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The volume (in mL) of 0.1 M AgNO3 required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of [Cr(H2O)6]Cl3, as silver chloride is close to

<no multiple choice options provided>

6

no

chemistry

In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 × 10^-10], 0.1 mol of CuCl [Ksp(CuCl) = 1.0 × 10^-6] is added. The resultant concentration of Ag+ in the solution is 1.6 × 10^-x. The value of "x" is

<no multiple choice options provided>

7

no

chemistry

The number of hexagonal faces that are present in a truncated octahedron is

<no multiple choice options provided>

8

no

chemistry

The maximum number of isomers (including stereoisomers) that are possible on mono-chlorination of the following compound, is CH3 \C\ CH2CH2\CH2CH3 \H

<image shows chemical structure>

8

yes

chemistry

The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the following carbocation is H3C-C(+)-CH2CH3 <image shows chemical structure>

<image shows chemical structure>

6

yes

chemistry

Match the transformations in column I with appropriate options in column II

Column I: (A) CO2(s) → CO2(g), (B) CaCO3(s) → CaO(s) + CO2(g), (C) 2 H• → H2(g), (D) P(white, solid) → P(red, solid) Column II: (p) phase transition, (q) allotropic change, (r) ΔH is positive, (s) ΔS is positive, (t) ΔS is negative

A: p, r and s B: r and s C: t D: p, q and t

no

chemistry

Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II

A: r, s and t; B: p and s; C: r and s; D: q and r

A: r, s and t; B: p and s; C: r and s; D: q and r

yes

chemistry

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected ( R ) and transmitted ( T ) intensities, both as function of θ, are plotted. The correct sketch is

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

C

yes

physics

A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

(A) 1/2 mV^2, (B) mV^2, (C) 3/2 mV^2, (D) 2mV^2

B

no

physics

A long insulated copper wire is closely wound as a spiral of 'N' turns. The spiral has inner radius 'a' and outer radius 'b'. The spiral lies in the X-Y plane and a steady current 'I' flows through the wire. The Z-component of the magnetic field at the center of the spiral is

(A) (μ₀N I / 2(b-a)) ln (b/a), (B) (μ₀N I / 2(b-a)) ln ((b+a)/(b-a)), (C) (μ₀N I / 2b) ln (b/a), (D) (μ₀N I / 2b) ln ((b+a)/(b-a))

A

yes

physics

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x₁(t) = A sin ωt and x₂(t) = A sin (ωt + 2π/3). Adding a third sinusoidal displacement x₃(t) = B sin (ωt + ϕ) brings the mass to a complete rest. The values of B and ϕ are

(A) √2 A, 3π/4, (B) A, 4π/3, (C) √3 A, 5π/6, (D) A, π/3

B

no

physics

Which of the field patterns given below is valid for electric field as well as for magnetic field?

A, B, C, D

C

yes

physics

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is

(A) 250 m/s, (B) 250√2 m/s, (C) 400 m/s, (D) 500 m/s

D

yes

physics

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

(A) 0.9%, (B) 2.4%, (C) 3.1%, (D) 4.2%

C

no

physics

A wooden block performs SHM on a frictionless surface with frequency, v0. The block carries a charge +Q on its surface. If now a uniform electric field E is switched-on as shown, then the SHM of the block will be

A) of the same frequency and with shifted mean position. B) of the same frequency and with the same mean position. C) of changed frequency and with shifted mean position. D) of changed frequency and with the same mean position.

A

yes

physics

Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

(A) dA < dF, (B) dB > dF, (C) dA > dF, (D) dA + dB = 2 dF

ABD

yes

physics

A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?

(A) IRA > IRB, (B) IRA < IRB, (C) VCA > VCB, (D) VCA < VCB

BC

no

physics

Which of the following statement(s) is/are correct?

(A) If the electric field due to a point charge varies as r^-2.5 instead of r^-2, then the Gauss law will still be valid. (B) The Gauss law can be used to calculate the field distribution around an electric dipole. (C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same. (D) The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB - VA).

CD

no

physics

A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision

(A) the ring has pure rotation about its stationary CM. (B) the ring comes to a complete stop. (C) friction between the ring and the ground is to the left. (D) there is no friction between the ring and the ground.

A OR AC

yes

physics

A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^2, is

No response choices provided

5

no

physics

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is

No response choices provided

4

yes

physics

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is

No response choices provided

5

yes

physics

Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of its image is at 'x' cm above the bottom of the tank. Then 'x' is

No response choices provided

2

yes

physics

A series R-C combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If the impedance of the R-C circuit is R√1.25, the time constant (in millisecond) of the circuit is

No response choices provided

4

no

physics

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A × 10 (where 1 < A < 10). The value of 'Z' is

No response choices provided

7

no

physics

One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Matrix response

A: p, r and t; B: p and r; C: q and s; D: r and t

yes

physics

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ1. Match each system with statements given in Column II describing the nature and wavelength of the standing waves.

(A) Pipe closed at one end, (B) Pipe open at both ends, (C) Stretched wire clamped at both ends, (D) Stretched wire clamped at both ends and at mid-point

A : p and t, B : p and s, C : q and s, D : q and r

yes

physics

Let P(6,3) be a point on the hyperbola (x^2/a^2) - (y^2/b^2) = 1. If the normal at the point P intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

(A) √5/2, (B) √3/2, (C) √2, (D) √3

B

no

mathematics

A value of b for which the equations x^2 + bx - 1 = 0 and x^2 + x + b = 0, have one root in common is

(A) -√2, (B) -i√3, (C) i√5, (D) √2

B

no

mathematics

Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form [1 a b; ω 1 c; ω^2 ω 1], where each of a, b, and c is either ω or ω^2. Then the number of distinct matrices in the set S is

(A) 2, (B) 6, (C) 4, (D) 8

A

no

mathematics

The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point

(A) (3/2,0), (B) (-5/2,2), (C) (3,5/2), (D) (-4,0)

D

no

mathematics

If lim [1+𝑥ln(1+𝑏²)] = 2𝑏sin²𝜃, 𝑏>0 and 𝜃∈(-𝜋,𝜋], then the value of 𝜃 is

A) ±𝜋/4, B) ±𝜋/3, C) ±𝜋/6, D) ±𝜋/2

D

no

mathematics

Let f:[-1,2]→(0,∞) be a continuous function such that f(x)=f(1-x) for all x∈[-1,2]. Let R₁= ∫xf(x)dx, and R₂ be the area of the region bounded by y=f(x), x=-1, x=2, and the x-axis. Then

A) R₁=2R₂, B) R₁=3R₂, C) 2R₁=R₂, D) 3R₁=R₂

C

no

mathematics

Let f(x)=x³ and g(x)=sinx for all x∈R. Then the set of all x satisfying (f∘g∘g∘f)(x)=(g∘g∘f)(x), where (f∘g)(x)=f(g(x)), is

A) ±√n𝜋, n∈{0,1,2,...}, B) ±√n𝜋, n∈{1,2,...}, C) 𝜋/2+2n𝜋, n∈{...,-2,-1,0,1,2,...}, D) 2n𝜋, n∈{...,-2,-1,0,1,2,...}

A

no

mathematics

Let (x,y) be any point on the parabola y²=4x. Let P be the point that divides the line segment from (0,0) to (x,y) in the ratio 1:3. Then the locus of P is

A) x²=y, B) y²=2x, C) y²=x, D) x²=2y

C

no

mathematics

If f(x)={ −x, π/2 ≤ x≤ π/2; −cos x, −π/2 < x ≤ 0; x−1, 0 < x ≤ 1; ln x, x>1,}, then

(A) f(x) is continuous at x = π/2, (B) f(x) is not differentiable at x = 0, (C) f(x) is differentiable at x = 1, (D) f(x) is differentiable at x = 3/2

ABCD

no

mathematics

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then

(A) P(E)=4/5, P(F)=3/5, (B) P(E)=1/5, P(F)=2/5, (C) P(E)=2/5, P(F)=1/5, (D) P(E)=3/5, P(F)=4/5

AD

no

mathematics

Let L be a normal to the parabola y^2 = 4x. If L passes through the point (9, 6), then L is given by

(A) y - x + 3 = 0, (B) y + 3x - 33 = 0, (C) y + x - 15 = 0, (D) y - 2x + 12 = 0

ABD

no

mathematics

Let f : (0,1) → R be defined by f(x) = (b - x)/(1 - bx), where b is a constant such that 0 < b < 1. Then

(A) f is not invertible on (0, 1), (B) f ≠ f^-1 on (0, 1) and f'(b) = 1/f'(0), (C) f = f^-1 on (0, 1) and f'(b) = 1/f'(0), (D) f^-1 is differentiable on (0, 1)

A

no

mathematics

Let ω = e^(2i/3), and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x, a + bω + cω^2 = y, a + bω^2 + cω = z. Then the value of |x|^2 + |y|^2 + |z|^2 / |a|^2 + |b|^2 + |c|^2 is

MARKS TO ALL

no

mathematics

The number of distinct real roots of x^4 - 4x^3 + 12x^2 + x - 1 = 0 is

2

no

mathematics

Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ∈ ℝ, where f'(x) denotes d f(x)/dx and g(x) is a given non-constant differentiable function on ℝ with g(0) = g(2) = 0. Then the value of y(2) is

0

no

mathematics

Let M be a 3x3 matrix satisfying M = [0 -1; 1 2; 0 3], M^-1 = [1 1; 1 1; 0 -1], and M^T = [1 0; 0 1; 1 12]. Then the sum of the diagonal entries of M is

9

no

mathematics

Let a = -i - k, b = -i + j and c = i + 2j + 3k be three given vectors. If r is a vector such that r × b = c × b and r . a = 0, then the value of r.b is

9

no

mathematics

The straight line 2x - 3y = 1 divides the circular region x^2 + y^2 ≤ 6 into two parts. If S = {(2, 3), (5, 3), (1, -1), (1, 1)}, then the number of point(s) in S lying inside the smaller part is

2

no

mathematics

Match the statements given in Column I with the values given in Column II

(A) If ā = j + √3 k̄ , b̄ = - j + √3 k̄ and c̄ = 2√3 k̄ form a triangle, then the internal angle of the triangle between ā and b̄ is (B) If ∫_0^π (f(x) - 3x)dx = a^2 - b^2, then the value of f(π/6) is (C) The value of ∫_(π/3)^(5π/6) (π^2/9) sec(πx) dx is (D) The maximum value of |Arg (1/(1-z))| for |z|=1, z≠1 is given by

A : q B : p or p, q, r, s and t C : s D : t

no

mathematics

Match the statements given in Column I with the intervals/union of intervals given in Column II

(A) The set {Re(2iz / (1-z^2)) : z is a complex number, |z|=1, z != +1} is (p) (-∞, -1) ∪ (1, ∞) (B) The domain of the function f(x) = sin^-1 (8(3)^(x+3) / (1-3^(x+1))) is (q) (-∞, 0) ∪ (0, ∞) (C) If f(θ) = [-tan θ tan θ 1 / -1 -tan θ 1], then the set {f(θ) : 0 ≤ θ < π/2} is (r) [2, ∞) (D) If f(x) = x^(2/3) (3x-10), x ≥ 0, then f(x) is increasing in (s) (-∞, -1] ∪ [1, ∞)

A: s B: t C: r D: r

no

mathematics

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque (|τ|) on the system about O, as a function of time is best represented by which plot?

A, B, C, D

B

yes

physics

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

(A) (65/2)*(1/T) (B) (97/4)*(1/T) (C) (97/2)*(1/T) (D) (97)*(1/T)

C

no

physics

Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field | E(r)| and the electric potential V(r) with the distance r from the centre, is best represented by which graph ?

(A) |E(r)| and V(r) graphs (B) |E(r)| and V(r) graphs (C) |E(r)| and V(r) graphs (D) |E(r)| and V(r) graphs

D

yes

physics

In the determination of Young's modulus (Y = 4ML/πd^3) by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement

(A) due to the errors in the measurements of d and l are the same. (B) due to the error in the measurement of d is twice that due to the error in the measurement of l. (C) due to the error in the measurement of l is twice that due to the error in the measurement of d. (D) due to the error in the measurement of d is four times that due to the error in the measurement of l.

A

no

physics

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency ω = π/2 rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s²)

(A) √50 m/s, (B) √51 m/s, (C) √52 m/s, (D) √53 m/s

A

yes

physics

Young's double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are βG, βR and βB, respectively. Then,

(A) βG > βB > βR, (B) βB > βG > βR, (C) βR > βB > βG, (D) βR > βG > βB

D

no

physics

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the angular momentum of the system, calculated about O and P are denoted by Lo and Lp respectively, then

A) Lo and Lp do not vary with time. B) Lo varies with time while Lp remains constant. C) Lo remains constant while Lp varies with time. D) Lo and Lp both vary with time.

C

yes

physics

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the r m s speeds (v_rms(helium))/(v_rms(argon)) is

(A) 0.32, (B) 0.45, (C) 2.24, (D) 3.16

D

no

physics

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then X is nearly

(A) 1 x 10^-3 V, (B) 1 x 10^-7 V, (C) 1 x 10^-9 V, (D) 1x 10^-10 V

C

no

physics

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be

(A) - 280.0 cm, (B) 40.0 cm, (C) 21.5 cm, (D) 13.3 cm

B

yes

physics

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, −q at (0, −a/4,0), +3q at (0,0,0) and −q at (0,+a/4,0). Choose the correct option(s).

(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane x = − a/2. (B) The net electric flux crossing the plane y = +a/2 is more than the net electric flux crossing the plane y = − a/2. (C) The net electric flux crossing the entire region is q/ε0. (D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane x = +a/2.

ACD

yes

physics

For the resistance network shown in the figure, choose the correct option(s).

(A) The current through P Q is zero. (B) I1 = 3 A. (C) The potential at S is less than that at Q. (D) I2 = 2 A.

ABCD

yes

physics

A small block of mass of 0.1 kg lies on a fixed inclined plane P Q which makes an angle θ with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 m/s²)

(A) θ = 45° (B) θ > 45° and a frictional force acts on the block towards P. (C) θ > 45° and a frictional force acts on the block towards Q. (D) θ < 45° and a frictional force acts on the block towards Q.

AC

yes

physics

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E = E0 j and B = B0 i. At time t = 0, this charge has velocity v in the x-y plane, making an angle θ with the x-axis. Which of the following option(s) is(are) correct for time t > 0?

(A) If θ = 0°, the charge moves in a circular path in the x-z plane. (B) If θ = 0°, the charge undergoes helical motion with constant pitch along the y-axis. (C) If θ = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis. (D) If θ = 90°, the charge undergoes linear but accelerated motion along the y-axis.

CD

no

physics

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

(A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed. (D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.

BD

no

physics

An infinitely long solid cylinder of radius R has a uniform volume charge density ρ. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression 23ρR/16πε₀. The value of k is

6

yes

physics

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by N/12 μ₀aJ, then the value of N is

5

yes

physics

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is Io and Ip, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio Ip/Io to the nearest integer is

No response choices provided

3

yes

physics

A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side a (a << R) having two turns is placed with its center at z = √3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the z-axis. If the mutual inductance between the loops is given by μ0a^2/2√2 R, then the value of p is

No response choices provided

7

yes

physics

A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is: (take the proton mass, mp = (5/3) x 10^-27 kg; h/e = 4.2 x 10^15 J.s/C; 4πε0 = 9 x 10^9 m/F; 1 fm = 10^-15 m)

No response choices provided

7

no

physics

In allene (C3H4), the type(s) of hybridisation of the carbon atoms is (are)

(A) sp and sp³ (B) sp and sp² (C) only sp² (D) sp² and sp³

B

no

chemistry

For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm.liter² mol⁻²) is

(A) 1.0 (B) 4.5 (C) 1.5 (D) 3.0

C

yes

chemistry

The number of optically active products obtained from the complete ozonolysis of the given compound is

(A) 0, (B) 1, (C) 2, (D) 4

A

yes

chemistry

A compound M¥Xq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is

(A) MX, (B) MX₂, (C) M₂X, (D) M₆X₁₄

B

yes

chemistry

The number of aldol reaction(s) that occurs in the given transformation is

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

C

yes

chemistry

The colour of light absorbed by an aqueous solution of CuSO4 is

(A) orange-red, (B) blue-green, (C) yellow, (D) violet

A

no

chemistry

The carboxyl functional group (–COOH) is present in

(A) picric acid, (B) barbituric acid, (C) ascorbic acid, (D) aspirin

D

no

chemistry

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr radius]

(A) (h^2)/(4π^2ma0^2), (B) (h^2)/(16π^2ma0^2), (C) (h^2)/(32π^2ma0^2), (D) (h^2)/(64π^2ma0^2)

C

no

chemistry

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

(A) HNO3, NO, NH4Cl, N2, (B) HNO3, NO, N2, NH4Cl, (C) HNO3, NH4Cl, NO, N2, (D) NO, HNO3, NH4Cl, N2

B

no

chemistry

As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is

(A) Tetraaquadiaminecobalt (III) chloride, (B) Tetraaquadimminecobalt (III) chloride, (C) Diaminetetraaquacobalt (III) chloride, (D) Diamminetraaquacobalt (III) chloride

D

no

chemistry

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction, as shown in the given scheme.

(A) C6H5OH and C6H5COOH, (B) C6H5COOH and C6H5CH3OH, (C) C6H5CH2OH and C6H5OH, (D) C6H5CH2OH and C6H5CH2COOH

BD

yes

chemistry

Choose the correct reason(s) for the stability of the lyophobic colloidal particles. (A) Preferential adsorption of ions on their surface from the solution, (B) Preferential adsorption of solvent on their surface from the solution, (C) Attraction between different particles having opposite charges on their surface, (D) Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles

(A) Preferential adsorption of ions on their surface from the solution, (B) Preferential adsorption of solvent on their surface from the solution, (C) Attraction between different particles having opposite charges on their surface, (D) Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles

AD

no

chemistry

Which of the following molecules, in pure form, is (are) unstable at room temperature?

(A) [Cyclohexane ring], (B) [Benzene ring], (C) [Cycloheptatriene oxide], (D) [Benzene oxide]

BC

yes

chemistry

Which of the following hydrogen halides react(s) with AgNO3(aq) to give a precipitate that dissolves in Na2S2O3(aq) ?

(A) HCl (B) HF (C) HBr (D) HI

ACD

no

chemistry

For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct ? [Take ∆S as change in entropy and w as work done]

(A) ∆Sx→z = ∆Sx→y + ∆Sy→z (B) wx→z = wx→y + wy→z (C) wx→y→z = wx→y (D) ∆Sx→y→z = ∆Sx→y

AC

yes

physics

The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positively charged at pH = 7.0 ?

4

yes

chemistry

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table ?

8

no

chemistry

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is CHO CH2 CHOH CHOH CHOH CH2OH

No response choices provided

8

no

chemistry

29.2% (w/w) HCl stock solution has a density of 1.25 g mL-1. The molecular weight of HCl is 36.5 g mol-1. The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is

No response choices provided

8

no

chemistry

An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of [t1/8] / [t1/10] x 10? (take loge2 = 0.3)

No response choices provided

9

no

chemistry

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

(A) 75, (B) 150, (C) 210, (D) 243

B

no

mathematics

Let f(x) = { (x^2 cos (π/x)), x ≠ 0, x ∈ R, 0, x = 0 } then f is

(A) differentiable both at x = 0 and at x = 2, (B) differentiable at x = 0 but not differentiable at x = 2, (C) not differentiable at x = 0 but differentiable at x = 2, (D) differentiable neither at x = 0 nor at x = 2

B

yes

mathematics

The function f : [0, 3] → [1, 29], defined by f(x) = 2x^3 − 15x^2 + 36x + 1, is

(A) one-one and onto, (B) onto but not one-one, (C) one-one but not onto, (D) neither one-one nor onto

B

no

mathematics

If lim (x→∞) (x^2 + x + 1 / x + 1) − ax − b = 4 , then

(A) a = 1, b = 4, (B) a = 1, b = − 4, (C) a = 2, b = − 3, (D) a = 2, b = 3

B

yes

mathematics

Let z be a complex number such that the imaginary part of z is nonzero and a = z² + z + 1 is real. Then a cannot take the value

(A) - 1, (B) 1/3, (C) 1/2, (D) 3/4

D

no

mathematics

The ellipse E₁ : x²/9 + y²/4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E₂ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E₂ is

(A) √2/2, (B) √3/2, (C) 1/2, (D) 3/4

C

no

mathematics

Let P = [aij] be a 3x3 matrix and let Q = [bij], where bij = 2^(i+j-2)*aij for 1 ≤ i, j ≤ 3. If the determinant of P is 2, then the determinant of the matrix Q is

(A) 2¹⁰, (B) 2¹¹, (C) 2¹², (D) 2¹³

D

no

mathematics

The integral ∫ (sec² x / (sec x + tan x)½) dx equals (for some arbitrary constant K)

(A) 1 / (sec x + tan x)¹/² {[1 / 11 - 1/7 (sec x + tan x)²] + K}, (B) 1 / (sec x + tan x)¹/² {[1 / 11 + 1/7 (sec x + tan x)²] + K}, (C) 1 / (sec x + tan x)¹/² {[1 / 11 - 1/7 (sec x + tan x)²] + K}, (D) 1 / (sec x + tan x)¹/² {[1 / 11 + 1/7 (sec x + tan x)²] + K}

C

no

mathematics

The point P is the intersection of the straight line joining the points Q(2,3.5) and R(1, -1, 4) with the plane 5x - 4y - z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length of the line segment PS is

(A) 1/√2, (B) √2, (C) 2, (D) 2√2

A

no

mathematics

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle x² + y² = 9 is

(A) 20(x² + y²) - 36x + 45y = 0, (B) 20(x² + y²) + 36x - 45y = 0, (C) 36(x² + y²) - 20x + 45y = 0, (D) 36(x² + y²) + 20x - 45y = 0

A

no

mathematics

Let θ, φ∈ [0, 2π] be such that 2 cos θ (1− sin φ) = sin^2 θ (tan (θ/2) + cot (θ/2)) cos φ − 1, tan ( 2π− θ ) > 0 and −1 < sin θ < − √3/2. Then φ cannot satisfy

(A) 0 < φ < π/2 (B) π/2 < φ < 4π/3 (C) 4π/3 < φ < 3π/2 (D) 3π/2 < φ < 2π

ACD

no

mathematics

Let S be the area of the region enclosed by y = e^(x^2), y = 0, x = 0, and x = 1. Then

(A) S ≥ 1/e (B) S ≥ 1 − 1/e (C) S ≤ 1/4 (1 + 1/√e) (D) S ≤ 1/√2 + 1/e (1 − 1/√2)

ABD

no

mathematics

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective probabilities 1/2, 1/4 and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the events that the engines E1, E2 and E3 are functioning. Which of the following is (are) true ?

(A) P [ X1^c | X ] = 3/16, (B) P (Exactly two engines of the ship are functioning | X) = 7/8, (C) P [ X | X2 ] = 5/16, (D) P [ X | X1 ] = 7/16

BD

no

mathematics