JEE Main 1 February 2024 Shift 1 Question Paper

Question 1

A bag contains $8$ balls, whose colours are either white or black. $4$ balls are drawn at random without replacement and it was found that $2$ balls are white and $2$ balls are black. The probability that the bag contains equal number of white and black balls is:

Accepted Answer

(B) $\dfrac{2}{7}$

Answer

(A) $\dfrac{2}{5}$

Answer

(C) $\dfrac{1}{7}$

Answer

(D) $\dfrac{1}{5}$

Question 2

The value of the integral $\displaystyle\int_0^{\pi/4}\dfrac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals:

Accepted Answer

(C) $\dfrac{\sqrt2\,\pi^2}{32}$

Answer

(A) $\dfrac{\sqrt2\,\pi^2}{8}$

Answer

(B) $\dfrac{\sqrt2\,\pi^2}{16}$

Answer

(D) $\dfrac{\sqrt2\,\pi^2}{64}$

Question 3

If $A=\begin{bmatrix}\sqrt2 & 1\ -1 & \sqrt2\end{bmatrix}$, $B=\begin{bmatrix}1 & 0\ 1 & 1\end{bmatrix}$, $C=ABA^T$ and $X=A^T C^2 A$, then $\det X$ is equal to:

Accepted Answer

(B) $729$

Answer

(A) $243$

Answer

(C) $27$

Answer

(D) $891$

Question 4

If $	an A=\dfrac{1}{\sqrt{x(x^2+x+1)}}$, $	an B=\dfrac{\sqrt x}{\sqrt{x^2+x+1}}$ and $	an C=\left(x^{-3}+x^{-2}+x^{-1}ight)^{1/2}$, $0<A,B,C<\dfrac\pi2$, then $A+B$ is equal to:

Accepted Answer

(A) $C$

Answer

(B) $\pi-C$

Answer

(C) $2\pi-C$

Answer

(D) $\dfrac\pi2-C$

Question 5

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to:

Accepted Answer

(C) $51$

Answer

(A) $47$

Answer

(B) $53$

Answer

(D) $43$

Question 6

Let $S=\{z\in\mathbb{C}:|z-1|=1$ and $(\sqrt2-1)(z+\bar z)-i(z-\bar z)=2\sqrt2\}$. Let $z_1,z_2\in S$ be such that $|z_1|=\max\limits_{z\in S}|z|$ and $|z_2|=\min\limits_{z\in S}|z|$. Then $\left|\sqrt2\,z_1-z_2\right|^2$ equals:

Accepted Answer

(D) $2$

Answer

(A) $1$

Answer

(B) $4$

Answer

(C) $3$

Question 7

If the median and mean deviation about the median of $170,125,230,190,210,a,b$ be $170$ and $\dfrac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

Accepted Answer

(C) $30$

Answer

(A) $31$

Answer

(B) $28$

Answer

(D) $32$

Question 8

Let $\vec a=-5\hat i+\hat j-3\hat k$, $\vec b=\hat i+2\hat j-4\hat k$ and $\vec c=\big(\big(\big((\vec a	imes\vec b)	imes\hat i\big)	imes\hat i\big)	imes\hat i\big)$. Then $\vec c\cdot(-\hat i+\hat j+\hat k)$ is equal to:

Accepted Answer

(A) $-12$

Answer

(B) $-10$

Answer

(C) $-13$

Answer

(D) $-15$

Question 9

Let $S=\{x\in\mathbb{R}:(\sqrt3+\sqrt2)^x+(\sqrt3-\sqrt2)^x=10\}$. Then the number of elements in $S$ is:

Accepted Answer

(C) $2$

Answer

(A) $4$

Answer

(B) $0$

Answer

(D) $1$

Question 10

The area enclosed by the curves $xy+4y=16$ and $x+y=6$ is equal to:

Accepted Answer

(C) $30-32\log_e 2$

Answer

(A) $28-30\log_e 2$

Answer

(B) $30-28\log_e 2$

Answer

(D) $32-30\log_e 2$

Question 11

Let $f:\mathbb{R}	o\mathbb{R}$ and $g:\mathbb{R}	o\mathbb{R}$ be defined as $f(x)=\begin{cases}\log_e x & ,\ x>0\ e^{-x} & ,\ x\le0\end{cases}$ and $g(x)=\begin{cases}x & ,\ x\ge0\ e^x & ,\ x<0\end{cases}$. Then $g\circ f:\mathbb{R}	o\mathbb{R}$ is:

Accepted Answer

(B) neither one-one nor onto

Answer

(A) one-one but not onto

Answer

(C) onto but not one-one

Answer

(D) both one-one and onto

Question 12

If the system of equations $2x+3y-z=5$, $x+\alpha y+3z=-4$, $3x-y+\beta z=7$ has infinitely many solutions, then $13\alpha\beta$ is equal to:

Accepted Answer

(B) $1120$

Answer

(A) $1110$

Answer

(C) $1210$

Answer

(D) $1220$

Question 13

For $0<	heta<\dfrac\pi2$, if the eccentricity of the hyperbola $x^2-y^2\csc^2	heta=5$ is $\sqrt7$ times the eccentricity of the ellipse $x^2\csc^2	heta+y^2=5$, then the value of $	heta$ is:

Accepted Answer

(C) $\dfrac\pi3$

Answer

(A) $\dfrac\pi6$

Answer

(B) $\dfrac{5\pi}{12}$

Answer

(D) $\dfrac\pi4$

Question 14

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}=2x(x+y)^3-x(x+y)-1$, $y(0)=1$. Then $\left(\dfrac{1}{\sqrt2}+y\left(\dfrac{1}{\sqrt2}\right)\right)^2$ equals:

Accepted Answer

(D) $\dfrac{1}{2-\sqrt e}$

Answer

(A) $\dfrac{1}{4+\sqrt e}$

Answer

(B) $\dfrac{3}{3-\sqrt e}$

Answer

(C) $\dfrac{2}{1+\sqrt e}$

Question 15

Let $f:\mathbb{R}	o\mathbb{R}$ be defined as $f(x)=\begin{cases}\dfrac{a-b\cos 2x}{x^2} & ,\ x<0\ x^2+cx+2 & ,\ 0\le x\le1\ 2x+1 & ,\ x>1\end{cases}$. If $f$ is continuous everywhere in $\mathbb{R}$ and $m$ is the number of points where $f$ is NOT differentiable then $m+a+b+c$ equals:

Accepted Answer

(D) $2$

Answer

(A) $1$

Answer

(B) $4$

Answer

(C) $3$

Question 16

Let $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$, be an ellipse, whose eccentricity is $\dfrac{1}{\sqrt2}$ and the length of the latus rectum is $\sqrt{14}$. Then the square of the eccentricity of $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ is:

Accepted Answer

(C) $\dfrac32$

Answer

(A) $3$

Answer

(B) $\dfrac72$

Answer

(D) $\dfrac52$

Question 17

Let $3,a,b,c$ be in A.P. and $3,a-1,b+1,c+9$ be in G.P. Then, the arithmetic mean of $a,b,c$ is:

Accepted Answer

(D) $11$

Answer

(A) $-4$

Answer

(B) $-1$

Answer

(C) $13$

Question 18

Let $C:x^2+y^2=4$ and $C':x^2+y^2-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $C$ and $C'$ intersect at two distinct points, is $\mathbb{R}-[a,b]$, then the point $(8a+12,16b-20)$ lies on the curve:

Accepted Answer

(D) $6x^2+y^2=42$

Answer

(A) $x^2+2y^2-5x+6y=3$

Answer

(B) $5x^2-y=-11$

Answer

(C) $x^2-4y^2=7$

Question 19

If $5f(x)+4f\left(\dfrac1xight)=x^2-2$, $\forall x
e0$ and $y=9x^2 f(x)$, then $y$ is strictly increasing in:

Accepted Answer

(B) $\left(-\dfrac{1}{\sqrt5},0\right)\cup\left(\dfrac{1}{\sqrt5},\infty\right)$

Answer

(A) $\left(0,\dfrac{1}{\sqrt5}\right)$

Answer

(C) $\left(-\dfrac{1}{\sqrt5},0\right)\cup\left(0,\dfrac{1}{\sqrt5}\right)$

Answer

(D) $\left(-\infty,-\dfrac{1}{\sqrt5}\right)\cup\left(0,\dfrac{1}{\sqrt5}\right)$

Question 20

If the shortest distance between the lines $\dfrac{x-\lambda}{-2}=\dfrac{y-2}{1}=\dfrac{z-1}{1}$ and $\dfrac{x-\sqrt3}{1}=\dfrac{y-1}{-2}=\dfrac{z-2}{2}$ is $1$, then the sum of all possible values of $\lambda$ is:

Accepted Answer

(B) $2\sqrt3$

Answer

(A) $0$

Answer

(C) $3\sqrt3$

Answer

(D) $-2\sqrt3$

Question 21

If $y=x(t)$ is the solution of the differential equation $(t+1)\,dx=\left(2x+(t+1)^4\right)dt$, $x(0)=2$, then $x(1)$ equals ___

Accepted Answer

14

Question 22

The number of elements in the set $S=\{(x,y,z):x,y,z\in\mathbb{Z},\ x+2y+3z=42,\ x,y,z\ge0\}$ equals ___

Accepted Answer

169

Question 23

If the coefficient of $x^{30}$ in the expansion of $\left(1+\dfrac1xight)^6(1+x^2)^7(1-x^3)^8$; $x
e0$ is $|\alpha|$, then $|\alpha|$ equals ___

Accepted Answer

678

Question 24

Let $3,7,11,15,\ldots,403$ and $2,5,8,11,\ldots,404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ___

Accepted Answer

6699

Question 25

Let $\{x\}$ denote the fractional part of $x$ and $f(x)=\dfrac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}$, $x
e0$. If $L$ and $R$ respectively denote the left hand limit and the right hand limit of $f(x)$ at $x=0$, then $\dfrac{32}{\pi^2}(L^2+R^2)$ is equal to ___

Accepted Answer

18

Question 26

Let the line $\sqrt2\,x+y=\alpha$ pass through the point of the intersection $P$ (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2y$. Let the line $L$ touch two circles $C_1$ and $C_2$ of equal radius $2\sqrt3$. If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the y-axis, then the square of the area of the triangle $PQ_1Q_2$ is equal to ___

Accepted Answer

72

Question 27

Let $P=\{z\in\mathbb{C}:|z+2-3i|\le\sqrt{11}\}$ and $Q=\{z\in\mathbb{C}:z(1+i)+\bar z(1-i)\le-8\}$. Let in $P\cap Q$, $|z-3+2i|$ be the maximum and minimum at $z_1$ and $z_2$ respectively. If $|z_1|^2+2|z_2|^2=\alpha+\beta\sqrt2$, where $\alpha,\beta$ are integers, then $\alpha+\beta$ equals ___

Accepted Answer

36

Question 28

If $\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{8\sqrt2\cos x\,dx}{(1+e^{\sin x})(1+\sin^4 x)}=\alpha\pi+\beta\log_e(3+2\sqrt2)$, where $\alpha,\beta$ are integers, then $\alpha^2+\beta^2$ equals ___

Accepted Answer

8

Question 29

Let the line of the shortest distance between the lines $L_1:\vec r=(\hat i+2\hat j+3\hat k)+\lambda(\hat i-\hat j+\hat k)$ and $L_2:\vec r=(4\hat i+5\hat j+6\hat k)+\mu(\hat i+\hat j-\hat k)$ intersect $L_1$ and $L_2$ at $P$ and $Q$ respectively. If $(\alpha,\beta,\gamma)$ is the midpoint of the line segment $PQ$, then $2(\alpha+\beta+\gamma)$ is equal to ___

Accepted Answer

21

Question 30

Let $A=\{1,2,3,\ldots,20\}$. Let $R_1$ and $R_2$ be two relations on $A$ such that $R_1=\{(a,b):b$ is divisible by $a\}$, $R_2=\{(a,b):a$ is an integral multiple of $b\}$. Then, number of elements in $R_1-R_2$ is equal to ___

Accepted Answer

46

Question 31

With rise in temperature, the Young’s modulus of elasticity:

Accepted Answer

(B) decreases

Answer

(A) changes erratically

Answer

(C) increases

Answer

(D) remains unchanged

Question 32

If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2\,m/s^2$, then the length of the second’s pendulum at a height $h=2R$ from the surface of earth will be:

Accepted Answer

(B) $\dfrac19\,m$

Answer

(A) $\dfrac29\,m$

Answer

(C) $\dfrac49\,m$

Answer

(D) $\dfrac89\,m$

Question 33

The reading in the ideal voltmeter $(V)$ shown in the given circuit diagram is:

Accepted Answer

(C) $0\,V$

Answer

(A) $5\,V$

Answer

(B) $10\,V$

Answer

(D) $3\,V$

Question 34

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2V$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

Accepted Answer

(A) $\dfrac14 CV^2$

Answer

(B) $2CV^2$

Answer

(C) $\dfrac12 CV^2$

Answer

(D) $\dfrac34 CV^2$

Question 35

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

Accepted Answer

(A) $\dfrac94 R$

Answer

(B) $\dfrac74 R$

Answer

(C) $\dfrac32 R$

Answer

(D) $\dfrac52 R$

Question 36

A ball of mass $0.5\,kg$ is attached to a string of length $50\,cm$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400\,N$. The maximum possible value of angular velocity of the ball in rad/s, is:

Accepted Answer

(B) $40$

Answer

(A) $1600$

Answer

(C) $1000$

Answer

(D) $20$

Question 37

A parallel plate capacitor has a capacitance $C=200\,pF$. It is connected to $230\,V$ ac supply with an angular frequency $300\,rad/s$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

Accepted Answer

(D) $13.8\,\mu A$ and $13.8\,\mu A$

Answer

(A) $1.38\,\mu A$ and $13.8\,\mu A$

Answer

(B) $14.3\,\mu A$ and $143\,\mu A$

Answer

(C) $13.8\,\mu A$ and $138\,\mu A$

Question 38

The pressure and volume of an ideal gas are related as $PV^{5/2}=K$ (Constant). The work done when the gas is taken from state $A(P_1,V_1,T_1)$ to state $B(P_2,V_2,T_2)$ is:

Accepted Answer

(A) $2(P_1V_1-P_2V_2)$

Answer

(B) $2(P_2V_2-P_1V_1)$

Answer

(C) $2\left(\sqrt{P_1V_1}-\sqrt{P_2V_2}\right)$

Answer

(D) $2\left(P_2\sqrt{V_2}-P_1\sqrt{V_1}\right)$

Question 39

A galvanometer has a resistance of $50\,\Omega$ and it allows maximum current of $5\,mA$. It can be converted into voltmeter to measure upto $100\,V$ by connecting in series a resistor of resistance:

Accepted Answer

(C) $19950\,\Omega$

Answer

(A) $5975\,\Omega$

Answer

(B) $20050\,\Omega$

Answer

(D) $19500\,\Omega$

Question 40

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

Accepted Answer

(D) $8:1$

Answer

(A) $1:8$

Answer

(B) $1:2$

Answer

(C) $4:1$

Question 41

$10$ divisions on the main scale of a Vernier calliper coincide with $11$ divisions on the Vernier scale. If each division on the main scale is of $5$ units, then the least count of the instrument is:

Accepted Answer

(D) $\dfrac{5}{11}$

Answer

(A) $\dfrac12$

Answer

(B) $\dfrac{10}{11}$

Answer

(C) $\dfrac{50}{11}$

Question 42

In series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be:

Accepted Answer

(C) reduced by $\dfrac34 L$

Answer

(A) reduced by $\dfrac14 L$

Answer

(B) increased by $2L$

Answer

(D) increased to $4L$

Question 43

The radius $(r)$, length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as $r=(0.35\pm0.05)\,cm$, $R=(100\pm10)$ ohm, $l=(15\pm0.2)\,cm$. The percentage error in resistivity of the material of the wire is:

Accepted Answer

(B) $39.9\%$

Answer

(A) $25.6\%$

Answer

(C) $37.3\%$

Answer

(D) $35.6\%$

Question 44

The dimensional formula of angular impulse is:

Accepted Answer

(B) $[ML^2T^{-1}]$

Answer

(A) $[ML^{-2}T^{-1}]$

Answer

(C) $[MLT^{-1}]$

Answer

(D) $[ML^2T^{-2}]$

Question 45

A simple pendulum of length $1\,m$ has a wooden bob of mass $1\,kg$. It is struck by a bullet of mass $10^{-2}\,kg$ moving with a speed of $2	imes10^2\,m/s$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $g=10\,m/s^2$)

Accepted Answer

(B) $0.20\,m$

Answer

(A) $0.30\,m$

Answer

(C) $0.35\,m$

Answer

(D) $0.40\,m$

Question 46

A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution. If this particle is projected with the same velocity at an angle $	heta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $	heta$ is then given by:

Accepted Answer

(A) $\sin^{-1}\left[\dfrac{2gT^2}{\pi^2 R}\right]^{1/2}$

Answer

(B) $\sin^{-1}\left[\dfrac{\pi^2 R}{2gT^2}\right]^{1/2}$

Answer

(C) $\cos^{-1}\left[\dfrac{2gT^2}{\pi^2 R}\right]^{1/2}$

Answer

(D) $\cos^{-1}\left[\dfrac{\pi R}{2gT^2}\right]^{1/2}$

Question 47

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$, the acceleration of the system in $m/s^2$ is: (Consider that the masses are massless and unstretchable and the pulley is also massless and frictionless)

Accepted Answer

(C) $2$

Answer

(A) $3$

Answer

(B) $4$

Answer

(D) $1.2$

Question 48

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

Accepted Answer

(D) $12.1\,eV$

Answer

(A) $1.5\,eV$

Answer

(B) $13.6\,eV$

Answer

(C) $1.9\,eV$

Question 49

A monochromatic light of wavelength $6000\,	ext{Å}$ is incident on the single slit of width $0.01\,mm$. If the diffraction pattern is formed at the focus of the convex lens of focal length $20\,cm$, the linear width of the central maximum is:

Accepted Answer

(B) $24\,mm$

Answer

(A) $60\,mm$

Answer

(C) $120\,mm$

Answer

(D) $12\,mm$

Question 50

A regular polygon of $6$ sides is formed by bending a wire of length $4\pi$ metre. If electric current of $4\pi\sqrt3\,A$ is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x	imes10^{-7}\,T$. The value of $x$ is ___

Accepted Answer

72

Question 51

A rectangular loop of sides $12\,cm$ and $5\,cm$, with its sides parallel to the x-axis and y-axis respectively moves with a velocity of $5\,cm/s$ in the positive x axis direction, in a space containing a variable magnetic field in the positive z direction. The field has a gradient of $10^{-3}\,T/cm$ along the negative x direction and it is decreasing with time at the rate of $10^{-3}\,T/s$. If the resistance of the loop is $6\,m\Omega$, the power dissipated by the loop as heat is ___ $	imes10^{-9}\,W$.

Accepted Answer

216

Question 52

The distance between object and its $3$ times magnified real image as produced by a convex lens is $20\,cm$. The focal length of the lens used is ___ $cm$.

Accepted Answer

3.75

Question 53

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $	heta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5\,g/cc$, the dielectric constant of water will be ___. (Take density of water $=1\,g/cc$)

Accepted Answer

3

Question 54

The radius of a nucleus of mass number $64$ is $4.8$ fermi. Then the mass number of another nucleus having radius of $4$ fermi is $\dfrac{1000}{x}$, where $x$ is ___

Accepted Answer

27

Question 55

The identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4\,m$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\dfrac{4\sqrt2}{x}$, where the value of $x$ is ___

Accepted Answer

3

Question 56

A tuning fork resonates with a sonometer wire of length $1\,m$ stretched with a tension of $6\,N$. When the tension in the wire is changed to $54\,N$, the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is ___ Hz.

Accepted Answer

6

Question 57

A plane is in level flight at constant speed and each of its two wings has an area of $40\,m^2$. If the speed of the air is $180\,km/h$ over the lower wing surface and $252\,km/h$ over the upper wing surface, the mass of the plane is ___ kg. (Take air density to be $1\,kg\,m^{-3}$ and $g=10\,m/s^2$)

Accepted Answer

9600

Question 58

The current in a conductor is expressed as $I=3t^2+4t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1\,s$ to $t=2\,s$ is ___ C.

Accepted Answer

22

Question 59

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was $16\,m$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3t^3+18t^2+16t$, where $x$ is in m and $t$ is in s. The velocity of the particle when its acceleration becomes zero is ___ m/s.

Accepted Answer

52

Question 60

If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is:

Accepted Answer

(B) TACGAAGT

Answer

(A) CATTAGCT

Answer

(C) GTACTTAC

Answer

(D) ATGCGACT

Question 61

Given below are two statements:
Assertion (A): Haloalkanes react with KCN to form alkyl cyanides as a main product while with AgCN form isocyanides as a main product.
Reason (R): KCN and AgCN both are highly ionic compounds. In the light of the above statement, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

In acidic medium, $K_2Cr_2O_7$ shows oxidising action as represented in the half reaction $Cr_2O_7^{2-}+XH^++Ye^-	o 2Cr^{3+}+ZH_2O$. $X$, $Y$, $Z$ and $A$ are respectively:

Accepted Answer

(D) $14,6,7$ and $Cr^{3+}$

Answer

(A) $8,6,4$ and $Cr_2O_5$

Answer

(B) $14,7,6$ and $Cr^{3+}$

Answer

(C) $8,4,6$ and $Cr_2O_5$

Question 63

Which of the following reactions are disproportionation reactions? (A) $Cu^+	o Cu^{2+}+Cu$ (B) $3MnO_4^{2-}+4H^+	o 2MnO_4^-+MnO_2+2H_2O$ (C) $2KMnO_4	o K_2MnO_4+MnO_2+O_2$ (D) $2MnO_4^-+3Mn^{2+}+2H_2O	o 5MnO_2+4H^+$. Choose the correct answer from the options given below:

Accepted Answer

(A) (A), (B)

Answer

(B) (B), (C), (D)

Answer

(C) (A), (B), (C)

Answer

(D) (A), (D)

Question 64

In case of isoelectronic species the size of $F^-$, $Ne$ and $Na^+$ is affected by:

Accepted Answer

(D) Nuclear charge (z)

Answer

(A) Principal quantum number (n) same

Answer

(B) None of the factors because their size is the same

Answer

(C) Electron-electron interaction in the outer orbitals

List-I (Reactions)	List-II (Reagents)
A. $CH_3(CH_2)_2COOC_2H_5\to CH_3(CH_2)_2CHO$	I. $CH_3MgBr,\ H_2O$
B. $C_6H_5COC_6H_5\to C_6H_5CH_2C_6H_5$	II.Zn(Hg) and conc. HCl
C. $C_6H_5CHO\to C_6H_5CH(OH)CH_3$	III. $NaBH_4,\ H^+$
D. $CH_3COCH_2COOC_2H_5\to CH_3CH(OH)CH_2COOC_2H_5$	IV.DIBAL-H, $H_2O$

JEE Main 1 February 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 1 February 2024 Shift 1

Chemistry — JEE Main 1 February 2024 Shift 1

Mathematics — JEE Main 1 February 2024 Shift 1

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