JEE Main 2020 January 7 Shift 2 Question Paper with Solutions PDF

The area (in sq. units) of the region
{(x, y) \( \in \) R² | 4x² \( \le \) y \( \le \) 8x + 12} is :

• (A) \( {{125} \over 3} \)
• (B) \( {{128} \over 3} \)
• (C) \( {{127} \over 3} \)
• (D) \( {{124} \over 3} \)

Let y = y(x) be the solution curve of the differential equation,

\( \left( {{y^2} - x} \right){{dy} \over {dx}} = 1 \), satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is :

• (A) 2 + e
• (B) -e
• (C) 2
• (D) 2 - e

Let \( {a_1} \) , \( {a_2} \) , \( {a_3} \) ,....... be a G.P. such that
\( {a_1} \) < 0, \( {a_1} \) + \( {a_2} \) = 4 and \( {a_3} \) + \( {a_4} \) = 16.
If \( \sum\limits_{i = 1}^9 {{a_i}} = 4\lambda \), then \( \lambda \) is equal to:

• (A) 171
• (B) -171
• (C) -513
• (D) \( {{511} \over 3} \)

The number of ordered pairs (r, k) for which
6.³⁵C_r = (k² - 3). ³⁶C_{r + 1}, where k is an integer, is :

• (A) 6
• (B) 3
• (C) 2
• (D) 4

Let \( \overrightarrow a \) , \( \overrightarrow b \) and \( \overrightarrow c \) be three unit vectors such that
\( \overrightarrow a + \vec b + \overrightarrow c = \overrightarrow 0 \). If \( \lambda = \overrightarrow a .\vec b + \vec b.\overrightarrow c + \overrightarrow c .\overrightarrow a \) and
\( \overrightarrow d = \overrightarrow a \times \vec b + \vec b \times \overrightarrow c + \overrightarrow c \times \overrightarrow a \), then the ordered pair, \( \left( {\lambda ,\overrightarrow d } \right) \) is equal to :

• (A) \( \left( {{3 \over 2},3\overrightarrow a \times \overrightarrow c } \right) \)
• (B) \( \left( { - {3 \over 2},3\overrightarrow c \times \overrightarrow b } \right) \)
• (C) \( \left( { - {3 \over 2},3\overrightarrow a \times \overrightarrow b } \right) \)
• (D) \( \left( {{3 \over 2},3\overrightarrow b \times \overrightarrow c } \right) \)

If \( \theta \)₁ and \( \theta \)₂ be respectively the smallest and the largest values of \( \theta \) in (0, 2\( \pi \)) - {\( \pi \)} which satisfy the equation,
2cot²\( \theta \) - \( {5 \over {\sin \theta }} \) + 4 = 0, then
\( \int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta } \) is equal to :

• (A) \( {\pi \over 9} \)
• (B) \( {{2\pi } \over 3} \)
• (C) \( {{\pi } \over 3} \)
• (D) \( {\pi \over 3} + {1 \over 6} \)

The value of \( \alpha \) for which
\( 4\alpha \int\limits_{ - 1}^2 {{e^{ - \alpha \left| x \right|}}dx} = 5 \), is:

• (A) \( {\log _e}2 \)
• (B) \( {\log _e}\sqrt 2 \)
• (C) \( {\log _e}\left( {{4 \over 3}} \right) \)
• (D) \( {\log _e}\left( {{3 \over 2}} \right) \)

Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If \( \mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4 \), then which one of the following is not true?

• (A) ƒ(1) - 4ƒ(-1) = 4.
• (B) x = 1 is a point of minima and x = -1 is a point of maxima of ƒ.
• (C) x = 1 is a point of maxima and x = -1 is a point of minimum of ƒ.
• (D) ƒ is an odd function.

The coefficient of \( x^7 \) in the expression \( \left(1+x\right)^{10}+x\left(1+x\right)^{9}+x^{2}\left(1+x\right)^{8}+...+x^{10} \) is :

• (A) \( 420 \)
• (B) \( 330 \)
• (C) \( 210 \)
• (D) \( 120 \)

The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is :

• (A) 3x - 2y = 0
• (B) 7x - 5y = 0
• (C) 2x - 3y = 0
• (D) 5x - 7y = 0

Let \( \alpha \) and \( \beta \) be the roots of the equation x² - x - 1 = 0.
If p_k = \( {\left( \alpha \right)^k} + {\left( \beta \right)^k} \) , k \( \ge \) 1, then which one of the following statements is not true?

• (A) (p₁ + p₂ + p₃ + p₄ + p₅) = 26
• (B) p₅ = 11
• (C) p₃ = p₅ – p₄
• (D) p₅ = p₂ · p₃

Let y = y(x) be a function of x satisfying

\( y\sqrt {1 - {x^2}} = k - x\sqrt {1 - {y^2}} \) where k is a constant and

\( y\left( {{1 \over 2}} \right) = - {1 \over 4} \). Then \( {{dy} \over {dx}} \) at x = \( {1 \over 2} \), is equal to :

• (A) \( {2 \over {\sqrt 5 }} \)
• (B) \( - {{\sqrt 5 } \over 2} \)
• (C) \( {{\sqrt 5 } \over 2} \)
• (D) \( - {{\sqrt 5 } \over 4} \)

If \( {{3 + i\sin \theta } \over {4 - i\cos \theta }} \), \( \theta \) \( \in \) [0, 2\( \theta \)], is a real number, then an argument of
sin\( \theta \) + icos\( \theta \) is :

• (A) \( \pi - {\tan ^{ - 1}}\left( {{3 \over 4}} \right) \)
• (B) \( - {\tan ^{ - 1}}\left( {{3 \over 4}} \right) \)
• (C) \( {\tan ^{ - 1}}\left( {{4 \over 3}} \right) \)
• (D) \( \pi - {\tan ^{ - 1}}\left( {{4 \over 3}} \right) \)

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is \( {{1 \over 4}} \) . If the probability that at most two machines will be out of service on the same day is \( {\left( {{3 \over 4}} \right)^3}k \), then k is equal to :

• (A) \( {{{17} \over 4}} \)
• (B) \( {{{17} \over 2}} \)
• (C) \( {{{17} \over 8}} \)
• (D) 4

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A \( \subseteq \) B and B \( \subseteq \) D, then A \( \subseteq \) C" is :

• (A) If A ⊈ C, then A ⊈ B or B ⊈ D
• (B) If A ⊈ C, then A ⊈ B and B \( \subseteq \) D
• (C) If A \( \subseteq \) C, then B \( \subset \) A or D \( \subset \) B
• (D) If A ⊈ C, then A \( \subseteq \) B and B \( \subseteq \) D

Let A = [a_ij] and B = [b_ij] be two 3 × 3 real matrices such that b_ij = (3)^(i+j-2)a_ji, where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:

• (A) 3
• (B) \( {1 \over 3} \)
• (C) \( {1 \over 9} \)
• (D) \( {1 \over {81}} \)

The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x³ - 4x² + 8x + 11, when x \( \in \) [0, 1] is:

• (A) \( {2 \over 3} \)
• (B) \( {{\sqrt 7 - 2} \over 3} \)
• (C) \( {{4 - \sqrt 5 } \over 3} \)
• (D) \( {{4 - \sqrt 7 } \over 3} \)

Let the tangents drawn from the origin to the circle,
x² + y² - 8x - 4y + 16 = 0 touch it at the points A and B. The (AB)² is equal to :

• (A) \( {{56} \over 5} \)
• (B) \( {{32} \over 5} \)
• (C) \( {{52} \over 5} \)
• (D) \( {{64} \over 5} \)

If the sum of the first 40 terms of the series,
3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :

• (A) 20
• (B) 5
• (C) 10
• (D) 25

If 3x + 4y = 12\( \sqrt 2 \) is a tangent to the ellipse
\( {{{x^2}} \over {{a^2}}} + {{{y^2}} \over 9} = 1 \) for some \( a \) \( \in \) R, then the distance between the foci of the ellipse is :

• (A) \( 2\sqrt 5 \)
• (B) \( 2\sqrt 7 \)
• (C) 4
• (D) \( 2\sqrt 2 \)

If the function ƒ defined on \( \left( { - {1 \over 3},{1 \over 3}} \right) \) by

f(x) = \( \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + 3x} \over {1 - 2x}}} \right),} & {when\,x \ne 0} \cr {k,} & {when\,x = 0} \cr } } \right. \)

is continuous, then k is equal to_______.

If the system of linear equations,
x + y + z = 6
x + 2y + 3z = 10
3x + 2y + \( \lambda \)z = \( \mu \)
has more than two solutions, then \( \mu \) - \( \lambda \)² is equal to ______.

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (\( \alpha \), 7, 1) is \( \left( {{5 \over 3},{7 \over 3},{{17} \over 3}} \right) \), then \( \alpha \) is equal to______.

Let X = {n \( \in \) N : 1 \( \le \) n \( \le \) 50}. If
A = {n \( \in \) X: n is a multiple of 2} and
B = {n \( \in \) X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.

Mass per unit area of a circular disc of radius \( a \) depends on the distance r from its centre as \( \sigma \left( r \right) \) = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and assing through its centre is:

• (A) \( 2\pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right) \)
• (B) \( \pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right) \)
• (C) \( 2\pi {a^4}\left( {{{aA} \over 4} + {B \over 5}} \right) \)
• (D) \( 2\pi {a^4}\left( {{A \over 4} + {B \over 5}} \right) \)

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 \( \Omega \) resistor. The ratio of the currents at time t = \( \infty \) and at t = 40 s is close to : (Take e² = 7.389)

• (A) 1.06
• (B) 0.84
• (C) 1.15
• (D) 1.46

The electric field of a plane electromagnetic wave is given by
\( \overrightarrow E = {E_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {kz + \omega t} \right) \)

At t = 0, a positively charged particle is at the point (x, y, z) = \( \left( {0,0,{\pi \over k}} \right) \).
If its instantaneous velocity at (t = 0) is \( {v_0}\widehat k \) , the force acting on it due to the wave is :

• (A) parallel to \( \widehat k \)
• (B) parallel to \( {{\widehat i + \widehat j} \over {\sqrt 2 }} \)
• (C) antiparallel to \( {{\widehat i + \widehat j} \over {\sqrt 2 }} \)
• (D) zero

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45^o with the vertical. Then F equal : (Take g = 10 ms^–2 and the rope to be massless)

• (A) 100 N
• (B) 75 N
• (C) 90 N
• (D) 70 N

In a Young's double slit experiment, the separation between the slits is 0.15 mm. in the experiment, a source of light of wavelengh 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is :

• (A) 4.9 mm
• (B) 5.9 mm
• (C) 6.9 mm
• (D) 3.9 mm

A particle of mass m and charge q has an initial velocity \( \overrightarrow v = {v_0}\widehat j \) . If an electric field \( \overrightarrow E = {E_0}\widehat i \) and magnetic field \( \overrightarrow B = {B_0}\widehat i \) act on the particle, its speed will double after a time:

• (A) \( {{3m{v_0}} \over {q{E_0}}} \)
• (B) \( {{\sqrt 2 m{v_0}} \over {q{E_0}}} \)
• (C) \( {{\sqrt 3 m{v_0}} \over {q{E_0}}} \)
• (D) \( {{2m{v_0}} \over {q{E_0}}} \)

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

• (A) \( {1 \over c}{\left( {{{2E} \over m}} \right)^{{1 \over 2}}} \)
• (B) \( {1 \over c}{\left( {{E \over {2m}}} \right)^{{1 \over 2}}} \)
• (C) \( {\left( {{E \over {2m}}} \right)^{{1 \over 2}}} \)
• (D) \( c{\left( {2mE} \right)^{{1 \over 2}}} \)

A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms^–2 at the north pole and the radius of the earth = 6400 km) :

• (A) 194.32 N
• (B) 195.66 N
• (C) 195.32 N
• (D) 194.66 N

The dimension of \( {{{B^2}} \over {2{\mu _0}}} \), where B is magnetic field and \( {{\mu _0}} \) is the magnetic permeability of vacuum, is :

• (A) ML²T^–2
• (B) MLT^–2
• (C) ML^-1T^–2
• (D) ML²T^–1

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are \( 6.4\, cm \) and \( 4.8\, cm \), respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

• (A) \( \frac{\sqrt{3}}{2} \)
• (B) \( \frac{3}{4} \)
• (C) \( \frac{81}{256} \)
• (D) \( \frac{9}{16} \)

A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

• (A) 2.5 s and 7.5 s
• (B) 5.0 s and 10.0 s
• (C) 5.0 s and 7.5 s
• (D) 2.5 s and 5.0 s

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s²) must be at least :

• (A) 48000 W
• (B) 62360 W
• (C) 56300 W
• (D) 66000 W

A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is f₁ , then the ratio \( {{{f_1}} \over f} \) is closest to the integer :

• (A) 17
• (B) 1
• (C) 9
• (D) 5

In a building there are \( 15 \) bulbs of \( 45\, W, 15 \) bulbs of \( 100\, W \), \( 15 \) small fans of \( 10\, W \) and \( 2 \) heaters of \( 1\, kW \). The voltage of electric main is \( 220\, V \). The minimum fuse capacity (rated value) of the building will be:

• (A) \( 25\, A \)
• (B) \( 15\, A \)
• (C) \( 10\, A \)
• (D) \( 20\, A \)

In the figure, potential difference between A and B is :

• (A) 10 V
• (B) 5 V
• (C) zero
• (D) 15 V

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \( {\tau _1} \) to \( {\tau _2} \) . If \( {{{C_p}} \over {{C_v}}} = \gamma \) for this gas then a good estimate for \( {{{\tau _2}} \over {{\tau _1}}} \) is given by :

• (A) \( {\left( 2 \right)^{{{1 + \gamma } \over 2}}} \)
• (B) 2
• (C) \( {\left( {{1 \over 2}} \right)^{{{1 + \gamma } \over 2}}} \)
• (D) \( {\left( {{1 \over 2}} \right)^\gamma } \)

The activity of a radioactive sample falls from \( 700\, s^{-1} \) to \( 500\, s^{-1} \) in 30 minutes. Its half life is close to :

• (A) \( 72 \) min
• (B) \( 62 \) min
• (C) \( 66 \) min
• (D) \( 52 \) min

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T₁ and T₂ . The temperature of the hot reservoir of the first engine is T₁ and the temperature of the cold reservoir of the second engine is T₂ . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T₁ and T₂ . If both engines perform equal amount of work?

• (A) \( T = {{2{T_1}{T_2}} \over {{T_1} + {T_2}}} \)
• (B) \( T = \sqrt {{T_1}{T_2}} \)
• (C) \( T = {{{T_1} + {T_2}} \over 2} \)
• (D) T = 0

• (A) 1.0 T, 50A/m and 1.5 T
• (B) 1.5 T, 50 A/m and 1.0 T
• (C) 1.5 T, 50 A/m and 2.0 T
• (D) 150 A/m, 1.0 T and 1.5 T

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v₀ = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :

• (A) 1 m/s
• (B) \( {1 \over 8} \) m/s
• (C) \( {1 \over 4} \) m/s
• (D) \( {1 \over 2} \) m/s

The sum of two forces \( \overrightarrow P \) and \( \overrightarrow Q \) is \( \overrightarrow R \) such that \( \left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right| \) . The angle \( \theta \) (in degrees) that the resultant of 2\( {\overrightarrow P } \) and \( {\overrightarrow Q } \) will make with \( {\overrightarrow Q } \) is , ..............

M grams of steam at 100^oC is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at 40^oC [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g] the value of M is ____

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) _____

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 \( \Omega \) is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the ceil is \( {N \over {10}} \) \( \Omega \) , where N is an integer then value of N is .............

Among the statements(a)-(d) the incorrect ones are :
(a) Octahedral CO(III) complexes with strong fields ligands have very high magnetic moments.
(b) When \( \Delta \)₀ < P, the d-electron configuration of Co(III) in an octahedral complex is \( t_{eg}^4e_g^2 \)
(c) Wavelength of light absorbed by [Co(en)₃]³⁺ is lower than that of [CoF₆]^3-
(d) If the \( \Delta \)₀ for an octahedral complex of CO(III) is 18,000 cm^-1, the \( \Delta \)_t for its tetrahedral complex with the same ligand be 16,000 cm^-1

• (A) (a) and (b) only
• (B) (b) and (c) only
• (C) (c) and (d) only
• (D) (a) and (d) only

Within each pair of elements F & Cl, S & Se, and Li & Na, respectively, the elements that release more energy upon and electron gain are :

• (A) F, S and Li
• (B) Cl, Se and Na
• (C) Cl, S and Li
• (D) F, Se and Na

In the following reactions sequence, structure of A and B respectively will be :

• (A)
• (B)
• (C)
• (D)

Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time:

• (A) the volume of the solution and the solvent does not change
• (B) the volume of the solution increases and the volume of the solvent decreases
• (C) the volume of the solution decreases and the volume of the solvent increases
• (D) the volume of the solution does not change and the volume of the solvent decreases

The correct order of stability for the following alkoxides is :

• (A) (C) > (B) > (A)
• (B) (C) > (A) > (B)
• (C) (B) > (C) > (A)
• (D) (B) > (A) > (C)

The bond order and the magnetic characteristics of CN^- are :

• (A) 3, paramagnetic
• (B) \( 2{1 \over 2} \), paramagnetic
• (C) 3, diamagnetic
• (D) \( 2{1 \over 2} \), diamagnetic

Which of the following statements is correct ?

• (A) Gluconic acid can from cyclic (acteal/hemiacetal) structure
• (B) Gluconic acid is a partial oxidation product of glucose
• (C) Gluconic acid is obtained by oxidation of glucose with (HNO₃)
• (D) Gluconic acid is a dicarboxylic acid.

The number of possible optical isomers for the complexes MA₂B₂ with sp³ and dsp² hydridized metal atom. respectively, is :
Note : A and B are unidentate netural and unidentate monoanionic ligands, respectively.

• (A) 0 and 2
• (B) 0 and 0
• (C) 0 and 1
• (D) 2 and 2

The redox reaction among the following is :

• (A) reaction of H₂SO₄ with NaOH.
• (B) formation of ozone form atmosphere oxygen in the presence of sunlight.
• (C) combination of dinitrogen with dioxygen at 2000 K
• (D) reaction of [Co(H₂O)₆]Cl₃ With AgNO₃

For the reaction
2H₂(g) + 2NO(g) \( \to \) N₂(g) + 2H₂O(g)
the observed rate expression is, rate = K_f[NO]²[H₂]. The rate expression for the reverse reaction is :

• (A) K_b[N₂][H₂O]
• (B) K_b[N₂][H₂O]²/[H₂]
• (C) K_b[N₂][H₂O]²/[NO]
• (D) K_b[N₂][H₂O]²

Consider the following reactions :
Which of these reactions are possible ?

• (A) (b), (c) and (d)
• (B) (a) and (b)
• (C) (a) and (d)
• (D) (b) and (d)

The equation that is incorrect is :

• (A) \( {\left( {\Lambda _m^0} \right)_{KCl}} - {\left( {\Lambda _m^0} \right)_{NaCl}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{NaBr}} \)
• (B) \( {\left( {\Lambda _m^0} \right)_{NaBr}} - {\left( {\Lambda _m^0} \right)_{NaI}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{NaBr}} \)
• (C) \( {\left( {\Lambda _m^0} \right)_{NaBr}} - {\left( {\Lambda _m^0} \right)_{NaCl}} = {\left( {\Lambda _m^0} \right)_{KBr}} - {\left( {\Lambda _m^0} \right)_{KCl}} \)
• (D) \( {\left( {\Lambda _m^0} \right)_{{H_2}O}} = {\left( {\Lambda _m^0} \right)_{HCl}} + {\left( {\Lambda _m^0} \right)_{NaOH}} - {\left( {\Lambda _m^0} \right)_{NaCl}} \)

For the following reactions


K_s and K_e, are respectively, the rate constants for substitution and elimination and \( \mu = {{{k_s}} \over {{k_e}}} \) the correct options is

• (A) \( {\mu _B} > {\mu _A} \) and K_e(A) > K_e(B)
• (B) \( {\mu _A} > {\mu _B} \) and K_e(B) > K_e(A)
• (C) \( {\mu _B} > {\mu _A} \) and K_e(B) > K_e(A)
• (D) \( {\mu _A} > {\mu _B} \) and K_e(A) > K_e(B)

A chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of compounds consisting of (A) benzanilide (B) aniline and (C) acetophenone. When the column is eluted with a mixture of solvents, hexane : ethylacelate (20:80), the sequence of obtained compounds is :

• (A) (A), (B) and (C)
• (B) (B), (A) and (C)
• (C) (C), (A) and (B)
• (D) (B), (C) and (A)

In the following reaction sequence,


The major product B is :

• (A)
• (B)
• (C)
• (D)

The ammonia (NH₃) released on quantitative reaction of 0.6 g urea (NH₂CONH₂) with sodium hydroxide (NaOH) can be neutralized by :

• (A) 200 ml of 0.02 N HCl
• (B) 100 ml of 0.2 N HCl
• (C) 100 ml of 0.1 HCl
• (D) 200 ml of 0.4 N HCl

In the following reaction, products (A) and (B) respectively, are :

NaOH + Cl₂ \( \to \) (A) + side products
(hot and conc.)

Ca(OH)₂ + Cl₂ \( \to \) (B) + side products (dry)

• (A) NaOCl and Ca(OCl)₂
• (B) NaClO₃ and Ca(ClO₃)₂
• (C) NaOCl and Ca(ClO₃)₂
• (D) NaClO₃ and Ca(OCl)₂

Among statements (a)-(d), the correct ones are: (a) Decomposition of hydrogen peroxide gives dioxygen. (b) Like hydrogen peroxide,compounds, such as \( KClO_3, Pb (NO_3)_2 \) and \( NaNO_3 \) when heated liberate dioxygen. (c) 2-Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide. (d) Hydrogen peroxide is used for the manufacture of sodium perborate.

• (A) (a), (b), (c) and (d)
• (B) (a), (b) and (c) only
• (C) (a), (c) and (d) only
• (D) (a) and (c) only Question

Identify the correct labels of A,B and C in the following graph from the options given below :


Root mean square speed (V_rms); most probable speed (V_mp); Average speed (V_av)

• (A) A - V_av ; B - V_rms ; C - V_mp
• (B) A - V_rms ; B - V_mp ; C - V_av
• (C) A - V_mp; B- V_av; C - V_rms
• (D) A - V_mp ; B - V_rms ; C - V_av

The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is :

• (A) liquation
• (B) vapour phase refining
• (C) distillation
• (D) zone refining

The flocculation value of HCl for arsenic sulphide sol.
is 30 m mol L^-1 If H₂SO₄ is used for the flocculatiopn of arsenic sulphide, the amount in grams, of H₂SO₄ in 250 ml required for the above purposed is ______.
(molecular mass of H₂SO₄ = 98 g/mol)

The standard heat of formation \( \left( {{\Delta _f}H_{298}^0} \right) \) of ethane (in kj/mol), if the heat of combustion of ethane, hydrogen and graphite are - 1560, -393.5 and -286 Kj/mol, respectively is :

3 g of acetic acid is added to 250 mL of 0.1 M HCL and the solution made up to 500 mL. To 20 mL of this solutions \( {1 \over 2} \) mL of 5 M NaOH is added. The pH of the solution is __________.

[Given : pKa of acetic acid = 4.75, molar mass of acetic of acid = 60 g/mol, log 3 = 0.4771] Neglect any changes in volume.

Consider the following reactions :

\( NaCl{\rm{ }} + {\rm{ }}{K_2}C{r_2}{O_7} + \mathop {{H_2}S{O_4}}\limits_{(conc.)} \)\( \to \) (A) + side products

(A) + NaOH \( \to \) (B) + Side products

\( \left( B \right){\rm{ }} + \mathop {{H_2}S{O_4}}\limits_{(dilute)} + {\rm{ }}{H_2}{O_2} \) \( \to \) (C) + Side products

The sum of the total number of atoms in one molecule each of (A) and (B) and (C) is

The number of sp² hybridised carbons present in "Aspartame" is