JEE Main 4 April 2024 Shift 1 Question Paper

Question 1

Let $f:\mathbb{R}	o\mathbb{R}$ be a function given by $f(x)=\begin{cases}\dfrac{1-\cos 2x}{x^2} & ,\ x<0\ \alpha & ,\ x=0\ \dfrac{\beta\sqrt{1-\cos x}}{x} & ,\ x>0\end{cases}$ where $\alpha,\beta\in\mathbb{R}$. If $f$ is continuous at $x=0$, then $\alpha^2+\beta^2$ is equal to:

Accepted Answer

(B) $12$

Answer

(A) $48$

Answer

(C) $3$

Answer

(D) $6$

Question 2

Three urns $A$, $B$ and $C$ contain $7$ red, $5$ black; $5$ red, $7$ black and $6$ red, $6$ black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn $A$ is:

Accepted Answer

(B) $\dfrac{5}{18}$

Answer

(A) $\dfrac{4}{17}$

Answer

(C) $\dfrac{7}{18}$

Answer

(D) $\dfrac{5}{16}$

Question 3

The vertices of a triangle are $A(-1,3)$, $B(-2,2)$ and $C(3,-1)$. A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is:

Accepted Answer

(C) $x+y-(2-\sqrt2)=0$

Answer

(A) $x-y-(2+\sqrt2)=0$

Answer

(B) $-x+y-(2-\sqrt2)=0$

Answer

(D) $x+y+(2-\sqrt2)=0$

Question 4

If the solution $y=y(x)$ of the differential equation $(x^4+2x^3+3x^2+2x+2)\,dy=(2x^2+2x+3)\,dx$ satisfies $y(-1)=-\dfrac\pi4$, then $y(0)$ is equal to:

Accepted Answer

(C) $\dfrac\pi4$

Answer

(A) $-\dfrac{\pi}{12}$

Answer

(B) $0$

Answer

(D) $\dfrac\pi2$

Question 5

Let the sum of the maximum and the minimum values of the function $f(x)=\dfrac{2x^2-3x+8}{2x^2+3x+8}$ be $\dfrac{m}{n}$, where $\gcd(m,n)=1$. Then $m+n$ is equal to:

Accepted Answer

(D) $201$

Answer

(A) $182$

Answer

(B) $217$

Answer

(C) $195$

Question 6

One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\dfrac1x$ is $\left(\dfrac12,2\right)$. Let the area of the region bounded by these curves be $\dfrac{1}{24}(\ell\sqrt5+m)-n\log_e(1+\sqrt5)$, where $\ell,m,n\in\mathbb{N}$. Then $\ell+m+n$ is equal to:

Accepted Answer

(B) $30$

Answer

(A) $32$

Answer

(C) $29$

Answer

(D) $31$

Question 7

Let the system of linear equations $x+(\sqrt2\sin\alpha)y+(\sqrt2\cos\alpha)z=0$, $x+(\cos\alpha)y+(\sin\alpha)z=0$, $x+(\sin\alpha)y-(\cos\alpha)z=0$ has a non-trivial solution, then $\alpha\in\left(0,\dfrac\pi2\right)$ is equal to:

Accepted Answer

(C) $\dfrac{5\pi}{24}$

Answer

(A) $\dfrac{3\pi}{4}$

Answer

(B) $\dfrac{7\pi}{24}$

Answer

(D) $\dfrac{11\pi}{24}$

Question 8

There are $5$ points $P_1,P_2,P_3,P_4,P_5$ on the side $AB$, excluding $A$ and $B$, of a triangle $ABC$. Similarly there are $6$ points $P_6,P_7,\ldots,P_{11}$ on the side $BC$ and $7$ points $P_{12},P_{13},\ldots,P_{18}$ on the side $CA$ of the triangle. The number of triangles, that can be formed using the points $P_1,P_2,\ldots,P_{18}$ as vertices, is:

Accepted Answer

(B) $751$

Answer

(A) $776$

Answer

(C) $796$

Answer

(D) $771$

Question 9

Let $f(x)=\begin{cases}-2 & ,\ -2\le x\le0\ x-2 & ,\ 0<x\le2\end{cases}$ and $h(x)=f(|x|)+|f(x)|$. Then $\displaystyle\int_{-2}^{2}h(x)\,dx$ is equal to:

Accepted Answer

(A) $2$

Answer

(B) $4$

Answer

(C) $1$

Answer

(D) $6$

Question 10

The sum of all rational terms in the expansion of $\left(2^{1/5}+5^{1/3}\right)^{15}$ is equal to:

Accepted Answer

(A) $3133$

Answer

(B) $633$

Answer

(C) $931$

Answer

(D) $6131$

Question 11

Let a unit vector which makes an angle of $60^\circ$ with $2\hat i+2\hat j-\hat k$ and an angle of $45^\circ$ with $\hat i-\hat k$ be $\vec C$. Then $\vec C+\left(-\dfrac12\hat i+\dfrac{1}{3\sqrt2}\hat j-\dfrac{\sqrt2}{3}\hat k\right)$ is:

Accepted Answer

(D) $\dfrac{\sqrt2}{3}\hat i-\dfrac12\hat k$

Answer

(A) $-\dfrac{\sqrt2}{3}\hat i+\dfrac{\sqrt2}{3}\hat j+\left(\dfrac12+\dfrac{2\sqrt2}{3}\right)\hat k$

Answer

(B) $\dfrac{\sqrt2}{3}\hat i+\dfrac{1}{3\sqrt2}\hat j-\dfrac12\hat k$

Answer

(C) $\left(\dfrac{1}{\sqrt3}+\dfrac12\right)\hat i+\left(\dfrac{1}{\sqrt3}-\dfrac{1}{3\sqrt2}\right)\hat j+\left(\dfrac{1}{\sqrt3}+\dfrac{\sqrt2}{3}\right)\hat k$

Question 12

Let the first three terms $2$, $p$ and $q$, with $q
e2$, of a G.P. be respectively the $7^{th}$, $8^{th}$ and $13^{th}$ terms of an A.P. If the $5^{th}$ term of the G.P. is the $n^{th}$ term of the A.P., then $n$ is equal to:

Accepted Answer

(D) $163$

Answer

(A) $151$

Answer

(B) $169$

Answer

(C) $177$

Question 13

Let $a,b\in\mathbb{R}$. Let the mean and the variance of $6$ observations $-3,4,7,-6,a,b$ be $2$ and $23$, respectively. The mean deviation about the mean of these $6$ observations is:

Accepted Answer

(A) $\dfrac{13}{3}$

Answer

(B) $\dfrac{16}{3}$

Answer

(C) $\dfrac{11}{3}$

Answer

(D) $\dfrac{14}{3}$

Question 14

If $2$ and $6$ are the roots of the equation $ax^2+bx+1=0$, then the quadratic equation, whose roots are $\dfrac{1}{2a+b}$ and $\dfrac{1}{6a+b}$, is:

Accepted Answer

(D) $x^2+8x+12=0$

Answer

(A) $2x^2+11x+12=0$

Answer

(B) $4x^2+14x+12=0$

Answer

(C) $x^2+10x+16=0$

Question 15

Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar z)^2+|z|=0$, $z\in\mathbb{C}$. Then $4(\alpha^2+\beta^2)$ is equal to:

Accepted Answer

(B) $4$

Answer

(A) $6$

Answer

(C) $8$

Answer

(D) $2$

Question 16

Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$, farther from the origin and at a distance of $9$ units from the point $P$, be $(\alpha,\beta,\gamma)$. Then $\alpha^2+\beta^2+\gamma^2$ is equal to:

Accepted Answer

(A) $155$

Answer

(B) $150$

Answer

(C) $160$

Answer

(D) $165$

Question 17

A square is inscribed in the circle $x^2+y^2-10x-6y+30=0$. One side of this square is parallel to $y=x+3$. If $(x_i,y_i)$ are the vertices of the square, then $\sum(x_i^2+y_i^2)$ is equal to:

Accepted Answer

(D) $152$

Answer

(A) $148$

Answer

(B) $156$

Answer

(C) $160$

Question 18

If the domain of the function $\sin^{-1}\left(\dfrac{3x-22}{2x-19}\right)+\log_e\left(\dfrac{3x^2-8x+5}{x^2-3x-10}\right)$ is $(\alpha,\beta]$, then $3\alpha+10\beta$ is equal to:

Accepted Answer

(A) $97$

Answer

(B) $100$

Answer

(C) $95$

Answer

(D) $98$

Question 19

Let $f(x)=x^5+2e^{x/4}$ for all $x\in\mathbb{R}$. Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x\in\mathbb{R}$. Then the value of $8g'(2)$ is:

Accepted Answer

(A) $16$

Answer

(B) $4$

Answer

(C) $8$

Answer

(D) $2$

Question 20

Let $\alpha\in(0,\infty)$ and $A=\begin{bmatrix}1 & 2 & \alpha\ 1 & 0 & 1\ 0 & 1 & 2\end{bmatrix}$. If $\det\big(\mathrm{adj}(2A-A^T)\cdot\mathrm{adj}(A-2A^T)\big)=2^8$, then $|A|^2$ is equal to:

Accepted Answer

(C) $16$

Answer

(A) $1$

Answer

(B) $49$

Answer

(D) $4$

Question 21

If $\displaystyle\lim_{x	o1}\dfrac{(5x+1)^{1/3}-(x+5)^{1/3}}{(2x+3)^{1/2}-(x+4)^{1/2}}=\dfrac{m\sqrt5}{n(2n)^{2/3}}$, where $\gcd(m,n)=1$, then $8m+12n$ is equal to ___

Accepted Answer

100

Question 22

In a survey of $220$ students of a higher secondary school, it was found that at least $125$ and at most $130$ studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these three subjects. Let $m$ and $n$ respectively be the least and the most number of students who studied all the three subjects. Then $m+n$ is equal to ___

Accepted Answer

45

Question 23

Let the solution $y=y(x)$ of the differential equation $\dfrac{dy}{dx}-y=1+4\sin x$ satisfy $y(\pi)=1$. Then $y\left(\dfrac\pi2\right)+10$ is equal to ___

Accepted Answer

7

Question 24

If the shortest distance between the lines $\dfrac{x+2}{2}=\dfrac{y+3}{3}=\dfrac{z-5}{4}$ and $\dfrac{x-3}{1}=\dfrac{y-2}{-3}=\dfrac{z+4}{2}$ is $\dfrac{38}{3\sqrt5}k$ and $\displaystyle\int_0^k[x^2]\,dx=\alpha-\sqrt\alpha$, where $[x]$ denotes the greatest integer function, then $6\alpha^3$ is equal to ___

Accepted Answer

48

Question 25

Let $a=1+\dfrac{{}^2C_2}{3!}+\dfrac{{}^3C_2}{4!}+\dfrac{{}^4C_2}{5!}+\ldots$ and $b=1+\dfrac{{}^1C_0+{}^1C_1+{}^2C_2}{1!}+\dfrac{{}^2C_0+{}^3C_1+{}^4C_2}{2!}+\dfrac{{}^3C_0+{}^4C_1+{}^5C_2}{3!}+\ldots$. Then $\dfrac{2b}{a^2}$ is equal to ___

Accepted Answer

8

Question 26

Let $A$ be a $3	imes3$ matrix of non-negative real elements such that $A\begin{bmatrix}1\1\1\end{bmatrix}=3\begin{bmatrix}1\1\1\end{bmatrix}$. Then the maximum value of $\det(A)$ is ___

Accepted Answer

27

Question 27

Let the length of the focal chord $PQ$ of the parabola $y^2=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$, then $10p^2$ is equal to ___

Accepted Answer

72

Question 28

Let $ABC$ be a triangle of area $15\sqrt2$ and the vectors $\vec{AB}=\hat i+2\hat j-7\hat k$, $\vec{BC}=a\hat i+b\hat j+c\hat k$ and $\vec{AC}=6\hat i+d\hat j-2\hat k$, $d>0$. Then the square of the length of the largest side of the triangle $ABC$ is ___

Accepted Answer

54

Question 29

If $\displaystyle\int_0^{\pi/4}\dfrac{\sin^2 x}{1+\sin x\cos x}\,dx=\dfrac1a\log_e\left(\dfrac a3\right)+\dfrac{\pi}{b\sqrt3}$, where $a,b\in\mathbb{N}$, then $a+b$ is equal to ___

Accepted Answer

8

Question 30

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

Accepted Answer

(B) the electron will continue to move with uniform velocity along the axis of the solenoid.

Answer

(A) the electron will be accelerated along the axis.

Answer

(C) the electron will be deflected to move along the circular path about axis.

Answer

(D) the electron will experience a force at $45^\circ$ to the axis and execute a helical path.

Question 31

The electric field in an electromagnetic wave is given by $\vec E=\hat i\,40\cos\omega\left(t-\dfrac zc\right)\,NC^{-1}$. The magnetic field induction of this wave is (in SI unit):

Accepted Answer

(D) $\vec B=\hat j\dfrac{40}{c}\cos\omega\left(t-\dfrac zc\right)$

Answer

(A) $\vec B=\hat i\dfrac{40}{c}\cos\omega\left(t-\dfrac zc\right)$

Answer

(B) $\vec B=\hat j\,40c\cos\omega\left(t-\dfrac zc\right)$

Answer

(C) $\vec B=\hat k\dfrac{40}{c}\cos\omega\left(t-\dfrac zc\right)$

Question 32

Which of the following nuclear fragments corresponding to nuclear fission between neutron $({}^1_0n)$ and uranium isotope $({}^{235}_{92}U)$ is correct:

Accepted Answer

(D) ${}^{144}_{56}Ba+{}^{89}_{36}Kr+3{}^1_0n$

Answer

(A) ${}^{144}_{56}Ba+{}^{89}_{36}Kr+4{}^1_0n$

Answer

(B) ${}^{140}_{54}Xe+{}^{94}_{38}Sr+3{}^1_0n$

Answer

(C) ${}^{153}_{51}Sb+{}^{99}_{41}Nb+3{}^1_0n$

Question 33

In an experiment to measure the focal length $(f)$ of a convex lens, the least count of the measuring scales for the position of object $(u)$ and for the position of image $(v)$ are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens is:

Accepted Answer

(B) $f^2\left(\dfrac{\Delta u}{u^2}+\dfrac{\Delta v}{v^2}\right)$

Answer

(A) $f^2\left(\dfrac{\Delta u}{u}+\dfrac{\Delta v}{v}\right)$

Answer

(C) $2f\left(\dfrac{\Delta u}{u}+\dfrac{\Delta v}{v}\right)$

Answer

(D) $f\left(\dfrac{\Delta u}{u}+\dfrac{\Delta v}{v}\right)$

Question 34

Given below are two statements:
Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_1-P_2=\rho g(h_2-h_1)$.
Statement II: In venturi tube shown $2gh=v_1^2-v_2^2$.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(D) Statement I is correct but Statement II is incorrect.

Answer

(A) Both Statement I and Statement II are correct.

Answer

(B) Statement I is incorrect but Statement II is correct.

Answer

(C) Both Statement I and Statement II are incorrect.

Question 35

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8\,\Omega$ and $10\,\Omega$ respectively. After inserting in a hot bath of temperature $400^\circ C$, the resistance of platinum wire is:

Accepted Answer

(B) $16\,\Omega$

Answer

(A) $2\,\Omega$

Answer

(C) $8\,\Omega$

Answer

(D) $10\,\Omega$

Question 36

A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

Accepted Answer

(D) $\dfrac{2GMm\pi}{L^2}$

Answer

(A) $\dfrac{GMm\pi}{2L^2}$

Answer

(B) $0$

Answer

(C) $\dfrac{GMm\pi}{L^2}$

Question 37

On celsius scale the temperature of body increases by $40^\circ C$. The increase in temperature on Fahrenheit scale is:

Accepted Answer

(C) $72^\circ F$

Answer

(A) $70^\circ F$

Answer

(B) $68^\circ F$

Answer

(D) $75^\circ F$

Question 38

An effective power of a combination of $5$ identical convex lenses which are kept in contact along the principal axis is $25\,D$. Focal length of each of the convex lens is:

Accepted Answer

(A) $20\,cm$

Answer

(B) $50\,cm$

Answer

(C) $500\,cm$

Answer

(D) $25\,cm$

Question 39

Which figure shows the correct variation of applied potential difference $(V)$ with photoelectric current $(I)$ at two different intensities of light $(I_1<I_2)$ of same wavelengths:

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 40

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$. Which of the following curve best describes acceleration of the block with time $t$:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 41

If a rubber ball falls from a height $h$ and rebounds upto the height of $h/2$. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are:

Accepted Answer

(D) $50\%,\ \sqrt{2gh}$

Answer

(A) $50\%,\ \sqrt{\dfrac{gh}{2}}$

Answer

(B) $50\%,\ \sqrt{gh}$

Answer

(C) $40\%,\ \sqrt{2gh}$

Question 42

The equation of stationary wave is $y=2a\sin\left(\dfrac{2\pi nt}{\lambda}\right)\cos\left(\dfrac{2\pi x}{\lambda}\right)$. Which of the following is NOT correct:

Accepted Answer

(C) The dimensions of $n/\lambda$ is $[T]$.

Answer

(A) The dimensions of $nt$ is $[L]$.

Answer

(B) The dimensions of $n$ is $[LT^{-1}]$.

Answer

(D) The dimensions of $x$ is $[L]$.

Question 43

A body travels $102.5\,m$ in $n^{th}$ second and $115.0\,m$ in $(n+2)^{th}$ second. The acceleration is:

Accepted Answer

(B) $6.25\,m/s^2$

Answer

(A) $9\,m/s^2$

Answer

(C) $12.5\,m/s^2$

Answer

(D) $5\,m/s^2$

Question 44

To measure the internal resistance of a battery, potentiometer is used. For $R=10\,\Omega$, the balance point is observed at $\ell=500\,cm$ and for $R=1\,\Omega$ the balance point is observed at $\ell=400\,cm$. The internal resistance of the battery is approximately:

Accepted Answer

(D) $0.3\,\Omega$

Answer

(A) $0.2\,\Omega$

Answer

(B) $0.4\,\Omega$

Answer

(C) $0.1\,\Omega$

Question 45

An infinitely long positively charged straight thread has a linear charge density $\lambda\,Cm^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 46

The value of net resistance of the network as shown in the given figure is:

Accepted Answer

(C) $6\,\Omega$

Answer

(A) $\dfrac52\,\Omega$

Answer

(B) $\dfrac{15}{4}\,\Omega$

Answer

(D) $\dfrac{30}{11}\,\Omega$

Question 47

P-T diagram of an ideal gas having three different densities $\rho_1,\rho_2,\rho_3$ (in three different cases) is shown in the figure. Which of the following is correct:

Accepted Answer

(B) $\rho_1>\rho_2$

Answer

(A) $\rho_2<\rho_1$

Answer

(C) $\rho_1<\rho_2$

Answer

(D) $\rho_1=\rho_2=\rho_3$

Question 48

The co-ordinates of a particle moving in x-y plane are given by $x=2+4t$, $y=3t+8t^2$. The motion of the particle is:

Accepted Answer

(D) uniformly accelerated having motion along a parabolic path.

Answer

(A) non-uniformly accelerated.

Answer

(B) uniformly accelerated having motion along a straight line.

Answer

(C) uniform motion along a straight line.

Question 49

In an a.c. circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below:

Accepted Answer

(D) A, B and D only

Answer

(A) A, B and C only

Answer

(B) B, C and D only

Answer

(C) A and B only

Question 50

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s\,C/m^2$ is placed on x-y plane. Another infinitely long line charge having uniform linear charge density $+\lambda_s\,C/m$ is placed at $z=4\,m$ plane and parallel to y-axis. If the magnitude when $|\sigma_s|=2|\lambda_s|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi\sqrt n:1$. The value of $n$ is ___

Accepted Answer

16

Question 51

A hydrogen atom changes its state from $n=3$ to $n=2$. Due to recoil, the percentage change in the wave length of emitted light is approximately $1	imes10^{-n}$. The value of $n$ is ___. (Given $Rhc=13.6\,eV$, $hc=1242\,eV\,nm$, $h=6.6	imes10^{-34}\,J\,s$, mass of hydrogen atom $=1.6	imes10^{-27}\,kg$)

Accepted Answer

7

Question 52

The magnetic field existing in a region is given by $\vec B=0.2(1+2x)\hat k$ T. A square loop of edge $50\,cm$ carrying $0.5\,A$ current is placed in x-y plane with its edges parallel to the x-y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is ___ mN.

Accepted Answer

50

Question 53

A alternating current at any instant is given by $i=\left[6+\sqrt{56}\sin\left(100\pi t+\dfrac\pi3\right)\right]\,A$. The rms value of the current is ___ A.

Accepted Answer

8

Question 54

Twelve wires each having resistance $2\,\Omega$ are joined to form a cube. A battery of $6\,V$ emf is joined across point $a$ and $c$. The voltage difference between $e$ and $f$ is ___ V.

Accepted Answer

1

Question 55

A soap bubble is blown to a diameter of $7\,cm$. $36960$ erg of work is done in blowing it further. If surface tension of soap solution is $40\,dyne/cm$ then the new radius is ___ cm. Take $\left(\pi=\dfrac{22}{7}\right)$

Accepted Answer

7

Question 56

Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment. $\lambda_1=450\,nm$ and $\lambda_2=650\,nm$. The minimum order of fringe produced by $\lambda_2$ which overlaps with the fringe produced by $\lambda_1$ is $n$. The value of $n$ is ___

Accepted Answer

9

Question 57

An elastic spring under tension of $3\,N$ has a length $a$. Its length is $b$ under tension $2\,N$. For its length $(3a-2b)$, the value of tension will be ___ N.

Accepted Answer

5

Question 58

Two forces $\vec F_1$ and $\vec F_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec F_1$ and $\vec F_2$ is $\cos^{-1}\left(\dfrac1n\right)$. The value of $|n|$ is ___

Accepted Answer

6

Question 59

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h_1$ and $h_2$, respectively, above the initial level. The ratio $h_1:h_2$ is $\dfrac{n}{10}$. The value of $n$ is ___

Accepted Answer

7

Question 60

What pressure (bar) of $H_2$ would be required to make emf of hydrogen electrode zero in pure water at $25^\circ C$?

Accepted Answer

(A) $10^{-14}$

Answer

(B) $10^{-7}$

Answer

(C) $1$

Answer

(D) $0.5$

Question 61

The correct sequence of ligands in the order of decreasing field strength is:

Accepted Answer

(A) $CO>H_2O>F^->S^{2-}$

Answer

(B) $^-OH>F^->NH_3>CN^-$

Answer

(C) $NCS^->EDTA^{4-}>CN^->CO$

Answer

(D) $S^{2-}>{}^-OH>EDTA^{4-}>CO$

Question 62

Match List-I (electronic-effect mechanism steps) with List-II (the electronic effect). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

What will be the decreasing order of basic strength of the following conjugate bases? $^-OH$, $RO^-$, $CH_3COO^-$, $Cl^-$

Accepted Answer

(B) RO >–OH > CH3CO O > Cl

Answer

(A) Cl > OH > R O > CH3COO

Answer

(C) –OH > RO  > CH3 COO > Cl

Answer

(D) Cl  > RO  > –OH > CH3CO O

Question 64

In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium hydroxide to:

Accepted Answer

(B) decrease concentration of $^-OH$ ions

Answer

(A) prevent interference by phosphate ions

Answer

(C) increase concentration of $Cl^-$ ions

Answer

(D) increase concentration of $NH_4^+$ ions

List-I (Mechanism step)	List-II (Effect)
A.see figure	I. $-E$ effect
B.see figure	II. $-R$ effect
C.see figure	III. $+E$ effect
D.see figure	IV. $+R$ effect

JEE Main 4 April 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 4 April 2024 Shift 1

Chemistry — JEE Main 4 April 2024 Shift 1

Mathematics — JEE Main 4 April 2024 Shift 1

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