question: Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

response_choices:
(A) II, III in haematite and III in magnetite
(B) II, III in haematite and II in magnetite
(C) II in haematite and II, III in magnetite
(D) III in haematite and II, III in magnetite

answer: D

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question_subject: chemistry


question:
Among the following complexes (K–P),
K3[Fe(CN)6] (K), [Co(NH3)6]Cl3 (L), Na3[Co(oxalate)3] (M), [Ni(H2O)6]Cl2 (N),
K3[Pt(CN)6] (O) and [Zn(H2O)6](NO3)2 (P)
the diamagnetic complexes are

response_choices: (A) K, L, M, N	(B) K, M, O, P	(C) L, M, O, P	(D) L, M, N, O

answer: C

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question_subject: chemistry


question:
Passing H2S gas into a mixture of Mn2+, Ni2+, Cu2+ and Hg2+ ions in an acidified aqueous
solution precipitates

response_choices:
(A) CuS and HgS		(B) MnS and CuS
(C) MnS and NiS		(D) NiS and HgS

answer: A

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question_subject: chemistry


question:
Consider the following cell reaction:
2Fe(s) + O2(g) + 4H+(aq) → 2Fe3+(aq) + 2H2O(l)		E° = 1.67 V
At [Fe3+] = 10–3 M, P(O2) = 0.1 atm and pH = 3, the cell potential at 25 °C is

answer: D

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question_subject: chemistry


question: The freezing point (in °C) of a solution containing 0.1 g of K4[Fe(CN)6] (Mol. Wt. 329) in 100 g of water (Kf = 1.86 K kg mol^-1) is

answer: A

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question_subject: chemistry


question: Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO2 in dil. HCl followed by addition to an alkaline solution of β-naphtholƖ(CH3)2     Ɣ    NH2      Ɣ  CH2NH2

response_choices: βCH3     NHCH3     H3C

answer: C

image_available: yes

question_subject: chemistry


question: The major product of the following reaction is RCH2OH ------> H⊕ (anhydrous)

response_choices: (A) a hemiacetal  (B) an acetal  (C) an ether  (D) an ester

answer: B

image_available: yes

question_subject: chemistry


question: The following carbohydrate is H OH HO HO HO H H

response_choices: (A) a ketohexose  (B) an aldohexose  (C) an α-furanose  (D) an α-pyranose

answer: B

image_available: yes

question_subject: chemistry


question: Reduction of the metal centre in aqueous permanganate ion involves

response_choices: (A) 3 electrons in neutral medium, (B) 5 electrons in neutral medium, (C) 3 electrons in alkaline medium, (D) 5 electrons in acidic medium

answer: ACD

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question_subject: chemistry


question: The equilibrium 2 Cu⁺ ⇌ Cu²⁺ + Cu⁰ in aqueous medium at 25 °C shifts towards the left in the presence of

response_choices: (A) NO₃⁻, (B) Cl⁻, (C) SCN⁻, (D) CN⁻

answer: BCD

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question_subject: chemistry


question:
For the first order reaction

2N2O5(g) → 4NO2(g) + O2(g)

response_choices:
(A) the concentration of the reactant decreases exponentially with time.
(B) the half-life of the reaction decreases with increasing temperature.
(C) the half-life of the reaction depends on the initial concentration of the reactant.
(D) the reaction proceeds to 99.6 % completion in eight half-life duration.

answer: ABD

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question_subject: chemistry


question:
The correct functional group X and the reagent/reaction conditions Y in the following scheme are

X—(CH2)4—X    (i) Y
                  —————————————————>   condensation polymer
                        O        O
                (ii)    \C—(CH2)4—C/
                            \    /
                             HO  OH
                            heat

response_choices:
(A) X = COOCH3 , Y = H2/Ni/heat
(B) X = CONH2 , Y = H2/Ni/heat
(C) X = CONH2 , Y = Br2/NaOH
(D) X = CN , Y = H2/Ni/heat

answer: CD

image_available: yes

question_subject: chemistry


question: Among the following, the number of compounds than can react with PCl5 to give POCl3 is O2, CO2, SO2, H2O, H2SO4, P2O10

response_choices: <no multiple choice options provided>

answer: 4

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question_subject: chemistry


question: 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

response_choices: <no multiple choice options provided>

answer: 6

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question_subject: chemistry


question: 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

response_choices: <no multiple choice options provided>

answer: 7

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question_subject: chemistry


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

response_choices: <no multiple choice options provided>

answer: 8

image_available: no

question_subject: chemistry


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

response_choices: <image shows chemical structure>

answer: 8

image_available: yes

question_subject: chemistry


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

response_choices: <image shows chemical structure>

answer: 6

image_available: yes

question_subject: chemistry


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

response_choices:
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

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

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question_subject: chemistry


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

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

image_available: yes

question_subject: chemistry


question: 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

answer: C

image_available: yes

question_subject: physics


question: 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

answer: B

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question_subject: physics


question: 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

answer: A

image_available: yes

question_subject: physics


question: 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

answer: B

image_available: no

question_subject: physics


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

response_choices: A, B, C, D

answer: C

image_available: yes

question_subject: physics


question: 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

answer: D

image_available: yes

question_subject: physics


question: 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

answer: C

image_available: no

question_subject: physics


question: 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

response_choices: 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.

answer: A

image_available: yes

question_subject: physics


question: 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

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

answer: ABD

image_available: yes

question_subject: physics


question: 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?

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

answer: BC

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question_subject: physics


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

response_choices: (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).

answer: CD

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question_subject: physics


question: 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

response_choices: (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.

answer: A OR AC

image_available: yes

question_subject: physics


question: 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

response_choices: No response choices provided

answer: 5

image_available: no

question_subject: physics


question: 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

response_choices: No response choices provided

answer: 4

image_available: yes

question_subject: physics


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

response_choices: No response choices provided

answer: 5

image_available: yes

question_subject: physics


question: 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

response_choices: No response choices provided

answer: 2

image_available: yes

question_subject: physics


question: 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

response_choices: No response choices provided

answer: 4

image_available: no

question_subject: physics


question: 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

response_choices: No response choices provided

answer: 7

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question_subject: physics


question: 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.

response_choices: Matrix response

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

image_available: yes

question_subject: physics


question: 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.

response_choices: (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

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

image_available: yes

question_subject: physics


question: 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

answer: B

image_available: no

question_subject: mathematics


question: 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

answer: B

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question_subject: mathematics


question: 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

answer: A

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question_subject: mathematics


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

answer: D

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question_subject: mathematics


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

answer: D

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question_subject: mathematics


question: 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

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

answer: C

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question_subject: mathematics


question: 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

answer: A

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question_subject: mathematics


question: 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

response_choices: A) x²=y, B) y²=2x, C) y²=x, D) x²=2y

answer: C

image_available: no

question_subject: mathematics


question: 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

response_choices: (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

answer: ABCD

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question_subject: mathematics


question: 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

answer: AD

image_available: no

question_subject: mathematics


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

answer: ABD

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question_subject: mathematics


question: 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

response_choices: (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)

answer: A

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question_subject: mathematics


question: 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

answer: MARKS TO ALL

image_available: no

question_subject: mathematics


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

answer: 2

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question_subject: mathematics


question: 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

answer: 0

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question_subject: mathematics


question: 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

answer: 9

image_available: no

question_subject: mathematics


question: 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

answer: 9

image_available: no

question_subject: mathematics


question: 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

answer: 2

image_available: no

question_subject: mathematics


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

response_choices:
(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

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

image_available: no

question_subject: mathematics


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

response_choices:
(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, ∞)

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

image_available: no

question_subject: mathematics