JEE Main 2021 Feb 26 Shift 2 Question Paper with Solution PDF- Download Here

Let \(f(x)\) be a differentiable function at \(x = a\) with \(f'(a) = 2\) and \(f(a) = 4\).
Then \(\displaystyle\lim_{x \to a} \frac{x f(a) - a f(x)}{x - a}\) equals :

• (1) \(4 - 2a\)
• (2) \(2a + 4\)
• (3) \(a + 4\)
• (4) \(2a - 4\)

Let \(A(1, 4)\) and \(B(1, -5)\) be two points. Let \(P\) be a point on the circle \((x - 1)^2 + (y - 1)^2 = 1\) such that \((PA)^2 + (PB)^2\) have maximum value, then the points, \(P\), \(A\) and \(B\) lie on :

• (1) a straight line
• (2) an ellipse
• (3) a parabola
• (4) a hyperbola

Consider the following system of equations :
\(x + 2y - 3z = a\)
\(2x + 6y - 11z = b\)
\(x - 2y + 7z = c\),
where \(a\), \(b\) and \(c\) are real constants. Then the system of equations :

• (1) has no solution for all \(a\), \(b\) and \(c\)
• (2) has a unique solution when \(5a = 2b + c\)
• (3) has infinite number of solutions when \(5a = 2b + c\)
• (4) has a unique solution for all \(a\), \(b\) and \(c\)

A natural number has prime factorization given by \(n = 2^x 3^y 5^z\), where \(y\) and \(z\) are such that \(y + z = 5\) and \(y^{-1} + z^{-1} = \frac{5}{6}\), \(y \gt z\). Then the number of odd divisions of \(n\), including 1, is :

• (1) \(11\)
• (2) \(6\)
• (3) \(12\)
• (4) \(6x\)

If \(0 \lt a, b \lt 1\), and \(\tan^{-1}a + \tan^{-1}b = \frac{\pi}{4}\), then the value of
\((a + b) - \left(\frac{a^2 + b^2}{2}\right) + \left(\frac{a^3 + b^3}{3}\right) - \left(\frac{a^4 + b^4}{4}\right) + \dots\)
is :

• (1) \(\log_e 2\)
• (2) \(e\)
• (3) \(\log_e\left(\frac{e}{2}\right)\)
• (4) \(e^2 = 1\)

Let \(f(x) = \displaystyle\int_0^x e^t f(t)\,dt + e^x\) be a differentiable function for all \(x \in R\). Then \(f(x)\) equals :

• (1) \(e^{(e^x - 1)}\)
• (2) \(2e^{e^x} - 1\)
• (3) \(2e^{e^x - 1} - 1\)
• (4) \(e^{e^x} - 1\)

For \(x \gt 0\), if \(f(x) = \displaystyle\int_1^x \frac{\log_e t}{(1 + t)}\,dt\), then \(f(e) + f\left(\frac{1}{e}\right)\) is equal to :

• (1) \(\frac{1}{2}\)
• (2) \(-1\)
• (3) \(0\)
• (4) \(1\)

Let \(A = \{1, 2, 3, \dots, 10\}\) and \(f : A \to A\) be defined as
\(f(k) = \begin{cases} k + 1 & \text{if } k \text{ is odd} \\ k & \text{if } k \text{ is even} \end{cases}\)
Then the number of possible functions \(g : A \to A\) such that \(g \circ f = f\) is :

• (1) \(5^5\)
• (2) \(10^5\)
• (3) \(5!\)
• (4) \({}^{10}C_5\)

Let \(A_1\) be the bounded area enclosed by the curves \(y=x^2+2\), \(x+y=8\) and \(y\)-axis that lies in the first quadrant. Let \(A_2\) be the bounded area enclosed by the curves \(y=x^2+2\), \(y^2=x\), \(x=2\) and \(y\)-axis that lies in the first quadrant. Then \(A_1-A_2\) is equal to

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

Let \(f(x) = \sin^{-1}x\) and \(g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}\). If \(g(2) = \displaystyle\lim_{x \to 2} g(x)\), then the domain of the function \(f \circ g\) is :

• (1) \((-\infty, -2] \cup \left[-\frac{4}{3}, \infty\right)\)
• (2) \((-\infty, -2] \cup [-1, \infty)\)
• (3) \((-\infty, -2] \cup \left[-\frac{3}{2}, \infty\right)\)
• (4) \((-\infty, -1] \cup [2, \infty)\)

Let \(f : R \to R\) be defined as
\(f(x) = \begin{cases} 2\sin\left(-\frac{\pi x}{2}\right), & \text{if } x \lt -1 \\ |ax^2 + x + b|, & \text{if } -1 \le x \le 1 \\ \sin(\pi x), & \text{if } x \gt 1 \end{cases}\)
If \(f(x)\) is continuous on \(R\), then \(a + b\) equals :

• (1) \(-3\)
• (2) \(3\)
• (3) \(-1\)
• (4) \(1\)

If the locus of the mid-point of the line segment from the point \((3, 2)\) to a point on the circle, \(x^2 + y^2 = 1\) is a circle of radius \(r\), then \(r\) is equal to :

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

If vectors \(\vec{a_1} = x\hat{i} - \hat{j} + \hat{k}\) and \(\vec{a_2} = \hat{i} + y\hat{j} + z\hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x\hat{i} + y\hat{j} + z\hat{k}\) is :

• (1) \(\frac{1}{\sqrt3}\left(\hat{i} - \hat{j} + \hat{k}\right)\)
• (2) \(\frac{1}{\sqrt2}\left(-\hat{j} + \hat{k}\right)\)
• (3) \(\frac{1}{\sqrt2}\left(\hat{i} - \hat{j}\right)\)
• (4) \(\frac{1}{\sqrt3}\left(\hat{i} + \hat{j} - \hat{k}\right)\)

A seven digit number is formed using digits \(3, 3, 4, 4, 4, 5, 5\). The probability, that number so formed is divisible by 2, is :

• (1) \(\frac{1}{7}\)
• (2) \(\frac{4}{7}\)
• (3) \(\frac{6}{7}\)
• (4) \(\frac{3}{7}\)

Let \(L\) be a line obtained from the intersection of two planes \(x + 2y + z = 6\) and \(y + 2z = 4\). If point \(P(\alpha, \beta, \gamma)\) is the foot of perpendicular from \((3, 2, 1)\) on \(L\), then the value of \(21(\alpha + \beta + \gamma)\) equals :

• (1) \(102\)
• (2) \(142\)
• (3) \(136\)
• (4) \(68\)

The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :

• (1) An equilateral triangle having each of its side of length \(\sqrt{3}\,r\).
• (2) An equilateral triangle of height \(\frac{2r}{3}\).
• (3) A right angle triangle having two of its sides of length \(2r\) and \(r\).
• (4) An isosceles triangle with base equal to \(2r\).

The sum of the series
\(\displaystyle\sum_{n=1}^{\infty}\frac{n^2+6n+10}{(2n+1)!}\)
is equal to :

• (1) \(\frac{41}{8}e+\frac{19}{8}e^{-1}-10\)
• (2) \(\frac{41}{8}e-\frac{19}{8}e^{-1}-10\)
• (3) \(\frac{41}{8}e+\frac{19}{8}e^{-1}+10\)
• (4) \(-\frac{41}{8}e+\frac{19}{8}e^{-1}-10\)

If the mirror image of the point \((1,3,5)\) with respect to the plane \(4x-5y+2z=8\) is \((\alpha,\beta,\gamma)\), then \(5(\alpha+\beta+\gamma)\) equals :

• (1) 39
• (2) 41
• (3) 47
• (4) 43

Let \(F_1(A,B,C)=(A\wedge\sim B)\vee[\sim C\wedge(A\vee B)]\vee\sim A\) and
\(F_2(A,B)=(A\vee B)\vee(B\to\sim A)\) be two logical expressions. Then :

• (1) Both F₁ and F₂ are not tautologies
• (2) F₁ and F₂ both are tautologies
• (3) F₁ is not a tautology but F₂ is a tautology
• (4) F₁ is a tautology but F₂ is not a tautology

Let slope of the tangent line to a curve at any point \(P(x,y)\) be given by \(\frac{xy^2+y}{x}\). If the curve intersects the line \(x+2y=4\) at \(x=-2\), then the value of \(y\), for which the point \((3,y)\) lies on the curve, is :

• (1) \(-\frac{18}{19}\)
• (2) \(-\frac{4}{3}\)
• (3) \(\frac{18}{35}\)
• (4) \(-\frac{18}{11}\)

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.

If the matrix \(A=\begin{bmatrix}1&0&0\\0&2&0\\3&0&-1\end{bmatrix}\) satisfies the equation
\(A^{20}+\alpha A^{19}+\beta A=\begin{bmatrix}1&0&0\\0&4&0\\0&0&1\end{bmatrix}\)
for some real numbers \(\alpha\) and \(\beta\), then \(\beta-\alpha\) is equal to ___________.

Let \(\alpha\) and \(\beta\) be two real numbers such that \(\alpha+\beta=1\) and \(\alpha\beta=-1\). Let \(p_n=(\alpha)^n+(\beta)^n\), \(p_{n-1}=11\) and \(p_{n+1}=29\) for some integer \(n\ge1\). Then, the value of \(p_n^2\) is ___________.

Let \(z\) be those complex numbers which satisfy
\(|z+5|\le4\) and \(z(1+i)+\overline{z}(1-i)\ge-10\), \(i=\sqrt{-1}\).
If the maximum value of \(|z+1|^2\) is \(\alpha+\beta\sqrt2\), then the value of \((\alpha+\beta)\) is ____________.

If the arithmetic mean and geometric mean of the \(p^{th}\) and \(q^{th}\) terms of the sequence \(-16,8,-4,2,\dots\) satisfy the equation \(4x^2-9x+5=0\), then \(p+q\) is equal to __________.

If \(I_{m,n}=\int_0^1x^{m-1}(1-x)^{n-1}dx\), for \(m,n\ge1\), and
\(\int_0^1\frac{x^{m-1}+x^{n-1}}{(1+x)^{m+1}}dx=\alpha I_{m,n}\), \(\alpha\in R\), then \(\alpha\) equals ___________.

Let \(X_1,X_2,\dots,X_{18}\) be eighteen observations such that
\(\sum_{i=1}^{18}(X_i-\alpha)=36\)
and
\(\sum_{i=1}^{18}(X_i-\beta)^2=90\)
, where \(\alpha\) and \(\beta\) are distinct real numbers. If the standard deviation of these observations is 1, then the value of \(|\alpha-\beta|\) is ____________.

Let \(a\) be an integer such that all the real roots of the polynomial \(2x^5+5x^4+10x^3+10x^2+10x+10\) lie in the interval \((a,a+1)\). Then, \(|a|\) is equal to ___________.

Let the normals at all the points on a given curve pass through a fixed point \((a,b)\). If the curve passes through \((3,-3)\) and \((4,-2\sqrt2)\), and given that \(a-2\sqrt2\,b=3\), then \((a^2+b^2+ab)\) is equal to __________.

Let \(L\) be a common tangent line to the curves
\(4x^2+9y^2=36\) and \((2x)^2+(2y)^2=31\). Then the square of the slope of the line \(L\) is __________.

Draw the output signal Y in the given combination of gates.

• (1)
• (2)
• (3)
• (4)

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is \(2.5 \times 10^{-4}\) Wb/m\(^2\) and the angle of dip is \(60^\circ\). The emf induced between the tips of the plane wings will be __________.

• (1) 88.37 mV
• (2) 62.50 mV
• (3) 54.125 mV
• (4) 108.25 mV

Find the peak current and resonant frequency of the following circuit (as shown in figure).

• (1) 2 A and 100 Hz
• (2) 2 A and 50 Hz
• (3) 0.2 A and 100 Hz
• (4) 0.2 A and 50 Hz

A scooter accelerates from rest for time \(t_1\) at constant rate \(a_1\) and then retards at constant rate \(a_2\) for time \(t_2\) and comes to rest. The correct value of \(\frac{t_1}{t_2}\) wil be :

• (1) \(\frac{a_1 + a_2}{a_2}\)
• (2) \(\frac{a_1 + a_2}{a_1}\)
• (3) \(\frac{a_2}{a_1}\)
• (4) \(\frac{a_1}{a_2}\)

Given below are two statements:

Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..

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

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of \(\lambda\) where C/V = \(\lambda\) ?

• (1) \([M^{-3}L^{-4}I^{3}T^{7}]\)
• (2) \([M^{-2}L^{-3}I^{2}T^{6}]\)
• (3) \([M^{-2}L^{-4}I^{3}T^{7}]\)
• (4) \([M^{-1}L^{-3}I^{-2}T^{-7}]\)

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

• (1) 4.34 m/s
• (2) 2.19 m/s
• (3) 3.25 m/s
• (4) 4.17 m/s

A wire of 1\(\Omega\) has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

• (1) 76%
• (2) 12.5%
• (3) 25%
• (4) 56%

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) respectively. Then choose the correct relation for these vectors.

• (1) \(\vec{b} = \vec{a} + 2\vec{c}\)
• (2) \(\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}\)
• (3) \(\vec{b} = 2\vec{a} + \vec{c}\)
• (4) \(\vec{b} = \vec{a} - \vec{c}\)

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is :

• (1) either monoatomic or diatomic.
• (2) monoatomic only.
• (3) polyatomic only.
• (4) diatomic only.

The length of metallic wire is \(l_1\) when tension in it is \(T_1\). It is \(l_2\) when the tension is \(T_2\). The original length of the wire will be :

• (1) \(\frac{T_1 l_1 - T_2 l_2}{T_2 - T_1}\)
• (2) \(\frac{l_1 + l_2}{2}\)
• (3) \(\frac{T_2 l_1 + T_1 l_2}{T_1 + T_2}\)
• (4) \(\frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}\)

The trajectory of a projectile in a vertical plane is \(y = \alpha x - \beta x^2\), where \(\alpha\) and \(\beta\) are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained H are respectively given by :

• (1) \(\tan^{-1}\alpha,\ \frac{\alpha^2}{4\beta}\)
• (2) \(\tan^{-1}\alpha,\ \frac{4\alpha^2}{\beta}\)
• (3) \(\tan^{-1}\left(\frac{\beta}{\alpha}\right),\ \frac{\alpha^2}{\beta}\)
• (4) \(\tan^{-1}\beta,\ \frac{\alpha^2}{2\beta}\)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 
Assertion (A): Electromagnetic waves carry energy but not momentum. 
Reason (R): Mass of a photon is zero. In the light of the above statements.
choose the most appropriate answer from the options given below:

• (1) Both (A) and (R) are true and (R) is the correct explanation of (A)
  
• (2) (A) is false but (R) is true
  
• (3) Both (A) and (R) are true but (R) is not the correct explanation of (A)
  
• (4) (A) is true but (R) is false
  

A body starts from rest on a long inclined plane of slope \(45^\circ\). The coefficient of friction between the body and the plane varies as \(\mu=0.3x\), where \(x\) is distance travelled down the plane. The body will have maximum speed (for \(g=10\ \mathrm{m/s^2}\)) when \(x=\)

• (1) 9.8 m
• (2) 27 m
• (3) 12 m
• (4) 3.33 m

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

• (1) \(\frac{MF}{F + Ma}\)
• (2) \(\frac{F + Ma}{M}\)
• (3) \(\frac{Ma - F}{M}\)
• (4) \(\frac{F - Ma}{M}\)

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be :

• (1) \(\frac{2mgh}{I + 2mr^2}\)
• (2) \(\frac{2mgh}{I + mr^2}\)
• (3) 2gh
• (4) \(\frac{2gh}{I + mr^2}\)

A particle executes S.H.M., the graph of velocity as a function of displacement is :

• (1) a parabola
• (2) a helix
• (3) an ellipse
• (4) a circle

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

• (1) 335 Hz
• (2) 345 Hz
• (3) 338 Hz
• (4) 342 Hz

Given below are two statements :

Statement I : A second's pendulum has a time period of 1 second.

Statement II : It takes precisely one second to move between the two extreme positions.

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

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

A radioactive sample is undergoing \(\alpha\) decay. At any time \(t_1\), its activity is \(A\) and another time \(t_2\), the activity is \(\frac{A}{5}\). What is the average life time for the sample?

• (1) \(\frac{\ln 5}{t_2 - t_1}\)
• (2) \(\frac{\ln(t_2 + t_1)}{2}\)
• (3) \(\frac{t_1 - t_2}{\ln 5}\)
• (4) \(\frac{t_2 - t_1}{\ln 5}\)

A monoatomic gas performs a work of \(\frac Q4\) where \(Q\) is the heat supplied to it. The molar heat capacity of the gas will be ____ \(R\) during this transformation. Where \(R\) is the gas constant.

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is \(\frac{\sqrt{x}\,a}{2}\). The value of \(x\) is __________.

Time period of a simple pendulum is \(T\). The time taken to complete \(\frac{5}{8}\) oscillations starting from mean position is \(\frac{\alpha}{\beta}T\). The value of \(\alpha\) is _________.

The zener diode has a \(V_z = 30\ \mathrm{V}\). The current passing through the diode for the following circuit is ________ mA.

The volume \(V\) of a given mass of monoatomic gas changes with temperature \(T\) according to the relation \(V = KT^{\frac{2}{3}}\). The workdone when temperature changes by 90K will be \(xR\). The value of \(x\) is _________. [R = universal gas constant]

A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is __________ cm.

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________.

Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

• (1) 1 : 2
• (2) 1:3
• (3) 2 : 3
• (4) 3 : 2

If the highest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are _________.

• (1) (a) \(\to\) (i), (b) \(\to\) (ii), (c) \(\to\) (iii), (d) \(\to\) (iv)
• (2) (a) \(\to\) (iv), (b) \(\to\) (iii), (c) \(\to\) (ii), (d) \(\to\) (i)
• (3) (a) \(\to\) (iii), (b) \(\to\) (iv), (c) \(\to\) (i), (d) \(\to\) (ii)
• (4) (a) \(\to\) (ii), (b) \(\to\) (i), (c) \(\to\) (iv), (d) \(\to\) (iii)

Ceric ammonium nitrate and \(\mathrm{CHCl_3}\)/alc. KOH are used for the identification of functional groups present in __________ and _______ respectively.

• (1) amine, alcohol
• (2) alcohol, phenol
• (3) alcohol, amine
• (4) amine, phenol

In \(\overset{1}{\mathrm{C}}\mathrm{H_2} = \overset{2}{\mathrm{C}} = \overset{3}{\mathrm{C}}\mathrm{H} - \overset{4}{\mathrm{C}}\mathrm{H_3}\) molecule, the hybridization of carbon 1, 2, 3 and 4 respectively, are :

• (1) \(sp^2,\ sp,\ sp^2,\ sp^3\)
• (2) \(sp^2,\ sp^2,\ sp^2,\ sp^3\)
• (3) \(sp^3,\ sp,\ sp^3,\ sp^3\)
• (4) \(sp^2,\ sp^3,\ sp^2,\ sp^3\)

A. Phenyl methanamine

B. N,N-Dimethylaniline

C. N-Methyl aniline

D. Benzenamine

Choose the correct order of basic nature of the above amines.

• (1) D > C > B > A
• (2) A > C > B > D
• (3) D > B > C > A
• (4) A > B > C > D

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

Assertion A : In \(\mathrm{TlI_3}\), isomorphous to \(\mathrm{CsI_3}\), the metal is present in +1 oxidation state.

Reason R : Tl metal has fourteen f electrons in its electronic configuration.

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

• (1) A is correct but R is not correct
• (2) A is not correct but R is correct
• (3) Both A and R are correct but R is NOT the correct explanation of A
• (4) Both A and R are correct and R is the correct explanation of A

Which of the following forms of hydrogen emits low energy \(\beta^-\) particles?

• (1) Tritium \(_1^3\mathrm{H}\)
• (2) Proton \(\mathrm{H^+}\)
• (3) Protium \(_1^1\mathrm{H}\)
• (4) Deuterium \(_1^2\mathrm{H}\)

Which pair of oxides is acidic in nature?

• (1) \(\mathrm{CaO,\ SiO_2}\)
• (2) \(\mathrm{B_2O_3,\ CaO}\)
• (3) \(\mathrm{B_2O_3,\ SiO_2}\)
• (4) \(\mathrm{N_2O,\ BaO}\)

Identify A in the given reaction.

• (1)
• (2)
• (3)
• (4)

Match List - I with List - II.

Choose the correct answer from the options given below :

• (1) (a) \(\to\) (ii), (b) \(\to\) (iv), (c) \(\to\) (i), (d) \(\to\) (iii)
• (2) (a) \(\to\) (iii), (b) \(\to\) (iv), (c) \(\to\) (i), (d) \(\to\) (ii)
• (3) (a) \(\to\) (iii), (b) \(\to\) (i), (c) \(\to\) (iv), (d) \(\to\) (ii)
• (4) (a) \(\to\) (ii), (b) \(\to\) (i), (c) \(\to\) (iv), (d) \(\to\) (iii)

Identify A in the following chemical reaction.

• (1)
• (2)
• (3)
• (4)

2, 4-DNP test can be used to identify :

• (1) ether
• (2) amine
• (3) aldehyde
• (4) halogens

Considering the above reaction, the major product among the following is :

• (1)
• (2)
• (3)
• (4)

Identify A in the given chemical reaction.

• (1)
• (2)
• (3)
• (4)

• (1) O > S > Se > Te
• (2) O < S < Se < Te
• (3) O < S > Se > Te
• (4) O < S > Se < Te

• (1) (a) \(\to\) (iii), (b) \(\to\) (ii), (c) \(\to\) (i)
• (2) (a) \(\to\) (i), (b) \(\to\) (iii), (c) \(\to\) (ii)
• (3) (a) \(\to\) (ii), (b) \(\to\) (i), (c) \(\to\) (iii)
• (4) (a) \(\to\) (iii), (b) \(\to\) (i), (c) \(\to\) (ii)

Seliwanoff test and Xanthoproteic test are used for the identification of ___________ and ________ respectively.

• (1) ketoses, proteins
• (2) proteins, ketoses
• (3) aldoses, ketoses
• (4) ketoses, aldoses

• (1) (a) \(\to\) (i), (b) \(\to\) (ii), (c) \(\to\) (iii), (d) \(\to\) (iv)
• (2) (a) \(\to\) (iii), (b) \(\to\) (i), (c) \(\to\) (v), (d) \(\to\) (ii)
• (3) (a) \(\to\) (i), (b) \(\to\) (ii), (c) \(\to\) (v), (d) \(\to\) (iii)
• (4) (a) \(\to\) (iii), (b) \(\to\) (v), (c) \(\to\) (i), (d) \(\to\) (iv)

• (1) (a) \(\to\) (iv), (b) \(\to\) (iii), (c) \(\to\) (i), (d) \(\to\) (ii)
• (2) (a) \(\to\) (iv), (b) \(\to\) (i), (c) \(\to\) (ii), (d) \(\to\) (iii)
• (3) (a) \(\to\) (iii), (b) \(\to\) (ii), (c) \(\to\) (i), (d) \(\to\) (iv)
• (4) (a) \(\to\) (i), (b) \(\to\) (iii), (c) \(\to\) (iv), (d) \(\to\) (ii)

The nature of charge on resulting colloidal particles when \(\mathrm{FeCl_3}\) is added to excess of hot water is :

• (1) neutral
• (2) sometimes positive and sometimes negative
• (3) positive
• (4) negative

Calgon is used for water treatment. Which of the following statement is \(NOT\) true about Calgon?

• (1) Calgon contains the \(2^{\text {nd }}\) most abundant element by weight in the Earth's crust.
• (2) It is polymeric compound and is water soluble.
• (3) It is also known as Graham's salt
• (4) It does not remove \(Ca ^{2+}\) ion by precipitation.

When 12.2 g of benzoic acid is dissolved in 100 g of water, the freezing point of solution was found to be \(-0.93^\circ\mathrm{C}\) (\(K_f(\mathrm{H_2O}) = 1.86\ \mathrm{K\ kg\ mol^{-1}}\)). The number (n) of benzoic acid molecules associated (assuming 100% association) is ___________.

If the activation energy of a reaction is 80.9 kJ mol^-1, the fraction of molecules at 700 K, having enough energy to react to form products is \(e^{-x}\). The value of x is __________. (Rounded off to the nearest integer) [Use \(R = 8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}\)]

In mildly alkaline medium, thiosulphate ion is oxidized by \(\mathrm{MnO_4^-}\) to "A". The oxidation state of sulphur in "A" is __________.

The average S-F bond energy in kJ mol⁻¹ of \(\mathrm{SF_6}\) is _____________. (Rounded off to the nearest integer)

[Given : The values of standard enthalpy of formation of \(\mathrm{SF_6(g)}\), \(\mathrm{S(g)}\) and \(\mathrm{F(g)}\) are - 1100, 275 and 80 kJ mol⁻¹ respectively.]

Emf of the following cell at 298K in V is x \(\times\) 10⁻².

\(\mathrm{Zn|Zn^{2+}(0.1\ M)||Ag^{+}(0.01\ M)|Ag}\)

The value of x is _________. (Rounded off to the nearest integer)

[Given : \(E^{\theta}_{Zn^{2+}/Zn} = -0.76\,V;\ E^{\theta}_{Ag^{2+}/Ag} = +0.80\,V;\ \frac{2.303RT}{F} = 0.059\)]

The pH of ammonium phosphate solution, if pk_a of phosphoric acid and pk_b of ammonium hydroxide are 5.23 and 4.75 respectively, is ___________.

The number of stereoisomers possible for \(\mathrm{[Co(ox)_2(Br)(NH_3)]^{2-}}\) is ___________. [ox = oxalate]

If the uncertainty in velocity and position of a minute particle in space are, \(2.4 × 10^{–26}\) \((m s^{–1)}\) and \(10^{–7} (m)\), respectively. The mass of the particle in g is _____ . (Nearest integer)
(Given : \(h = 6.626 × 10^{–34} Js\))

The \(\mathrm{NaNO_3}\) weighed out to make 50 mL of an aqueous solution containing 70.0 mg \(\mathrm{Na^+}\) per mL is _________ g. (Rounded off to the nearest integer)

[Given : Atomic weight in g mol⁻¹ - Na : 23; N : 14; O : 16]

The number of octahedral voids per lattice site in a lattice is _________. (Rounded off to the nearest integer)