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Apr 11, 2023

JEE Mains

Shift: 2

Total Questions Available: 70

Question 1

Which one of the following pairs is an example of polar molecular solids?

Options:

A)

HCl(s),AlN(s)\mathrm{HCl}(\mathrm{s}), \mathrm{AlN}(\mathrm{s})

B)

MgO(s),SO2(s)\mathrm{MgO}(\mathrm{s}), \mathrm{SO}_{2}(\mathrm{s})

C)

SO2(s),NH3(s)\mathrm{SO}_{2}(\mathrm{s}), \mathrm{NH}_{3}(\mathrm{s})

D)

SO2(s),CO2(s)\mathrm{SO}_{2}(\mathrm{s}), \mathrm{CO}_{2}(\mathrm{s})

Question 2

The major product formed in the following reaction is

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Hydrocarbons Question 17 English 1JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Hydrocarbons Question 17 English 2

Choose the correct answer from the options given below :

Options:

A)

D only

B)

B only

C)

A only

D)

C only

Question 3

Compound 'B' is

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 21 English

Options:

A)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 21 English Option 1

B)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 21 English Option 2

C)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 21 English Option 3

D)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 21 English Option 4

Question 4

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : [CoCl(NH3)5]2+\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+} absorbs at lower wavelength of light with respect to [Co(NH3)5(H2O)]3+\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}

Reason R : It is because the wavelength of the light absorbed depends on the oxidation state of the metal ion.

In the light of the above statements, choose the correct answer from the options given below:

Options:

A)

A\mathrm{A} is false but R\mathrm{R} is true

B)

Both A\mathrm{A} and R\mathrm{R} are true but R\mathrm{R} is NOT the correct explanation of AA

C)

Both A\mathrm{A} and R\mathrm{R} are true and R\mathrm{R} is the correct explanation of A\mathrm{A}

D)

A\mathrm{A} is true but R\mathrm{R} is false

Question 5

If Ni2+\mathrm{Ni}^{2+} is replaced by Pt2+\mathrm{Pt}^{2+} in the complex [NiCl2Br2]2\left[\mathrm{NiCl}_{2} \mathrm{Br}_{2}\right]^{2-}, which of the following properties are expected to get changed ?

A. Geometry

B. Geometrical isomerism

C. Optical isomerism

D. Magnetic properties

Options:

A)

A and D

B)

A, B and D

C)

A, B and C

D)

B and C

Question 6

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : A solution of the product obtained by heating a mole of glycine with a mole of chlorine in presence of red phosphorous generates chiral carbon atom.

Reason R : A molecule with 2 chiral carbons is always optically active.

In the light of the above statements, choose the correct answer from the options given below:

Options:

A)

Both A and R are true and R is the correct explanation of A

B)

Both A and R are true but R is NOT the correct explanation of A

C)

A is true but R is false

D)

A is false but R is true

Question 7

Match List I with List II

LIST I
Complex
LIST II
Colour
A. Mg(NH4)PO4Mg(N{H_4})P{O_4} I. brown
B. K3[Co(NO2)6]{K_3}[Co{(N{O_2})_6}] II. white
C. MnO(OH)2MnO{(OH)_2} III. yellow
D. Fe4[Fe(CN)6]3F{e_4}{[Fe{(CN)_6}]_3} IV. blue

Choose the correct answer from the options given below :

Options:

A)

A-II, B-IV, C-I, D-III

B)

A-II, B-III, C-I, D-IV

C)

A-III, B-IV, C-II, D-I

D)

A-II, B-III, C-IV, D-I

Question 8

What weight of glucose must be dissolved in 100 g100 \mathrm{~g} of water to lower the vapour pressure by 0.20 mm Hg0.20 \mathrm{~mm} ~\mathrm{Hg} ?

(Assume dilute solution is being formed)

Given : Vapour pressure of pure water is 54.2 mm Hg54.2 \mathrm{~mm} ~\mathrm{Hg} at room temperature. Molar mass of glucose is 180 g mol1180 \mathrm{~g} \mathrm{~mol}^{-1}

Options:

A)

3.69 g

B)

2.59 g

C)

3.59 g

D)

4.69 g

Question 9

A solution is prepared by adding 2 g2 \mathrm{~g} of "X\mathrm{X}" to 1 mole of water. Mass percent of "X\mathrm{X}" in the solution is :

Options:

A)

20%

B)

10%

C)

2%

D)

5%

Question 10

Compound from the following that will not produce precipitate on reaction with AgNO3\mathrm{AgNO}_{3} is :

Options:

A)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 22 English Option 1

B)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 22 English Option 2

C)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 22 English Option 3

D)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 22 English Option 4

Question 11

The magnetic moment is measured in Bohr Magneton (BM).

Spin only magnetic moment of Fe\mathrm{Fe} in [Fe(H2O)6]3+\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} and [Fe(CN)6]3\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} complexes respectively is :

Options:

A)

3.87 B.M. and 1.732 B.M.

B)

5.92 B.M. and 1.732 B.M.

C)

6.92 B.M. in both

D)

4.89 B.M. and 6.92 B.M.

Question 12

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Hydrocarbons Question 18 English

In the light of the above statements, choose the correct answer from the options given below:

Options:

A)

Both A and R are true and R is the correct explanation of A

B)

A is false but R is true

C)

A is true but R is false

D)

Both A and R are true but R is NOT the correct explanation of A

Question 13

For a chemical reaction A+B\mathrm{A}+\mathrm{B} \rightarrow Product, the order is 1 with respect to A\mathrm{A} and B\mathrm{B}.

Rate\mathrm{Rate}
mol L1 S1\mathrm{mol~L^{-1}~S^{-1}}
[A]\mathrm{[A]}
mol L1\mathrm{mol~L^{-1}}
[B]\mathrm{[B]}
mol L1\mathrm{mol~L^{-1}}
0.10 20 0.5
0.40 xx 0.5
0.80 40 yy

What is the value of xx and yy ?

Options:

A)

80 and 4

B)

160 and 4

C)

80 and 2

D)

40 and 4

Question 14

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 22 English

Product [X] formed in the above reaction is :

Options:

A)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 22 English Option 1

B)

JEE Main 2023 (Online) 11th April Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 22 English Option 2

C)

H3CCH=CHCH3\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}

D)

H3CCH2CH=CH2\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}

Numerical TypeQuestion 15

The number of possible isomeric products formed when 3-chloro-1-butene reacts with HCl\mathrm{HCl} through carbocation formation is __________.

Numerical TypeQuestion 16

The maximum number of lone pairs of electrons on the central atom from the following species is ____________.

ClO3,XeF4,SF4\mathrm{ClO}_{3}{ }^{-}, \mathrm{XeF}_{4}, \mathrm{SF}_{4} and I3\mathrm{I}_{3}{ }^{-}

Numerical TypeQuestion 17

The total number of intensive properties from the following is __________

Volume, Molar heat capacity, Molarity, Eθ\mathrm{E}^{\theta} cell, Gibbs free energy change, Molar mass, Mole

Numerical TypeQuestion 18

Number of compounds from the following which will not produce orange red precipitate with Benedict solution is ___________.

Glucose, maltose, sucrose, ribose, 2-deoxyribose, amylose, lactose

Numerical TypeQuestion 19

The number of correct statements from the following is ___________.

A. For 1s1 \mathrm{s} orbital, the probability density is maximum at the nucleus

B. For 2s2 \mathrm{s} orbital, the probability density first increases to maximum and then decreases sharply to zero.

C. Boundary surface diagrams of the orbitals encloses a region of 100%100 \% probability of finding the electron.

D. p and d-orbitals have 1 and 2 angular nodes respectively.

E. probability density of p-orbital is zero at the nucleus

Numerical TypeQuestion 20

4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI\mathrm{HI} were found. The equilibrium constant for H2( g)+I2( g)2HI(g)\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) is _________.

Numerical TypeQuestion 21

The number of correct statements from the following is __________

A. Ecell \mathrm{E_{\text {cell }}} is an intensive parameter

B. A negative E\mathrm{E}^{\ominus} means that the redox couple is a stronger reducing agent than the H+/H2\mathrm{H}^{+} / \mathrm{H}_{2} couple.

C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction.

D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte.

Numerical TypeQuestion 22

The volume of hydrogen liberated at STP by treating 2.4 g2.4 \mathrm{~g} of magnesium with excess of hydrochloric acid is _________ × 102 L\times ~10^{-2} \mathrm{~L}

Given : Molar volume of gas is 22.4 L22.4 \mathrm{~L} at STP.

Molar mass of magnesium is 24 g mol124 \mathrm{~g} \mathrm{~mol}^{-1}

Question 23

Let a,b,ca, b, c and dd be positive real numbers such that a+b+c+d=11a+b+c+d=11. If the maximum value of a5b3c2da^{5} b^{3} c^{2} d is 3750β3750 \beta, then the value of β\beta is

Options:

A)

110

B)

108

C)

90

D)

55

Question 24

The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)n+2(1+\mathrm{x})^{\mathrm{n}+2}, which are in the ratio 1:3:51: 3: 5, is equal to :

Options:

A)

63

B)

92

C)

25

D)

41

Question 25

If the system of linear equations

7x+11y+αz=135x+4y+7z=β175x+194y+57z=361 \begin{aligned} & 7 x+11 y+\alpha z=13 \\\\ & 5 x+4 y+7 z=\beta \\\\ & 175 x+194 y+57 z=361 \end{aligned}

has infinitely many solutions, then α+β+2\alpha+\beta+2 is equal to :

Options:

A)

6

B)

4

C)

5

D)

3

Question 26

For aCa \in \mathbb{C}, let A={zC:Re(a+zˉ)>Im(aˉ+z)}\mathrm{A}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z}) > \operatorname{Im}(\bar{a}+z)\} and B={zC:Re(a+zˉ)<Im(aˉ+z)}\mathrm{B}=\{z \in \mathbb{C}: \operatorname{Re}(a+\bar{z})<\operatorname{Im}(\bar{a}+z)\}. Then among the two statements :

(S1): If Re(a),Im(a)>0\operatorname{Re}(a), \operatorname{Im}(a) > 0, then the set A contains all the real numbers

(S2) : If Re(a),Im(a)<0\operatorname{Re}(a), \operatorname{Im}(a) < 0, then the set B contains all the real numbers,

Options:

A)

both are false

B)

only (S1) is true

C)

only (S2) is true

D)

both are true

Question 27

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :

Options:

A)

103

B)

104

C)

102

D)

101

Question 28

Let A={1,3,4,6,9}\mathrm{A}=\{1,3,4,6,9\} and B={2,4,5,8,10}\mathrm{B}=\{2,4,5,8,10\}. Let R\mathrm{R} be a relation defined on A×B\mathrm{A} \times \mathrm{B} such that R={((a1,b1),(a2,b2)):a1b2\mathrm{R}=\left\{\left(\left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right)\right): a_{1} \leq b_{2}\right. and b1a2}\left.b_{1} \leq a_{2}\right\}. Then the number of elements in the set R is :

Options:

A)

180

B)

26

C)

52

D)

160

Question 29

If the 1011th 1011^{\text {th }} term from the end in the binominal expansion of (4x552x)2022\left(\frac{4 x}{5}-\frac{5}{2 x}\right)^{2022} is 1024 times 1011th 1011^{\text {th }}R term from the beginning, then x|x| is equal to

Options:

A)

516 \frac{5}{16}

B)

8

C)

12

D)

15

Question 30

x+1xxxx+λxxxx+λ2=98(103x+81)\left|\begin{array}{ccc}x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^{2}\end{array}\right|=\frac{9}{8}(103 x+81), then λ,λ3\lambda, \frac{\lambda}{3} are the roots of the equation :

Options:

A)

4x2+24x27=04 x^{2}+24 x-27=0

B)

4x224x+27=04 x^{2}-24 x+27=0

C)

4x224x27=04 x^{2}-24 x-27=0

D)

4x2+24x+27=04 x^{2}+24 x+27=0

Question 31

Let the mean of 6 observations 1,2,4,5,x1,2,4,5, \mathrm{x} and y\mathrm{y} be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :

Options:

A)

103\frac{10}{3}

B)

83\frac{8}{3}

C)

73\frac{7}{3}

D)

3

Question 32

If f:RRf: \mathbb{R} \rightarrow \mathbb{R} be a continuous function satisfying \int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0, then the value of α\alpha is :

Options:

A)

3-\sqrt{3}

B)

2\sqrt{2}

C)

2-\sqrt{2}

D)

3\sqrt{3}

Question 33

Let ff and gg be two functions defined by

f(x)={x+1,x<0x1,x0f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ |x-1|, & x \geq 0\end{array}\right. and g(x)={x+1,x<01,x0\mathrm{g}(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ 1, & x \geq 0\end{array}\right.

Then (gf)(x)(g \circ f)(x) is :

Options:

A)

continuous everywhere but not differentiable at x=1x=1

B)

differentiable everywhere

C)

not continuous at x=1x=-1

D)

continuous everywhere but not differentiable exactly at one point

Question 34

Let y=y(x)y=y(x) be the solution of the differential equation dydx+5x(x5+1)y=(x5+1)2x7,x>0\frac{d y}{d x}+\frac{5}{x\left(x^{5}+1\right)} y=\frac{\left(x^{5}+1\right)^{2}}{x^{7}}, x > 0. If y(1)=2y(1)=2, then y(2)y(2) is equal to :

Options:

A)

693128\frac{693}{128}

B)

697128\frac{697}{128}

C)

637128\frac{637}{128}

D)

679128\frac{679}{128}

Question 35

Let the function f:[0,2]Rf:[0,2] \rightarrow \mathbb{R} be defined as

f(x)={emin{x2,x[x]},x[0,1)e[xlogex],x[1,2]f(x)= \begin{cases}e^{\min \left\{x^{2}, x-[x]\right\},} & x \in[0,1) \\ e^{\left[x-\log _{e} x\right]}, & x \in[1,2]\end{cases}

where [t][t] denotes the greatest integer less than or equal to tt. Then the value of the integral \int_\limits{0}^{2} x f(x) d x is :

Options:

A)

2e12 e-1

B)

2e122 e-\frac{1}{2}

C)

1+3e21+\frac{3 e}{2}

D)

(e1)(e2+12)(e-1)\left(e^{2}+\frac{1}{2}\right)

Question 36

The domain of the function f(x)=1[x]23[x]10f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]-10}} is : ( where [x][\mathrm{x}] denotes the greatest integer less than or equal to xx )

Options:

A)

(,2)[6,)(-\infty,-2) \cup[6, \infty)

B)

(,3][6,)(-\infty,-3] \cup[6, \infty)

C)

(,2)(5,)(-\infty,-2) \cup(5, \infty)

D)

(,3](5,)(-\infty,-3] \cup(5, \infty)

Numerical TypeQuestion 37

Let a=i^+2j^+3k^\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k} and b=i^+j^k^\vec{b}=\hat{i}+\hat{j}-\hat{k}. If c\vec{c} is a vector such that \vec{a} \cdot \vec{c}=11, \vec{b} \cdot(\vec{a} \times \vec{c})=27\( and \)\vec{b} \cdot \vec{c}=-\sqrt{3}|\vec{b}|\(, then \)|\vec{a} \times \vec{c}|^{2} is equal to _________.

Numerical TypeQuestion 38

Let A={1,2,3,4,5}\mathrm{A}=\{1,2,3,4,5\} and B={1,2,3,4,5,6}\mathrm{B}=\{1,2,3,4,5,6\}. Then the number of functions f:ABf: \mathrm{A} \rightarrow \mathrm{B} satisfying f(1)+f(2)=f(4)1f(1)+f(2)=f(4)-1 is equal to __________.

Numerical TypeQuestion 39

Let the probability of getting head for a biased coin be 14\frac{1}{4}. It is tossed repeatedly until a head appears. Let N\mathrm{N} be the number of tosses required. If the probability that the equation 64x2+5Nx+1=064 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0 has no real root is pq\frac{\mathrm{p}}{\mathrm{q}}, where p\mathrm{p} and q\mathrm{q} are coprime, then qpq-p is equal to ________.

Numerical TypeQuestion 40

If A is the area in the first quadrant enclosed by the curve C:2x2y+1=0\mathrm{C: 2 x^{2}-y+1=0}, the tangent to C\mathrm{C} at the point (1,3)(1,3) and the line x+y=1\mathrm{x}+\mathrm{y}=1, then the value of 60 A60 \mathrm{~A} is _________.

Numerical TypeQuestion 41

Let S={zC{i,2i}:z2+8iz15z23iz2R}\mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^{2}+8 i z-15}{z^{2}-3 i z-2} \in \mathbb{R}\right\}. If α1311iS,αR{0}\alpha-\frac{13}{11} i \in \mathrm{S}, \alpha \in \mathbb{R}-\{0\}, then 242α2242 \alpha^{2} is equal to _________.

Numerical TypeQuestion 42

The number of points, where the curve f(x)=e8xe6x3e4xe2x+1,xRf(x)=\mathrm{e}^{8 x}-\mathrm{e}^{6 x}-3 \mathrm{e}^{4 x}-\mathrm{e}^{2 x}+1, x \in \mathbb{R} cuts xx-axis, is equal to _________.

Question 43

JEE Main 2023 (Online) 11th April Evening Shift Physics - Current Electricity Question 40 English

The current flowing through R2_2 is :

Options:

A)

12 A\frac{1}{2} \mathrm{~A}

B)

13 A\frac{1}{3} \mathrm{~A}

C)

14 A\frac{1}{4} \mathrm{~A}

D)

23 A\frac{2}{3} \mathrm{~A}

Question 44

A plane electromagnetic wave of frequency 20 MHz20 ~\mathrm{MHz} propagates in free space along x\mathrm{x}-direction. At a particular space and time, E=6.6j^ V/m\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}. What is B\overrightarrow{\mathrm{B}} at this point?

Options:

A)

2.2×108i^T-2.2 \times 10^{-8} \hat{i} T

B)

2.2×108i^T2.2 \times 10^{-8} \hat{i} T

C)

2.2×108k^T2.2 \times 10^{-8} \hat{k} T

D)

2.2×108k^T-2.2 \times 10^{-8} \hat{k} T

Question 45

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

A. The electron will experience magnetic force along the axis of the solenoid.

B. The electron will not experience magnetic force.

C. The electron will continue to move along the axis of the solenoid.

D. The electron will be accelerated along the axis of the solenoid.

E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

Options:

A)

B, C and D only

B)

B and C only

C)

A and D only

D)

B and E only

Question 46

The Thermodynamic process, in which internal energy of the system remains constant is

Options:

A)

Isobaric

B)

Isochoric

C)

Adiabatic

D)

Isothermal

Question 47

Given below are two statements: one is labelled as Assertion A\mathbf{A} and the other is labelled as Reason R\mathbf{R}

Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass.

Reason R: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar.

In the light of the above statements, choose the correct answer from the options given below

Options:

A)

A is true but R is false

B)

A is false but R is true

C)

Both A and R are true but R is NOT the correct explanation of A

D)

Both A and R are true and R is the correct explanation of A

Question 48

The energy of He+\mathrm{He}^{+} ion in its first excited state is, (The ground state energy for the Hydrogen atom is 13.6 eV)-13.6 ~\mathrm{eV}) :

Options:

A)

13.6 eV-13.6 ~\mathrm{eV}

B)

27.2 eV-27.2 ~\mathrm{eV}

C)

3.4 eV-3.4 ~\mathrm{eV}

D)

54.4 eV-54.4 ~\mathrm{eV}

Question 49

When one light ray is reflected from a plane mirror with 3030^{\circ} angle of reflection, the angle of deviation of the ray after reflection is :

Options:

A)

140140^{\circ}

B)

130130^{\circ}

C)

120120^{\circ}

D)

110110^{\circ}

Question 50

A capacitor of capacitance C\mathrm{C} is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

Options:

A)

Zero

B)

CVε0\frac{C V}{\varepsilon_{0}}

C)

CV2ε0\frac{C V}{2 \varepsilon_{0}}

D)

2CVε0\frac{2 C V}{\varepsilon_{0}}

Question 51

The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy :

(Assume mp=me×1849m_{p}=m_{e} \times 1849 )

Options:

A)

1:43

B)

1:62

C)

2:43

D)

1:30

Question 52

Eight equal drops of water are falling through air with a steady speed of 10 cm/s10 \mathrm{~cm} / \mathrm{s}. If the drops coalesce, the new velocity is:-

Options:

A)

40 cm/s40 \mathrm{~cm} / \mathrm{s}

B)

16 cm/s16 \mathrm{~cm} / \mathrm{s}

C)

10 cm/s10 \mathrm{~cm} / \mathrm{s}

D)

5 cm/s5 \mathrm{~cm} / \mathrm{s}

Question 53

The logic operations performed by the given digital circuit is equivalent to:

JEE Main 2023 (Online) 11th April Evening Shift Physics - Semiconductor Question 19 English

Options:

A)

NOR

B)

AND

C)

NAND

D)

OR

Question 54

A projectile is projected at 3030^{\circ} from horizontal with initial velocity 40 ms140 \mathrm{~ms}^{-1}. The velocity of the projectile at t=2 s\mathrm{t}=2 \mathrm{~s} from the start will be : (Given g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^{2} )

Options:

A)

203 ms120 \sqrt{3} \mathrm{~ms}^{-1}

B)

Zero

C)

20 ms120 \mathrm{~ms}^{-1}

D)

403 ms140 \sqrt{3} \mathrm{~ms}^{-1}

Question 55

A body of mass 500 g500 \mathrm{~g} moves along x\mathrm{x}-axis such that it's velocity varies with displacement x\mathrm{x} according to the relation v=10x m/sv=10 \sqrt{x} \mathrm{~m} / \mathrm{s} the force acting on the body is:-

Options:

A)

166 N

B)

5 N

C)

25 N

D)

125 N

Question 56

A space ship of mass 2×104 kg2 \times 10^{4} \mathrm{~kg} is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^{2} and radius of earth =6400 km=6400 \mathrm{~km} ):

Options:

A)

7.9(21)km/s7.9(\sqrt{2}-1) \mathrm{km} / \mathrm{s}

B)

11.2(21)km/s11.2(\sqrt{2}-1) \mathrm{km} / \mathrm{s}

C)

7.4(21)km/s7.4(\sqrt{2}-1) \mathrm{km} / \mathrm{s}

D)

8(21)km/s8(\sqrt{2}-1) \mathrm{km} / \mathrm{s}

Question 57

When vector A=2i^+3j^+2k^\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k} is subtracted from vector B\overrightarrow{\mathrm{B}}, it gives a vector equal to 2j^2 \hat{j}. Then the magnitude of vector B\overrightarrow{\mathrm{B}} will be :

Options:

A)

3

B)

33\sqrt{33}

C)

6\sqrt6

D)

5\sqrt5

Question 58

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

Options:

A)

FV2 T2\mathrm{FV}^{-2} \mathrm{~T}^{2}

B)

FV4 T6\mathrm{FV}^{4} \mathrm{~T}^{-6}

C)

F2 V2 T6\mathrm{F}^{2} \mathrm{~V}^{-2} \mathrm{~T}^{6}

D)

FV4 T2\mathrm{FV}^{-4} \mathrm{~T}^{-2}

Question 59

If V\mathrm{V} is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

Options:

A)

3 V2\frac{3 \mathrm{~V}}{2}

B)

V2\frac{\mathrm{V}}{2}

C)

43 V\frac{4}{3} \mathrm{~V}

D)

V\mathrm{V}

Question 60

The root mean square speed of molecules of nitrogen gas at 27C27^{\circ} \mathrm{C} is approximately : (Given mass of a nitrogen molecule =4.6×1026 kg=4.6 \times 10^{-26} \mathrm{~kg} and take Boltzmann constant kB=1.4×1023JK1\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{JK}^{-1} )

Options:

A)

91 m/s

B)

1260 m/s

C)

27.4 m/s

D)

523 m/s

Numerical TypeQuestion 61

As shown in the figure, a plane mirror is fixed at a height of 50 cm50 \mathrm{~cm} from the bottom of tank containing water (μ=43)\left(\mu=\frac{4}{3}\right). The height of water in the tank is 8 cm8 \mathrm{~cm}. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ___________ cm\mathrm{cm}.

JEE Main 2023 (Online) 11th April Evening Shift Physics - Geometrical Optics Question 25 English

Numerical TypeQuestion 62

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity ω\omega. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be Ex\frac{E}{x}. The value of xx is

Numerical TypeQuestion 63

The surface tension of soap solution is 3.5×102 Nm13.5 \times 10^{-2} \mathrm{~Nm}^{-1}. The amount of work done required to increase the radius of soap bubble from 10 cm10 \mathrm{~cm} to 20 cm20 \mathrm{~cm} is _________ × 104 J\times ~10^{-4} \mathrm{~J}.

(takeπ=22/7)(\operatorname{take} \pi=22 / 7)

Numerical TypeQuestion 64

A wire of density 8×103 kg/m38 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} is stretched between two clamps 0.5 m0.5 \mathrm{~m} apart. The extension developed in the wire is 3.2×104 m3.2 \times 10^{-4} \mathrm{~m}. If Y=8×1010 N/m2Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}, the fundamental frequency of vibration in the wire will be ___________ Hz\mathrm{Hz}.

Numerical TypeQuestion 65

A metallic cube of side 15 cm15 \mathrm{~cm} moving along yy-axis at a uniform velocity of 2 ms12 \mathrm{~ms}^{-1}. In a region of uniform magnetic field of magnitude 0.5 T0.5 \mathrm{~T} directed along zz-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

JEE Main 2023 (Online) 11th April Evening Shift Physics - Electromagnetic Induction Question 23 English

Numerical TypeQuestion 66

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1:21/31: 2^{1 / 3}. Their respective speed have a ratio of n:1n: 1. The value of nn is __________.

Numerical TypeQuestion 67

A block of mass 5 kg5 \mathrm{~kg} starting from rest pulled up on a smooth incline plane making an angle of 3030^{\circ} with horizontal with an affective acceleration of 1 ms21 \mathrm{~ms}^{-2}. The power delivered by the pulling force at t=10 st=10 \mathrm{~s} from the start is ___________ W.

[use g=10 ms2\mathrm{g}=10 \mathrm{~ms}^{-2} ]

(calculate the nearest integer value)

Numerical TypeQuestion 68

In the given circuit, C1=2μF,C2=0.2μF,C3=2μF,C4=4μF,C5=2μF,C6=2μF\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=0.2 \mu \mathrm{F}, \mathrm{C}_{3}=2 \mu \mathrm{F}, \mathrm{C}_{4}=4 \mu \mathrm{F}, \mathrm{C}_{5}=2 \mu \mathrm{F}, \mathrm{C}_{6}=2 \mu \mathrm{F}, The charge stored on capacitor C4\mathrm{C}_{4} is ____________ μC\mu \mathrm{C}.

JEE Main 2023 (Online) 11th April Evening Shift Physics - Capacitor Question 16 English

Numerical TypeQuestion 69

A coil has an inductance of 2H2 \mathrm{H} and resistance of 4 Ω4 ~\Omega. A 10 V10 \mathrm{~V} is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ___________ ×102 J\times 10^{-2} \mathrm{~J}.

Numerical TypeQuestion 70

Two identical cells each of emf 1.5 V1.5 \mathrm{~V} are connected in series across a 10 Ω10 ~\Omega resistance. An ideal voltmeter connected across 10 Ω10 ~\Omega resistance reads 1.5 V1.5 \mathrm{~V}. The internal resistance of each cell is __________ Ω\Omega.