JEE Main 2020 B.E./B.Tech Question Paper with Answer Keys (September 4, 2020- Morning Session)

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

• (1) 3
• (2) 5
• (3) 7
• (4) 9

Let \(\alpha\) and \(\beta\) be the roots of \(x^2-3x+p=0\) and \(\gamma\) and \(\delta\) be the roots of \(x^2-6x+q=0\). If \(\alpha,\beta,\gamma,\delta\) form a geometric progression. Then ratio \((2q+p):(2q-p)\) is :

• (1) 33 : 31
• (2) 9 : 7
• (3) 5 : 3
• (4) 3 : 1

Let \(f(x)=|x-2|\) and \(g(x)=f(f(x)),\ x\in[0,4]\). Then \(\int_0^3 \left(g(x)-f(x)\right)dx\) is equal to :

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

The integral \(\int\left(\frac{x}{x\sin x+\cos x}\right)^2dx\) is equal to (where C is a constant of integration) :

• (1) \(\sec x+\frac{x\tan x}{x\sin x+\cos x}+C\)
• (2) \(\sec x-\frac{x\tan x}{x\sin x+\cos x}+C\)
• (3) \(\tan x+\frac{x\sec x}{x\sin x+\cos x}+C\)
• (4) \(\tan x-\frac{x\sec x}{x\sin x+\cos x}+C\)

Let \(f(x)=\int\frac{\sqrt{x}}{(1+x)^2}dx\ (x\ge 0)\). Then \(f(3)-f(1)\) is equal to :

• (1) \(-\frac{\pi}{12}+\frac{1}{2}+\frac{\sqrt{3}}{4}\)
• (2) \(\frac{\pi}{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}\)
• (3) \(\frac{\pi}{6}+\frac{1}{2}-\frac{\sqrt{3}}{4}\)
• (4) \(-\frac{\pi}{6}+\frac{1}{2}+\frac{\sqrt{3}}{4}\)

Two vertical poles \(AB=15\) m and \(CD=10\) m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :

• (1) 6
• (2) 10/3
• (3) 20/3
• (4) 5

Let \(y=y(x)\) be the solution of the differential equation, \(xy^{\prime}-y=x^2(x\cos x+\sin x),\ x>0\). If \(y(\pi)=\pi\), then \(y^{\prime\prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)\) is equal to :

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

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If \(x\)% of the people read both the newspapers, then a possible value of \(x\) can be :

• (1) 29
• (2) 55
• (3) 65
• (4) 37

If \(A=\begin{bmatrix}\cos\theta & i\sin\theta\\ i\sin\theta & \cos\theta\end{bmatrix},\ \left(\theta=\frac{\pi}{24}\right)\) and \(A^5=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\), where \(i=\sqrt{-1}\), then which one of the following is not true?

• (1) \(a^2-d^2=0\)
• (2) \(a^2-b^2=\frac{1}{2}\)
• (3) \(0\le a^2+b^2\le 1\)
• (4) \(a^2-c^2=1\)

Let \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\ (a>b)\) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, \(\phi(t)=\frac{5}{12}+t-t^2\), then \(a^2+b^2\) is equal to :

• (1) 116
• (2) 126
• (3) 135
• (4) 145

Let \([t]\) denote the greatest integer \(\le t\). Then the equation in \(x\), \([x]^2+2[x+2]-7=0\) has :

• (1) no integral solution.
• (2) exactly two solutions.
• (3) exactly four integral solutions.
• (4) infinitely many solutions.

Let \(u=\frac{2z+i}{z-ki},\ z=x+iy\) and \(k>0\). If the curve represented by \(\mathrm{Re}(u)+\mathrm{Im}(u)=1\) intersects the \(y\)-axis at the points P and Q where \(PQ=5\), then the value of \(k\) is :

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

If \((a+\sqrt{2}\,b\cos x)(a-\sqrt{2}\,b\cos y)=a^2-b^2\), where \(a \gt b \gt 0\), then \(\frac{dx}{dy}\) at \(\left(\frac{\pi}{4},\frac{\pi}{4}\right)\) is :

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

Let \(f\) be a twice differentiable function on \(R\). 
If \(f ^{\prime}(0)=4\) and \(f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,\) 
then \((2 a+1)^5 a^2\) is equal to ______.

If \(1+(1-2^2\cdot 1)+(1-4^2\cdot 3)+(1-6^2\cdot 5)+\ldots+(1-20^2\cdot 19)=\alpha-220\beta\), then an ordered pair \((\alpha,\beta)\) is equal to :

• (1) (10, 97)
• (2) (10, 103)
• (3) (11, 103)
• (4) (11, 97)

Let \(x_0\) be the point of local maxima of \(f(x)=\vec{a}\cdot(\vec{b}\times\vec{c})\), where \(\vec{a}=x\hat{i}-2\hat{j}+3\hat{k}\), \(\vec{b}=-2\hat{i}+x\hat{j}-\hat{k}\) and \(\vec{c}=7\hat{i}-2\hat{j}+x\hat{k}\). Then the value of \(\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}\) at \(x=x_0\) is :

• (1) \(-30\)
• (2) \(-22\)
• (3) \(-4\)
• (4) \(14\)

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If \(\angle BAC=90^\circ\), and \(\mathrm{ar}(\Delta ABC)=5\sqrt{5}\) sq. units, then the abscissa of the vertex C is :

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

Consider the two statements :
(S1) : \((p \to q) \lor (\neg q \to p)\) is a tautology.
(S2) : \((p \land \neg q) \land (\neg p \lor q)\) is a fallacy.
Then :

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

The value of \(\sum_{r=0}^{20}{}^{50-r}C_6\) is equal to :

• (1) \({}^{50}C_6-{}^{30}C_6\)
• (2) \({}^{50}C_7-{}^{30}C_7\)
• (3) \({}^{51}C_7-{}^{30}C_7\)
• (4) \({}^{51}C_7+{}^{30}C_7\)

Let P(3, 3) be a point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\). If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair \((a^2, e^2)\) is equal to :

• (1) \(\left(\frac{9}{2},2\right)\)
• (2) \((9,3)\)
• (3) \(\left(\frac{3}{2},2\right)\)
• (4) \(\left(\frac{9}{2},3\right)\)

If the system of equations
\(x-2y+3z=9\)
\(2x+y+z=b\)
\(x-7y+az=24\),
has infinitely many solutions, then \(a-b\) is equal to ______.

Suppose a differentiable function \(f(x)\) satisfies the identity \(f(x+y)=f(x)+f(y)+xy^2+x^2y\), for all real \(x\) and \(y\). If \(\lim_{x\to 0}\frac{f(x)}{x}=1\), then \(f'(3)\) is equal to ______.

The probability of a man hitting a target is \(\frac{2}{5}\). He fires at the target \(k\) times (\(k\), a given number). Then the minimum \(k\), so that the probability of hitting the target at least once is more than \(\frac{7}{10}\), is :

• (1) 3
• (2) 5
• (3) 2
• (4) 4

Let \((2x^2+3x+4)^{10}=\sum_{r=0}^{20}a_rx^r\). Then \(\frac{a_7}{a_{13}}\) is equal to ______.

If the equation of a plane P, passing through the intersection of the planes, \(x+4y-z+7=0\) and \(3x+y+5z=8\) is \(ax+by+6z=15\) for some \(a,b\in\mathbf{R}\), then the distance of the point (3, 2, \(-1\)) from the plane P is ______.

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s^-2. The density of water is 1 gm cm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s²).

• (1) 1.52 gm
• (2) 3.15 gm
• (3) 4.15 gm
• (4) 4.51 gm

On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by \(\frac{Ax}{(x^2+a^2)^{3/2}}\) in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is :

• (1) \(\frac{A}{(x^2+a^2)^{3/2}}\)
• (2) \(\frac{A}{(x^2+a^2)^{1/2}}\)
• (3) \(A(x^2+a^2)^{3/2}\)
• (4) \(A(x^2+a^2)^{1/2}\)

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of: (Given, Planck’s constant = \(6.6 × 10^{–34}\) Js).

• (1) \(2.10 × 10^{–34}\) Js
• (2) \(1.05 × 10^{–34}\) Js
• (3) \(3.15 × 10^{–34}\) Js
• (4) \(4.2 × 10^{–34}\) Js

A short bar magnet placed with its axis at \(30^\circ\) with an external magnetic field of \(800\) Gauss experiences a torque of \(0.016\,\text{N m}\). The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3}\,\text{J}\). The value of \(\alpha\) is ___.

Starting from the origin at time \(t=0\), with initial velocity \(5 \hat{ j } \,ms ^{-1},\) a particle moves in the \(x - y\) plane with a constant acceleration of \((10 \hat{ i }+4 \hat{ j }) ms ^{-2} .\) At time \(t\), its coordinates are (20 \(\left. m , y _{0} m \right)\). The values of \(t\) and \(y _{0}\), are respectively

• (1) \(4 \,s\) and \(52\, m\)
• (2) \(2\, s\) and \(24\, m\)
• (3) \(2\, s\) and \(18\, m\)
• (4) \(5\, s\) and \(25\, m\)

Three point charges q, –2q and 2q are placed on x-axis at a distance x = 0, x = \(\frac{3}{ 4}\) R and x = R respectively from origin as shown. If q = 2 × 10^-6 C and R = 2 cm, the magnitude of net force experienced by the charge –2q is ________ N.

Take the breakdown voltage of the zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of the output voltage is :
(Graphs drawn are schematic and not to scale)

• (1)
• (2)
• (3)
• (4)

A battery of \(3.0\ \mathrm{V}\) is connected to a resistor dissipating \(0.5\ \mathrm{W}\) of power. If the terminal voltage of the battery is \(2.5\ \mathrm{V}\), the power dissipated within the internal resistance is :

• (1) \(0.125\ \mathrm{W}\)
• (2) \(0.50\ \mathrm{W}\)
• (3) \(0.072\ \mathrm{W}\)
• (4) \(0.10\ \mathrm{W}\)

A beam of plane polarised light of large cross-sectional area and uniform intensity of \(3.3\ \mathrm{W\,m^{-2}}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\ \mathrm{m^2}\)) which rotates about its axis with an angular speed of \(31.4\ \mathrm{rad/s}\). The energy of light passing through the polariser per revolution, is close to :

• (1) \(1.0 \times 10^{-5}\ \mathrm{J}\)
• (2) \(1.0 \times 10^{-4}\ \mathrm{J}\)
• (3) \(1.5 \times 10^{-4}\ \mathrm{J}\)
• (4) \(5.0 \times 10^{-4}\ \mathrm{J}\)

Two charged thin infinite plane sheets of uniform surface charge density \(\sigma_+\) and \(\sigma_-\), where \(|\sigma_+| \gt |\sigma_-|\), intersect at right angle. Which of the following best represents the electric field lines for this system :

• (1)
• (2)
• (3)
• (4)

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :

• (1) \(1, 2, 3, \ldots\)
• (2) \(1, 3, 5, \ldots\)
• (3) \(\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\)
• (4) \(\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots\)

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is :

• (1) 6 : 5
• (2) 2 : 5
• (3) 4 : 6
• (4) 6 : 4

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

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil ?

Three positions shown describe : (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit.

• (1)
• (2)
• (3)
• (4)

The specific heat of water \(= 4200\ \mathrm{J\,kg^{-1}K^{-1}}\) and the latent heat of ice \(= 3.4 \times 10^{5}\ \mathrm{J\,kg^{-1}}\). 100 grams of ice at \(0^{\circ}\mathrm{C}\) is placed in 200 g of water at \(25^{\circ}\mathrm{C}\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ}\mathrm{C}\) is close to (in grams) :

• (1) 69.3
• (2) 61.7
• (3) 64.6
• (4) 63.8

A Tennis ball is released from a height \(h\) and after freely falling on a wooden floor it rebounds and reaches height \(\frac{h}{2}\). The velocity versus height of the ball during its motion may be represented graphically by :
(graph are drawn schematically and on not to scale)

• (1)
• (2)
• (3)
• (4)

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum :

• (1) \(\lambda_{\text{radio waves}} \gt \lambda_{\text{micro waves}} \gt \lambda_{\text{visible}} \gt \lambda_{x\text{-rays}}\)
• (2) \(\lambda_{\text{visible}} \gt \lambda_{x\text{-rays}} \gt \lambda_{\text{radio waves}} \gt \lambda_{\text{micro waves}}\)
• (3) \(\lambda_{x\text{-rays}} \lt \lambda_{\text{micro waves}} \lt \lambda_{\text{radio waves}} \lt \lambda_{\text{visible}}\)
• (4) \(\lambda_{\text{visible}} \lt \lambda_{\text{micro waves}} \lt \lambda_{\text{radio waves}} \lt \lambda_{x\text{-rays}}\)

Particle A of mass \(m_A = \frac{m}{2}\) moving along the x-axis with velocity \(v_0\) collides elastically with another particle B at rest having mass \(m_B = \frac{m}{3}\). If both particles move along the x-axis after the collision, the change \(\Delta\lambda\) in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength (\(\lambda_0\)) before collision is :

• (1) \(\Delta\lambda = \frac{3}{2}\lambda_0\)
• (2) \(\Delta\lambda = 2\lambda_0\)
• (3) \(\Delta\lambda = \frac{5}{2}\lambda_0\)
• (4) \(\Delta\lambda = 4\lambda_0\)

Blocks of masses \(m\), \(2m\), \(4m\) and \(8m\) are arranged in a line on a frictionless floor. Another block of mass \(m\), moving with speed \(v\) along the same line (see figure) collides with mass \(m\) in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass \(8m\) starts moving the total energy loss is \(p\%\) of the original energy. Value of 'p' is close to :

• (1) 37
• (2) 77
• (3) 87
• (4) 94

Dimensional formula for thermal conductivity is (here \(K\) denotes the temperature)

• (1) \(MLT ^{-3} K\)
• (2) \(MLT ^{-2} K\)
• (3) \(MLT ^{-2} K ^{-2}\)
• (4) \(MLT ^{-3} K ^{-1}\)

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is \(I_0\). If part ADE is removed, the moment of inertia of the remaining part about the same axis is \(\frac{NI_0}{16}\) where N is an integer. Value of N is ____.

A circular disc of mass M and radius R is rotating about its axis with angular speed \(\omega_1\). If another stationary disc having radius \(\frac{R}{2}\) and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_2\). The energy lost in the process is p% of the initial energy. Value of p is __________.

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.

In a microscope, the objective has a focal length \(f_o=2\) cm and the eye-piece has a focal length \(f_e=4\) cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is_____.

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is 304 \(\mathrm{\AA}\). The corresponding difference for the Paschen series (in \(\mathrm{\AA}\)) is ____.

\(E^{\circ}_{\mathrm{Cu^{2+}|Cu}} = +0.34\ \mathrm{V}\)
\(E^{\circ}_{\mathrm{Zn^{2+}|Zn}} = -0.76\ \mathrm{V}\)
Identify the incorrect statement from the options below for the above cell :

• (1) If \(E_{ext} \lt 1.1\ \mathrm{V}\), Zn dissolves at anode and Cu deposits at cathode
• (2) If \(E_{ext} = 1.1\ \mathrm{V}\), no flow of \(e^-\) or current occurs
• (3) If \(E_{ext} \gt 1.1\ \mathrm{V}\), \(e^-\) flows from Cu to Zn
• (4) If \(E_{ext} \gt 1.1\ \mathrm{V}\), Zn dissolves at Zn electrode and Cu deposits at Cu electrode

For the equilibrium \(\mathrm{A} \rightleftharpoons \mathrm{B}\), the variation of the rate of the forward (a) and reverse (b) reaction with time is given by :

• (1)
• (2)
• (3)
• (4)

[P] on treatment with \(\mathrm{Br_2/FeBr_3}\) in \(\mathrm{CCl_4}\) produced a single isomer \(\mathrm{C_8H_7O_2Br}\) while heating [P] with sodalime gave toluene. The compound [P] is :

• (1)
• (2)
• (3)
• (4)

The decreasing order of reactivity of the following organic molecules towards \(\mathrm{AgNO_3}\) solution is :

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

What are the functional groups present in the structure of maltose?

• (1) One acetal and one ketal
• (2) One ketal and one hemiketal
• (3) Two acetals
• (4) One acetal and one hemiacetal

The number of isomers possible for \(\mathrm{[Pt(en)(NO_2)_2]}\) is :

• (1) 3
• (2) 1
• (3) 4
• (4) 2

The elements with atomic numbers 101 and 104 belong to, respectively :

• (1) Group 6 and Actinoids
• (2) Actinoids and Group 4
• (3) Group 11 and Group 4
• (4) Actinoids and Group 6

An organic compound (A) (molecular formula \(\mathrm{C_6H_{12}O_2}\)) was hydrolysed with dil. \(\mathrm{H_2SO_4}\) to give a carboxylic acid (B) and an alcohol (C). 'C' gives white turbidity immediately when treated with anhydrous \(\mathrm{ZnCl_2}\) and conc. HCl. The organic compound (A) is :

• (1)
• (2)
• (3)
• (4)

The intermolecular potential energy for the molecules A, B, C and D given below suggests that :

• (1) A–A has the largest bond enthalpy.
• (2) A–B has the stiffest bond.
• (3) A–D has the shortest bond length.
• (4) D is more electronegative than other atoms.

The pair in which both the species have the same magnetic moment (spin only) is :

• (1) \([\mathrm{Cr(H_2O)_6}]^{2+}\) and \([\mathrm{CoCl_4}]^{2-}\)
• (2) \([\mathrm{Cr(H_2O)_6}]^{2+}\) and \([\mathrm{Fe(H_2O)_6}]^{2+}\)
• (3) \([\mathrm{Mn(H_2O)_6}]^{2+}\) and \([\mathrm{Cr(H_2O)}]^{2+}\)
• (4) \([\mathrm{Co(OH)_4}]^{2-}\) and \([\mathrm{Fe(NH_3)_6}]^{2+}\)

When neopentyl alcohol is heated with an acid, it slowly converted into an 85 : 15 mixture of alkenes A and B, respectively. What are these alkenes ?

• (1)
• (2)
• (3)
• (4)

The region in the electromagnetic spectrum where the Balmer series lines appear is :

• (1) Ultraviolet
• (2) Visible
• (3) Infrared
• (4) Microwave

The IUPAC name of the following compound is :

• (1) 3–Bromo–5–methylcyclopentanoic acid
• (2) 4–Bromo–2–methylcyclopentane carboxylic acid
• (3) 3–Bromo–5–methylcyclopentane carboxylic acid
• (4) 5–Bromo–3–methylcyclopentanoic acid

The ionic radii of \(\mathrm{O^{2-}}\), \(\mathrm{F^-}\), \(\mathrm{Na^+}\) and \(\mathrm{Mg^{2+}}\) are in the order :

• (1) \(\mathrm{O^{2-}} \gt \mathrm{F^-} \gt \mathrm{Na^+} \gt \mathrm{Mg^{2+}}\)
• (2) \(\mathrm{Mg^{2+}} \gt \mathrm{Na^+} \gt \mathrm{F^-} \gt \mathrm{O^{2-}}\)
• (3) \(\mathrm{O^{2-}} \gt \mathrm{F^-} \gt \mathrm{Mg^{2+}} \gt \mathrm{Na^+}\)
• (4) \(\mathrm{F^-} \gt \mathrm{O^{2-}} \gt \mathrm{Na^+} \gt \mathrm{Mg^{2+}}\)

For one mole of an ideal gas, which of these statements must be true ?
(a) U and H each depends only on temperature
(b) Compressibility factor z is not equal to 1
(c) \(C_{P,m} - C_{V,m} = R\)
(d) \(dU = C_V dT\) for any process

• (1) (c) and (d)
• (2) (a) and (c)
• (3) (b), (c) and (d)
• (4) (a), (c) and (d)

Which of the following will react with \(\mathrm{CHCl_3}\) + alc. KOH ?

• (1) Adenine and proline
• (2) Adenine and thymine
• (3) Adenine and lysine
• (4) Thymine and proline

The main oxides formed on combustion of \(Li, Na\) and \(K\) in excess of air are, respectively :

• (1) \(Li_2O, Na_2O\) and \(KO_2\)
• (2) \(LiO_2, Na_2O_2\) and \(K_2O\)
• (3) \(Li_2O_2, Na_2O_2 \) and \(KO_2\)
• (4) \(Li_2O, Na_2O\) and \( KO_2\)

On heating, lead (II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid (C) is :

• (1) +2
• (2) +3
• (3) +4
• (4) +5

Among statements (a) - (d), the correct ones are :
(a) Lime stone is decomposed to CaO during the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted as an anionic complex.
(c) Nickel is purified by Mond's process.
(d) Zr and Ti are purified by Van Arkel method.

• (1) (b), (c) and (d) only
• (2) (a), (b), (c) and (d)
• (3) (c) and (d) only
• (4) (a), (c) and (d) only

• (1) (i)-(e), (ii)-(c), (iii)-(a), (iv)-(f)
• (2) (i)-(b), (ii)-(c), (iii)-(e), (iv)-(d)
• (3) (i)-(d), (ii)-(b), (iii)-(e), (iv)-(f)
• (4) (i)-(d), (ii)-(b), (iii)-(a), (iv)-(e)

At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of Hg. What is the vapour pressure in mm Hg of n-heptane in its pure state ______ ?

If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed in approximately (in minutes) __________.
(Take : \(\log 2 = 0.30\); \(\log 2.5 = 0.40\))

The number of chiral centres present in [B] is ________.

(Reaction scheme as drawn: 3-methylcyclohexyl-CH(CH₃)-C\(\equiv\)N; (i) C₂H₅MgBr, (ii) H₃O⁺ gives [A]; the same nitrile with (i) CH₃MgBr, (ii) H₂O gives [B].)

The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is ________.

A 20.0 mL solution containing 0.2 g impure H₂O₂ reacts completely with 0.316 g of KMnO₄ in acid solution. The purity of H₂O₂ (in %) is ____________ (mol. wt. of H₂O₂ = 34; mol. wt. of KMnO₄ = 158)