NTA JEE Main 25th July 2021 Shift 2

NTA JEE Main 25th July 2021 Shift 2 - Question 1

Report

Two vectors $$\vec{X}$$ and $$\vec{Y}$$ have equal magnitude. The magnitude of $$\left(\vec{X} - \vec{Y}\right)$$ is $$n$$ times the magnitude of $$\left(\vec{X} + \vec{Y}\right)$$. The angle between $$\vec{X}$$ and $$\vec{Y}$$ is:

A

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

B

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

C

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

D

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

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 2

Report

The force is given in terms of time $$t$$ and displacement $$x$$ by the equation $$F = A \cos Bx + C \sin Dt$$. The dimensional formula of $$\frac{AD}{B}$$ is:

A

$$[M^0 \, L \, T^{-1}]$$

B

$$[M L^2 \, T^{-3}]$$

C

$$[M^1 \, L^1 \, T^{-2}]$$

D

$$[M^2 \, L^2 \, T^{-3}]$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 3

Report

The relation between time $$t$$ and distance $$x$$ for a moving body is given as $$t = mx^2 + nx$$, where $$m$$ and $$n$$ are constants. The retardation of the motion is: (When $$v$$ stands for velocity)

A

$$2mv^3$$

B

$$2mnv^3$$

C

$$2nv^3$$

D

$$2n^2v^3$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 4

Report

A balloon was moving upwards with a uniform velocity of 10 m s$$^{-1}$$. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of g as 10 m s$$^{-2}$$)

A

300 m

B

200 m

C

125 m

D

250 m

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 5

Report

The instantaneous velocity of a particle moving in a straight line is given as $$v = \alpha t + \beta t^2$$, where $$\alpha$$ and $$\beta$$ are constants. The distance travelled by the particle between 1 s and 2 s is:

A

$$3\alpha + 7\beta$$

B

$$\frac{3}{2}\alpha + \frac{7}{3}\beta$$

C

$$\frac{\alpha}{2} + \frac{\beta}{3}$$

D

$$\frac{3}{2}\alpha + \frac{7}{2}\beta$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 6

Report

A force $$\vec{F} = \left(40\hat{i} + 10\hat{j}\right)$$ N acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\vec{r}$$ at time $$t = 10$$ s will be

A

$$\left(100\hat{i} + 400\hat{j}\right)$$ m

B

$$\left(100\hat{i} + 100\hat{j}\right)$$ m

C

$$\left(400\hat{i} + 100\hat{j}\right)$$ m

D

$$\left(400\hat{i} + 400\hat{j}\right)$$ m

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 7

Report

Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is $$W$$, the weight of the same object on that planet will be:

A

$$2W$$

B

$$W$$

C

$$2^{\frac{1}{3}}W$$

D

$$\sqrt{2} \, W$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 8

Report

A heat engine has an efficiency of $$\frac{1}{6}$$. When the temperature of sink is reduced by 62°C, its efficiency gets doubled. The temperature of the source is:

A

124°C

B

37°C

C

62°C

D

99°C

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 9

Report

Two spherical soap bubbles of radii $$r_1$$ and $$r_2$$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

A

$$\frac{r_1 r_2}{r_1 + r_2}$$

B

$$\sqrt{r_1 r_2}$$

C

$$\sqrt{r_1^2 + r_2^2}$$

D

$$\frac{r_1 + r_2}{2}$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 10

Report

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

A

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

B

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

C

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

D

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

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 11

Report

Two ideal electric dipoles $$A$$ and $$B$$, having their dipole moment $$p_1$$ and $$p_2$$ respectively are placed on a plane with their centres at $$O$$ as shown in the figure. At point $$C$$ on the axis of dipole $$A$$, the resultant electric field is making an angle of 37° with the axis. The ratio of the dipole moment of $$A$$ and $$B$$, $$\frac{p_1}{p_2}$$ is: (take sin 37° = $$\frac{3}{5}$$)

A

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

B

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

C

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

D

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

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 12

Report

If $$q_f$$ is the free charge on the capacitor plates and $$q_b$$ is the bound charge on the dielectric slab of dielectric constant $$k$$ placed between the capacitor plates, then bound charge $$q_b$$ can be expressed as:

A

$$q_b = q_f\left(1 - \frac{1}{\sqrt{k}}\right)$$

B

$$q_b = q_f\left(1 - \frac{1}{k}\right)$$

C

$$q_b = q_f\left(1 + \frac{1}{\sqrt{k}}\right)$$

D

$$q_b = q_f\left(1 + \frac{1}{k}\right)$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 13

Report

In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells $$\frac{\varepsilon_1}{\varepsilon_2}$$ is:

A

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

B

$$\frac{8}{5}$$

C

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

D

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

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 14

Report

The given potentiometer has its wire of resistance 10 $$\Omega$$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2 $$\Omega$$ resistor is:

A

10 V

B

5 V

C

$$\frac{40}{9}$$ V

D

$$\frac{40}{11}$$ V

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 15

Report

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is,

A

1 : 4

B

4 : 3

C

3 : 1

D

2 : 3

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 16

Report

A 10 $$\Omega$$ resistance is connected across 220 V - 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is:

A

2.5 ms

B

1.5 ms

C

3.0 ms

D

4.5 ms

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 17

Report

A prism of refractive index $$\mu$$ and angle of prism $$A$$ is placed in the position of minimum angle of deviation. If minimum angle of deviation is also $$A$$, then in terms of refractive index,

A

$$2\cos^{-1}\left(\frac{\mu}{2}\right)$$

B

$$\sin^{-1}\left(\frac{\mu}{2}\right)$$

C

$$\sin^{-1}\left(\sqrt{\frac{\mu - 1}{2}}\right)$$

D

$$\cos^{-1}\left(\frac{\mu}{2}\right)$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 18

Report

A ray of light entering from air into a denser medium of refractive index $$\frac{4}{3}$$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $$\theta$$ should be equal to:

A

$$\sin^{-1}\frac{\sqrt{7}}{3}$$

B

$$\sin^{-1}\frac{\sqrt{5}}{4}$$

C

$$\sin^{-1}\frac{\sqrt{7}}{4}$$

D

$$\sin^{-1}\frac{\sqrt{5}}{3}$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 19

Report

An electron moving with speed $$v$$ and a photon moving with speed $$c$$, have the same D-Broglie wavelength. The ratio of the kinetic energy of the electron to that of a photon is:

A

$$\frac{3c}{v}$$

B

$$\frac{v}{3c}$$

C

$$\frac{v}{2c}$$

D

$$\frac{2c}{v}$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 20

Report

When radiation of wavelength $$\lambda$$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is:

A

$$2\lambda$$

B

$$4\lambda$$

C

$$8\lambda$$

D

$$6\lambda$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 21

Report

A force of $$F = (5y + 20)\hat{j}$$ N acts on a particle. The work done by this force when the particle is moved from $$y = 0$$ m to $$y = 10$$ m is _________ J.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 22

Report

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is _________ $$\pi \times 10^{-1}$$ N m

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 23

Report

A system consists of two types of gas molecules $$A$$ and $$B$$ having the same number density $$2 \times 10^{25}$$ m$$^{-3}$$. The diameter of $$A$$ and $$B$$ are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule $$A$$ to that of $$B$$ between two successive collisions is _________ $$\times 10^{-2}$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 24

Report

A 16 $$\Omega$$ wire is bent to form a square loop. A 9 V supply having an internal resistance of 1 $$\Omega$$ is connected across one of its sides. The potential drop across the diagonals of the square loop is _________ $$\times 10^{-1}$$ V.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 25

Report

Two circuits are shown in figure (a) and (b). At a frequency of _________ rad s$$^{-1}$$ the average power dissipated in one cycle will be the same in both the circuits.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 26

Report

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity $$B$$. The electrons emitted perpendicular to the magnetic field $$B$$, with maximum kinetic energy are bent into a circular arc of radius 30 cm. The value of $$B$$ is _________ $$\times 10^{-7}$$ T.
Given $$hc = 20 \times 10^{-26}$$ J m, the mass of the electron = $$9 \times 10^{-31}$$ kg.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 27

Report

From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is _________ $$x \times 10^{-3}$$ J
Mass of neutron = 1.00866 u
Mass of proton = 1.00726 u
Mass of Aluminium nucleus = 27.18846 u
(Assume 1 u corresponds to $$x$$ J of energy)
(Round off to the nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 28

Report

The nuclear activity of a radioactive element becomes $$\left(\frac{1}{8}\right)^{th}$$ of its initial value in 30 years. The half-life of radioactive element is _________ years.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 29

Report

In a semiconductor, the number density of intrinsic charge carriers at 27°C is $$1.5 \times 10^{16}$$ m$$^{-3}$$. If the semiconductor is doped with an impurity atom, the hole density increases to $$4.5 \times 10^{22}$$ m$$^{-3}$$. The electron density in the doped semiconductor is _________ $$\times 10^{9}$$ m$$^{-3}$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 30

Report

A message signal of frequency 20 kHz and peak voltage of 20 V is used to modulate a carrier wave of frequency 1 MHz and peak voltage of 20 V. The modulation index will be:

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 31

Report

The spin only magnetic moments (in BM) for free Ti$$^{3+}$$, V$$^{2+}$$ and Sc$$^{3+}$$ ions respectively are (At.No. Sc : 21, Ti : 22, V : 23)

A

3.87, 1.73, 0

B

1.73, 3.87, 0

C

1.73, 0, 3.87

D

0, 3.87, 1.73

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 32

Report

The ionic radii of F$$^-$$ and O$$^{2-}$$ respectively are 1.33 A and 1.4A, while the covalent radius of N is 0.74A. The correct statement for the ionic radius of N$$^{3-}$$ from the following is:

A

It is smaller than F$$^-$$ and N

B

It is bigger than O$$^{2-}$$ and F$$^-$$

C

It is bigger than F$$^-$$ and N, but smaller than O$$^{2-}$$

D

It is smaller than O$$^{2-}$$ and F$$^-$$, but bigger than N

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 33

Report

In the following the correct bond order sequence is:

A

$$O_2^{2-} \gt O_2^{+} \gt O_2^{-} \gt O_2$$

B

$$O_2^{+} \gt O_2^{-} \gt O_2^{2-} \gt O_2$$

C

$$O_2^{+} \gt O_2 \gt O_2^{-} \gt O_2^{2-}$$

D

$$O_2 \gt O_2^{-} \gt O_2^{2-} \gt O_2^{+}$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 34

Report

Identify the species having one $$\pi$$-bond and maximum number of canonical forms from the following:

A

$$SO_3$$

B

$$O_2$$

C

$$SO_2$$

D

$$CO_3^{2-}$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 35

Report

Identify the process in which change in the oxidation state is five:

A

$$Cr_2O_7^{2-} \rightarrow 2Cr^{3+}$$

B

$$MnO_4^{-} \rightarrow Mn^{2+}$$

C

$$CrO_4^{2-} \rightarrow Cr^{3+}$$

D

$$C_2O_4^{2-} \rightarrow 2CO_2$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 36

Report

Which one of the following metals forms interstitial hydride easily?

A

Cr

B

Fe

C

Mn

D

Co

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 37

Report

Match List I with List II:
List-I (Elements)   List-II (Properties)
(a) Li   (i) Poor water solubility of I$$^-$$ salt
(b) Na   (ii) Most abundant element in cell fluid
(c) K   (iii) Bicarbonate salt used in fire extinguisher
(d) Cs   (iv) Carbonate salt decomposes easily on heating
Choose the correct answer from the options given below:

A

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

B

(a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)

C

(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

D

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 38

Report

The correct decreasing order of densities of the following compounds is:

A

(D) > (C) > (B) > (A)

B

(C) > (D) > (A) > (B)

C

(C) > (B) > (A) > (D)

D

(A) > (B) > (C) > (D)

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 39

Report

Which among the following is the strongest acid?

A

$$CH_3CH_2CH_2CH_3$$

B

C

D

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 40

Report

Given below are two statements:
Statement I : Chlorofluoro carbons breakdown by radiation in the visible energy region and release chlorine gas in the atmosphere which then reacts with stratospheric ozone.
Statement II : Atmospheric ozone reacts with nitric oxide to give nitrogen and oxygen gases, which add to the atmosphere.
For the above statements choose the correct answer from the options given below:

A

Statement I is incorrect but statement II is true

B

Both statement I and II are false

C

Statement I is correct but statement II is false

D

Both statement I and II are correct

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 41

Report

Match List I with List II:
List-I (Example of colloids)          List-II (Classification)
(a) Cheese                                 (i) dispersion of liquid in liquid
(b) Pumice stone                      (ii) dispersion of liquid in gas
(c) Hair cream                           (iii) dispersion of gas in solid
(d) Cloud                                    (iv) dispersion of liquid in solid
Choose the most appropriate answer from the options given below:

A

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

B

(a)-(iv), (b)-(i), (c)-(iii), (d)-(ii)

C

(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

D

(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 42

Report

Match List I with List II: (Both having metallurgical terms)
List-I                                      List-II
(a) Concentration of Ag ore    (i) Reverberatory furnace
(b) Blast furnace                   (ii) Pig iron
(c) Blister copper                  (iii) Leaching with dilute NaCN solution
(d) Froth floatation method   (iv) Sulfide ores
Choose the correct answer from the options given below:

A

(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

B

(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

C

(a)-(iv), (b)-(i), (c)-(iii), (d)-(ii)

D

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 43

Report

Which one of the following metal complexes is most stable?

A

$$[Co(en)(NH_3)_4]Cl_2$$

B

$$[Co(en)_3]Cl_2$$

C

$$[Co(en)_2(NH_3)_2]Cl_2$$

D

$$[Co(NH_3)_6]Cl_2$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 44

Report

Consider the above reaction sequence, Product "A" and Product "B" formed respectively are:

A

B

C

D

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 45

Report

What is the major product "P" of the following reaction?

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 46

Report

Maleic anhydride
Maleic anhydride can be prepared by:

A

Heating trans-but-2-enedioic acid

B

Heating cis-but-2-enedioic acid

C

Treating cis-but-2-enedioic acid with alcohol and acid

D

Treating trans-but-2-enedioic acid with alcohol and acid

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 47

Report

Consider the above reaction, the Product "P" is:

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 48

Report

A reaction of benzonitrile with one equivalent CH$$_3$$MgBr followed by hydrolysis produces a yellow liquid "P". The compound "P" will give positive _________ test.

A

Iodoform test

B

Schiff's test

C

Ninhydrin's test

D

Tollen's test

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 49

Report

A biodegradable polyamide can be made from:

A

Glycine and isoprene

B

Hexamethylene diamine and adipic acid

C

Glycine and aminocaproic acid

D

Styrene and caproic acid

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 50

Report

Which one of the following is correct structure for cytosine?

A

B

C

D

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 51

Report

The number of significant figures in 0.00340 is _________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 52

Report

An accelerated electron has a speed of $$5 \times 10^6$$ ms$$^{-1}$$ with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is $$x \times 10^{-9}$$ m. The value of $$x$$ is _________. (Nearest integer)
[Use mass of electron = $$9.1 \times 10^{-31}$$ kg, h = $$6.63 \times 10^{-34}$$ Js, $$\pi$$ = 3.14]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 53

Report

An LPG cylinder contains gas at a pressure of 300 kPa at 27°C. The cylinder can withstand the pressure of $$1.2 \times 10^6$$ Pa. The room in which the cylinder is kept catches fire. The minimum temperature at which the bursting of cylinder will take place is _________ °C. (Nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 54

Report

A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change in internal energy is _________J. (Nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 55

Report

Assuming that Ba(OH)$$_2$$ is completely ionised in aqueous solution under the given conditions the concentration of H$$_3$$O$$^+$$ ions in 0.005M aqueous solution of Ba(OH)$$_2$$ at 298 K is _________ $$\times 10^{-12}$$ mol L$$^{-1}$$. (Nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 56

Report

0.8 g of an organic compound was analysed by Kjeldahl's method for the estimation of nitrogen. If the percentage of nitrogen in the compound was found to be 42%, then _________ mL of 1M H$$_2$$SO$$_4$$ would have been neutralized by the ammonia evolved during the analysis.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 57

Report

Consider the above chemical reaction. The total number of stereoisomers possible for Product "P" is _________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 58

Report

When 3.00 g of a substance X' is dissolved in 100 g of CCl$$_4$$, it raises the boiling point by 0.60 K. The molar mass of the substance 'X' is _________ g mol$$^{-1}$$. (Nearest integer).
[Given K$$_b$$ for CCl$$_4$$ is 5.0 K kg mol$$^{-1}$$]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 59

Report

For a chemical reaction A $$\rightarrow$$ B, it was found that concentration of B is increased by 0.2 mol L$$^{-1}$$ in 30 min. The average rate of the reaction is _________ $$\times 10^{-1}$$ mol L$$^{-1}$$ h$$^{-1}$$. (in nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 60

Report

Number of electrons present in 4f orbital of Ho$$^{3+}$$ ion is _________ (Given Atomic No. of Ho = 67)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 61

Report

The number of real solutions of the equation, $$x^2 - |x| - 12 = 0$$ is:

A

2

B

3

C

1

D

4

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 62

Report

The sum of all those terms which are rational numbers in the expansion of $$\left(2^{\frac{1}{3}} + 3^{\frac{1}{4}}\right)^{12}$$ is:

A

89

B

27

C

35

D

43

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 63

Report

If the greatest value of the term independent of $$x$$ in the expansion of $$\left(x \sin \alpha + a\frac{\cos \alpha}{x}\right)^{10}$$ is $$\frac{10!}{(5!)^2}$$, then the value of $$a$$ is equal to:

A

$$-1$$

B

1

C

$$-2$$

D

2

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 64

Report

The lowest integer which is greater than $$\left(1 + \frac{1}{10^{100}}\right)^{10^{100}}$$ is

A

3

B

4

C

2

D

1

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 65

Report

If $$^nP_r = ^nP_{r+1}$$ and $$^nC_r = ^nC_{r-1}$$, then the value of $$r$$ is equal to:

A

1

B

4

C

2

D

3

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 66

Report

The value of $$\cot \frac{\pi}{24}$$ is:

A

$$\sqrt{2} + \sqrt{3} + 2 - \sqrt{6}$$

B

$$\sqrt{2} + \sqrt{3} + 2 + \sqrt{6}$$

C

$$\sqrt{2} - \sqrt{3} - 2 + \sqrt{6}$$

D

$$3\sqrt{2} - \sqrt{3} - \sqrt{6}$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 67

Report

The number of distinct real roots of $$\begin{vmatrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{vmatrix} = 0$$ in the interval $$-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$$ is:

A

4

B

1

C

2

D

3

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 68

Report

Let the equation of the pair of lines, $$y = px$$ and $$y = qx$$, can be written as $$(y - px)(y - qx) = 0$$. Then the equation of the pair of the angle bisectors of the lines $$x^2 - 4xy - 5y^2 = 0$$ is:

A

$$x^2 - 3xy + y^2 = 0$$

B

$$x^2 + 4xy - y^2 = 0$$

C

$$x^2 + 3xy - y^2 = 0$$

D

$$x^2 - 3xy - y^2 = 0$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 69

Report

If a tangent to the ellipse $$x^2 + 4y^2 = 4$$ meets the tangents at the extremities of its major axis at $$B$$ and $$C$$, then the circle with $$BC$$ as diameter passes through the point.

A

$$(\sqrt{3}, 0)$$

B

$$(\sqrt{2}, 0)$$

C

$$(1, 1)$$

D

$$(-1, 1)$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 70

Report

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

A

The match will not be played and weather is not good and ground is wet.

B

If the match will not be played, then either weather is not good or ground is wet.

C

The match will be played and weather is not good or ground is wet.

D

The match will not be played or weather is good and ground is not wet.

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 71

Report

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $$\sqrt{13.44}$$, then the standard deviation of the second sample is:

A

8

B

6

C

4

D

5

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 72

Report

If $$P = \begin{bmatrix} 1 & 0 \\ \frac{1}{2} & 1 \end{bmatrix}$$, then $$P^{50}$$ is:

A

$$\begin{bmatrix} 1 & 0 \\ 25 & 1 \end{bmatrix}$$

B

$$\begin{bmatrix} 1 & 50 \\ 0 & 1 \end{bmatrix}$$

C

$$\begin{bmatrix} 1 & 25 \\ 0 & 1 \end{bmatrix}$$

D

$$\begin{bmatrix} 1 & 0 \\ 50 & 1 \end{bmatrix}$$

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 73

Report

If $$[x]$$ be the greatest integer less than or equal to $$x$$, then $$\sum_{n=8}^{100} \left[\frac{(-1)^n n}{2}\right]$$ is equal to:

A

0

B

4

C

$$-2$$

D

2

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 74

Report

Consider function $$f : A \rightarrow B$$ and $$g : B \rightarrow C$$ $$(A, B, C \subseteq R)$$ such that $$(gof)^{-1}$$ exists, then:

A

$$f$$ and $$g$$ both are one-one

B

$$f$$ and $$g$$ both are onto

C

$$f$$ is one-one and $$g$$ is onto

D

$$f$$ is onto and $$g$$ is one-one

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 75

Report

If $$f(x) = \begin{cases} \int_0^x (5 + |1 - t|) \, dt, & x > 2 \\ 5x + 1, & x \leq 2 \end{cases}$$, then

A

$$f(x)$$ is not continuous at $$x = 2$$

B

$$f(x)$$ is everywhere differentiable

C

$$f(x)$$ is continuous but not differentiable at $$x = 2$$

D

$$f(x)$$ is not differentiable at $$x = 1$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 76

Report

The value of the integral $$\int_{-1}^{1} \log\left(x + \sqrt{x^2 + 1}\right) dx$$ is:

A

2

B

0

C

$$-1$$

D

1

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 77

Report

Let $$y = y(x)$$ be the solution of the differential equation $$x \, dy = (y + x^3 \cos x) \, dx$$ with $$y(\pi) = 0$$, then $$y\left(\frac{\pi}{2}\right)$$ is equal to:

A

$$\frac{\pi^2}{4} + \frac{\pi}{2}$$

B

$$\frac{\pi^2}{2} + \frac{\pi}{4}$$

C

$$\frac{\pi^2}{2} - \frac{\pi}{4}$$

D

$$\frac{\pi^2}{4} - \frac{\pi}{2}$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 78

Report

Let $$a, b$$ and $$c$$ be distinct positive numbers. If the vectors $$a\hat{i} + a\hat{j} + c\hat{k}$$, $$\hat{i} + \hat{k}$$ and $$c\hat{i} + c\hat{j} + b\hat{k}$$ are co-planar, then $$c$$ is equal to:

A

$$\frac{2}{\frac{1}{a} + \frac{1}{b}}$$

B

$$\frac{a + b}{2}$$

C

$$\frac{1}{a} + \frac{1}{b}$$

D

$$\sqrt{ab}$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 79

Report

If $$|\vec{a}| = 2$$, $$|\vec{b}| = 5$$ and $$|\vec{a} \times \vec{b}| = 8$$, then $$|\vec{a} \cdot \vec{b}|$$ is equal to:

A

6

B

4

C

3

D

5

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 80

Report

Let $$X$$ be a random variable such that the probability function of a distribution is given by $$P(X = 0) = \frac{1}{2}$$, $$P(X = j) = \frac{1}{3^j}$$ $$(j = 1, 2, 3, \ldots, \infty)$$. Then the mean of the distribution and $$P(X$$ is positive and even) respectively, are:

A

$$\frac{3}{8}$$ and $$\frac{1}{8}$$

B

$$\frac{3}{4}$$ and $$\frac{1}{8}$$

C

$$\frac{3}{4}$$ and $$\frac{1}{9}$$

D

$$\frac{3}{4}$$ and $$\frac{1}{16}$$

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 81

Report

If $$a + b + c = 1$$, $$ab + bc + ca = 2$$ and $$abc = 3$$, then the value of $$a^4 + b^4 + c^4$$ is equal to:

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 82

Report

The equation of a circle is $$\text{Re}(z^2) + 2(\text{Im}(z))^2 + 2\text{Re}(z) = 0$$, where $$z = x + iy$$. A line which passes through the centre of the given circle and the vertex of the parabola, $$x^2 - 6x - y + 13 = 0$$, has $$y$$-intercept equal to _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 83

Report

Let $$n \in \mathbf{N}$$ and $$[x]$$ denote the greatest integer less than or equal to $$x$$. If the sum of $$(n + 1)$$ terms of $$^nC_0, 3 \cdot ^nC_1, 5 \cdot ^nC_2, 7 \cdot ^nC_3, \ldots$$ is equal to $$2^{100} \cdot 101$$, then $$2\left[\frac{n-1}{2}\right]$$ is equal to

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 84

Report

If the co-efficient of $$x^7$$ and $$x^8$$ in the expansion of $$\left(2 + \frac{x}{3}\right)^n$$ are equal, then the value of $$n$$ is equal to:

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 85

Report

Consider the function $$f(x) = \frac{P(x)}{\sin(x - 2)}$$, $$x \neq 2$$, and $$f(x) = 7$$, $$x = 2$$ where $$P(x)$$ is a polynomial such that $$P''(x)$$ is always a constant and $$P(3) = 9$$. If $$f(x)$$ is continuous at $$x = 2$$, then $$P(5)$$ is equal to _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 86

Report

If a rectangle is inscribed in an equilateral triangle of side length $$2\sqrt{2}$$ as shown in the figure, then the square of the largest area of such a rectangle is _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 87

Report

Let a curve $$y = f(x)$$ pass through the point $$\left(2, (\log_e 2)^2\right)$$ and have slope $$\frac{2y}{x \log_e x}$$ for all positive real values of $$x$$. Then the value of $$f(e)$$ is equal to _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 88

Report

If $$\vec{a}$$ and $$\vec{b}$$ are unit vectors and $$\left(\vec{a} + 3\vec{b}\right)$$ is perpendicular to $$\left(7\vec{a} - 5\vec{b}\right)$$ and $$\left(\vec{a} - 4\vec{b}\right)$$ is perpendicular to $$\left(7\vec{a} - 2\vec{b}\right)$$, then the angle between $$\vec{a}$$ and $$\vec{b}$$ (in degrees) is _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 89

Report

If the lines $$\frac{x - k}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$$ and $$\frac{x + 1}{3} = \frac{y + 2}{2} = \frac{z + 3}{1}$$ are co-planar, then the value of $$k$$ is _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th July 2021 Shift 2 - Question 90

Report

A fair coin is tossed $$n-$$ times such that the probability of getting at least one head is at least 0.9. Then the minimum value of $$n$$ is _________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution