JEE Main 2023 Jan 24 Shift 1 Question Paper with Solution PDF- Download Here

Let \(p , q \in R\) and \((1-\sqrt{3})^{200}=2^{199}(p+i q), t=\sqrt{-1}\) Then \(p + q + q ^2\) and \(p - q + q ^2\) are roots of the equation

• (1) \(x^2-4 x+1=0\)
• (2) \(x^2+4 x+1=0\)
• (3) \(x^2-4 x-1=0\)
• (4) \(x^2+4 x-1=0\)

Let \(N\) denote the number that turns up when a fair die is rolled If the probability that the system of equations\( x+y+z=1 \) \( 2 x + Ny +2 z=2 \) \( 3 x +3 y+ N z=3\) has unique solution is \(\frac{k}{6}\), then the sum of value of \(k\) and all possible values of \(N\) is

• (1) 18
• (2) 19
• (3) 20
• (4) 21

The relation \(R =\{(a, b)\) : \(\operatorname{gcd}(a, b)=1,2 a \neq b, a, b \in Z\}\) is :

• (1) reflexive but not symmetric
• (2) transitive but not reflexive
• (3) symmetric but not transitive
• (4) neither symmetric nor transitive

\(\displaystyle\lim _{t \rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots+n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}\) is equal to

• (1) \(n ^2\)
• (2) \(n ^2+ n\)
• (3) \(n\)
• (4) \(\frac{n(n+1)}{2}\)

\(tan^{-1}(\frac {1+\sqrt 3}{3+\sqrt 3})+sec^{-1}(\sqrt {\frac {8+4\sqrt 3}{3+3\sqrt 3})}\) is equal to:

• (1) \(\frac \pi6\)
• (2) \(\frac \pi3\)
• (3) \(\frac \pi4\)
• (4) \(\frac \pi2\)

Let \(y=y(x)\) be the solution of the differential equation \(x^3 d y+(x y-1) d x=0, x>0\), \(y\left(\frac{1}{2}\right)=3- e\) Then \(y(1)\) is equal to

• (1) \(2-e\)
• (2) e
• (3) 1
• (4) 3

Let \(\Omega\) be the sample space and \(A \subseteq \Omega\) be an event .
Given below are two statements : 
(S1): If \(P ( A )=0\), then \(A =\emptyset\) 
(S2): If \(P(A)=1\), then \(A=\Omega\)
Then

• (1) both (S1) and (S2) are true
• (2) only ( \(S 1)\) is true
• (3) only (S2) is true
• (4) both (S1) and (S2) are false

The area enclosed by the curves \(y^2+4 x=4\) and \(y-2 x=2\) is :

• (1) 9
• (2) \( \frac{22}{3} \)
• (3) \(\frac{23}{3} \)
• (4) \(\frac{25}{3}\)

The equation \(x^2-4 x+[x]+3=x[x]\), where \([x]\) denotes the greatest integer function, has :

• (1) no solution
• (2) exactly two solutions in \((-\infty, \infty)\)
• (3) a unique solution in \((-\infty, 1)\)
• (4) a unique solution in \((-\infty, \infty)\)

If \(A\) and \(B\) are two non-zero \(n \times n\) matrics such that \(A ^2+ B = A ^2 B\), then

• (1) \(A ^2= I\) or \(B = I\)
• (2) \(A ^2 B = BA ^2\)
• (3) \(AB = I\)
• (4) \(A ^2 B = I\)

For three positive integers \(p , q , r , x^{p q^2}=y^{y r}=z^{p^2 r }\) and \(r = pq +1\) such that \(3,3 \log _y x, 3 \log _z y\) \(7 \log _x z\) are in AP with common difference \(\frac{1}{2}\) Then \(r-p-q\) is equal to

• (1) 6
• (2) 2
• (3) 12
• (4) \(-6\)

Let \(P Q R\) be a triangle. The points \(A, B\) and \(C\) are on the sides \(Q R, R P\) and \(P Q\) respectively such that \(\frac{Q A}{A R}=\frac{R B}{B P}=\frac{P C}{C Q}=\frac{1}{2}\). Then \(\frac{A \text { Area }(\triangle P Q R)}{\text { Area }(\triangle A B C)}\) is equal to

• (1) 4
• (2) 3
• (3) 2
• (4) \(\frac{5}{2}\)

Let \(f(x)=\begin{cases}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\ 0 & , x=0\end{cases}\)Then at \(x=0\)

• (1) \(f\) is continuous but not differentiable
• (2) \(f\) is continuous but \(f^{\prime}\) is not continuous
• (3) \(f^{\prime}\) is continuous but not differentiable
• (4) \(f\) and \(f^{\prime}\) both are continuous

Let a tangent to the curve \(y^2=24 x\) meet the curve \(x y=2\) at the points \(A\) and \(B\) Then the mid points of such line segments \(A B\) lie on a parabola with the

• (1) length of latus rectum \(\frac{3}{2}\)
• (2) length of latus rectum 2
• (3) directrix \(4 x =3\)
• (4) directrix \(4 x=-3\)

The value of \(\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r\) is

• (1) \({ }^{45} C _{24}\)
• (2) \({ }^{45} C_{23}\)
• (3) \({ }^{44} C _{23}\)
• (4) \({ }^{44} C_{22}\)

The distance of the point \((7,-3,-4)\) from the plane passing through the points \((2,-3,1),(-1,1,-2)\) and \((3,-4,2)\) is :

• (1) \(5 \sqrt{2}\)
• (2) \(4 \sqrt{2}\)
• (3) 4
• (4) 5

The compound statement \((-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))\) is equivalent to

• (1) \(((\sim P) \vee Q) \wedge((\sim Q) \vee P)\)
• (2) \((\sim Q) \vee P\)
• (3) \(((-P) \vee Q) \wedge(-Q)\)
• (4) \((-P) \vee Q\)

The distance of the point \((-1,9,-16)\) from the plane \(2 x+3 y-z=5\) measured parallel to the line \(\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}\) is

• (1) \(20 \sqrt{2}\)
• (2) 31
• (3) \(13 \sqrt{2}\)
• (4) 26

Let \(\vec{u}=\hat{i}-\hat{j}-2 \hat{k}, \vec{v}=2 \hat{i}+\hat{j}-\hat{k}, \vec{v} \cdot \vec{w}=2\) and \(\vec{v} \times \vec{w}=\vec{u}+\lambda \vec{v}\).  Then \(\vec{u} \cdot \vec{w}\) is equal to

• (1) 1
• (2) 2
• (3) \(\frac{3}{2}\)
• (4) \(-\frac{2}{3}\)

Let \(\alpha\) be a root of the equation \((a-c) x^2+(b-a) x+(c-b)=0\)where \(a , b , c\) are distinct real numbers such that the matrix \(\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}\)is singular Then, the value of \(\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}\) is

• (1) 6
• (2) 3
• (3) 9
• (4) 12

Let \(\lambda \in R\) and let the equation \(E\) be \(|x|^2-2|x|+|\lambda-3|=0\). Then the largest element in the set \(S=\) \(\{x+\lambda: x\) is an integer solution of \(E\}\) is

The shortest distance between the lines \(\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}\) and \(\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}\) is equal to

The \(4^{\text {th }}\) term of \(G P\) is \(500\) and its common ratio is \(\frac{1}{m}, m \in N\) Let \(S_n\) denote the sum of the first \(n\) terms of this GP If \(S_6>S_5+1\) and \(S_7< S_6+\frac{1}{2}\), then the number of possible values of \(m\) is

Let \(C\) be the largest circle centred at \((2,0)\) and inscribed in the ellipse \(\frac{x^2}{36}+\frac{y^2}{16}=1\)If \((1, a)\) lies on \(C\), then \(10 \alpha^2\) is equal to

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses If he can choose at most two language courses, then the number of ways he can choose five courses is

The value of \(12 \int\limits_0^3\left|x^2-3 x+2\right| d x\) is

The value of \(\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x\) is

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is

Let a tangent to the curve \(9 x^2+16 y^2=144\) intersect the coordinate axes at the points \(A\) and \(B\). Then, the minimum length of the line segment \(AB\) is

Suppose \(\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}\) Then the value of \(\alpha\) is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement
Reason R: The current in the forward bias is more than the current in the reverse bias for a \(p-n\) junction diode
In the light of the above statements, choose the correct answer from the options given below:

• (1) A is true but \(R\) is false
• (2) Both \(A\) and \(R\) are true and \(R\) is the correct explanation of \(A\)
• (3) A is false but \(R\) is true
• (4) Both \(A\) and \(R\) are true but \(R\) is \(N O T\) the correct explanation of \(A\)

As per given figure, a weightless pulley \(P\) is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if \(g =10 \,/ s ^2\) )

• (1) \((4 \sqrt{3}-1) N\)
• (2) \(4(\sqrt{3}-1) N\)
• (3) \(4(\sqrt{3}+1) N\)
• (4) \((4 \sqrt{3}+1) N\)

Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is \(\theta_{ B }\), then the Brewster's angle for the light propagating from glass to air is \(\frac{\pi}{2}-\theta_m\)
Statement II : The Brewster's angle for the light propagating from glass to air is \(\tan ^{-1}\left(\mu_{ g }\right)\) where \(\mu_{ g }\) is the refractive index of glass
In the light of the above statements choose the correct answer from the options given below:

• (1) Both Statement I and Statement II are true
• (2) Both Statement I and Statement II are false
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

A \(100\, m\) long wire having cross-sectional area \(625 \times 10^{-4} \, m ^2\) and Young's modulus is \(10^{10} Nm ^{-2}\) is subjected to a load of \(250 \, N\), then the elongation in the wire will be:

• (1) \(6.25 \times 10^{-3} m\)
• (2) \(4 \times 10^{-3} m\)
• (3) \(4 \times 10^{-4} m\)
• (4) \(6.25 \times 10^{-6} m\)

The weight of a body at the surface of earth is \(18\, N\) The weight of the body at an altitude of \(3200 \,km\) above the earth's surface is (given, radius of earth \(R _{ e }=6400 \,km\) ):

• (1) 19.6 N
• (2) 9.8 N
• (3) 4.9 N
• (4) 8 N

From the photoelectric effect experiment, following observations are made Identify which of these are correct 
A. The stopping potential depends only on the work function of the metal 
B. The saturation current increases as the intensity of incident light increases 
C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light 
D. Photoelectric effect can be explained using wave theory of light 
Choose the correct answer from the options given below:

• (1) A, B, D only
• (2) B only
• (3) A, C, D only
• (4) B, C only

Two long straight wires \(P\) and \(Q\) carrying equal current \(10\, A\) each were kept parallel to each other at \(5 \, cm\) distance Magnitude of magnetic force experienced by \(10 \, cm\) length of wire \(P\) is \(F_1\) If distance between wires is halved and currents on them are doubled, force \(F_2\) on \(10 \, cm\) length of wire \(P\) will be:

• (1) \(10 F _1\)
• (2) \(8 F _1\)
• (3) \(\frac{F_1}{8}\)
• (4) \(\frac{F_1}{10}\)

A circular loop of radius \(r\) is carrying current \(I A\) The ratio of magnetic field at the center of circular loop and at a distance \(r\) from the center of the loop on its axis is:

• (1) \(1: 3 \sqrt{2}\)
• (2) \(2 \sqrt{2}: 1\)
• (3) \(3 \sqrt{2}: 2\)
• (4) \(1: \sqrt{2}\)

If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\) What will be the equivalent distance between charges in air for the same electrostatic force?

• (1) \(k \sqrt{d}\)
• (2) \(1 \cdot 5 d \sqrt{k}\)
• (3) \(2 d \sqrt{k}\)
• (4) \(d \sqrt{k}\)

A conducting circular loop of radius \(\frac{10}{\sqrt{\pi}} cm\) is placed perpendicular to a uniform magnetic field of \(0.5 T\) The magnetic field is decreased to zero in \(0.5 s\) at a steady rate The induced emf in the circular loop at \(0.25 s\) is:

• (1) \(emf =1 mV\)
• (2) \(emf =100 mV\)
• (3) \(emf =5 mV\)
• (4) \(emf =10 mV\)

\(1 \,g\) of a liquid is converted to vapour at \(3 \times 10^5 Pa\) pressure If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600 \, cm ^3\) during this phase change, then the increase in internal energy in the process will be:

• (1) \(4800 \, J\)
• (2) \(4320 \, J\)
• (3) \(4.32 \times 10^8 \, J\)
• (4) \(432000 \, J\)

As shown in the figure, a network of resistors is connected to a battery of \(24 V\) with an internal resistance of \(3 \Omega\) The currents through the resistors \(R_4\) and \(R_5\) are \(I_4\) and \(I_5\) respectively The values of \(I _4\) and \(I _5\) are:\((24 V , 3 \Omega)\)

• (1) \(I _4=\frac{8}{5} A\) and \(I _5=\frac{2}{5} A\)
• (2) \(I _4=\frac{6}{5} A\) and \(I _5=\frac{24}{5} A\)
• (3) \(I _4=\frac{2}{5} A\) and \(I _5=\frac{8}{5} A\)
• (4) \(I _4=\frac{24}{5} A\) and \(I _5=\frac{6}{5} A\)

A travelling wave is described by the equation \(y(x, t)=[0.05 \sin (8 x-4 t)] m\) The velocity of the wave is : [all the quantities are in SI unit]

• (1) \(4 \,ms ^{-1}\)
• (2) \(8 \,ms ^{-1}\)
• (3) \(0.5 \, ms ^{-1}\)
• (4) \(2 \,ms ^{-1}\)

The maximum vertical height to which a man can throw a ball is \(136 \,m\) The maximum horizontal distance upto which he can throw the same ball is:

• (1) \(68\, m\)
• (2) \(136\, m\)
• (3) \(192\, m\)
• (4) \(272\, m\)

Given below are two statements : 
Statement I : The temperature of a gas is \(-73^{\circ} C\) When the gas is heated to \(527^{\circ} C\), the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:

• (1) Statement I is false but Statement II is true
• (2) Both Statement I and Statement II are true
• (3) Both Statement I and Statement II are false
• (4) Statement I is true but Statement II is false

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

• (1) Statement I is false but Statement II is true
• (2) Statement I is true but Statement II is false
• (3) Both statement I and Statement II are false
• (4) Both Statement I and Statement II are true

In \(\vec{E}\) and \(\vec{K}\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by:\((\omega-\) angular frequency):

• (1) \(\frac{1}{\omega}(\vec{K}\times\vec{E})\)
• (2) \(\omega(\vec{E}\times\vec{K})\)
• (3) \(\vec{K}\times\vec{E}\)
• (4) \(\omega(\vec{ K } \times \vec{ E })\)

A modulating signal is a square wave, as shown in the figure If the carrier wave is given as \(c ( t )=2 \sin (8 \pi t)\) volts, the modulation index is:

• (1) \(\frac{1}{3}\)
• (2) 1
• (3) \(\frac{1}{2}\)
• (4) \(\frac{1}{4}\)

Consider the following radioactive decay process \({ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6\) The mass number and the atomic number of \(A_6\) are given by:

• (1) 211 and 80
• (2) 210 and 80
• (3) 210 and 82
• (4) 210 and 84

A hollow cylindrical conductor has length of \(314\, m\), while its inner and outer diameters are \(4 \, mm\) and \(8 \, mm\) respectively The resistance of the conductor is \(n \times 10^{-3} \Omega\).If the resistivity of the material is \(24 \times 10^{-8} \Omega m\) The value of \(n\) is ___

A block of a mass \(2\, kg\) is attached with two identical springs of spring constant \(20\, N / m\) each The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure) When the mass is displaced from its equilibrium position, it executes a simple harmonic motion The time period of oscillation is \(\frac{\pi}{\sqrt{x}}\) in SI unit The value of \(x\) is

Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of \(a\) to \(b\) is \(\frac{x}{2}\) The value of \(x\) is __

A hole is drilled in a metal sheet At \(27^{\circ} C\), the diameter of hole is \(5 cm\) When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\) The value of \(d\) will be ___ if coefficient of linear expansion of the metal is \(16 \times 10^{-5} { }^{\circ} C\)

Solid sphere \(A\) is rotating about an axis \(PQ\) If the radius of the sphere is \(5 cm\) then its radius of gyration about \(PQ\) will be \(\sqrt{x} cm\) The value of \(x\) is __

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity The radius of curvature of both the lenses is \(30 \,cm\) and refraction index of the material for both the lenses is \(175\) Both the lenses are placed at distance of \(40 \,cm\) from each other Due to the combination, the image of the object is formed at distance \(x=\)__ \(cm\), from concave lens.

A stream of a positively charged particles having \(\frac{q}{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\vec{v}_0=3 \times 10^7 \hat{i} m / s\) is deflected by an electric field \(18 kV / m\) The electric field exists in a region of \(10 cm\) along \(x\) direction Due to the electric field, the deflection of the charge particles in the \(y\) direction is___ \(mm\)

A spherical body of mass \(2\, kg\) starting from rest acquires a kinetic energy of \(10000\, J\) at the end of \(5^{\text {th }}\) second The force acted on the body is ___\(N\)

In the circuit shown in the figure, the ratio of the quality factor and the band width is__s

Assume that protons and neutrons have equal masses Mass of a mucleon is \(16 \times 10^{-27} kg\) and radius of nucleus is \(15 \times 10^{-15} A ^{1 / 3} m\) The approximate ratio of the nuclear density and water density is \(n \times 10^{13}\) The value of \(n\) is ___

The primary and secondary valencies of cobalt respectively in \([ Co(NH_3)_5Cl]Cl_2\) are :

• (1) 3 and 5
• (2) 2 and 6
• (3) 2 and 8
• (4) 3 and 6

' \(A\)' and ' \(B\) ' formed in the following set of reactions are:

• (1)
• (2)
• (3)
• (4)

Decreasing order of the hydrogen bonding in following forms of water is correctly represented by
A. Liquid water
B. Ice
C. Impure water 
Choose the correct answer from the options given below:

• (1) \(C \gt B \gt A\)
• (2) \(B \gt A \gt C\)
• (3) \(A=B \gt C\)
• (4) \(A \gt B\gt C\)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases
Reason R: \(\,I ^{-}\)is a good nucleophile as well as a good leaving group
In the light of the above statements, choose the correct answer from the options given below

• (1) A is false but \(R\) is true
• (2) A is true but \(R\) is false
• (3) Both \(A\) and \(R\) are true but \(R\) is \(N O T\) the correct explanation of \(A\)
• (4) Both \(A\) and \(R\) are true and \(R\) is the correct explanation of \(A\)

An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime The metal ion is:

• (1) \(Co ^{2+}\)
• (2) \(Fe ^{2+}\)
• (3) \(Ni ^{2+}\)
• (4) \(Cu ^{2+}\)

In the following given reaction, ' \(A\) ' is

• (1)
• (2)
• (3)
• (4)

'R formed in the following sequence of reactions is :

• (1)
• (2)
• (3)
• (4)

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

• (1) \(T_1^{2+}\)
• (2) \(Mn ^{2+}\)
• (3) \(V ^{2+}\)
• (4) \(Cr ^{2+}\)

Compound \(( X )\) undergoes following sequence of reactions to give the Lactone \(( Y )\)

• (1)
• (2)
• (3)
• (4)

• (1) A only
• (2) \(B\) and \(C\) only
• (3) A and C only
• (4) A and D only

Order of Covalent bond:
A. \(KF > KI ; LiF > KF\) 
B. \(KF < KI ; LiF > KF\) 
C. \(SnCl _4> SnCl _2 ; CuCl > NaCl\) 
D. \(LiF > KF ; CuCl <NaCl\)
E. \(KF < KI ; CuCl > NaCl\) 
Choose the correct answer from the options given below:

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

It is observed that characteristic \(X\)-ray spectra of elements show regularity When frequency to the power " \(n\) " ie \(v^n\) of \(X\)-rays emitted is plotted against atomic number " \(Z\) ", following graph is obtained

• (1) 2
• (2) 3
• (3) 1
• (4) \(\frac{1}{2}\)

Increasing order of stability of the resonance structures is:
 
Choose the correct answer from the options given below:

• (1) \(D , C , A , B\)
• (2) C, D, A, B
• (3) D, C, B, A
• (4) \(C, D , A , B\)

Which of the following statements is correct about freons?

• (1) All radicals are known as freons.
• (2) Freons cause skin cancer.
• (3) Freons are chlorofluoro carbon.
• (4) Freons are used in sunscreen lotion.

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

Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at the same concentration 
Statement II: For colloidal particles, the potential difference between the fixed layer and the diffused layer of the same charges is called the electrokinetic potential or zeta potential
In the light of the above statements, choose the correct answer from the options given below

• (1) Statement I is false but Statement II is true
• (2) Both Statement I and Statement II are true
• (3) Statement I is true but Statement II is false
• (4) Both Statement I and Statement II are false

• (1) A-R, B-Q, C-S, D-P
• (2) A-Q, B-P, C-S, D-R
• (3) A-P, B-S, C-Q, D-R
• (4) A-S, B-P, C-R, D-Q

Reaction of \(BeO\) with ammonia and hydrogen fluoride gives A which on thermal decomposition gives \(BeF _2\) and \(NH _4 F\) What is ' \(A ^{\prime}\) ?

• (1) \(\left( NH _4\right) BeF _3\)
• (2) \(H _3 NBeF _3\)
• (3) \(\left( NH _4\right) Be _2 F _5\)
• (4) \(\left( NH _4\right)_2 BeF _4\)

• (1) Both Statement-I and Statement-II are correct.
• (2) Both Statement-I and Statement-II are incorrect.
• (3) Statement-I is correct but Statement-II is incorrect.
• (4) Statement-I is incorrect but Statement-II is correct.

Which of the Phosphorus oxoacid can create silver mirror from \(AgNO _3\) solution?

• (1) \(H _4 P _2 O _7\)
• (2) \(\left( HPO _3\right)_n\)
• (3) \(H _4 P _2 O _6\)
• (4) \(H _4 P _2 O _5\)

When \(Fe _{0.93} O\) is heated in presence of oxygen, it converts to \(Fe _2 O _3\) The number of correct statement/s from the following is
A. The equivalent weight of \(Fe _{093} O\) is Molecular wejght \(0.79\)
B. The number of moles of \(Fe ^{2+}\) and \(Fe ^{3+}\) in 1 mole of \(Fe _{0.93} O\) is \(0.79\) and \(014\) respectively
C. \(Fe _{0.93} O\) is metal deficient with lattice comprising of cubic closed packed arrangement of \(O ^{2-}\) ions
D. The \(\%\) composition of \(Fe ^{2+}\) and \(Fe ^{3+}\) in \(Fe _{093} O\) is \(85 \%\) and \(15 \%\) respectively

\(5 \,g\) of \(NaOH\) was dissolved in deionized water to prepare a \(450 \,mL\) stock solution What volume (in \(mL\) ) of this solution would be required to prepare \(500 \,mL\) of \(01\, M\) solution? Given: Molar Mass of \(Na, O\) and \(H\) is 23,16 and \(1 \,g\, mol ^{-1}\) respectively

Uracil is a base present in RNA with the following structure \(\%\) of \(N\) in uracil is ___

Number of moles of \(AgCl\) formed in the following reaction is

The number of correct statement/s from the following is
A. Larger the activation energy, smaller is the value of the rate constant
B. The higher is the activation energy, higher is the value of the temperature coefficient 
C. At lower temperatures, increase in temperature causes more change in the value of \(k\) than at higher temperature 
D. A plot of \(\ln k\) vs \(\frac{1}{T}\) is a straight line with slope equal to \(-\frac{E_a}{R}\)

The dissociation constant of acetic acid is \(x \times 10^{-5}\) When \(25 \,mL\) of \(0.2 \,M \,CH _3 COONa\) solution is mixed with \(25 \,mL\) of \(0.02\, M \,CH _3 COOH\) solution, the \(pH\) of the resultant solution is found to be equal to 5. The value of \(x\) is ___

At \(298 \,K\), a 1 litre solution containing \(10\, m\,mol\) of \(Cr _2 O _7{ }^{2-}\) and \(100\, m\,mol\) of \(Cr ^{3+}\) shows a pH of 30.

Given: \(Cr _2 O _7^{2-} \rightarrow Cr ^{3+} ; E ^{\circ}=1330 V\) and \(\frac{2303 RT }{ F }=0059 V\).

The potential for the half cell reaction is \(x \times 10^{-3} V\). The value of \(x\) is ___ .

The d-electronic configuration of \(\left[ CoCl _4\right]^{2-}\) in tetrahedral crystal field is \(e ^{ m } t _2 ^n\) Sum of "\(m\)" and "number of unpaired electrons" is

If wavelength of the first line of the Paschen series of hydrogen atom is _____ nm, then the wavelength of the second line of this series is nm (Nearest integer)