JEE Main 2022 27th July Evening Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQlaws of motion

+4 / -1

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta$ . The magnitude of the contact force will be :

A

Mg

B

\mathrm{Mg} \cos \theta

C

\sqrt{\mathrm{Mg} \sin \theta+\mathrm{Mg} \cos \theta}

D

\operatorname{Mg} \sin \theta \sqrt{1+\mu}

Q 2PhysicsSection A • MCQwave optics

+4 / -1

Two coherent sources of light interfere. The intensity ratio of two sources is $1: 4$ . For this interference pattern if the value of $\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$ is equal to $\frac{2 \alpha+1}{\beta+3}$ , then $\frac{\alpha}{\beta}$ will be :

A

1.5

B

2

C

0.5

D

1

Q 3PhysicsSection B • Numericalwaves

+4 / -1

A wire of length 30 cm, stretched between rigid supports, has it's n^th and (n + 1)^th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ____________ kg/m.

Answer Format:Enter numerical value rounded to the nearest integer

Q 4PhysicsSection B • Numericalproperties of matter

+4 / -1

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 5PhysicsSection A • MCQelectromagnetic waves

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Identify the correct statements from the following descriptions of various properties of electromagnetic waves.

(A) In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

(B) The energy in electromagnetic wave is divided equally between electric and magnetic fields.

(C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

(D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

(E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

Choose the most appropriate answer from the options given below :

A

(D) only

B

(B) and (D) only

C

(B), (C) and (E) only

D

(A), (B) and (E) only

Q 6PhysicsSection B • Numericalray optics

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A thin prism of angle $6^{\circ}$ and refractive index for yellow light $\left(\mathrm{n}_{\mathrm{Y}}\right) 1.5$ is combined with another prism of angle $5^{\circ}$ and $\mathrm{n}_{\mathrm{Y}}=1.55$ . The combination produces no dispersion. The net average deviation $(\delta)$ produced by the combination is $\left(\frac{1}{x}\right)^{\circ}$ . The value of $x$ is ____________.

$qImage-refraction-tir-and-prism-geometrical-optics-optics-Jeemate$

Answer Format:Enter numerical value rounded to the nearest integer

Q 7PhysicsSection B • Numericalcurrent electricity

+4 / -1

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is $40 \mathrm{~cm}$ . The balancing length, if the radius of the wire $\mathrm{AB}$ is doubled, will be ______________ $\mathrm{cm}$ .

qImage-meter-bridge-current-electricity-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 8PhysicsSection A • MCQlaws of motion

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A block 'A' takes 2 s to slide down a frictionless incline of 30 $^\circ$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45 $^\circ$ , the time taken by the block, to slide down the incline, will be approximately :

A

2.66 s

B

0.83 s

C

1.68 s

D

0.70 s

Q 9PhysicsSection B • Numericalcapacitor

+4 / -1

A parallel plate capacitor with width $4 \mathrm{~cm}$ , length $8 \mathrm{~cm}$ and separation between the plates of $4 \mathrm{~mm}$ is connected to a battery of $20 \mathrm{~V}$ . A dielectric slab of dielectric constant 5 having length $1 \mathrm{~cm}$ , width $4 \mathrm{~cm}$ and thickness $4 \mathrm{~mm}$ is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ____________ $\epsilon_{0}$ J. (Where $\epsilon_{0}$ is the permittivity of free space)

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection A • MCQheat and thermodynamics

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Which statements are correct about degrees of freedom ?

(A) A molecule with n degrees of freedom has n $^{2}$ different ways of storing energy.

(B) Each degree of freedom is associated with $\frac{1}{2}$ RT average energy per mole.

(C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom.

(D) $\mathrm{CH}_{4}$ has a total of 6 degrees of freedom.

Choose the correct answer from the options given below :

A

(B) and (C) only

B

(B) and (D) only

C

(A) and (B) only

D

(C) and (D) only

Q 11PhysicsSection A • MCQunits and measurements

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An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$ , where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and t is the temperature. The dimensions of $\beta$ will be :

A

\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\right]

B

\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]

C

\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]

D

\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]

Q 12PhysicsSection A • MCQcommunication systems

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A square wave of the modulating signal is shown in the figure. The carrier wave is given by $C(t)=5 \sin (8 \pi t)$ Volt. The modulation index is :

qImage-modulation-and-demodulation-communication-systems-modern-physics-Jeemate

A

0.2

B

0.1

C

0.3

D

0.4

Q 13PhysicsSection A • MCQcurrent electricity

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(A) The drift velocity of electrons decreases with the increase in the temperature of conductor.

(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.

(C) The drift velocity does not depend on the applied potential difference to the conductor.

(D) The drift velocity of electron is inversely proportional to the length of the conductor.

(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below :

A

(A) and (B) only

B

(A) and (D) only

C

(B) and (E) only

D

(B) and (C) only

Q 14PhysicsSection A • MCQalternating current

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A series LCR circuit has $\mathrm{L}=0.01\, \mathrm{H}, \mathrm{R}=10\, \Omega$ and $\mathrm{C}=1 \mu \mathrm{F}$ and it is connected to ac voltage of amplitude $\left(\mathrm{V}_{\mathrm{m}}\right) 50 \mathrm{~V}$ . At frequency $60 \%$ lower than resonant frequency, the amplitude of current will be approximately :

A

466 mA

B

312 mA

C

238 mA

D

196 mA

Q 15PhysicsSection B • Numericalproperties of matter

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In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ , and $5 \mathrm{~m})$ but of same cross section $\left(2 \mathrm{~mm}^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11} \,\mathrm{Nm}^{-2}$ , then the value of $x$ is __________.

qImage-mechanical-properties-of-solids-properties-of-matter-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 16PhysicsSection A • MCQmagnetic properties of matter

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A compass needle of oscillation magnetometer oscillates 20 times per minute at a place $\mathrm{P}$ of $\operatorname{dip} 30^{\circ}$ . The number of oscillations per minute become 10 at another place $\mathrm{Q}$ of $60^{\circ}$ dip. The ratio of the total magnetic field at the two places $\left(B_{Q}: B_{P}\right)$ is :

A

\sqrt{3}: 4

B

4: \sqrt{3}

C

\sqrt{3}: 2

D

2: \sqrt{3}

Q 17PhysicsSection A • MCQmagnetics

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A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0 \mathrm{~T}$ and the radius of the cyclotron 'dees' is $60 \mathrm{~cm}$ , the kinetic energy of the accelerated protons in MeV will be :

$[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C}$ ]

A

12

B

18

C

16

D

32

Q 18PhysicsSection B • Numericalelectromagnetic induction

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A conducting circular loop is placed in $X-Y$ plane in presence of magnetic field $\overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right)$ in SI unit. If the radius of the loop is $1 \mathrm{~m}$ , the induced emf in the loop, at time, $\mathrm{t}=2 \mathrm{~s}$ is $\mathrm{n} \pi \,\mathrm{V}$ . The value of $\mathrm{n}$ is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 19PhysicsSection B • Numericalcapacitor

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As show in the figure, in steady state, the charge stored in the capacitor is ____________ $\times\, 10^{-6}$ C.

qImage-rc-circuit-capacitor-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 20PhysicsSection A • MCQheat and thermodynamics

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In $1^{\text {st }}$ case, Carnot engine operates between temperatures $300 \mathrm{~K}$ and $100 \mathrm{~K}$ . In $2^{\text {nd }}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\text {nd }}$ case) will be :

qImage-heat-engine-second-law-of-thermodynamics-and-carnot-engine-heat-and-thermodynamics-mechanics-Jeemate

A

same as the

1^{\text {st }}

case.

B

always greater than the

1^{\text {st }}

case.

C

always less than the

1^{\text {st }}

case.

D

may increase or decrease with respect to the

1^{\text {st }}

case.

Q 21PhysicsSection A • MCQproperties of matter

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A steel wire of length $3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$ , both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$ . The load applied, in Newton, will be: $\quad\left(\right.$ Given $\pi=\frac{22}{7}$ )

A

360

B

180

C

1080

D

154

Q 22PhysicsSection A • MCQatoms and nuclei

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The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is 5 days. The activity will become $5 \times 10^{-6}$ curie after :

A

7 days

B

15 days

C

25 days

D

35 days

Q 23PhysicsSection A • MCQelectronic devices

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For a constant collector-emitter voltage of $8 \mathrm{~V}$ , the collector current of a transistor reached to the value of $6 \mathrm{~mA}$ from $4 \mathrm{~mA}$ , whereas base current changed from $20 \,\mu \mathrm{A}$ to $25 \,\mu \mathrm{A}$ value. If transistor is in active state, small signal current gain (current amplification factor) will be :

A

240

B

400

C

0.0025

D

200

Q 24PhysicsSection B • Numericalrotational motion

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A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $4 \mathrm{~ms}^{-1}$ , is ____________ cm. (take g = $10 \mathrm{~ms}^{-2}$ )

qImage-moment-of-inertia-rotational-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 25PhysicsSection A • MCQelectrostatics

+4 / -1

A charge of $4 \,\mu \mathrm{C}$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

A

1 \,\mu \mathrm{C}

and

3 \,\mu\mathrm{C}

B

2 \,\mu \mathrm{C}

and

2\, \mu \mathrm{C}

C

0 and

4\, \mu\, \mathrm{C}

D

1.5 \,\mu \mathrm{C}

and

2.5\, \mu \mathrm{C}

Q 26PhysicsSection A • MCQcenter of mass

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A body of mass $10 \mathrm{~kg}$ is projected at an angle of $45^{\circ}$ with the horizontal. The trajectory of the body is observed to pass through a point $(20,10)$ . If $\mathrm{T}$ is the time of flight, then its momentum vector, at time $\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$ , is _____________.

[Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ]

A

100 \hat{i}+(100 \sqrt{2}-200) \hat{j}

B

100 \sqrt{2} \hat{i}+(100-200 \sqrt{2}) \hat{j}

C

100 \hat{i}+(100-200 \sqrt{2}) \hat{j}

D

100 \sqrt{2} \hat{i}+(100 \sqrt{2}-200) \hat{j}

Q 27PhysicsSection A • MCQdual nature of radiation

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With reference to the observations in photo-electric effect, identify the correct statements from below :

(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.

(B) The value of saturation current increases on moving the source of light away from the metal surface.

(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light.

(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.

(E) Existence of threshold wavelength can not be explained by wave nature of light/ electromagnetic waves.

Choose the correct answer from the options given below :

A

(A) and (B) only

B

(A) and (E) only

C

(C) and (E) only

D

(D) and (E) only

Q 28PhysicsSection B • Numericalmotion

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Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t(\sqrt{2}+1)$ s. The value of t is ___________.

(use $\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

qImage-projectile-motion-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 29PhysicsSection A • MCQgravitation

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A body of mass $\mathrm{m}$ is projected with velocity $\lambda \,v_{\mathrm{e}}$ in vertically upward direction from the surface of the earth into space. It is given that $v_{\mathrm{e}}$ is escape velocity and $\lambda<1$ . If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :

(R : radius of earth)

A

\frac{\mathrm{R}}{1+\lambda^{2}}

B

\frac{R}{1-\lambda^{2}}

C

\frac{R}{1-\lambda}

D

\frac{\lambda^{2} \mathrm{R}}{1-\lambda^{2}}

Q 30PhysicsSection A • MCQmotion

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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :

A

2.0

B

1.0

C

0.5

D

1.5

Q 31ChemistrySection A • MCQatomic structure

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Outermost electronic configurations of four elements A, B, C, D are given below :

(A) $3 s^{2}$

(B) $3 s^{2} 3 p^{1}$

(C) $3 s^{2} 3 p^{3}$

(D) $3 s^{2} 3 p^{4}$

The correct order of first ionization enthalpy for them is :

A

(A) < (B) < (C) < (D)

B

(B) < (A) < (D) < (C)

C

(B) < (D) < (A) < (C)

D

(B) < (A) < (C) < (D)

Q 32ChemistrySection B • Numericalchemical bonding and molecular structure

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The number of molecule(s) or ion(s) from the following having non-planar structure is ____________.

$\mathrm{NO}_{3}^{-}, \mathrm{H}_{2} \mathrm{O}_{2}, \mathrm{BF}_{3}, \mathrm{PCl}_{3}, \mathrm{XeF}_{4}, \mathrm{SF}_{4}, \mathrm{XeO}_{3}, \mathrm{PH}_{4}^{+}, \mathrm{SO}_{3},\left[\mathrm{Al}(\mathrm{OH})_{4}\right]^{-}$

Answer Format:Enter numerical value rounded to the nearest integer

Q 33ChemistrySection B • Numericalthermodynamics

+4 / -1

A gas (Molar mass = 280 $\mathrm{~g} \mathrm{~mol}^{-1}$ ) was burnt in excess $\mathrm{O}_{2}$ in a constant volume calorimeter and during combustion the temperature of calorimeter increased from $298.0 \mathrm{~K}$ to $298.45$ $\mathrm{K}$ . If the heat capacity of calorimeter is $2.5 \mathrm{~kJ} \mathrm{~K}^{-1}$ and enthalpy of combustion of gas is $9 \mathrm{~kJ} \mathrm{~mol}^{-1}$ then amount of gas burnt is _____________ g. (Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 34ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

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$\matrix{ {[A]} & \to & {[B]} \cr {{\mathop{\rm Reactant}\nolimits} } & {} & {{\mathop{\rm Product}\nolimits} } \cr }$

If formation of compound $[\mathrm{B}]$ follows the first order of kinetics and after 70 minutes the concentration of $[\mathrm{A}]$ was found to be half of its initial concentration. Then the rate constant of the reaction is $x \times 10^{-6} \mathrm{~s}^{-1}$ . The value of $x$ is ______________. (Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 35ChemistrySection A • MCQchemical bonding and molecular structure

+4 / -1

Match List - I with List - II.

	List - I		List - II
(A)	$\psi_{\mathrm{MO}}=\psi_{\mathrm{A}}-\psi_{\mathrm{B}}$	(I)	Dipole moment
(B)	$\mu=Q \times r$	(II)	Bonding molecular orbital
(C)	$\frac{\mathrm{N}_{\mathrm{b}}-\mathrm{N}_{\mathrm{a}}}{2}$	(III)	Anti-bonding molecular orbital
(D)	$\psi_{\mathrm{MO}}=\psi_{\mathrm{A}}+\psi_{\mathrm{B}}$	(IV)	Bond order

Choose the correct answer from the options given below :

A

(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{IV}),(\mathrm{D})-(\mathrm{III})

B

(\mathrm{A})-(\mathrm{III}),(\mathrm{B})-(\mathrm{IV}),(\mathrm{C})-(\mathrm{I}),(\mathrm{D})-(\mathrm{II})

C

(\mathrm{A})-(\mathrm{III}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{IV}),(\mathrm{D})-(\mathrm{II})

D

(\mathrm{A})-(\mathrm{III}),(\mathrm{B})-(\mathrm{IV}),(\mathrm{C})-(\mathrm{II}),(\mathrm{D})-(\mathrm{I})

Q 36ChemistrySection A • MCQs block elements

+4 / -1

An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is :

A

Mg

B

Be

C

Ca

D

Sr

Q 37ChemistrySection B • Numericalgaseous state

+4 / -1

For a real gas at $25^{\circ} \mathrm{C}$ temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant 'b' should be __________ $\times 10^{-2} \mathrm{~L} \mathrm{~mol}^{-1}$ (Nearest integer)

(Given $\mathrm{R}=0.083 \mathrm{~L}$ bar $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ )

Answer Format:Enter numerical value rounded to the nearest integer

Q 38ChemistrySection A • MCQatomic structure

+4 / -1

The correct decreasing order of energy for the orbitals having, following set of quantum numbers :

(A) n = 3, l = 0, m = 0

(B) n = 4, l = 0, m = 0

(C) n = 3, l = 1, m = 0

(D) n = 3, l = 2, m = 1

is :

A

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

B

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

C

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

D

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

Q 39ChemistrySection A • MCQelectrochemistry

+4 / -1

Given below are two statements :

Statement I : For KI, molar conductivity increases steeply with dilution

Statement II : For carbonic acid, molar conductivity increases slowly with dilution

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

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

Q 40ChemistrySection A • MCQionic equilibrium

+4 / -1

The plot of $\mathrm{pH}$ -metric titration of weak base $\mathrm{NH}_{4} \mathrm{OH}$ vs strong acid HCl looks like :

A

B

C

D

Q 41ChemistrySection A • MCQp block elements

+4 / -1

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

Assertion (A) : Boron is unable to form $\mathrm{BF}_{6}^{3-}$ .

Reason (R) : Size of B is very small.

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

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

Q 42ChemistrySection A • MCQcoordination compounds

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$\mathrm{Fe}^{3+}$ cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of :

A

\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]_{2}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]

B

\mathrm{Fe}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]_{2}

C

\mathrm{Fe}_{3}\left[\mathrm{Fe}(\mathrm{OH})_{2}(\mathrm{CN})_{4}\right]_{2}

D

\mathrm{Fe}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]_{3}

Q 43ChemistrySection A • MCQpolymers

+4 / -1

Match List - I with List - II.

	List - I (Polymer)		List - II (Monomer)
(A)	Neoprene	(I)	Acrylonitrile
(B)	Teflon	(II)	Chloroprene
(C)	Acrilan	(III)	Tetrafluoroethene
(D)	Natural rubber	(IV)	Isoprene

Choose the correct answer from the options given below :

A

(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{III}),(\mathrm{C})-(\mathrm{I}),(\mathrm{D})-(\mathrm{IV})

B

(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{III}),(\mathrm{D})-(\mathrm{IV})

C

(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{I}),(\mathrm{C})-(\mathrm{IV}),(\mathrm{D})-(\mathrm{III})

D

(\mathrm{A})-(\mathrm{I}),(\mathrm{B})-(\mathrm{II}),(\mathrm{C})-(\mathrm{III}),(\mathrm{D})-(\mathrm{IV})

Q 44ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Given below are two statements:

Statement I : The non bio-degradable fly ash and slag from steel industry can be used by cement industry.

Statement II : The fuel obtained from plastic waste is lead free.

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

A

Both Statement I and Statement II are correct

B

Both Statement I and Statement II are incorrect

C

Statement I is correct but Statement II is incorrect

D

Statement I is incorrect but Statement II is correct

Q 45ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Match List - I with List - II.

	List - I (Mixture)		List - II (Purification Process)
(A)	Chloroform & Aniline	(I)	Steam distillation
(B)	Benzoic acid & Napthalene	(II)	Sublimation
(C)	Water & Aniline	(III)	Distillation
(D)	Napthalene & Sodium chloride	(IV)	Crystallisation

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

Q 46ChemistrySection B • Numericalisolation of elements

+4 / -1

Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of principal ores if iron is _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 47ChemistrySection A • MCQbiomolecules

+4 / -1

Match List - I with Match List - II.

	List - I		List - II
(A)	Glucose + HI	(I)	Gluconic acid
(B)	Glucose + Br $_2$ water	(II)	Glucose pentacetate
(C)	Glucose + acetic anhydride	(III)	Saccharic acid
(D)	Glucose + HNO $_3$	(IV)	Hexane

Choose the correct answer from the options given below:

A

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

B

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

C

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

D

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

Q 48ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

The structure of A in the given reaction is :

qImage-preparation-methods-for-both-aldehydes-and-ketones-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

A

B

C

D

Q 49ChemistrySection B • Numericalaldehydes ketones and carboxylic acids

+4 / -1

The spin only magnetic moment of the complex present in Fehling's reagent is __________ B.M. (Nearest integer).

Answer Format:Enter numerical value rounded to the nearest integer

Q 50ChemistrySection B • Numericalhydrogen

+4 / -1

The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic medium is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 51ChemistrySection A • MCQcompounds containing nitrogen

+4 / -1

An organic compound $'\mathrm{A}'$ contains nitrogen and chlorine. It dissolves readily in water to give a solution that turns litmus red. Titration of compound $'\mathrm{A}'$ with standard base indicates that the molecular weight of $'\mathrm{A}'$ is $131 \pm 2$ . When a sample of $'\mathrm{A}'$ is treated with aq. $\mathrm{NaOH}$ , a liquid separates which contains $\mathrm{N}$ but not $\mathrm{Cl}$ . Treatment of the obtained liquid with nitrous acid followed by phenol gives orange precipitate. The compound $'\mathrm{A}'$ is :

A

B

C

D

Q 52ChemistrySection A • MCQsurface chemistry

+4 / -1

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

Assertion (A) : Dissolved substances can be removed from a colloidal solution by diffusion through a parchment paper.

Reason (R) : Particles in a true solution cannot pass through parchment paper but the colloidal particles can pass through the parchment paper.

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

A

Both (A) and (R) are correct and (R) is the correct explanation of (A)

B

Both (A) and (R) are correct but (R) is not the correct explanation of (A)

C

(A) is correct but (R) is not correct

D

(A) is not correct but (R) is correct

Q 53ChemistrySection A • MCQcoordination compounds

+4 / -1

Low oxidation state of metals in their complexes are common when ligands :

A

have good

\pi

-accepting character

B

have good

\sigma

-donor character

C

are having good

\pi

-donating ability

D

are having poor

\sigma

-donating ability

Q 54ChemistrySection B • Numericalredox reactions

+4 / -1

The normality of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in the solution obtained on mixing $100 \mathrm{~mL}$ of $0.1 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}$ with $50 \mathrm{~mL}$ of $0.1 \,\mathrm{M}\, \mathrm{NaOH}$ is _______________ $\times 10^{-1} \mathrm{~N}$ . (Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 55ChemistrySection B • Numericalsolutions

+4 / -1

When a certain amount of solid A is dissolved in $100 \mathrm{~g}$ of water at $25^{\circ} \mathrm{C}$ to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is $23.76 \,\mathrm{mmHg}$ . The number of moles of solute A added is _____________. (Nearest Integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 56ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Match List - I with List - II.

	List - I		List - II
(A)		(I)	Gatterman Koch reaction
(B)	$C{H_3} - CN\mathrel{\mathop{\kern0pt\longrightarrow}<br>\limits_{{H_3}{O^ + }}^{SnC{l_2}/HCl}} C{H_3} - CHO$	(II)	Etard reaction
(C)		(III)	Stephen reaction
(D)		(IV)	Rosenmund reaction

Choose the correct answer from the options given below :

A

(\mathrm{A})-(\mathrm{IV}),(\mathrm{B})-(\mathrm{III}),(\mathrm{C})-(\mathrm{II}),(\mathrm{D})-(\mathrm{I})

B

(\mathrm{A})-(\mathrm{I}),(\mathrm{B})-(\mathrm{II}),(\mathrm{C})-(\mathrm{III}),(\mathrm{D})-(\mathrm{IV})

C

(\mathrm{A})-(\mathrm{II}),(\mathrm{B})-(\mathrm{III}),(\mathrm{C})-(\mathrm{IV}),(\mathrm{D})-(\mathrm{I})

D

(\mathrm{A})-(\mathrm{III}),(\mathrm{B})-(\mathrm{II}),(\mathrm{C})-(\mathrm{I}),(\mathrm{D})-(\mathrm{IV})

Q 57ChemistrySection A • MCQd and f block elements

+4 / -1

In neutral or alkaline solution, $\mathrm{MnO}_{4}^{-}$ oxidises thiosulphate to :

A

\mathrm{S}_{2} \mathrm{O}_{7}^{2-}

B

\mathrm{S}_{2} \mathrm{O}_{8}^{2-}

C

\mathrm{SO}_{3}^{2-}

D

\mathrm{SO}_{4}^{2-}

Q 58ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

Major product ' $\mathrm{B}$ ' of the following reaction sequence is :

qImage-haloalkanes-haloalkanes-and-haloarenes-organic-chemistry-Jeemate

A

B

C

D

Q 59ChemistrySection B • Numericalpractical organic chemistry

+4 / -1

qImage-chemistry-involved-in-the-preparation-of-organic-and-inorganic-compounds-practical-organic-chemistry-organic-chemistry-Jeemate

In the above reaction, $5 \mathrm{~g}$ of toluene is converted into benzaldehyde with $92 \%$ yield. The amount of benzaldehyde produced is ______________ $\times 10^{-2} \mathrm{~g}$ . (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 60ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Which of the following enhances the lathering property of soap?

A

Sodium stearate

B

Sodium carbonate

C

Sodium rosinate

D

Trisodium phosphate

Q 61MathematicsSection B • Numericaldefinite integration

+4 / -1

Let $f(x)=\min \{[x-1],[x-2], \ldots,[x-10]\}$ where [t] denotes the greatest integer $\leq \mathrm{t}$ . Then $\int\limits_{0}^{10} f(x) \mathrm{d} x+\int\limits_{0}^{10}(f(x))^{2} \mathrm{~d} x+\int\limits_{0}^{10}|f(x)| \mathrm{d} x$ is equal to ________________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 62MathematicsSection A • MCQcomplex numbers

+4 / -1

Let S be the set of all $(\alpha, \beta), \pi<\alpha, \beta<2 \pi$ , for which the complex number $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely imaginary and $\frac{1+i \cos \beta}{1-2 i \cos \beta}$ is purely real. Let $Z_{\alpha \beta}=\sin 2 \alpha+i \cos 2 \beta,(\alpha, \beta) \in S$ . Then $\sum\limits_{(\alpha, \beta) \in S}\left(i Z_{\alpha \beta}+\frac{1}{i \bar{Z}_{\alpha \beta}}\right)$ is equal to :

A

3

B

3 i

C

1

D

2

-

i

Q 63MathematicsSection A • MCQcircle

+4 / -1

A circle $C_{1}$ passes through the origin $\mathrm{O}$ and has diameter 4 on the positive $x$ -axis. The line $y=2 x$ gives a chord $\mathrm{OA}$ of circle $\mathrm{C}_{1}$ . Let $\mathrm{C}_{2}$ be the circle with $\mathrm{OA}$ as a diameter. If the tangent to $\mathrm{C}_{2}$ at the point $\mathrm{A}$ meets the $x$ -axis at $\mathrm{P}$ and $y$ -axis at $\mathrm{Q}$ , then $\mathrm{QA}: \mathrm{AP}$ is equal to :

A

1 : 4

B

1 : 5

C

2 : 5

D

1 : 3

Q 64MathematicsSection B • Numericaldefinite integration

+4 / -1

Let f be a differentiable function satisfying $f(x)=\frac{2}{\sqrt{3}} \int\limits_{0}^{\sqrt{3}} f\left(\frac{\lambda^{2} x}{3}\right) \mathrm{d} \lambda, x>0$ and $f(1)=\sqrt{3}$ . If $y=f(x)$ passes through the point $(\alpha, 6)$ , then $\alpha$ is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 65MathematicsSection A • MCQquadratic equation and inequalities

+4 / -1

If $\alpha, \beta$ are the roots of the equation

$x^{2}-\left(5+3^{\sqrt{\log _{3} 5}}-5^{\sqrt{\log _{5} 3}}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0$ ,

then the equation, whose roots are $\alpha+\frac{1}{\beta}$ and $\beta+\frac{1}{\alpha}$ , is :

A

3 x^{2}-20 x-12=0

B

3 x^{2}-10 x-4=0

C

3 x^{2}-10 x+2=0

D

3 x^{2}-20 x+16=0

Q 66MathematicsSection A • MCQarea under the curves

+4 / -1

The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to :

A

\frac{40}{3}

B

\frac{56}{3}

C

\frac{112}{3}

D

\frac{80}{3}

Q 67MathematicsSection A • MCQtrigonometric functions and equations

+4 / -1

Let $S=\left\{\theta \in\left(0, \frac{\pi}{2}\right): \sum\limits_{m=1}^{9} \sec \left(\theta+(m-1) \frac{\pi}{6}\right) \sec \left(\theta+\frac{m \pi}{6}\right)=-\frac{8}{\sqrt{3}}\right\}$ . Then

A

S=\left\{\frac{\pi}{12}\right\}

B

S=\left\{\frac{2 \pi}{3}\right\}

C

\sum\limits_{\theta \in S} \theta=\frac{\pi}{2}

D

\sum\limits_{\theta \in S} \theta=\frac{3\pi}{4}

Q 68MathematicsSection B • Numericaldifferentiation

+4 / -1

For the curve $C:\left(x^{2}+y^{2}-3\right)+\left(x^{2}-y^{2}-1\right)^{5}=0$ , the value of $3 y^{\prime}-y^{3} y^{\prime \prime}$ , at the point $(\alpha, \alpha)$ , $\alpha>0$ , on C, is equal to ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 69MathematicsSection A • MCQstraight lines and pair of straight lines

+4 / -1

The equations of the sides $\mathrm{AB}, \mathrm{BC}$ and CA of a triangle ABC are $2 x+y=0, x+\mathrm{p} y=39$ and $x-y=3$ respectively and $\mathrm{P}(2,3)$ is its circumcentre. Then which of the following is NOT true?

A

(\mathrm{AC})^{2}=9 \mathrm{p}

B

(\mathrm{AC})^{2}+\mathrm{p}^{2}=136

C

32<\operatorname{area}\,(\Delta \mathrm{ABC})<36

D

34<\operatorname{area}\,(\triangle \mathrm{ABC})<38

Q 70MathematicsSection A • MCQdefinite integration

+4 / -1

$\int\limits_{0}^{2}\left(\left|2 x^{2}-3 x\right|+\left[x-\frac{1}{2}\right]\right) \mathrm{d} x$ , where [t] is the greatest integer function, is equal to :

A

\frac{7}{6}

B

\frac{19}{12}

C

\frac{31}{12}

D

\frac{3}{2}

Q 71MathematicsSection A • MCQprobability

+4 / -1

A six faced die is biased such that

$3 \times \mathrm{P}($ a prime number $)\,=6 \times \mathrm{P}($ a composite number $)\,=2 \times \mathrm{P}(1)$ .

Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

A

\frac{3}{11}

B

\frac{5}{11}

C

\frac{7}{11}

D

\frac{8}{11}

Q 72MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

If for $\mathrm{p} \neq \mathrm{q} \neq 0$ , the function $f(x)=\frac{\sqrt[7]{\mathrm{p}(729+x)}-3}{\sqrt[3]{729+\mathrm{q} x}-9}$ is continuous at $x=0$ , then :

A

7 p q \,f(0)-1=0

B

63 q \,f(0)-\mathrm{p}^{2}=0

C

21 q \,f(0)-\mathrm{p}^{2}=0

D

7 p q \,f(0)-9=0

Q 73MathematicsSection B • Numericalvector algebra

+4 / -1

Let $\overrightarrow a$ , $\overrightarrow b$ , $\overrightarrow c$ be three non-coplanar vectors such that $\overrightarrow a$ $\times$ $\overrightarrow b$ = 4 $\overrightarrow c$ , $\overrightarrow b$ $\times$ $\overrightarrow c$ = 9 $\overrightarrow a$ and $\overrightarrow c$ $\times$ $\overrightarrow a$ = $\alpha$ $\overrightarrow b$ , $\alpha$ > 0. If $\left| {\overrightarrow a } \right| + \left| {\overrightarrow b } \right| + \left| {\overrightarrow c } \right| = {1 \over {36}}$ , then $\alpha$ is equal to __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 74MathematicsSection A • MCQheight and distance

+4 / -1

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $45^{\circ}$ . Let R be a point on AQ and from a point B, vertically above $\mathrm{R}$ , the angle of elevation of $\mathrm{P}$ is $60^{\circ}$ . If $\angle \mathrm{BAQ}=30^{\circ}, \mathrm{AB}=\mathrm{d}$ and the area of the trapezium $\mathrm{PQRB}$ is $\alpha$ , then the ordered pair $(\mathrm{d}, \alpha)$ is :

A

(10(\sqrt{3}-1), 25)

B

\left(10(\sqrt{3}-1), \frac{25}{2}\right)

C

(10(\sqrt{3}+1), 25)

D

\left(10(\sqrt{3}+1), \frac{25}{2}\right)

Q 75MathematicsSection B • Numericalfunctions

+4 / -1

The number of functions $f$ , from the set $\mathrm{A}=\left\{x \in \mathbf{N}: x^{2}-10 x+9 \leq 0\right\}$ to the set $\mathrm{B}=\left\{\mathrm{n}^{2}: \mathrm{n} \in \mathbf{N}\right\}$ such that $f(x) \leq(x-3)^{2}+1$ , for every $x \in \mathrm{A}$ , is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 76MathematicsSection A • MCQinverse trigonometric functions

+4 / -1

The domain of the function $f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\right)\right)$ , where [t] is the greatest integer function, is :

A

\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)

B

\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)

C

\left(1, \frac{5-\sqrt{5}}{2}\right)

D

\left[1, \frac{5+\sqrt{5}}{2}\right)

Q 77MathematicsSection A • MCQarea under the curves

+4 / -1

Consider a curve $y=y(x)$ in the first quadrant as shown in the figure. Let the area $\mathrm{A}_{1}$ is twice the area $\mathrm{A}_{2}$ . Then the normal to the curve perpendicular to the line $2 x-12 y=15$ does NOT pass through the point.

qImage-area-bounded-between-the-curves-area-under-the-curves-calculus-Jeemate

A

(6, 21)

B

(8, 9)

C

(10,

-

4)

D

(12,

-

15)

Q 78MathematicsSection B • Numericalmatrices and determinants

+4 / -1

Consider a matrix $A=\left[\begin{array}{ccc}\alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta\end{array}\right]$ , where $\alpha, \beta, \gamma$ are three distinct natural numbers.

If $\frac{\operatorname{det}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))))}{(\alpha-\beta)^{16}(\beta-\gamma)^{16}(\gamma-\alpha)^{16}}=2^{32} \times 3^{16}$ , then the number of such 3 - tuples $(\alpha, \beta, \gamma)$ is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 79MathematicsSection A • MCQ3d geometry

+4 / -1

If the line of intersection of the planes $a x+b y=3$ and $a x+b y+c z=0$ , a $>0$ makes an angle $30^{\circ}$ with the plane $y-z+2=0$ , then the direction cosines of the line are :

A

\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0

B

\frac{1}{\sqrt{2}}, \pm \,\frac{1}{\sqrt{2}}, 0

C

\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}}, 0

D

\frac{1}{2},-\frac{\sqrt{3}}{2}, 0

Q 80MathematicsSection A • MCQdefinite integration

+4 / -1

Let $f(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}$ .

Consider

$(\mathrm{S} 1): f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2$

$(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12$

Then,

A

both (S1) and (S2) are correct

B

both (S1) and (S2) are wrong

C

only (S1) is correct

D

only (S2) is correct

Q 81MathematicsSection A • MCQprobability

+4 / -1

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $P(X>n-3)=\frac{k}{2^{n}}$ , then k is equal to :

A

528

B

529

C

629

D

630

Q 82MathematicsSection A • MCQparabola

+4 / -1

If the length of the latus rectum of a parabola, whose focus is $(a, a)$ and the tangent at its vertex is $x+y=a$ , is 16, then $|a|$ is equal to :

A

2 \sqrt{2}

B

2 \sqrt{3}

C

4 \sqrt{2}

D

4

Q 83MathematicsSection B • Numericalbinomial theorem

+4 / -1

Let for the $9^{\text {th }}$ term in the binomial expansion of $(3+6 x)^{\mathrm{n}}$ , in the increasing powers of $6 x$ , to be the greatest for $x=\frac{3}{2}$ , the least value of $\mathrm{n}$ is $\mathrm{n}_{0}$ . If $\mathrm{k}$ is the ratio of the coefficient of $x^{6}$ to the coefficient of $x^{3}$ , then $\mathrm{k}+\mathrm{n}_{0}$ is equal to :

Answer Format:Enter numerical value rounded to the nearest integer

Q 84MathematicsSection A • MCQ3d geometry

+4 / -1

If the length of the perpendicular drawn from the point $P(a, 4,2)$ , a $>0$ on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$ is $2 \sqrt{6}$ units and $Q\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$ is the image of the point P in this line, then $\mathrm{a}+\sum\limits_{i=1}^{3} \alpha_{i}$ is equal to :

A

7

B

8

C

12

D

14

Q 85MathematicsSection A • MCQmathematical reasoning

+4 / -1

If the truth value of the statement $(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$ is F, then the truth value of which of the following is $\mathrm{F}$ ?

A

\mathrm{P} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{R}

B

\mathrm{R} \vee \mathrm{Q} \rightarrow \,\sim \mathrm{P}

C

\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}

D

\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \,\sim \mathrm{P}

Q 86MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let $A=\left(\begin{array}{rr}4 & -2 \\ \alpha & \beta\end{array}\right)$ .

If $\mathrm{A}^{2}+\gamma \mathrm{A}+18 \mathrm{I}=\mathrm{O}$ , then $\operatorname{det}(\mathrm{A})$ is equal to _____________.

A

-

18

B

18

C

-

50

D

50

Q 87MathematicsSection A • MCQsequences and series

+4 / -1

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be $\frac{98}{25}$ . Then the sum of the first 21 terms of an AP, whose first term is $10\mathrm{a r}, \mathrm{n}^{\text {th }}$ term is $\mathrm{a}_{\mathrm{n}}$ and the common difference is $10 \mathrm{ar}^{2}$ , is equal to :

A

21 \,\mathrm{a}_{11}

B

22 \,\mathrm{a}_{11}

C

15 \,\mathrm{a}_{16}

D

14 \,\mathrm{a}_{16}

Q 88MathematicsSection B • Numericalhyperbola

+4 / -1

A common tangent $\mathrm{T}$ to the curves $\mathrm{C}_{1}: \frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ and $C_{2}: \frac{x^{2}}{42}-\frac{y^{2}}{143}=1$ does not pass through the fourth quadrant. If $\mathrm{T}$ touches $\mathrm{C}_{1}$ at $\left(x_{1}, y_{1}\right)$ and $\mathrm{C}_{2}$ at $\left(x_{2}, y_{2}\right)$ , then $\left|2 x_{1}+x_{2}\right|$ is equal to ______________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 89MathematicsSection B • Numericalsequences and series

+4 / -1

$\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\cdots+ \frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}$ is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 90MathematicsSection B • Numericalapplication of derivatives

+4 / -1

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $\tan ^{-1} \frac{3}{4}$ . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is ______________.

Answer Format:Enter numerical value rounded to the nearest integer

JEE Main 2022 27th July Evening Shift Question Paper with Solutions