation states. This is due to:

A

Diagonal relationship

B

Lattice effect

C

Lanthanoid contraction

D

Inert pair effect

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 34

Report

According to molecular orbital theory, which of the following is true with respect to $$Li_2^+$$ and $$Li_2^-$$?

A

$$Li_2^+$$ is stable and $$Li_2^-$$ is unstable

B

Both are unstable

C

Both are stable

D

$$Li_2^+$$ is unstable and $$Li_2^-$$ is stable

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 35

Report

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m$$^3$$ at 1000 K. Given, R is the gas constant in JK$$^{-1}$$mol$$^{-1}$$, x is:

A

$$\frac{4 + R}{2R}$$

B

$$\frac{2R}{4 + R}$$

C

$$\frac{4 - R}{2R}$$

D

$$\frac{2R}{4 - R}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 36

Report

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $$T_1$$ and $$T_2$$ ($$T_1 < T_2$$). The correct graphical depiction of the dependence of work done $$w$$ vs the final volume $$V$$ is:

A

B

C

D

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 37

Report

20 ml of 0.1 M $$H_2SO_4$$ solution is added to 30 mL of 0.2 M $$NH_4OH$$ solution. The pH of the resultant mixture is: ($$pK_b$$ of $$NH_4OH = 4.7$$)

A

5.0

B

5.2

C

9.4

D

9.0

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 38

Report

The isotopes of hydrogen are:

A

Protium, deuterium and tritium

B

Tritium and protium only

C

Protium and deuterium only

D

Deuterium and tritium only

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 39

Report

The alkaline earth metal nitrate that does not crystallise with molecules is:

A

$$Ba(NO_3)_2$$

B

$$Sr(NO_3)_2$$

C

$$Mg(NO_3)_2$$

D

$$Ca(NO_3)_2$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 40

Report

Correct statements among regarding silicones are:
(a) They are polymers with hydrophobic character.
(b) They are biocompatible.
(c) In general, they have high thermal stability and low dielectric strength.
(d) Usually, they are resistant to oxidation and used as greases.

A

(a), (b) and (c) only

B

(a) and (b) only

C

(a), (b), (c) and (d)

D

(a), (b) and (d) only

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 41

Report

Arrange the following amines in the decreasing order of basicity.

A

III > I > II

B

I > III > II

C

III > II > I

D

I > II > III

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 42

Report

Which amongst the following is the strongest acid?

A

$$CHCN_3$$

B

$$CHI_3$$

C

$$CHBr_3$$

D

$$CHCl_3$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 43

Report

The compounds A and B in the following reaction are, respectively:

A

A = Benzyl alcohol, B = Benzyl isocyanide

B

A = Benzyl chloride, B = Benzyl isocyanide

C

A = Benzyl alcohol, B = Benzyl cyanide

D

A = Benzyl chloride, B = Benzyl cyanide

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 44

Report

A water sample has ppm level concentration of the following metals: Fe = 0.2; Mn = 5.0; Cu = 3.0; Zn = 5.0. The metal that makes the water sample unsuitable for drinking is:

A

Zn

B

Fe

C

Mn

D

Cu

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 45

Report

The one that is extensively used as a piezoelectric material is:

A

Tridymite

B

Quartz

C

Amorphous silica

D

Mica

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 46

Report

A solution of sodium sulphate contains 92 g of Na$$^+$$ ions per kilogram of water. The molality of Na$$^+$$ ions in that solution in mol kg$$^{-1}$$ is:

A

16

B

4

C

12

D

8

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 47

Report

Which one of the following statements regarding Henry's law is not correct?

A

Different gases have different $$K_H$$ (Henry's law constant) values at the same temperature

B

The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution

C

Higher the value of $$K_H$$ at a given pressure, higher is the solubility of the gas in the liquids

D

The value of $$K_H$$ increases with increase of temperature and $$K_H$$ is function of the nature of the gas

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 48

Report

The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of $$PbSO_4$$ electrolyzed in g during the process is: (Molar mass of $$PbSO_4 = 303$$ g mol$$^{-1}$$)

A

22.8

B

15.2

C

11.4

D

7.6

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 49

Report

The following results were obtained during kinetic studies of the reaction.
$$2A + B \rightarrow$$ product

Experiment I: A = 0.10 mol L$$^{-1}$$, B = 0.20 mol L$$^{-1}$$, Rate = $$6.93 \times 10^{-3}$$ mol L$$^{-1}$$ min$$^{-1}$$
Experiment II: A = 0.10 mol L$$^{-1}$$, B = 0.25 mol L$$^{-1}$$, Rate = $$6.93 \times 10^{-3}$$ mol L$$^{-1}$$ min$$^{-1}$$
Experiment III: A = 0.20 mol L$$^{-1}$$, B = 0.30 mol L$$^{-1}$$, Rate = $$1.386 \times 10^{-2}$$ mol L$$^{-1}$$ min$$^{-1}$$

The time (in minutes) required to consume half of A is:

A

100

B

10

C

5

D

1

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 50

Report

Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, $$x$$ is the mass of the gas adsorbed on mass $$m$$ of the adsorbent at pressure P. $$\frac{x}{m}$$ is proportional to:

A

$$p^{\frac{1}{4}}$$

B

$$p$$

C

$$p^2$$

D

$$p^{\frac{1}{2}}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 51

Report

The ore that contains both iron and copper is:

A

Azurite

B

Malachite

C

Dolomite

D

Copper pyrites

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 52

Report

The major product of the following reaction is:

A

$$RCOOH$$

B

$$RCHO$$

C

$$RCH_2NH_2$$

D

$$RCONH_2$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 53

Report

Two complexes $$[CrH_2O)_6]Cl_3$$ (A) and $$[Cr(NH_3)_6]Cl_3$$ (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is:

A

Both are paramagnetic with three unpaired electrons

B

$$\Delta_0$$ value of A is less than that of B

C

$$\Delta_0$$ values of A and B are calculated from the energies violet and yellow light, respectively.

D

Both absorb energies corresponding to their complementary colors.

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 54

Report

In the reaction given below what will be the major product at the end:

Options:

A

B

C

D

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 55

Report

Major product of the given reaction is:

Options:

A

B

C

D

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 56

Report

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is:

A

4.90 BM

B

3.87 BM

C

6.93 BM

D

5.92 BM

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 57

Report

Acid strength given below the correct decreasing order will be:

A

$$NO_2CH_2COOH > FCH_2COOH > CNCH_2COOH > ClCH_2COOH$$

B

$$FCH_2COOH > NCCH_2COOH > NO_2CH_2COOH > ClCH_2COOH$$

C

$$CNCH_2COOH > O_2NCH_2COOH > FCH_2COOH > ClCH_2COOH$$

D

$$O_2NCH_2COOH > FCH_2COOH > ClCH_2COOH > NCCH_2COOH$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 58

Report

Major product of the given below reaction:

Options:

A

B

C

D

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 59

Report

The correct match between column-I and column-II is:
Column-I (drug)              Column-II (test)
(A) Chloroxylenol           (P) Carbylamine test
(B) Norethindrone         (Q) Sodium hydrogen carbonate test
(C) Sulphapyridine        (R) Ferric chloride test
(D) Penicillin                  (S) Baeyer's test

A

A $$\rightarrow$$ R, B $$\rightarrow$$ P, C $$\rightarrow$$ S, D $$\rightarrow$$ Q

B

A $$\rightarrow$$ Q, B $$\rightarrow$$ S, C $$\rightarrow$$ P, D $$\rightarrow$$ R

C

A $$\rightarrow$$ Q, B $$\rightarrow$$ P, C $$\rightarrow$$ S, D $$\rightarrow$$ R

D

A $$\rightarrow$$ R, B $$\rightarrow$$ S, C $$\rightarrow$$ P, D $$\rightarrow$$ Q

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 60

Report

The increasing order of pKa of the following amino acids in aqueous solution is: Glycine, Aspartate, Lysine, Arginine.

A

Arginine < Lysine < Glycine < Aspartate

B

Aspartate < Glycine < Arginine < Lysine

C

Glycine < Aspartate < Arginine < Lysine

D

Aspartate < Glycine < Lysine < Arginine

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 61

Report

Let $$\alpha$$ and $$\beta$$ be the roots of the equation $$x^2 + 2x + 2 = 0$$, then $$\alpha^{15} + \beta^{15}$$ is equal to:

A

-512

B

128

C

512

D

-256

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 62

Report

Let $$A = \{\theta \in (-\frac{\pi}{2}, \pi): \frac{3 + 2i\sin\theta}{1 - 2i\sin\theta}$$ is purely imaginary$$\}$$. Then the sum of the elements in $$A$$ is:

A

$$\frac{5\pi}{6}$$

B

$$\pi$$

C

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

D

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

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 63

Report

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

A

300

B

200

C

500

D

350

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 64

Report

If $$a$$, $$b$$ and $$c$$ be three distinct real numbers in G.P. and $$a + b + c = xb$$, then $$x$$ cannot be:

A

-3

B

2

C

4

D

-2

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 65

Report

Let $$a_1, a_2, \ldots, a_{30}$$ be an A.P., $$S = \sum_{i=1}^{30} a_i$$ and $$T = \sum_{i=1}^{15} a_{(2i-1)}$$. If $$a_5 = 27$$ and $$S - 2T = 75$$, then $$a_{10}$$ is equal to:

A

52

B

47

C

42

D

57

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 66

Report

If the fractional part of the number $$\frac{2^{403}}{15}$$ is $$\frac{k}{15}$$, then $$k$$ is equal to:

A

4

B

14

C

8

D

6

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 67

Report

For any $$\theta\in\left(\frac{\pi}{4},\frac{\pi}{2}\right)$$, the expression $$3\left(\sin\theta\ -\cos\theta\ \right)^4+6\left(\sin\theta\ +\cos\theta\ \right)^2+4\sin^6\theta\ $$ equals:

A

$$13 - 4\cos^2\theta + 6\cos^4\theta$$

B

$$13 - 4\cos^2\theta + 6\sin^2\theta\cos^2\theta$$

C

$$13 - 4\cos^6\theta$$

D

$$13 - 4\cos^4\theta + 2\sin^2\theta\cos^2\theta$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 68

Report

Consider the set of all lines $$px + qy + r = 0$$ such that $$3p + 2q + 4r = 0$$. Which one of the following statements is true?

A

The lines are not concurrent.

B

The lines are concurrent at the point $$\left(\frac{3}{4}, \frac{1}{2}\right)$$.

C

The lines are all parallel.

D

Each line passes through the origin.

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 69

Report

Three circles of radii $$a$$, $$b$$, $$c$$ ($$a < b < c$$) touch each other externally. If they have $$x$$-axis as a common tangent, then:

A

$$\frac{1}{\sqrt{a}} = \frac{1}{\sqrt{b}} + \frac{1}{\sqrt{c}}$$

B

$$a$$, $$b$$, $$c$$ are in A.P.

C

$$\frac{1}{\sqrt{b}} = \frac{1}{\sqrt{a}} + \frac{1}{\sqrt{c}}$$

D

$$\sqrt{a}$$, $$\sqrt{b}$$, $$\sqrt{c}$$ are in A.P.

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 70

Report

Axis of a parabola lies along $$x$$-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive $$x$$-axis then which of following points does not lie on it?

A

$$\left(6, 4\sqrt{2}\right)$$

B

$$\left(5, 2\sqrt{6}\right)$$

C

$$\left(8, 6\right)$$

D

$$\left(4, -4\right)$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 71

Report

Equation of a common tangent to the circle, $$x^2 + y^2 - 6x = 0$$ and the parabola, $$y^2 = 4x$$ is:

A

$$2\sqrt{3}y = -x - 12$$

B

$$\sqrt{3}y = x + 3$$

C

$$\sqrt{3}y = 3x + 1$$

D

$$2\sqrt{3}y = 12x + 1$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 72

Report

Let $$0 < \theta < \frac{\pi}{2}$$. If the eccentricity of the hyperbola $$\frac{x^2}{\cos^2\theta} - \frac{y^2}{\sin^2\theta} = 1$$ is greater than 2, then the length of its latus rectum lies in the interval:

A

$$(3, \infty)$$

B

$$\left(1, \frac{3}{2}\right)$$

C

$$(2, 3)$$

D

$$\left(\frac{3}{2}, 2\right)$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 73

Report

The value of $$\lim_{y \to 0} \frac{\sqrt{1 + \sqrt{1 + y^4}} - \sqrt{2}}{y^4}$$ is:

A

exists and equals $$\frac{1}{2\sqrt{2}}$$

B

exists and equals $$\frac{1}{4\sqrt{2}}$$

C

does not exist

D

exists and equals $$\frac{1}{2\sqrt{2}(\sqrt{2}+1)}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 74

Report

If the Boolean expression $$p \oplus q \wedge \sim p \odot q$$ is equivalent to $$p \wedge q$$, where $$\oplus$$, $$\odot \in \{\wedge, \vee\}$$, then the ordered pair $$(\oplus, \odot)$$ is:

A

$$(\vee, \wedge)$$

B

$$(\wedge, \wedge)$$

C

$$(\vee, \vee)$$

D

$$(\wedge, \vee)$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 75

Report

5 students of a class have an average height 150 cm and variance 18 cm$$^2$$. A new student, whose height is 156 cm, joined them. The variance in cm$$^2$$ of the height of these six students is:

A

22

B

16

C

18

D

20

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 76

Report

If $$A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$$, then the matrix $$A^{-50}$$ when $$\theta = \frac{\pi}{12}$$, is equal to:

A

$$\begin{pmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{pmatrix}$$

B

$$\begin{pmatrix} \frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix}$$

C

$$\begin{pmatrix} \frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2} \end{pmatrix}$$

D

$$\begin{pmatrix} \frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 77

Report

The system of linear equations
$$x + y + z = 2$$
$$2x + 3y + 2z = 5$$
$$2x + 3y + (a^2 - 1)z = a + 1$$

A

is inconsistent when $$a = \sqrt{3}$$

B

has a unique solution for $$a = \sqrt{3}$$

C

has infinitely many solutions for $$a = 4$$

D

is inconsistent when $$a = 4$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 78

Report

If $$\cos^{-1}\left(\frac{2}{3x}\right) + \cos^{-1}\left(\frac{3}{4x}\right) = \frac{\pi}{2}$$, ($$x > \frac{3}{4}$$), then $$x$$ is equal to:

A

$$\frac{\sqrt{145}}{10}$$

B

$$\frac{\sqrt{145}}{11}$$

C

$$\frac{\sqrt{146}}{12}$$

D

$$\frac{\sqrt{145}}{12}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 79

Report

For $$x \in R - \{0, 1\}$$, let $$f_1(x) = \frac{1}{x}$$, $$f_2(x) = 1 - x$$ and $$f_3(x) = \frac{1}{1-x}$$ be three given functions. If a function, $$J(x)$$ satisfies $$(f_2 \circ J \circ f_1)(x) = f_3(x)$$ then $$J(x)$$ is equal to:

A

$$f_3(x)$$

B

$$\frac{1}{x}f_3(x)$$

C

$$f_1(x)$$

D

$$f_2(x)$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 80

Report

Let $$f: R \to R$$ be a function defined as
$$f(x) = \begin{cases} 5, & \text{if } x \leq 1 \\ a + bx, & \text{if } 1 < x < 3 \\ b + 5x, & \text{if } 3 \leq x < 5 \\ 30, & \text{if } x \geq 5 \end{cases}$$

Then $$f$$ is:

A

continuous if $$a = -5$$ and $$b = 10$$

B

continuous if $$a = 0$$ and $$b = 5$$

C

not continuous for any values of $$a$$ and $$b$$

D

continuous if $$a = 5$$ and $$b = 5$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 81

Report

The maximum volume in cu.m of the right circular cone having slant height 3 m is:

A

$$2\sqrt{3}\pi$$

B

$$3\sqrt{3}\pi$$

C

$$6\pi$$

D

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

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 82

Report

If $$\theta$$ denotes the acute angle between the curves, $$y = 10 - x^2$$ and $$y = 2 + x^2$$ at a point of their intersection, then $$\tan\theta$$ is equal to:

A

$$\frac{4}{9}$$

B

$$\frac{8}{17}$$

C

$$\frac{7}{17}$$

D

$$\frac{8}{15}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 83

Report

For $$x^2 \neq n\pi + 1$$, $$n \in N$$ (the set of natural numbers), the integral $$\int x\sqrt{\frac{2\sin(x^2-1) - \sin 2(x^2-1)}{2\sin(x^2-1) + \sin 2(x^2-1)}} \; dx$$ is equal to (where c is a constant of integration):

A

$$\log_e \left|\sec\frac{x^2-1}{4}\right| + c$$

B

$$\frac{1}{2}\log_e \left|\sec^2(x^2-1)\right| - 1 + c$$

C

$$\frac{1}{2}\log_e \left|\sec^2\frac{x^2-1}{2}\right| + c$$

D

$$\log_e \left|\sec^2\frac{x^2-1}{2}\right| + c$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 84

Report

The value of $$\int_0^{\pi} \|cos x|^3 \; dx$$ is:

A

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

B

0

C

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

D

$$-\frac{4}{3}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 85

Report

The area (in sq. units) bounded by the parabola $$y = x^2 - 1$$, the tangent at the point (2, 3) to it and the $$y$$-axis is:

A

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

B

$$\frac{8}{3}$$

C

$$\frac{32}{3}$$

D

$$\frac{56}{3}$$

View Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 86

Report

If $$y = y(x)$$ is the solution of the differential equation, $$x\frac{dy}{dx} + 2y = x^2$$ satisfying $$y(1) = 1$$, then $$y\left(\frac{1}{2}\right)$$ is equal to:

A

$$\frac{7}{64}$$

B

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

C

$$\frac{13}{16}$$

D

$$\frac{49}{16}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 87

Report

Let $$\vec{a} = \hat{i} - \hat{j}$$, $$\vec{b} = \hat{i} + \hat{j} + \hat{k}$$ and $$\vec{c}$$ be a vector such that $$\vec{a} \times \vec{c} + \vec{b} = \vec{0}$$ and $$\vec{a} \cdot \vec{c} = 4$$, then $$|\vec{c}|^2$$ is equal to:

A

$$\frac{19}{2}$$

B

9

C

$$\frac{17}{2}$$

D

8

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 88

Report

The plane through the intersection of the planes $$x + y + z = 1$$ and $$2x + 3y - z + 4 = 0$$ and parallel to $$y$$-axis also passes through the point:

A

$$(3, 3, -1)$$

B

$$(-3, 1, 1)$$

C

$$(3, 2, 1)$$

D

$$(-3, 0, -1)$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 89

Report

The equation of the line passing through $$(-4, 3, 1)$$, parallel to the plane $$x + 2y - z - 5 = 0$$ and intersecting the line $$\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z-2}{-1}$$ is:

A

$$\frac{x+4}{3} = \frac{y-3}{-1} = \frac{z-1}{1}$$

B

$$\frac{x+4}{1} = \frac{y-3}{1} = \frac{z-1}{3}$$

C

$$\frac{x+4}{-1} = \frac{y-3}{1} = \frac{z-1}{1}$$

D

$$\frac{x-4}{2} = \frac{y+3}{1} = \frac{z+1}{4}$$

View Solution Video Solution

NTA JEE Main 9th January 2019 Shift 1 - Question 90

Report

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then $$P(X = 1) + P(X = 2)$$ equals:

A

$$\frac{24}{169}$$

B

$$\frac{52}{169}$$

C

$$\frac{49}{169}$$

D

$$\frac{25}{169}$$

View Solution Video Solution