question: The complex showing a spin-only magnetic moment of 2.82 B.M. is

answer: B

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question_subject: chemistry


question: The species having pyramidal shape is

response_choices: A) SO3    B) BrF3    C) SiO32-    D) OSF2

answer: D

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question_subject: chemistry


question: In the reaction H3C-(ring structure)-C-NH2    (1) NaOH/Br2    T    (2) (ring structure)-C-Cl    the structure of the Product T is

response_choices: A) (structure)    B) (structure)    C) (structure)    D) (structure)

answer: C

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question_subject: chemistry


question: The compounds P, Q and S were separately subjected to nitration using HNO3/H2SO4 mixture. The major product formed in each case respectively, is

response_choices: A) HO-NO2, H3C-NO2, O2N-; B) HO-NO2, H3C-NO2, -NO2; C) HO-NO2, H3C-NO2, -NO2; D) HO-NO2, H3C-NO2, O-NO2

answer: C

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question_subject: chemistry


question: The packing efficiency of the two-dimensional square unit cell shown below is

answer: D

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question_subject: chemistry


question: Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule B2 is

response_choices: A) 1 and diamagnetic, B) 0 and diamagnetic, C) 1 and paramagnetic, D) 0 and paramagnetic

answer: A

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question_subject: chemistry


question: The total number of diprotic acids among the following is H3PO4, H2SO4, H3PO3, H2CO3, H2S2O7, H3BO3, H3PO2, H2CrO4, H2SO3

answer: 6

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question_subject: chemistry


question: Total number of geometrical isomers for the complex [RhCl(CO)(PPh3)(NH3)] is

answer: 3

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question_subject: chemistry


question: Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, Na, Ti

answer: 2

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question_subject: chemistry


question: Silver (atomic weight = 108 g mol⁻¹) has a density of 10.5 g cm⁻³. The number of silver atoms on a surface of area 10⁻¹² m² can be expressed in scientific notation as y × 10^x. The value of x is

answer: 7

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question_subject: chemistry


question: One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ws and that along the dotted line path is wd, then the integer closest to the ratio wd/ws is

response_choices: Not Available

answer: 2

image_available: yes

question_subject: physics


question: The compounds P and Q respectively are

response_choices: A) H3C-CH2-CH-C-H and H3C-C-H, B) H3C-CH-C-H and C-H, C) H3C-CH2-CH-C-H and H3C-C-H, D) H3C-CH2-CH-C-H and H-C-H

answer: B

image_available: yes

question_subject: chemistry


question: The compound R is

response_choices: A) H3C-C-C-H, B) H3C-C=C-H, CH3, C-CH-CH, CH3, OH, D) H3C-CH-CH-H, CH3, CH2-OH

answer: A

image_available: yes

question_subject: chemistry


question: The compound S is

response_choices: A) H3C-CH-CH-H, CH2-CN, B) H3C-C-H, CH2-CN, C) H3C-CH-CH-OH, CH3, CN, CH2-OH, D) H3C-CH-OH, CH3-OH

answer: D

image_available: yes

question_subject: chemistry


question: The state S1 is

answer: B

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question_subject: chemistry


question: Energy of the state S1 in units of the hydrogen atom ground state energy is

answer: C

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question_subject: chemistry


question: The orbital angular momentum quantum number of the state S2 is

answer: B

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question_subject: chemistry


question: Match the reactions in Column I with appropriate options in Column II.

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

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

image_available: yes

question_subject: chemistry


question: All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

response_choices:
Column I: A) (CH3)2SiCl2, B) XeF4, C) Cl2, D) VCl3
 Column II: p) Hydrogen halide formation, q) Redox reaction, r) Reacts with glass, s) Polymerization, t) O2 formation

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

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question_subject: chemistry


question:
For r = 0, 1, ..., 10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the expansions of (1+x)10, (1+x)20 and (1+x)30. Then
 10 ∑ Ar (B10Br - C10Ar)
r=1
is equal to

answer: D

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question_subject: mathematics


question: Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to

answer: D

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question_subject: mathematics


question: Let f be a real-valued function defined on the interval (-1, 1) such that e^-x f(x) = 2 + ∫(√(t^4 + 1 dt), for all x ∈ (-1, 1), and let f^-1 be the inverse function of f. Then (f^-1)' (2) is equal to

answer: B

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question_subject: mathematics


question: If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = α , where α > 0, is 5, then the foot of the perpendicular from P to the plane is

answer: A

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question_subject: mathematics


question: Two adjacent sides of a parallelogram ABCD are given by AB = 2i + 10j + 11k and AD = - i + 2j + 2k The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α is given by

answer: B

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question_subject: mathematics


question: A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is

answer: C

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question_subject: mathematics


question: Two parallel chords of a circle of radius 2 are at a distance √3 + 1 apart. If the chords subtend at the center, angles of π/k and 2π/k, where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]

answer: 3

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question_subject: mathematics


question: Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r^2 is equal to

answer: 3

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question_subject: mathematics


question: Let f be a function defined on R (the set of all real numbers) such that f(x)=2010(x−2009)(x−2010)^2(x−2011)^3(x−2012)^4, for all x ∈ R. If g is a function defined on R with values in the interval (0, ∞) such that f(x) = ℓn (g (x)), for all x ∈ R, then the number of points in R at which g has a local maximum is

answer: 1

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question_subject: mathematics


question: Let a1, a2, a3, ... , a11 be real numbers satisfying a1 = 15, 27 - 2a2 > 0 and ak = 2ak-1 - ak-2 for k = 3, 4, ..., 11. If (a1^2 + a2^2 + ... + a11^2)/11 = 90, then the value of (a1 + a2 + ... + a11)/11 is equal to

answer: 0

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question_subject: mathematics


question: Let k be a positive real number and let A= [2k-1 √2k 2√k; 2√k 1 -2k; -2√k 2k -1] and B=[0 2k-1 √k; 1-2k 0 2√k; -√k -2√k 0] If det (adj A) + det(adj B) =10^6, then [k] is equal to

response_choices: Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to [k].

answer: 4

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question_subject: mathematics


question: The real number s lies in the interval

answer: C

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question_subject: mathematics


question: The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval

answer: A

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question_subject: mathematics


question: The function f(x) is

response_choices:
A) increasing in (−t, -1/4) and decreasing in (−1/4, t)
B) decreasing in (−t, -1/4) and increasing in (−1/4, t)
C) increasing in (-t, t)
D) decreasing in (-t, t)

answer: B

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question_subject: mathematics


question: The coordinates of A and B are

answer: D

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question_subject: mathematics


question: The orthocenter of the triangle PAB is

answer: C

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question_subject: mathematics


question: The equation of the locus of the point whose distances from the point P and the line AB are equal, is

answer: A

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question_subject: mathematics


question: Match the statements in Column-I with those in Column-II. [Note: Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.]

response_choices: Column I: A) The set of points z satisfying |z-1|z|=|z+1|z|, B) The set of points z satisfying |z+4|+|z-4|=10, C) If |w|=2, then the set of points z=w-1/w, D) If |w|=1, then the set of points z=w+1/w; Column II: p) an ellipse with eccentricity 4/5, q) the set of points z satisfying Im z=0, r) the set of points z satisfying |Im z|≤1, s) the set of points z satisfying |Re z|≤2, t) the set of points z satisfying |z|≤3

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

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question_subject: mathematics


question: Match the statements in Column-I with the values in Column-II.

response_choices:
A) A line from the origin meets the lines x-2=y-1=z+1 and x-8/3=y+3/2=-z-1/1 at P and Q respectively. If length PQ = d, then d^2 is p) - 4
B) The values of x satisfying tan^-1 (x + 3) - tan^-1 (x - 3) = sin^-1 (3/5) are q) 0
C) Non-zero vectors ā, b̄ and c̄ satisfy ā.b̄ = 0, (b̄ - ā).(b̄ + c̄) = 0 and 2|b̄ + c̄| = |b̄ - ā|. If ā = μb̄ + 4c̄, then the possible values of μ are r) 4
D) Let f be the function on [-π, π] given by f(0) = 9 and f(x) = sin((9x/2)/sin(x/2)) for x ≠ 0. The value of (2/π) ∫[-π]^π f(x) dx is s) 5
t) 6

answer:
A: t
B: p and r
C: either q or (q and s)
D: r

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question_subject: mathematics


question: A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

answer: D

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question_subject: physics


question: A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms^-1, the mass of the string is

response_choices: A) 5 grams, B) 10 grams, C) 20 grams, D) 40 grams

answer: B

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question_subject: physics


question: A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

response_choices: A) virtual and at a distance of 16 cm from the mirror, B) real and at a distance of 16 cm from the mirror, C) virtual and at a distance of 20 cm from the mirror, D) real and at a distance of 20 cm from the mirror

answer: B

image_available: yes

question_subject: physics


question: A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

answer: C

image_available: yes

question_subject: physics


question: A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81π/104 Vm−1. When the field is switched off, the drop is observed to fall with terminal velocity 2 × 10−3 m s−1. Given g = 9.8 m s−2, viscosity of the air = 1.8 × 10−5 Ns m−2 and the density of oil = 900 kg m−3, the magnitude of q is

answer: D

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question_subject: physics


question: A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to

answer: A

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question_subject: physics


question: A diatomic ideal gas is compressed adiabatically to (1/32) of its initial volume. In the initial temperature of the gas is T₁ (in Kelvin) and the final temperature is αT₁, the value of α is

answer: 4

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question_subject: physics


question: At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?

answer: 2

image_available: yes

question_subject: physics


question: Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from (25/3) m to (50/7) m in 30 seconds. What is the speed of the object in km per hour ?

answer: 3

image_available: no

question_subject: physics


question: A large glass slab (μ = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?

answer: 6

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question_subject: physics


question: To determine the half life of a radioactive element, a student plots a graph of |dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is

answer: 8

image_available: yes

question_subject: physics


question: If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r<<R) is

response_choices: A) 2πrT, B) 2πRT, C) 2π^2T/R, D) 2πR^2T/r

answer: C

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question_subject: physics


question: If r = 5x10^-4 m, p = 10^3 kgm^-3, g = 10 ms^-2, T = 0.11 Nm^-1, the radius of the drop when it detaches from the dropper is approximately

answer: A

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question_subject: physics


question: After the drop detaches, its surface energy is

answer: B

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question_subject: physics


question: A diatomic molecule has moment of inertia I. By Bohr's quantization condition its rotational energy in the nth level (n = 0 is not allowed) is

answer: D

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question_subject: physics


question: It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 4/π×10¹¹ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take ℏ = 2 π x 10^-34 J s)

answer: B

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question_subject: physics


question: In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.), where 1 a.m.u. = 5/3×10^-27 kg, is close to

answer: C

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question_subject: chemistry


question: Two transparent media of refractive indices μ1 and μ3 have a solid lens shaped transparent material of refractive index  μ2 between them as shown in figures in Column II. A traversing these media is also shown in the figures. In Column I different relationship between μ1, μ2 and μ3 are given. Match them to the ray diagrams shown in Column I

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

image_available: yes

question_subject: physics


question: You are given many resistances, capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are related as shown in column I. Match the two

response_choices:
A) I ≠ 0, V1 is proportional to I
B) I ≠ 0, V2 > V1
C) V1 = 0, V2 = V
D) I ≠ 0, V2 is proportional to I

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

image_available: yes

question_subject: physics