JEE Main 2022 — 25 Jul Shift 1 (Previous Year Paper)

The total number of functions, $f:\{1,2,3,4\}\to\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to:

1. A.60
2. B.90✓
3. C.108
4. D.126

Correct answer: B

If $\alpha,\beta,\gamma,\delta$ are the roots of the equation $x^4+x^3+x^2+x+1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to:

1. A.$-4$
2. B.$-1$✓
3. C.1
4. D.4

Correct answer: B

The number of $\theta\in(0,4\pi)$ for which the system of linear equations $3(\sin3\theta)x-y+z=2$, $3(\cos2\theta)x+4y+3z=3$, $6x+7y+7z=9$ has no solution, is:

1. A.6
2. B.7✓
3. C.8
4. D.9

Correct answer: B

If $\lim_{n\to\infty}\left(\sqrt{n^2-n-1}+n\alpha+\beta\right)=0$, then $8(\alpha+\beta)$ is equal to:

1. A.4
2. B.$-8$
3. C.$-4$✓
4. D.8

Correct answer: C

If the absolute maximum value of the function $f(x)=(x^2-2x+7)e^{(4x^3-12x^2-180x+31)}$ in the interval $[-3,0]$ is $f(\alpha)$, then:

1. A.$\alpha=0$
2. B.$\alpha=-3$✓
3. C.$\alpha\in(-1,0)$
4. D.$\alpha\in(-3,-1]$

Correct answer: B

The curve $y(x)=ax^3+bx^2+cx+5$ touches the $x$-axis at the point $P(-2,0)$ and cuts the $y$-axis at the point Q, where $y'$ is equal to 3. Then the local maximum value of $y(x)$ is:

1. A.$\frac{27}{4}$✓
2. B.$\frac{29}{4}$
3. C.$\frac{37}{4}$
4. D.$\frac92$

Correct answer: A

The area of the region given by $A=\{(x,y): x^2\le y\le\min\{x+2,4-3x\}\}$ is:

1. A.$\frac{31}{8}$
2. B.$\frac{17}{6}$✓
3. C.$\frac{19}{6}$
4. D.$\frac{27}{8}$

Correct answer: B

For any real number $x$, let $[x]$ denote the largest integer less than equal to $x$. Let $f$ be a real valued function defined on the interval $[-10,10]$ by $f(x)=\begin{cases}x-[x], & \text{if }[x]\text{ is odd}\\ 1+[x]-x, & \text{if }[x]\text{ is even}\end{cases}$. Then the value of $\frac{\pi^2}{10}\int_{-10}^{10}f(x)\cos\pi x\,dx$ is:

1. A.4✓
2. B.2
3. C.1
4. D.0

Correct answer: A

The slope of the tangent to a curve $C: y=y(x)$ at any point $(x,y)$ on it is $\frac{2e^{2x}-6e^{-x}+9}{2+9e^{-2x}}$. If C passes through the points $\left(0,\frac12+\frac{\pi}{2\sqrt2}\right)$ and $\left(\alpha,\frac12e^{2\alpha}\right)$, then $e^\alpha$ is equal to:

1. A.$\frac{3+\sqrt2}{3-\sqrt2}$
2. B.$\frac{3}{\sqrt2}\left(\frac{3+\sqrt2}{3-\sqrt2}\right)$✓
3. C.$\frac{1}{\sqrt2}\left(\frac{\sqrt2+1}{\sqrt2-1}\right)$
4. D.$\frac{\sqrt2+1}{\sqrt2-1}$

Correct answer: B

The general solution of the differential equation $(x-y^2)dx+y(5x+y^2)dy=0$ is:

1. A.$(y^2+x)^4=C|(y^2+2x)^3|$✓
2. B.$(y^2+2x)^4=C|(y^2+x)^3|$
3. C.$|(y^2+x)^3|=C(2y^2+x)^4$
4. D.$|(y^2+2x)^3|=C(2y^2+x)^4$

Correct answer: A

A line, with the slope greater than one, passes through the point $A(4,3)$ and intersects the line $x-y-2=0$ at the point B. If the length of the line segment AB is $\frac{\sqrt{29}}{3}$, then B also lies on the line:

1. A.$2x+y=9$
2. B.$3x-2y=7$
3. C.$x+2y=6$✓
4. D.$2x-3y=3$

Correct answer: C

Let the locus of the centre $(\alpha,\beta)$, $\beta>0$, of the circle which touches the circle $x^2+(y-1)^2=1$ externally and also touches the $x$-axis be L. Then the area bounded by L and the line $y=4$ is:

1. A.$\frac{32\sqrt2}{3}$
2. B.$\frac{40\sqrt2}{3}$
3. C.$\frac{64}{3}$✓
4. D.$\frac{32}{3}$

Correct answer: C

Let P be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac x2=\frac y3=\frac z5$ and $\frac x3=\frac y7=\frac z8$. If d is the distance of P from the point $(2,-5,11)$, then $d^2$ is equal to:

1. A.$\frac{147}{2}$
2. B.96
3. C.$\frac{32}{3}$✓
4. D.54

Correct answer: C

Let ABC be a triangle such that $\overrightarrow{BC}=\vec a$, $\overrightarrow{CA}=\vec b$, $\overrightarrow{AB}=\vec c$, $|\vec a|=6\sqrt2$, $|\vec b|=2\sqrt3$ and $\vec b\cdot\vec c=12$. Consider the statements: (S1): $|(\vec a\times\vec b)+(\vec c\times\vec b)|-|\vec c|=6(2\sqrt2-1)$ (S2): $\angle ACB=\cos^{-1}\left(\sqrt{\frac23}\right)$. Then

1. A.both (S1) and (S2) are true
2. B.only (S1) is true
3. C.only (S2) is true✓
4. D.both (S1) and (S2) are false

Correct answer: C

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is:

1. A.$\frac{33}{2^{32}}$
2. B.$\frac{33}{2^{29}}$
3. C.$\frac{33}{2^{28}}$✓
4. D.$\frac{33}{2^{27}}$

Correct answer: C

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^2+\alpha x+\beta>0$, for all $x\in\mathbb{R}$, is:

1. A.$\frac{17}{36}$✓
2. B.$\frac49$
3. C.$\frac12$
4. D.$\frac{19}{36}$

Correct answer: A

The number of solutions of $|\cos x|=\sin x$, such that $-4\pi\le x\le4\pi$ is:

1. A.4
2. B.6
3. C.8✓
4. D.12

Correct answer: C

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is:

1. A.$5(2\sqrt3+3)$ m✓
2. B.$5(\sqrt3+3)$ m
3. C.$10(\sqrt3+1)$ m
4. D.$10(2\sqrt3+1)$ m

Correct answer: A

Which of the following statements is a tautology?

1. A.$((\sim p)\vee q)\Rightarrow p$
2. B.$p\Rightarrow((\sim p)\vee q)$
3. C.$((\sim p)\vee q)\Rightarrow q$
4. D.$q\Rightarrow((\sim p)\vee q)$✓

Correct answer: D

Let $A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}$ and $B=A-I$. If $\omega=\frac{\sqrt3i-1}{2}$, then the number of elements in the set $\{n\in\{1,2,\dots,100\}: A^n+(\omega B)^n=A+B\}$ is equal to ________.

Correct answer: 17

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is ________.

Correct answer: 1492

If the maximum value of the term independent of $t$ in the expansion of $\left(t^2x^{\frac15}+\frac{(1-x)^{\frac1{10}}}{t}\right)^{15}$, $x\ge0$, is K, then 8K is equal to ________.

Correct answer: 6006

Let a, b be two non-zero real numbers. If p and r are the roots of the equation $x^2-8ax+2a=0$ and q and s are the roots of the equation $x^2+12bx+6b=0$, such that $\frac1p,\frac1q,\frac1r,\frac1s$ are in A.P., then $a^{-1}-b^{-1}$ is equal to ________.

Correct answer: 38

Let $a_1=b_1=1$, $a_n=a_{n-1}+2$ and $b_n=a_n+b_{n-1}$ for every natural number $n\ge2$. Then $\sum_{n=1}^{15}a_n\cdot b_n$ is equal to ________.

Correct answer: 27560

Let $f(x)=\begin{cases}|4x^2-8x+5|, & \text{if }8x^2-6x+1\ge0\\ [4x^2-8x+5], & \text{if }8x^2-6x+1<0\end{cases}$ where $[\alpha]$ denotes the greatest integer less than or equal to $\alpha$. Then the number of points in $\mathbb{R}$ where $f$ is not differentiable is ________.

Correct answer: 3

If $\lim_{n\to\infty}\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+\dots+(nk+n)]=33\cdot\lim_{n\to\infty}\frac{1}{n^{k+1}}\cdot[1^k+2^k+3^k+\dots+n^k]$, then the integral value of k is equal to ________.

Correct answer: 5

Let the equation of two diameters of a circle $x^2+y^2-2x+2fy+1=0$ be $2px-y=1$ and $2x+py=4p$. Then the slope $m\in(0,\infty)$ of the tangent to the hyperbola $3x^2-y^2=3$ passing through the centre of the circle is equal to ________.

Correct answer: 2

The sum of diameters of the circles that touch (i) the parabola $75x^2=64(5y-3)$ at the point $\left(\frac85,\frac65\right)$ and (ii) the $y$-axis, is equal to ________.

Correct answer: 10

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:

1. A.$[PA^{-1}T^0]$✓
2. B.$[PAT^{-1}]$
3. C.$[PA^{-1}T]$
4. D.$[PA^{-1}T^{-1}]$

Correct answer: A

Which of the following physical quantities have the same dimensions?

1. A.Electric displacement ($\vec D$) and surface charge density✓
2. B.Displacement current and electric field
3. C.Current density and surface charge density
4. D.Electric potential and energy

Correct answer: A

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be: (Given $\cos135^\circ=-0.7$)

1. A.42 m
2. B.47 m✓
3. C.19 m
4. D.40 m

Correct answer: B

A body of mass 0.5 kg travels on straight line path with velocity $v=(3x^2+4)$ m/s. The net workdone by the force during its displacement from $x=0$ to $x=2$ m is:

1. A.64 J
2. B.60 J✓
3. C.120 J
4. D.128 J

Correct answer: B

A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be:

1. A.$\sqrt{\frac53}$
2. B.$\sqrt{\frac45}$
3. C.$\sqrt{\frac35}$
4. D.$\sqrt{\frac{14}{15}}$✓

Correct answer: D

Three identical particles A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately:

1. A.21 G
2. B.100 G✓
3. C.59 G
4. D.42 G

Correct answer: B

A certain amount of gas of volume V at 27°C temperature and pressure $2\times10^7$ Nm$^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$):

1. A.$3.536\times10^5$ Pa
2. B.$3.536\times10^6$ Pa✓
3. C.$1.25\times10^6$ Pa
4. D.$1.25\times10^5$ Pa

Correct answer: B

Following statements are given: (A) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (C) The average kinetic energy of a gas molecule decreases with increase in volume. (D) Pressure of a gas increases with increase in temperature at constant pressure. (E) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

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

Correct answer: A

In figure (A), mass '2 m' is fixed on mass 'm' which is attached to two springs of spring constant k. In figure (B), mass 'm' is attached to two springs of spring constant 'k' and '2k'. If mass 'm' in (A) and in (B) are displaced by distance 'x' horizontally and then released, then time period $T_1$ and $T_2$ corresponding to (A) and (B) respectively follow the relation.

1. A.$\frac{T_1}{T_2}=\frac{3}{\sqrt2}$✓
2. B.$\frac{T_1}{T_2}=\sqrt{\frac32}$
3. C.$\frac{T_1}{T_2}=\sqrt{\frac23}$
4. D.$\frac{T_1}{T_2}=\frac{\sqrt2}{3}$

Correct answer: A

A condenser of 2 $\mu$F capacitance is charged steadily from 0 to 5 C. Which of the following graph represents correctly the variation of potential difference (V) across it\'s plates with respect to the charge (Q) on the condenser?

1. A.Straight line from origin reaching V = 2.5 x 10^6 V at Q = 5 C✓
2. B.Curve bending upward (convex) from origin reaching V = 5 x 10^6 V at Q = 5 C
3. C.Straight line from origin reaching V = 5 x 10^6 V at Q = 5 C
4. D.Curve rising and saturating near V = 2.5 x 10^6 V by Q = 5 C

Correct answer: A

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5 and their respective masses ratio is 9 : 4. Then, the ratio of their charges will be:

1. A.8 : 5
2. B.5 : 4✓
3. C.5 : 3
4. D.8 : 7

Correct answer: B

To increase the resonant frequency in series LCR circuit,

1. A.source frequency should be increased.
2. B.another resistance should be added in series with the first resistance.
3. C.another capacitor should be added in series with the first capacitor.✓
4. D.the source frequency should be decreased.

Correct answer: C

A small square loop of wire of side $l$ is placed inside a large square loop of wire L ($L\gg l$). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is:

1. A.$\frac{2\sqrt2\mu_0L^2}{\pi l}$
2. B.$\frac{\mu_0l^2}{2\sqrt2\pi L}$
3. C.$\frac{2\sqrt2\mu_0l^2}{\pi L}$✓
4. D.$\frac{\mu_0L^2}{2\sqrt2\pi l}$

Correct answer: C

The rms value of conduction current in a parallel plate capacitor is 6.9 $\mu$A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be:

1. A.5 pF
2. B.50 pF✓
3. C.100 pF
4. D.200 pF

Correct answer: B

Which of the following statement is correct?

1. A.In primary rainbow, observer sees red colour on the top and violet on the bottom✓
2. B.In primary rainbow, observer sees violet colour on the top and red on the bottom
3. C.In primary rainbow, light wave suffers total internal reflection twice before coming out of water drops.
4. D.Primary rainbow is less bright than secondary rainbow.

Correct answer: A

Time taken by light to travel in two different materials A and B of refractive indices $\mu_A$ and $\mu_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times10^{-10}$ s and the ratio of $\mu_A$ to $\mu_B$ is 1 : 2. Then, the thickness of material, in meter is: (Given $v_A$ and $v_B$ are velocities of light in A and B materials respectively.)

1. A.$5\times10^{-10}v_A$ m✓
2. B.$5\times10^{-10}$ m
3. C.$1.5\times10^{-10}$ m
4. D.$5\times10^{-10}v_B$ m

Correct answer: A

A metal exposed to light of wavelength 800 nm and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 nm is used. The workfunction of the metal is: (Take hc = 1230 eV-nm).

1. A.1.537 eV
2. B.2.46 eV
3. C.0.615 eV✓
4. D.1.23 eV

Correct answer: C

The momentum of an electron revolving in $n^{th}$ orbit is given by: (Symbols have their usual meanings)

1. A.$\frac{nh}{2\pi r}$✓
2. B.$\frac{nh}{2r}$
3. C.$\frac{nh}{2\pi}$
4. D.$\frac{2\pi r}{nh}$

Correct answer: A

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

1. A.$\vec\mu_L=\frac{e\vec L}{2m}$
2. B.$\vec\mu_L=-\frac{e\vec L}{2m}$✓
3. C.$\vec\mu_l=-\frac{e\vec L}{m}$
4. D.$\vec\mu_l=\frac{2e\vec L}{m}$

Correct answer: B

In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5 V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V. The truth table of the given circuit will be:

1. A.A B Y: 0 0 0; 1 0 0; 0 1 0; 1 1 1✓
2. B.A B Y: 0 0 0; 1 0 1; 0 1 1; 1 1 1
3. C.A B Y: 0 0 0; 1 0 0; 0 1 0; 1 1 0
4. D.A B Y: 0 0 1; 1 0 1; 0 1 1; 1 1 0

Correct answer: A

A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ________ m distance.

Correct answer: 3

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1:x$ where $x$ = ________.

Correct answer: 3

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ________ cm.

Correct answer: 5

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be ________ cm. ($\alpha_{iron}=1.2\times10^{-5}$ K$^{-1}$ and $\alpha_{brass}=1.8\times10^{-5}$ K$^{-1}$).

Correct answer: 60

An observer is riding on a bicycle and moving towards a hill at 18 kmh$^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be ________ Hz.

Correct answer: 20

The volume charge density of a sphere of radius 6 m is 2 $\mu$C cm$^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is ________ $\times10^{10}$ NC$^{-1}$. [Given: Permittivity of vacuum $\epsilon_0=8.85\times10^{-12}$ C$^2$ N$^{-1}$-m$^{-2}$]

Correct answer: 45

In the given figure, the value of $V_o$ will be ________ V.

Correct answer: 4

Eight copper wire of length $l$ and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length $2l$ have the same resistance (R) then its diameter will be ________ d.

Correct answer: 4

The energy band gap of semiconducting material to produce violet (wavelength = 4000 Å) LED is ________ eV. (Round off to the nearest integer).

Correct answer: 3

The required height of a TV tower which can cover the population of 6.03 lakh is h. If the average population density is 100 per square km and the radius of earth is 6400 km, then the value of h will be ________ m.

Correct answer: 150

SO$_2$Cl$_2$ on reaction with excess of water results into acidic mixture $\mathrm{SO_2Cl_2+2H_2O\rightarrow H_2SO_4+2HCl}$. 16 moles of NaOH is required for the complete neutralisation of the resultant acidic mixture. The number of moles of SO$_2$Cl$_2$ used is:

1. A.16
2. B.8
3. C.4✓
4. D.2

Correct answer: C

Which of the following sets of quantum numbers is not allowed?

1. A.$n=3, l=2, m_l=0, s=+\frac12$
2. B.$n=3, l=2, m_l=-2, s=+\frac12$
3. C.$n=3, l=3, m_l=-3, s=-\frac12$✓
4. D.$n=3, l=0, m_l=0, s=-\frac12$

Correct answer: C

The depression in freezing point observed for a formic acid solution of concentration 0.5 mL L$^{-1}$ is 0.0405°C. Density of formic acid is 1.05 g mL$^{-1}$. The Van't Hoff factor of the formic acid solution is nearly: (Given for water $k_f$ = 1.86 k kg mol$^{-1}$)

1. A.0.8
2. B.1.1
3. C.1.9✓
4. D.2.4

Correct answer: C

20 mL of 0.1 M NH$_4$OH is mixed with 40 mL of 0.05 M HCl. The pH of the mixture is nearest to: (Given: $K_b$(NH$_4$OH) = $1\times10^{-5}$, log 2 = 0.30, log 3 = 0.48, log 5 = 0.69, log 7 = 0.84, log 11 = 1.04)

1. A.3.2
2. B.4.2
3. C.5.2✓
4. D.6.2

Correct answer: C

Match List - I with List - II. List - I: (A) $\mathrm{N_2(g)+3H_2(g)\rightarrow2NH_3(g)}$ (B) $\mathrm{CO(g)+3H_2(g)\rightarrow CH_4(g)+H_2O(g)}$ (C) $\mathrm{CO(g)+H_2(g)\rightarrow HCHO(g)}$ (D) $\mathrm{CO(g)+2H_2(g)\rightarrow CH_3OH(g)}$. List - II: (I) Cu (II) Cu/ZnO–Cr$_2$O$_3$ (III) Fe$_x$O$_y$ + K$_2$O + Al$_2$O$_3$ (IV) Ni. Choose the correct answer from the options given below:

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

Correct answer: C

The IUPAC nomenclature of an element with electronic configuration [Rn] 5f$^{14}$6d$^1$7s$^2$ is:

1. A.Unnilbium
2. B.Unnilunium
3. C.Unnilquadium
4. D.Unniltrium✓

Correct answer: D

The compound(s) that is(are) removed as slag during the extraction of copper is: (A) CaO (B) FeO (C) Al$_2$O$_3$ (D) ZnO (E) NiO. Choose the correct answer from the options given below:

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

Correct answer: D

The reaction of H$_2$O$_2$ with potassium permanganate in acidic medium leads to the formation of mainly:

1. A.Mn$^{2+}$✓
2. B.Mn$^{4+}$
3. C.Mn$^{3+}$
4. D.Mn$^{6+}$

Correct answer: A

Choose the correct order of density of the alkali metals:

1. A.Li < K < Na < Rb < Cs✓
2. B.Li < Na < K < Rb < Cs
3. C.Cs < Rb < K < Na < Li
4. D.Li < Na < K < Cs < Rb

Correct answer: A

The geometry around boron in the product 'B' formed from the following reaction is $\mathrm{BF_3+NaH\xrightarrow{450\,K}A+NaF}$; $\mathrm{A+NMe_3\rightarrow B}$

1. A.trigonal planar
2. B.tetrahedral✓
3. C.pyramidal
4. D.square planar

Correct answer: B

The interhalogen compound formed from the reaction of bromine with excess of fluorine is a:

1. A.hypohalite
2. B.halate✓
3. C.perhalate
4. D.halite

Correct answer: B

The photochemical smog does not generally contain:

1. A.NO
2. B.NO$_2$
3. C.SO$_2$✓
4. D.HCHO

Correct answer: C

A compound 'A' on reaction with 'X' and 'Y' produces the same major product but different by product 'a' and 'b'. Oxidation of 'a' gives a substance produced by ants. Compound 'A' = $\mathrm{H_2C=C(CH_3)-CH_2-C(CH_3)_2-CH_3}$; with X: a + $\mathrm{O=C(CH_3)-CH_2-C(CH_3)_2-CH_3}$; with Y: b + $\mathrm{O=C(CH_3)-CH_2-C(CH_3)_2-CH_3}$. 'X' and 'Y' respectively are

1. A.KMnO$_4$/H$^+$ and dil. KMnO$_4$, 273 K
2. B.KMnO$_4$(dilute), 273 K and KMnO$_4$/H$^+$
3. C.KMnO$_4$/H$^+$ and O$_3$, H$_2$O/Zn
4. D.O$_3$, H$_2$O/Zn and KMnO$_4$/H$^+$✓