JEE Main 2021 July 20 Shift 2 Question Paper with Solution PDF- Download Here

The value of
\(\tan\left(2\tan^{-1}\left(\frac{3}{5}\right)+\sin^{-1}\left(\frac{5}{13}\right)\right)\)
is equal to :

• (1) \(\frac{-181}{69}\)
• (2) \(\frac{220}{21}\)
• (3) \(\frac{-291}{76}\)
• (4) \(\frac{151}{63}\)

The lines \(x=ay-1=z-2\) and \(x=3y-2=bz-2\), \((ab\ne0)\) are coplanar, if :

• (1) \(b=1,\ a\in R-\{0\}\)
• (2) \(a=1,\ b\in R-\{0\}\)
• (3) \(a=2,\ b=2\)
• (4) \(a=2,\ b=3\)

If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int_{-\pi/2}^{\pi/2}[[x]-\sin x]\,dx\) is equal to :

• (1) \(-\pi\)
• (2) \(\pi\)
• (3) 0
• (4) 1

If the real part of the complex number \((1-\cos\theta+2i\sin\theta)^{-1}\) is \(\frac15\) for \(\theta\in(0,\pi)\), then the value of the integral \(\int_0^{\theta}\sin x\,dx\) is equal to:

• (1) 1
• (2) 2
• (3) \(-1\)
• (4) 0

Let \(f:R-\left\{\frac{\alpha}{6}\right\}\to R\) be defined by \(f(x)=\frac{5x+3}{6x-\alpha}\). Then the value of \(\alpha\) for which \((f\circ f)(x)=x\), for all \(x\in R-\left\{\frac{\alpha}{6}\right\}\), is :

• (1) No such \(\alpha\) exists
• (2) 5
• (3) 8
• (4) 6

If \(f:R\to R\) is given by \(f(x)=x+1\), then the value of
\(\lim_{n\to\infty}\frac{1}{n}\left[f(0)+f\left(\frac{5}{n}\right)+f\left(\frac{10}{n}\right)+\ldots\ldots+f\left(\frac{5(n-1)}{n}\right)\right]\)
is :

• (1) \(\frac{3}{2}\)
• (2) \(\frac{5}{2}\)
• (3) \(\frac{1}{2}\)
• (4) \(\frac{7}{2}\)

Let A, B and C be three events such that the probability that exactly one of A and B occurs is \((1-k)\), the probability that exactly one of B and C occurs is \((1-2k)\), the probability that exactly one of C and A occurs is \((1-k)\) and the probability of all A, B and C occur simultaneously is \(k^2\), where \(0\lt k\lt1\). Then the probability that at least one of A, B and C occur is :

• (1) greater than \(\frac{1}{8}\) but less than \(\frac{1}{4}\)
• (2) greater than \(\frac{1}{2}\)
• (3) greater than \(\frac{1}{4}\) but less than \(\frac{1}{2}\)
• (4) exactly equal to \(\frac{1}{2}\)

The sum of all the local minimum values of the twice differentiable function \(f:R\to R\) defined by
\(f(x)=x^3-3x^2-\frac{3f^{\prime\prime}(2)}{2}x+f^{\prime\prime}(1)\)
is :

• (1) \(-22\)
• (2) 5
• (3) \(-27\)
• (4) 0

Let \(y=y(x)\) satisfies the equation
\(\frac{dy}{dx}-|A|=0\)
for all \(x\gt0\), where
\(A=\begin{bmatrix}y&\sin x&1\\0&-1&1\\2&0&\frac1x\end{bmatrix}\).
If \(y(\pi)=\pi+2\), then the value of \(y\left(\frac\pi2\right)\) is :

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

The mean and variance of the observations x, y, 5, 7, 9, 11, 13, 15 are 10 and 20 respectively. If x \(>\) y, then the value of x - y is:

• (1) 2
• (2) 4
• (3) 6
• (4) 8
  

Let \(g(t)=\int_{-\pi/2}^{\pi/2}\cos\left(\frac\pi4t+f(x)\right)dx\), where \(f(x)=\log_e\left(x+\sqrt{x^2+1}\right),\ x\in R\). Then which one of the following is correct?

• (1) \(g(1)=g(0)\)
• (2) \(\sqrt2\,g(1)=g(0)\)
• (3) \(g(1)=\sqrt2\,g(0)\)
• (4) \(g(1)+g(0)=0\)

Let P be a variable point on the parabola \(y=4x^2+1\). Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line \(y=x\) is :

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

The value of \(k\in R\), for which the following system of linear equations
\(3x-y+4z=3,\)
\(x+2y-3z=-2,\)
\(6x+5y+kz=-3,\)
has infinitely many solutions, is :

• (1) 3
• (2) \(-5\)
• (3) 5
• (4) \(-3\)

In a triangle ABC, if \(\left|\overrightarrow{BC}\right|=3\), \(\left|\overrightarrow{CA}\right|=5\) and \(\left|\overrightarrow{BA}\right|=7\), then the projection of the vector \(\overrightarrow{BA}\) on \(\overrightarrow{BC}\) is equal to :

• (1) \(\frac{19}{2}\)
• (2) \(\frac{13}{2}\)
• (3) \(\frac{11}{2}\)
• (4) \(\frac{15}{2}\)

For the natural numbers m, n, if \((1-y)^m(1+y)^n=1+a_1y+a_2y^2+\ldots.+a_{m+n}y^{m+n}\) and \(a_1=a_2=10\), then the value of \((m+n)\) is equal to :

• (1) 88
• (2) 64
• (3) 100
• (4) 80

Let \(r_1\) and \(r_2\) be the radii of the largest and smallest circles, respectively, which pass through the point \((-4,1)\) and having their centres on the circumference of the circle \(x^2+y^2+2x+4y-4=0\). If \(\frac{r_1}{r_2}=a+b\sqrt2\), then \(a+b\) is equal to :

• (1) 3
• (2) 11
• (3) 5
• (4) 7

Consider the following three statements :

(A) If 3 + 3 = 7 then 4 + 3 = 8

(B) If 5 + 3 = 8 then earth is flat.

(C) If both (A) and (B) are true then 5 + 6 = 17.

Then, which of the following statements is correct?

• (1) (A) is false, but (B) and (C) re true
• (2) (A) and (C) are true while (B) is false
• (3) (A) is true while (B) and (C) are false
• (4) (A) and (B) are false while (C) is true

Let in a right angled triangle, the smallest angle be \(\theta\). If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then \(\sin\theta\) is equal to :

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

Consider the line L given by the equation
\(\frac{x-3}{2} = \frac{y-1}{1} = \frac{z-2}{1}\).
Let Q be the mirror image of the point \((2, 3, -1)\) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P?

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

If sum of the first 21 terms of the series \(\log_{9^{1/2}} x + \log_{9^{1/3}} x + \log_{9^{1/4}} x + \ldots\ldots\), where \(x \gt 0\) is 504, then x is equal to

• (1) 243
• (2) 9
• (3) 7
• (4) 81

The number of solutions of the equation
\(\log_{(x+1)}(2x^2 + 7x + 5) + \log_{(2x+5)}(x+1)^2 - 4 = 0\)
, \(x \gt 0\), is :

Let \(y = y(x)\) be a solution curve of the differential equation \[(1 - x^2 y)\,dx = y\,dx + x\,dy.\] If the line \(x = 1\) intersects the curve \(y = y(x)\) at \(y = 2\) and the line \(x = 2\) intersects the curve \(y = y(x)\) at \(y = \alpha\), then a value of \(\alpha\) is:

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

For \(p \gt 0\), a vector
\(\vec{v}_2 = 2\hat{i} + (p+1)\hat{j}\)
is obtained by rotating the vector
\(\vec{v}_1 = \sqrt{3}\,p\hat{i} + \hat{j}\)
by an angle \(\theta\) about origin in counter clockwise direction. If
\(\tan\theta = \frac{(\alpha\sqrt{3} - 2)}{(4\sqrt{3} + 3)}\)
, then the value of \(\alpha\) is equal to ______________.

Consider a triangle having vertices A\((-2, 3)\), B\((1, 9)\) and C\((3, 8)\). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point
\(\left(0, \frac{\alpha}{2}\right)\)
, then the value of real number \(\alpha\) is ______________.

If the tangent to the curve y = x³ – x² + x at the point (a, b) is also tangent to the curve y = 5x² + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to _____ .

Let a function \(g : [0, 4] \to R\) be defined as
\(g(x) = \begin{cases} \max\limits_{0 \le t \le x} \{t^3 - 6t^2 + 9t - 3),\quad 0 \le x \le 3 \\ 4 - x,\quad 3 \lt x \le 4 \end{cases}\)
, then the number of points in the interval (0, 4) where g(x) is NOT differentiable, is ______________.

If
\(\lim_{x \to 0} \frac{\alpha x e^{x} - \beta \log_e(1+x) + \gamma x^2 e^{-x}}{x \sin^2 x} = 10\), \(\alpha, \beta, \gamma \in R\)
, then the value of \(\alpha + \beta + \gamma\) is ______________.

Let
\(A = \{a_{ij}\}\)
be a \(3 \times 3\) matrix,
where
\(a_{ij} = \begin{cases} (-1)^{j-i}\ \text{if } i \lt j, \\ 2\ \text{if } i = j, \\ (-1)^{i+j}\ \text{if } i \gt j \end{cases}\)
then \(\det(3\,\mathrm{Adj}(2A^{-1}))\) is equal to ______________.

For \(k \in N\), let
\(\frac{1}{\alpha(\alpha+1)(\alpha+2)\ldots\ldots\ldots(\alpha+20)} = \sum\limits_{K=0}^{20} \frac{A_k}{\alpha + k}\)
, where
\(\alpha \gt 0\)
. Then the value of
\(100\left(\frac{A_{14} + A_{15}}{A_{13}}\right)^2\)
is equal to ______________.

Let
\(\{a_n\}_{n=1}^{\infty}\)
be a sequence such that \(a_1 = 1\), \(a_2 = 1\) and
\(a_{n+2} = 2a_{n+1} + a_n\)
for all \(n \ge 1\). Then the value of
\(47\sum\limits_{n=1}^{\infty} \frac{a_n}{2^{3n}}\)
is equal to ______________.

If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

• (1) 100%
• (2) 200%
• (3) 300%
• (4) 400%

A person climbs up a stalled escalator in \(60\, s\) . If standing on the same but escalator running with constant velocity he takes \(40\, s\). How much time is taken by the person to walk up the moving escalator ?

• (1) 37 s
• (2) 27 s
• (3) 24 s
• (4) 45 s

A satellite is launched into a circular orbit of radius \( R \) around the earth. A second satellite is launched into an orbit of radius \( 1.03R \). The time period of revolution of the second satellite is larger than the first one approximately by:

• (1) 3 %
  
• (2) 4.5 %
  
• (3) 9 %
  
• (4) 2.5 %

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 \(\mathring{A}\) is observed at 5896 \(\mathring{A}\) ?

• (1) 306 km/sec
• (2) 322 km/sec
• (3) 296 km/sec
• (4) 336 km/sec

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) \(\frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}\)

In an electromagnetic wave the electric field vector and magnetic field vector are given as \(\vec{E} = E_0\hat{i}\) and \(\vec{B} = B_0\hat{k}\) respectively. The direction of propagation of electromagnetic wave is along :

• (1) \(\left(\hat{k}\right)\)
• (2) \(\hat{j}\)
• (3) \(\left(-\hat{k}\right)\)
• (4) \(\left(-\hat{j}\right)\)

For a series LCR circuit with R = 100 \(\Omega\), L = 0.5 mH and C = 0.1 pF connected across 220V\(-\)50 Hz AC supply, the phase angle between current and supplied voltage and the nature of the circuit is :

• (1) 0\(^\circ\), resistive circuit
• (2) \(\approx\) 90\(^\circ\), predominantly inductive circuit
• (3) 0\(^\circ\), resonance circuit
• (4) \(\approx\) 90\(^\circ\), predominantly capacitive circuit

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

• (1)
• (2)
• (3)
• (4)

A particle is making simple harmonic motion along the X-axis. If at a distances \(x_1\) and \(x_2\) from the mean position the velocities of the particle are \(v_1\) and \(v_2\) respectively. The time period of its oscillation is given as :

• (1) \(T = 2\pi\sqrt{\dfrac{x_2^2 + x_1^2}{v_1^2 - v_2^2}}\)
• (2) \(T = 2\pi\sqrt{\dfrac{x_2^2 + x_1^2}{v_1^2 + v_2^2}}\)
• (3) \(T = 2\pi\sqrt{\dfrac{x_2^2 - x_1^2}{v_1^2 + v_2^2}}\)
• (4) \(T = 2\pi\sqrt{\dfrac{x_2^2 - x_1^2}{v_1^2 - v_2^2}}\)

An electron having de-Broglie wavelength \(\lambda\) is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is :

• (1) 0
• (2) \(\dfrac{2m^2c^2\lambda^2}{h^2}\)
• (3) \(\dfrac{2mc\lambda^2}{h}\)
• (4) \(\dfrac{hc}{mc}\)

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :

• (1) Solid sphere
• (2) Solid cylinder
• (3) Hollow cylinder
• (4) Ring

If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass (m) in terms of t, v and l is :

• (1) \([t^{-1}v^{1}l^{-2}]\)
• (2) \([t^{1}v^{2}l^{-1}]\)
• (3) \([t^{-2}v^{-1}l^{1}]\)
• (4) \([t^{-1}v^{-2}l^{1}]\)

The correct relation between the degrees of freedom f and the ratio of specific heat \(\gamma\) is :

• (1) \(f = \dfrac{2}{\gamma - 1}\)
• (2) \(f = \dfrac{2}{\gamma + 1}\)
• (3) \(f = \dfrac{\gamma + 1}{2}\)
• (4) \(f = \dfrac{1}{\gamma + 1}\)

Consider a binary star system of star A and star B with masses \(m_A\) and \(m_B\) revolving in a circular orbit of radii \(r_A\) an \(r_B\), respectively. If \(T_A\) and \(T_B\) are the time period of star A and star B, respectively,

Then :

• (1) \(\dfrac{T_A}{T_B} = \left(\dfrac{r_A}{r_B}\right)^{\frac{3}{2}}\)
• (2) \(T_A = T_B\)
• (3) \(T_A \gt T_B\) (if \(m_A \gt m_B\))
• (4) \(T_A \gt T_B\) (if \(r_A \gt r_B\))

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :

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

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

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :

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

The susceptibility of a paramagnetic material is \(99\). The permeability of the material in Wb/A-m, is 
[Permeability of free space \(μ_0\) = \(4π × 10^{–7}\) Wb/A-m]

• (1) \(4π × 10^{–7}\)
• (2) \(4π × 10^{–4}\)
• (3) \(4π × 10^{–5}\)
• (4) \(4π × 10^{–6}\)

For a certain radioactive process the graph between ln R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :

• (1) 9.15 sec
• (2) 6.93 sec
• (3) 2.62 sec
• (4) 4.62 sec

At an angle of 30\(^\circ\) to the magnetic meridian, the apparent dip is 45\(^\circ\). Find the true dip :

• (1) \(\tan^{-1}\sqrt{3}\)
• (2) \(\tan^{-1}\dfrac{1}{\sqrt{3}}\)
• (3) \(\tan^{-1}\dfrac{2}{\sqrt{3}}\)
• (4) \(\tan^{-1}\dfrac{\sqrt{3}}{2}\)

A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance \(R_p\) is .................... \(\Omega\).

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30\(^\circ\) with the horizontal. The coefficient of friction between the body and plane is \(\dfrac{\sqrt{x}}{5}\) if the time of ascent is half of the time of descent. The value of x is __________.

In the given figure switches \(S_1\) and \(S_2\) are in open condition. The resistance across ab when the switches \(S_1\) and \(S_2\) are closed is _____________ \(\Omega\).

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is \(\frac{\sqrt{x}}{2}\). Then, the value of x is _____________.

The I–V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of 2 V and 4 V respectively, is

• (1) 1:2
• (2) 5:1
• (3) 1:40
• (4) 20:1

A series LCR circuit of R = 5 \(\Omega\), L = 20 mH and C = 0.5 \(\mu\)F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ______________ \(\times\) \(10^{2}\) W.

One mole of an ideal gas at \(27^\circ\) is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be _________ \(\times\) \(10^{-1}\) J. [Given : R = 8.3 J/mole K, ln2 = 0.6931] (Round off to the nearest integer)

When a metal surface is illuminated by light of wavelength \( \lambda \), the stopping potential is 8V. When the same surface is illuminated by light of wavelength \( 3\lambda \), the stopping potential is 2V. The threshold wavelength for this surface is:

• (1) 5\( \lambda \)
• (2) 3\( \lambda \)
• (3) 9\( \lambda \)
• (4) 4.5\( \lambda \)

A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is ___________.

A radioactive substance decays to \(\left(\frac{1}{16}\right)^{th}\) of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.

Which one of the following pairs of isomers is an example of metamerism?

• (1)
• (2)
• (3)
• (4)

• (1)

• (2)

• (3)

• (4)

The major product (P) in the following reaction is :

• (1)
• (2)
• (3)
• (4)

A solution is 0.1 M in \(\mathrm{Cl^-}\) and 0.001 M in \(\mathrm{CrO_4^{2-}}\). Solid \(\mathrm{AgNO_3}\) is gradually added to it. Assuming that the addition does not change in volume and \(K_{sp}(\mathrm{AgCl}) = 1.7\times10^{-10}\ \mathrm{M^2}\) and \(K_{sp}(\mathrm{Ag_2CrO_4}) = 1.9\times10^{-12}\ \mathrm{M^3}\).
Select correct statement from the following :

• (1) AgCl precipitates first because its \(K_{sp}\) is high.
• (2) \(\mathrm{Ag_2CrO_4}\) precipitates first as its \(K_{sp}\) is low.
• (3) \(\mathrm{Ag_2CrO_4}\) precipitates first because the amount of \(\mathrm{Ag^+}\) needed is low.
• (4) AgCl will precipitate first as the amount of \(\mathrm{Ag^+}\) needed to precipitate is low.

Outermost electronic configuration of a group 13 element, E, is \(4s^2, 4p^1\). The electronic configuration of an element of p-block period-five placed diagonally to element, E is :

• (1) [Kr] \(3d^{10}\) \(4s^2\) \(4p^2\)
• (2) [Ar] \(3d^{10}\) \(4s^2\) \(4p^2\)
• (3) [Xe] \(5d^{10}\) \(6s^2\) \(6p^2\)
• (4) [Kr] \(4d^{10}\) \(5s^2\) \(5p^2\)

Metallic sodium does not react normally with :

• (1) gaseous ammonia
• (2) But-2-yne
• (3) Ethyne
• (4) tert-butyl alcohol

Spin only magnetic moment of an octahedral complex of \(\mathrm{Fe^{2+}}\) in the presence of a strong field ligand in BM is :

• (1) 4.89
• (2) 2.82
• (3) 0
• (4) 3.46

Which one of the following species doesn't have a magnetic moment of 1.73 BM, (spin only value)?

• (1) \(\mathrm{O_2^+}\)
• (2) CuI
• (3) \(\mathrm{[Cu(NH_3)_4]Cl_2}\)
• (4) \(\mathrm{O_2^-}\)

Which one of the following statements is not true about enzymes?

• (1) Enzymes are non-specific for a reaction and substrate.
• (2) Almost all enzymes are proteins.
• (3) Enzymes work as catalysts by lowering the activation energy of a biochemical reaction.
• (4) The action of enzymes is temperature and pH specific.

The hybridisations of the atomic orbitals of nitrogen in \(\mathrm{NO_2^-}\), \(\mathrm{NO_2^+}\) and \(\mathrm{NH_4^+}\) respectively are.

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

Benzene on nitration gives nitrobenzene in presence of \(\mathrm{HNO_3}\) and \(\mathrm{H_2SO_4}\) mixture, where :

• (1) both \(\mathrm{H_2SO_4}\) and \(\mathrm{HNO_3}\) act as a bases
• (2) \(\mathrm{HNO_3}\) acts as an acid and \(\mathrm{H_2SO_4}\) acts as a base
• (3) both \(\mathrm{H_2SO_4}\) and \(\mathrm{HNO_3}\) act as an acids
• (4) \(\mathrm{HNO_3}\) acts as a base and \(\mathrm{H_2SO_4}\) acts as an acid

Consider the above reaction, compound B is :

• (1)
• (2)
• (3)
• (4)

Major product P of above reaction, is :

• (1)
• (2)
• (3)
• (4)

\(\mathrm{Cu^{2+}}\) salt reacts with potassium iodide to give

• (1) \(\mathrm{Cu_2I_2}\)
• (2) \(\mathrm{Cu_2I_3}\)
• (3) \(\mathrm{CuI}\)
• (4) \(\mathrm{Cu(I_3)_2}\)

In Carius method, halogen containing organic compound is heated with fuming nitric acid in the presence of :

• (1) \(\mathrm{HNO_3}\)
• (2) \(\mathrm{AgNO_3}\)
• (3) \(\mathrm{CuSO_4}\)
• (4) \(\mathrm{BaSO_4}\)

The correct order of their reactivity towards hydrolysis at room temperature is :

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

The single largest industrial application of dihydrogen is :

• (1) Manufacture of metal hybrides
• (2) Rocket fuel in space research
• (3) In the synthesis of ammonia
• (4) In the synthesis of nitric acid

Consider two chemical reactions (A) and (B) that take place during metallurgical process:
(A) \(\mathrm{ZnCO_{3(s)} \xrightarrow{\Delta} ZnO_{(s)} + CO_{2(g)}}\)
(B) \(\mathrm{2ZnS_{(s)} + 3O_{2(g)} \xrightarrow{\Delta} 2ZnO_{(s)} + 2SO_{2(g)}}\)
The correct option of names given to them respectively is :

• (1) (A) is calcination and (B) is roasting
• (2) Both (A) and (B) are producing same product so both are roasting
• (3) Both (A) and (B) are producing same product so both are calcination
• (4) (A) is roasting and (B) is calcination

Bakelite is a cross-linked polymer of formaldehyde and :

• (1) PHBV
• (2) Buna-S
• (3) Novolac
• (4) Dacron

Which one of the following gases is reported to retard photosynthesis?

• (1) \(\mathrm{CO}\)
• (2) CFCs
• (3) \(\mathrm{CO_2}\)
• (4) \(\mathrm{NO_2}\)

For a given chemical reaction A \(\rightarrow\) B at 300 K the free energy change is \(-49.4\) kJ \(\mathrm{mol^{-1}}\) and the enthalpy of reaction is 51.4 kJ \(\mathrm{mol^{-1}}\). The entropy change of the reaction is _____________ \(\mathrm{JK^{-1}\,mol^{-1}}\).

The wavelength of an electron of kinetic energy \(4.50 \times 10^{-29}\) J is ___________ \(\times 10^{-5}\) m. (Nearest integer)
Given : mass of electron is \(9 \times 10^{-31}\) kg, \(h = 6.6 \times 10^{-34}\) J s

The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr, respectively. If the liquid mixture, contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is \(\frac {x}{17}\). The value of x is _____.

4g equimolar mixture of NaOH and \(\mathrm{Na_2CO_3}\) contains x g of NaOH and y g of \(\mathrm{Na_2CO_3}\). The value of x is ____________ g. (Nearest integer)

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is ________________ × 10^-1% (Nearest integer).
(Given: Molar mass of Ag is 108 and Br is 80 g mol^-1)

\(\mathrm{PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g)}\)
In the above first order reaction the concentration of \(\mathrm{PCl_5}\) reduces from initial concentration 50 mol \(\mathrm{L^{-1}}\) to 10 mol \(\mathrm{L^{-1}}\) in 120 minutes at 300 K. The rate constant for the reaction at 300 K is x \(\times\) \(10^{-2}\) \(\mathrm{min^{-1}}\). The value of x is __________. [Given log5 = 0.6989]

An aqueous solution of \(\mathrm{NiCl_2}\) was heated with excess sodium cyanide in presence of strong oxidizing agent to form \(\mathrm{[Ni(CN)_6]^{2-}}\). The total change in number of unpaired electrons on metal centre is _______________.

Potassium chlorate is prepared by electrolysis of KCl in basic solution as shown by following equation.
\(\mathrm{6OH^- + Cl^- \rightarrow ClO_3^- + 3H_2O + 6e^-}\)
A current of xA has to be passed for 10h to produce 10.0g of potassium chlorate. The value of x is ____________. (Nearest integer)
(Molar mass of \(\mathrm{KClO_3}\) = 122.6 g \(\mathrm{mol^{-1}}\), F = 96500 C)

100 ml of 0.0018% (w/v) solution of \(\mathrm{Cl^-}\) ion was the minimum concentration of \(\mathrm{Cl^-}\) required to precipitate a negative sol in one h. The coagulating value of \(\mathrm{Cl^-}\) ion is _________ (Nearest integer)

Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ____________.