JEE Main 5 April 2024 Shift 2 question paper with solutions

Question 1

Maths · Continuity and Differentiability · Single correct

Let $f : [-1, 2] \to \mathbb{R}$ be given by $f(x) = 2x^2 + x + \lfloor x^2 \rfloor - \lfloor x \rfloor$, where $\lfloor t \rfloor$ denotes the greatest integer less than or equal to $t$. The number of points, where $f$ is not continuous, is :

1. 5
2. 6
3. 3
4. 4

Answer: (d)

Question 2

Maths · Differential Equations · Single correct

The differential equation of the family of circles passing through the origin and having centre at the line $y = x$ is :

1. $(x^2 - y^2 + 2xy) \, dx = (x^2 - y^2 - 2xy) \, dy$
2. $(x^2 + y^2 + 2xy) \, dx = (x^2 + y^2 - 2xy) \, dy$
3. $(x^2 + y^2 - 2xy) \, dx = (x^2 + y^2 + 2xy) \, dy$
4. $(x^2 - y^2 + 2xy) \, dx = (x^2 - y^2 + 2xy) \, dy$

Answer: (a)

Question 3

Maths · Complex Numbers and Quadratic Equations · Single correct

Let $S_1 = \{ z \in \mathbb{C} : |z| \leq 5 \}, S_2 = \{ z \in \mathbb{C} : \mathrm{Im} \left( \frac{z+1-\sqrt{3}i}{1-\sqrt{3}i} \right) \geq 0 \}$ and $S_3 = \{ z \in \mathbb{C} : \mathrm{Re}(z) \geq 0 \}$. Then the area of the region $S_1 \cap S_2 \cap S_3$ is:

1. $\frac{125\pi}{12}$
2. $\frac{125\pi}{4}$
3. $\frac{125\pi}{24}$
4. $\frac{125\pi}{6}$

Answer: (a)

Question 4

Maths · Applications of Integrals · Single correct

The area enclosed between the curves $y = x|x|$ and $y = x - |x|$ is :

1. $\frac{4}{3}$
2. 1
3. $\frac{2}{3}$
4. $\frac{8}{3}$

Answer: (a)

Question 5

Maths · Permutations and Combinations · Single correct

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50^{\text{th}}$ word is

1. JBBOH
2. OBBJH
3. OBBHJ
4. HBBJO

Answer: (b)

Question 6

Maths · Vector Algebra · Single correct

Let $\vec{a}$ = 2$\hat{i}$ + 5$\hat{j}$ - $\hat{k}$, $\vec{b}$ = 2$\hat{i}$ - 2$\hat{j}$ + 2$\hat{k}$ and $\vec{c}$ be three vectors such that ($\vec{c}$ + $\hat{i}$) $\times$ ($\vec{a}$ + $\vec{b}$ + $\hat{i}$) = $\vec{a}$ $\times$ ($\vec{c}$ + $\hat{i}$). If $\($ $\vec{a}$ $\cdot$ $\vec{c}$ = -29 $\)$, then $\vec{c}$ $\cdot$ (-2$\hat{i}$ + $\hat{j}$ + $\hat{k}$) is equal to:

1. 15
2. 12
3. 10
4. 5

Answer: (d)

Question 7

Maths · Vector Algebra · Single correct

Consider three vectors $\vec{a}, \vec{b}, \vec{c}$. Let $|\vec{a}| = 2$, $|\vec{b}| = 3$ and $\vec{a} = \vec{b} \times \vec{c}$. If $\alpha \in \left[0, \frac{\pi}{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$, then the minimum value of $27|\vec{c} - \vec{a}|^2$ is equal to:

1. 110
2. 124
3. 121
4. 105

Answer: (b)

Question 8

Maths · Straight Lines and Pair of Straight Lines · Single correct

Let $A(-1, 1)$ and $B(2, 3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $\triangle PAB$ is $10$. If the locus of $P$ is $ax + by = 15$, then $5a + 2b$ is:

1. 6
2. -$\frac{6}{5}$
3. 4
4. -$\frac{12}{5}$

Answer: (d)

Question 9

Maths · Three Dimensional Geometry · Single correct

Let $(\alpha, \beta, \gamma)$ be the image of the point $(8, 5, 7)$ in the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}$. Then $\alpha + \beta + \gamma$ is equal to :

1. 16
2. 20
3. 14
4. 18

Answer: (c)

Question 10

Maths · Binomial Theorem · Single correct

If the constant term in the expansion of $\left(\dfrac{\sqrt[5]{3}}{x} + \dfrac{2x}{\sqrt[3]{5}}\right)^{12}$, $x \neq 0$, is $\alpha \times 2^8 \times \sqrt[5]{3}$, then $25\alpha$ is equal to:

1. 724
2. 742
3. 639
4. 693

Answer: (d)

Question 11

Maths · Relations and Functions · Single correct

Let $f, g : \mathbb{R} \to \mathbb{R}$ be defined as : $$f(x) = |x - 1| and g(x) = \begin{cases} e^x, & x \geq 0 \\ x + 1, & x \leq 0 \end{cases}$$ Then the function $f(g(x))$ is

1. neither one-one nor onto.
2. one-one but not onto.
3. onto but not one-one.
4. both one-one and onto.

Answer: (a)

Question 12

Maths · Conic Sections · Single correct

Let the circle $C_1 : x^2 + y^2 - 2(x + y) + 1 = 0$ and $C_2$ be a circle having centre at $(-1, 0)$ and radius $2$. If the line of the common chord of $C_1$ and $C_2$ intersects the $y$-axis at the point $P$, then the square of the distance of $P$ from the centre of $C_1$ is:

1. 2
2. 1
3. 4
4. 6

Answer: (a)

Question 13

Maths · Sets · Single correct

Let the set $S = \{2, 4, 8, 16, \ldots, 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$. The maximum number of such possible partitions of $S$ is equal to:

1. 1680
2. 1640
3. 1520
4. 1710

Answer: (a)

Question 14

Maths · Determinants · Single correct

The values of $m, n$, for which the system of equations $$x + y + z = 4,$$ $$2x + 5y + 5z = 17,$$ $$x + 2y + mz = n$$ has infinitely many solutions, satisfy the equation:

1. $m^2 + n^2 - mn = 39$
2. $m^2 + n^2 - m - n = 46$
3. $m^2 + n^2 + m + n = 64$
4. $m^2 + n^2 + mn = 68$

Answer: (a)

Question 15

Maths · Probability · Single correct

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are from the set {$1, 2, 3, 4, 5, 6$\}. If the probability of this equation having one real root bigger than the other is $p$, then $216 \, p$ equals:

1. 57
2. 76
3. 38
4. 19

Answer: (c)

Question 16

Maths · Conic Sections · Single correct

Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies:

1. r = 0
2. 2r^2 - 4r + 1 = 0
3. 2r^2 - 8r + 7 = 0
4. r^2 - 8r + 8 = 0

Answer: (d)

Question 17

Maths · Integrals · Single correct

Let $\beta(m, n) = \int_0^1 x^{m-1} (1-x)^{n-1} \, dx$, $m, n > 0$. If $\int_0^1 (1-x^{10})^{20} \, dx = a \times \beta(b, c)$, then $100(a+b+c)$ equals

1. 1021
2. 2120
3. 2012
4. 1120

Answer: (b)

Question 18

Maths · Determinants · Single correct

Let $\alpha \beta \neq 0$ and $A = \begin{bmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha \end{bmatrix}$. If $B = \begin{bmatrix} 3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta \end{bmatrix}$ is the matrix of cofactors of the elements of $A$, then $\det(AB)$ is equal to:

1. 64
2. 216
3. 343
4. 125

Answer: (b)

Question 19

Maths · Continuity and Differentiability · Single correct

If $y(\theta) = \frac{2 \cos \theta + \cos 2\theta}{\cos 3\theta + 4 \cos 2\theta + 5 \cos \theta + 2}$, then at $\theta = \frac{\pi}{2}$, $y'' + y' + y$ is equal to:

1. $\frac{1}{2}$
2. $1$
3. $2$
4. $\frac{3}{2}$

Answer: (c)

Question 20

Maths · Sequences and Series · Single correct

For $x \geq 0$, the least value of $K$, for which $4^{1+x} + 4^{1-x}, \frac{K}{2}, 16^x + 16^{-x}$ are three consecutive terms of an A.P., is equal to:

1. 8
2. 4
3. 10
4. 16

Answer: (c)

Question 21

Maths · Probability · Numerical

Let the mean and the standard deviation of the probability distribution \[ \begin{tabular}{|c|c|c|c|c|} \hline $X$ & $\alpha$ & $1$ & $0$ & $-3$ \\ \hline $P(X)$ & $\dfrac13$ & $k$ & $\dfrac16$ & $\dfrac14$ \\ \hline \end{tabular} be $\mu$ and $\sigma$, respectively. If $\sigma - \mu = 2$, then $\sigma + \mu$ is equal to _______

Answer: 5

Question 22

Maths · Differential Equations · Numerical

Let $y = y(x)$ be the solution of the differential equation $$\frac{dy}{dx} + \frac{2x}{(1+x^2)^2}y = xe^{\frac{1}{(1+x^2)}}; \; y(0) = 0.$$ Then the area enclosed by the curve $f(x) = y(x)e^{-\frac{1}{(1+x^2)}}$ and the line $y - x = 4$ is

Answer: 18

Question 23

Maths · Trigonometric Functions · Fill in the blank

The number of solutions of $\sin^2 x + (2 + 2x - x^2) \sin x - 3(x - 1)^2 = 0$, where $-\pi \leq x \leq \pi$, is ________

Answer: 2

Question 24

Maths · Three Dimensional Geometry · Numerical

Let the point $(-1, \alpha, \beta)$ lie on the line of the shortest distance between the lines $\frac{x+2}{-3} = \frac{y-2}{4} = \frac{z-5}{2}$ and $\frac{x+2}{-1} = \frac{y+6}{2} = \frac{z-1}{0}$. Then $(\alpha - \beta)^2$ is equal to

Answer: 25

Question 25

Maths · Sequences and Series · Numerical

If $1 + \frac{\sqrt{3} - \sqrt{2}}{2\sqrt{3}} + \frac{5 - 2\sqrt{6}}{18} + \frac{9\sqrt{3} - 11\sqrt{2}}{36\sqrt{3}} + \frac{49 - 20\sqrt{6}}{180} + \dots \text{ upto } \infty = 2 + \left( \sqrt{\frac{b}{a}} + 1 \right) \log_e \left( \frac{a}{b} \right)$, where $a$ and $b$ are integers with $\gcd(a, b) = 1$, then $11a + 18b$ is equal to \text{_____}.

Answer: 76

Question 26

Maths · Limits and Derivatives · Numerical

Let $a > 0$ be a root of the equation $2x^2 + x - 2 = 0$. If $\lim_{x \to \frac{1}{a}} \frac{16(1 - \cos(2 + x - 2x^2))}{(1 - ax)^2} = \alpha + \beta \sqrt{17}$, where $\alpha, \beta \in \mathbb{Z}$, then $\alpha + \beta$ is equal to _____.

Answer: 170

Question 27

Maths · Integrals · Numerical

If $f(t) = \int_{0}^{\pi} \frac{2x \, dx}{1 - \cos^2 t \sin^2 x}$, $0 < t < \pi$, then the value of $\int_{0}^{\frac{\pi}{2}} \frac{\pi^2 \, dt}{f(t)}$ equals

Answer: 1

Question 28

Maths · Applications of Derivatives · Numerical

Let the maximum and minimum values of $\left( \sqrt{8x - x^2 - 12 - 4} \right)^2 + (x - 7)^2, x \in \mathbb{R}$ be M and m, respectively. Then $M^2 - m^2$ is equal to

Answer: 1600

Question 29

Maths · Conic Sections · Numerical

Let a line perpendicular to the line $2x - y = 10$ touch the parabola $y^2 = 4(x - 9)$ at the point $P$. The distance of the point $P$ from the centre of the circle $x^2 + y^2 - 14x - 8y + 56 = 0$ is

Answer: 10

Question 30

Maths · Complex Numbers and Quadratic Equations · Numerical

The number of real solutions of the equation $x|x + 5| + 2|x + 7| - 2 = 0$ is ________

Answer: 3

Question 31

Physics · Ray Optics and Optical Instruments · Single correct

Given below are two statements: Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II: The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, chose the correct answer from the options given below:

1. Statement I is false but Statement II is true
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

Answer: (c)

Question 32

Physics · Dual Nature of Radiation and Matter · Single correct

Which of the following statement is not true about stopping potential $(V_0)$?

1. It is $1/e$ times the maximum kinetic energy of electrons emitted.
2. It increases with increase in intensity of the incident light.
3. It depends on the nature of emitter material.
4. It depends upon frequency of the incident light.

Answer: (b)

Question 33

Physics · Atoms · Single correct

The angular momentum of an electron in a hydrogen atom is proportional to: (Where $r$ is the radius of orbit of electron)

1. $r$
2. $\sqrt{r}$
3. $\frac{1}{\sqrt{r}}$
4. $\frac{1}{r}$

Answer: (b)

Question 34

Physics · Current Electricity · Single correct

A galvanometer of resistance $100\,\Omega$ when connected in series with $400\,\Omega$ measures a voltage of upto $10\,\mathrm{V}$. The value of resistance required to convert the galvanometer into ammeter to read upto $10\,\mathrm{A}$ is $x \times 10^{-2}\,\Omega$. The value of $x$ is :

1. 2
2. 800
3. 20
4. 200

Answer: (c)

Question 35

Physics · Electric Charges and Fields · Single correct

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

1. To protect tyres from catching dirt from ground
2. To alert other vehicles
3. It is a custom
4. To conduct excess charge due to air friction to ground and prevent sparking

Answer: (d)

Question 36

Physics · Kinetic Theory · Single correct

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by:

1. $\sqrt{2n\pi d^2}$
2. $\frac{1}{\sqrt{2n\pi d^2}}$
3. $\frac{1}{\sqrt{2n\pi d^2}}$
4. $\frac{1}{\sqrt{2n^2\pi^2 d^2}}$

Answer: (c)

Question 37

Physics · Mathematics in Physics · Single correct

A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$. If $k$ is constant, the angle between $\vec{F}$ and $\vec{p}$ will be:

1. $\frac{\pi}{4}$
2. $\frac{\pi}{6}$
3. $\frac{\pi}{2}$
4. $\frac{\pi}{3}$

Answer: (c)

Question 38

Physics · Moving Charges and Magnetism · Single correct

The electrostatic force $\left( \vec{F}_1 \right)$ and magnetic force $\left( \vec{F}_2 \right)$ acting on a charge $q$ moving with velocity $v$ can be written:

1. $\vec{F}_1 = q\vec{E}, \vec{F}_2 = q(\vec{V} \times \vec{B})$
2. $\vec{F}_1 = q\vec{B}, \vec{F}_2 = q(\vec{B} \times \vec{V})$
3. $\vec{F}_1 = q\vec{E}, \vec{F}_2 = q(\vec{B} \times \vec{V})$
4. $\vec{F}_1 = q\vec{V} \cdot \vec{E}, \vec{F}_2 = q(\vec{B} \cdot \vec{V})$

Answer: (a)

Question 39

Physics · Laws of Motion · Single correct

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \, \mathrm{m}$ and completes $120$ revolutions in $3$ minutes. The magnitude of centripetal acceleration of the monkey is \text{_____} $\mathrm{m/s^2}$.

1. 57600$\pi^2$ $\mathrm{ms}^{-2}$
2. Zero
3. 4$\pi^2$ $\mathrm{ms}^{-2}$
4. 16$\pi^2$ $\mathrm{ms}^{-2}$

Answer: (d)

Question 40

Physics · Alternating Current · Single correct

A series LCR circuit is subjected to an ac signal of $200 \, \mathrm{V}$, $50 \, \mathrm{Hz}$. If the voltage across the inductor ($L = 10 \, \mathrm{mH}$) is $31.4 \, \mathrm{V}$, then the current in this circuit is _____.

1. $68\,\mathrm{A}$
2. $63\,\mathrm{A}$
3. $10\,\mathrm{A}$
4. $10\,\mathrm{mA}$

Answer: (c)

Question 41

Physics · Physical World, Units and Measurements · Single correct

What is the dimensional formula of $ab^{-1}$ in the equation $$\left( P + \frac{a}{V^2} \right) (V - b) = RT$$, where letters have their usual meaning.

1. $[M^{-1}L^5T^{3}]$
2. $[M^{5}L^7T^{4}]$
3. $[ML^2T^{-2}]$
4. $[M^0L^3T^{-2}]$

Answer: (c)

Question 42

Physics · Semiconductor Electronics: Materials, Devices and Simple Circuits · Single correct

The output ($Y$) of logic circuit given below is 0 only when :

1. $A = 1$, $B = 0$
2. $A = 0$, $B = 1$
3. $A = 0$, $B = 0$
4. $A = 1$, $B = 1$

Answer: (c)

Question 43

Physics · Work, Energy and Power · Single correct

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $t$ is proportional to:

1. $t$
2. $t^{3/2}$
3. $t^2$
4. $t^{2/3}$

Answer: (b)

Question 44

Physics · Current Electricity · Single correct

Match List-I with List-II : Choose the correct answer from the options given below:

1. $(A)-(III), (B)-(II), (C)-(IV), (D)-(I)$
2. $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$
3. $(A)-(IV), (B)-(III), (C)-(II), (D)-(I)$
4. $(A)-(I), (B)-(III), (C)-(II), (D)-(IV)$

Answer: (a)

Question 45

Physics · Kinetic Theory · Single correct

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_P}{C_V}$ for the gas is :

1. $\frac{5}{3}$
2. $\frac{9}{7}$
3. $\frac{3}{2}$
4. $\frac{7}{5}$

Answer: (c)

Question 46

Physics · Current Electricity · Single correct

Match List-I with List-II : Choose the correct answer from the options given below :

1. $(A)$–(IV), $(B)$–(II), $(C)$–(III), $(D)$–(I)
2. $(A)$–(III), $(B)$–(IV), $(C)$–(I), $(D)$–(II)
3. $(A)$–(II), $(B)$–(IV), $(C)$–(I), $(D)$–(III)
4. $(A)$–(III), $(B)$–(I), $(C)$–(II), $(D)$–(IV)

Answer: (b)

Question 47

Physics · Physical World, Units and Measurements · Single correct

A vernier callipers has 20 divisions on the vernier scale, which coincide with the $19^{\text{th}}$ division on the main scale. The least count of the instrument is $0.1\,\mathrm{mm}$. One main scale division is equal to \text{_____} $\mathrm{mm}$.

1. 0.5
2. 2
3. 5
4. 1

Answer: (b)

Question 48

Physics · Laws of Motion · Single correct

A heavy box of mass $50 \, \mathrm{kg}$ is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is $0.3$ then force of kinetic friction is :

1. 1.47 N
2. 147 N
3. 14.7 N
4. 1470 N

Answer: (b)

Question 49

Physics · Gravitation · Single correct

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : ( Given = Radius of geo-stationary orbit for earth is $4.2 \times 10^4$ km )

1. $1.4 \times 10^4$ km
2. $1.05 \times 10^4$ km
3. $8.4 \times 10^4$ km
4. $1.68 \times 10^5$ km

Answer: (b)

Question 50

Physics · Current Electricity · Single correct

The ratio of heat dissipated per second through the resistance $5\,\Omega$ and $10\,\Omega$ in the circuit given below is :

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 1

Answer: (b)

Question 51

Physics · Moving Charges and Magnetism · Numerical

A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' m ' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \, \mathrm{T}$ then the value of $m$ is _____.

Answer: 500

Question 52

Physics · Atoms · Numerical

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\,\mathrm{\mathring{A}}$. The longest wavelength of spectral lines in the Balmer series will be \text{_____} $\mathrm{\mathring{A}}$.

Answer: 6588

Question 53

Physics · Wave Optics · Numerical

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10^{-5}$ m. The value of $x$ is :

Answer: 275

Question 54

Physics · Waves · Numerical

A sonometer wire of resonating length 90 $\mathrm{\ cm}$ has a fundamental frequency of 400 $\mathrm{\ Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of 600 $\mathrm{\ Hz}$ under same tension _____ cm.

Answer: 60

Question 55

Physics · System of Particles and Rotational Motion · Numerical

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is .

Answer: 2

Question 56

Physics · Mechanical Properties of Fluids · Numerical

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \, \mathrm{N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _____N.

Answer: 1000

Question 57

Physics · Electric Charges and Fields · Numerical

The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be $\frac{E}{x}$. The value of $x$:

Answer: 16

Question 58

Physics · Motion in a Plane · Fill in the blank

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is _____ m.

Answer: 16

Question 59

Physics · Current Electricity · Numerical

A wire of resistance $20\,\Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _____ $\Omega$.

Answer: 5

Question 60

Physics · Electromagnetic Induction · Numerical

The current in an inductor is given by $I = (3t + 8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is $12\,\mathrm{mV}$. The self-inductance of the inductor ____ mH.

Answer: 4

Question 61

Chemistry · Chemical Bonding and Molecular Structure · Single correct

Match List I with List II List - I \begin{tabular}{|c|c|c|l|} \hline \multicolumn{2}{|c|}{List - I} & \multicolumn{2}{c|}{List - II} \\ \hline (A) & ICl & (I) & T-shape \\ \hline (B) & ICl$_3$ & (II) & pyramidal \\ \hline (C) & ClF$_5$ & (III) & Pentagonal bipyramidal \\ \hline (D) & XeF$_2$ & (IV) & Linear \\ \hline \end{tabular} Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(I), $(C)$-(II), (D)-(III)
2. (A)-(I), (B)-(IV), $(C)$-(III), (D)-(II)
3. (A) -(IV), (B)-(III), $(C)$-(II), (D)-(I)
4. (A) -(I), (B)-(III), $(C)$-(II), (D)-(IV)

Answer: (a)

Question 62

Chemistry · The d-and f-Block Elements · Single correct

While preparing crystals of Mohr's salt, dil $\mathrm{H_2SO_4}$ is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil $\mathrm{H_2SO_4}$ is added here to:

1. prevent the hydrolysis of ferrous sulphate
2. prevent the hydrolysis of ammonium sulphate
3. make the medium strongly acidic
4. increase the rate of formation of crystals

Answer: (a)

Question 63

Chemistry · Haloalkanes and Haloarenes · Single correct

Identify the major product in the following reaction.

Answer: (c)

Question 64

Chemistry · Organic Chemistry — Some Basic Principles & Techniques · Single correct

The correct nomenclature for the following compound is :

1. 2-formyl-4-hydroxyhept-7-enoic acid
2. 2-formyl-4-hydroxyhept-6-enoic acid
3. 2-carboxy-4-hydroxyhept-7-enal
4. 2-carboxy-4-hydroxyhept-6-enal

Answer: (b)

Question 65

Chemistry · Chemical Bonding and Molecular Structure · Single correct

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason $(R)$. Assertion (A) : $\mathrm{NH}_3$ and $\mathrm{NF}_3$ molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole moment of $\mathrm{NH}_3$ is greater than that of $\mathrm{NF}_3$. Reason $(R)$ : In $\mathrm{NH}_3$, the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the $\mathrm{N} - \mathrm{H}$ bonds. $\mathrm{F}$ is the most electronegative element. In the light of the above statements, choose the correct answer from the options given below :

1. Both (A) and $(R)$ are true and $(R)$ is the correct explanation of (A)
2. is false but $(R)$ is true
3. Both (A) and $(R)$ are true but $(R)$ is NOT the correct explanation of (A)
4. is true but $(R)$ is false

Answer: (a)

Question 66

Chemistry · Equilibrium · Single correct

Given below are two statements : Statement I : On passing $\mathrm{HCl}_{(g)}$ through a saturated solution of $\mathrm{BaCl}_2$, at room temperature white turbidity appears. Statement II : When $\mathrm{HCl}$ gas is passed through a saturated solution of $\mathrm{NaCl}$, sodium chloride is precipitated due to common ion effect. In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both Statement I and Statement II are correct
2. Statement I is correct but Statement II is incorrect
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct

Answer: (b)

Question 67

Chemistry · Co-ordination Compounds · Single correct

The metal atom present in the complex MABXL (where A, B, X and L are unidentate ligands and M is metal) involves $sp^3$ hybridization. The number of geometrical isomers exhibited by the complex is:

1. 2
2. 0
3. 4
4. 3

Answer: (b)

Question 68

Chemistry · Co-ordination Compounds · Single correct

Match List I with List II Choose the correct answer from the options given below :

1. (A)-(II), (B)-(I), $(C)$-(IV), (D)-(III)
2. (A)-(III), (B)-(I), $(C)$-(II), (D)-(IV)
3. (A)-(I), (B)-(III), $(C)$-(IV), (D)-(II)
4. (A)-(III), (B)-(I), $(C)$-(IV), (D)-(II)

Answer: (d)

Question 69

Chemistry · Electrochemistry · Single correct

The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO_3}$ solution:

1. 1 g of silver
2. 1 electrochemical equivalent of silver
3. 1 chemical equivalent of silver
4. 0.1 g atom of silver

Answer: (b)

Question 70

Chemistry · Alcohols, Phenols and Ethers · Single correct

Which one of the following reactions is NOT possible?

Answer: (c)

Question 71

Chemistry · Classification of Elements and Periodicity in Properties · Single correct

Given below are two statements : Statement I : The metallic radius of Na is 1.86 $\mathrm{\AA}$ and the ionic radius of $\mathrm{Na^+}$ is lesser than 1.86 $\mathrm{\AA}$ . Statement II : Ions are always smaller in size than the corresponding elements. In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are false
2. Statement I is incorrect but Statement II is true
3. Both Statement I and Statement II are true
4. Statement I is correct but Statement II is false

Answer: (d)

Question 72

Chemistry · Alcohols, Phenols and Ethers · Single correct

Consider the above reaction sequence and identify the major product $P$.

1. Methoxymethane
2. Methanoic acid
3. Methanal
4. Methane

Answer: (d)

Question 73

Chemistry · Hydrocarbons · Single correct

Consider the given chemical reaction: Product "A" is:

1. picric acid
2. acetic acid
3. adipic acid
4. oxalic acid

Answer: (c)

Question 74

Chemistry · Electrochemistry · Single correct

For the electro chemical cell $\mathrm{M}|\mathrm{M}^{2+}||\mathrm{X}|\mathrm{X}^{2-}$ If $\mathrm{E}^0_{(\mathrm{M}^{2+}/\mathrm{M})} = 0.46 \, \mathrm{V}$ and $\mathrm{E}^0_{(\mathrm{X}/\mathrm{X}^{2-})} = 0.34 \, \mathrm{V}$. Which of the following is \textbf{correct} ?

1. $\mathrm{M} + \mathrm{X} \rightarrow \mathrm{M}^{2+} + \mathrm{X}^{2-}$ is a spontaneous reaction
2. $\mathrm{E}_{cell} = 0.80 \, \mathrm{V}$
3. $\mathrm{E}_{cell} = -0.80 \, \mathrm{V}$
4. $\mathrm{M}^{2+} + \mathrm{X}^{2-} \rightarrow \mathrm{M} + \mathrm{X}$ is a spontaneous reaction

Answer: (d)

Question 75

Chemistry · Some Basic Concepts of Chemistry · Single correct

The number of moles of methane required to produce 11 $\mathrm{gCO}_2(g)$ after complete combustion is: (Given molar mass of methane in $\mathrm{g \ mol}^{-1}$: 16)

1. 0.35
2. 0.5
3. 0.75
4. 0.25

Answer: (d)

Question 76

Chemistry · Co-ordination Compounds · Single correct

The number of complexes from the following with no electrons in the $t_2$ orbital is $\mathrm{TiCl}_4$, $[\mathrm{MnO}_4]^-$, $[\mathrm{FeO}_4]^{2-}$, $[\mathrm{FeCl}_4]^-$, $[\mathrm{CoCl}_4]^{2-}$

1. 1
2. 4
3. 3
4. 2

Answer: (c)

Question 77

Chemistry · The d-and f-Block Elements · Single correct

The number of ions from the following that have the ability to liberate hydrogen from a dilute acid is _____. $\mathrm{Ti}^{2+}$, $\mathrm{Cr}^{2+}$ and $\mathrm{V}^{2+}$

1. 2
2. 3
3. 1
4. 0

Answer: (b)

Question 78

Chemistry · Hydrocarbons · Single correct

Identify $A$ and $B$ in the given chemical reaction sequence:

Answer: (c)

Question 79

Chemistry · The p-Block Elements (Group-13 and 14) · Single correct

The correct statements from the following are: (A) The decreasing order of atomic radii of group 13 elements is Tl > In > Ga > Al > B. (B) Down the group 13 electronegativity decreases from top to bottom. (C) Al dissolves in dil. HCl and liberate $\mathrm{H}_2$, but conc. $\mathrm{HNO}_3$ renders Al passive by forming a protective oxide layer on the surface. (D) All elements of group 13 exhibits highly stable +1 oxidation state. (E) Hybridisation of Al in $[\mathrm{Al}(\mathrm{H}_2\mathrm{O})_6]^{3+}$ ion is $\mathrm{sp}^3\mathrm{d}^2$. Choose the correct answer from the options given below:

1. (C) and (E) only
2. (A), (C) and (E) only
3. (A), (B), (C) and (E) only
4. (A) and (C) only

Answer: (a)

Question 80

Chemistry · Biomolecules · Single correct

Coagulation of egg, on heating is because of:

1. The secondary structure of protein remains unchanged
2. Denaturation of protein occurs
3. Biological property of protein remains unchanged
4. Breaking of the peptide linkage in the primary structure of protein occurs

Answer: (b)

Question 81

Chemistry · Thermodynamics · Numerical

Combustion of 1 mole of benzene is expressed at $C_6H_6(l) + \frac{15}{2} O_2(g) \rightarrow 6CO_2(g) + 3H_2O(l)$ The standard enthalpy of combustion of 2 mol of benzene is $-x\,\text{kJ}$. $x = \underline{\hspace{1.5cm}}$ \textbf{Given:} 1. Standard enthalpy of formation of 1 mol of $\mathrm{C_6H_6(l)}$, for the reaction $\mathrm{6C(graphite) + 3H_2(g) \rightarrow C_6H_6(l)}$ is $48.5\,\text{kJ mol}^{-1}$. 2. Standard enthalpy of formation of 1 mol of $\mathrm{CO_2(g)}$, for the reaction $\mathrm{C(graphite) + O_2(g) \rightarrow CO_2(g)}$ is $-393.5\,\text{kJ mol}^{-1}$. 3. Standard enthalpy of formation of 1 mol of $\mathrm{H_2O(l)}$, for the reaction $\mathrm{H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)}$ is $-286\,\text{kJ mol}^{-1}$.

Answer: 6534

Question 82

Chemistry · The d-and f-Block Elements · Numerical

The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products $A$ and $B$ along with the evolution of $\mathrm{CO}_2$. The sum of spin-only magnetic moment values of $A$ and $B$ is \text{_____} B.M. (Nearest integer) [Given atomic number : $\mathrm{C} : 6, \mathrm{Na} : 11, \mathrm{O} : 8, \mathrm{Fe} : 26, \mathrm{Cr} : 24$]

Answer: 6

Question 83

Chemistry · Amines · Numerical

X g of ethanamine was subjected to reaction with NaNO$_2$/HCl followed by hydrolysis to liberate N$_2$ and HCl. The HCl generated was completely neutralised by 0.2 moles of NaOH. X is _____ g.

Answer: 9

Question 84

Chemistry · Structure of Atom · Numerical

In an atom, total number of electrons having quantum numbers $n = 4$, $|m_l| = 1$ and $m_s = -\frac{1}{2}$ is

Answer: 6

Question 85

Chemistry · Organic Chemistry — Some Basic Principles & Techniques · Numerical

Using the given figure, the ratio of $R_f$ values of sample A and sample C is $x \times 10^{-2}$. Value of $x$ is _____

Answer: 50

Question 86

Chemistry · Aldehydes, Ketones and Carboxylic Acids · Numerical

In the Claisen-Schmidt reaction to prepare 351 g of dibenzalacetone using 87 g of acetone, the amount of benzaldehyde required is ______ g. (Nearest integer)

Answer: 318

Question 87

Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical

Consider the following single step reaction in gas phase at constant temperature. $$2 \mathrm{A}_{(g)} + \mathrm{B}_{(g)} \rightarrow \mathrm{C}_{(g)}$$ The initial rate of the reaction is recorded as $r_1$ when the reaction starts with $1.5 \, \mathrm{atm}$ pressure of A and $0.7 \, \mathrm{atm}$ pressure of B. After some time, the rate $r_2$ is recorded when the pressure of C becomes $0.5 \, \mathrm{atm}$. The ratio $r_1 : r_2$ is ______ $\times 10^{-1}$. (Nearest integer)

Answer: 315

Question 88

Chemistry · Aldehydes, Ketones and Carboxylic Acids · Numerical

The product $(C)$ in the following sequence of reactions has _____ $\pi$ bonds.

Answer: 4

Question 89

Chemistry · Solutions · Numerical

Considering acetic acid dissociates in water, its dissociation constant is $6.25 \times 10^{-5}$. If $5 \, \mathrm{mL}$ of acetic acid is dissolved in $1 \, \mathrm{litre}$ water, the solution will freeze at $-x \times 10^{-2} \degree \mathrm{C}$, provided pure water freezes at $0 \degree \mathrm{C}$. $x =$ \text{_____}. (Nearest integer) Given : $\left(K_f\right)_{\mathrm{water}} = 1.86 \, \mathrm{K \, kg \, mol}^{-1}$. density of acetic acid is $1.2 \, \mathrm{g \, mL}^{-1}$. molar mass of water $= 18 \, \mathrm{g \, mol}^{-1}$. molar mass of acetic acid $=60 \, \mathrm{g \, mol}^{-1}$. density of water $= 1 \, \mathrm{g \, cm}^{-3}$. Acetic acid dissociates as $\mathrm{CH_3COOH \rightleftharpoons CH_3COO^- + H^+}$

Answer: 19

Question 90

Chemistry · Chemical Bonding and Molecular Structure · Numerical

Number of compounds from the following with zero dipole moment is $HF, H_2, H_2 S, CO_2, NH_3, BF_3, CH_4, CHCl_3, SiF_4, H_2O, BeF_2$

Answer: 6