question: A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v^2/4g with respect to the initial position. The object is

response_choices: (A) ring (B) solid sphere (C) hollow sphere (D) disc

answer: D

image_available: yes

question_subject: physics


question: Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is P0. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

answer: B

image_available: yes

question_subject: physics


question: A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

response_choices: (A) zero everywhere, (B) non-zero and uniform, (C) non-uniform, (D) zero only at its center

answer: B

image_available: yes

question_subject: physics


question: Positive and negative point charges of equal magnitude are kept at (0, 0, a/2) and (0, 0, -a/2), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is

response_choices: (A) positive, (B) negative, (C) zero, (D) depends on the path connecting the initial and final positions

answer: C

image_available: no

question_subject: physics


question: A magnetic field B = B0j exists in the region. a < x < 2a and B = -B0j, in the region 2a < x < 3a, where B0 is a positive constant. A positive point charge moving with a velocity v = v0i, where v0 is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,

answer: (A)

image_available: yes

question_subject: physics


question: Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

answer: (A)

image_available: no

question_subject: physics


question:
STATEMENT-1

If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

because

STATEMENT-2

The linear momentum of an isolated system remains constant.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

answer: D

image_available: no

question_subject: physics


question:
STATEMENT-1

A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

because

STATEMENT-2

For every action there is an equal and opposite reaction.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

answer: B

image_available: no

question_subject: physics


question:
STATEMENT-1

A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.

because

STATEMENT-2

In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

answer: B

image_available: yes

question_subject: physics


question:
STATEMENT-1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

because

STATEMENT-2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

answer: B

image_available: no

question_subject: physics


question: The speed of sound of the whistle is

response_choices: (A) 340 m/s for passengers in A and 310 m/s for passengers in B, (B) 360 m/s for passengers in A and 310 m/s for passengers in B, (C) 310 m/s for passengers in A and 360 m/s for passengers in B, (D) 340 m/s for passengers in both the trains

answer: B

image_available: no

question_subject: physics


question: The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by

answer: A

image_available: yes

question_subject: physics


question: The spread of frequency as observed by the passengers in train B is

answer: A

image_available: no

question_subject: physics


question: Light travels as a

response_choices: (A) parallel beam in each medium, (B) convergent beam in each medium, (C) divergent beam in each medium, (D) divergent beam in one medium and convergent beam in the other medium

answer: A

image_available: no

question_subject: physics


question: The phases of the light wave at c, d, e and f are φc, φd, φe and φf respectively. It is given that φe ≠ φf.

response_choices: (A) φc cannot be equal to φd, (B) φd can be equal to φc, (C) (φd - φf) is equal to (φc - φe), (D) (φd - φe) is not equal to (φf - φc)

answer: C

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question_subject: physics


question: Speed of light is

response_choices: (A) the same in medium-1 and medium-2, (B) larger in medium-1 than in medium-2, (C) larger in medium-2 than in medium-1, (D) different at b and d

answer: B

image_available: no

question_subject: physics


question: Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices: A) The object moves on the x-axis under a conservative force in such a way that its "speed" and "position" satisfy v = c₁√(c₂ - x²), where c₁ and c₂ are positive constants. (B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy v = -kx, where k is a positive constant. (C) The object is attached to one end of a mass-less spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. (D) The object is projected from the earth's surface vertically upwards with a speed 2√(GM/R), where, M is the mass of the earth and R is the radius of the earth. Neglect forces from objects other than the earth.

answer:
First option: p,c
Second option: d

image_available: yes

question_subject: physics


question: Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices: (A) Point P is situated midway between the wires. (B) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (C) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (D) Point P is situated at the common center of the wires.

answer: ACBCBDAD or ACBCBDDA

image_available: yes

question_subject: physics


question: Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices: (A) Bimetallic strip, (B) Steam engine, (C) Incandescent lamp, (D) Electric fuse / (p) Radiation from a hot body, (q) Energy conversion, (r) Melting, (s) Thermal expansion of solids

answer: A - 's, q'  OR  's' alone, B - 'q', C - 'p, q'  OR  'p' alone, D - 'q, r'  OR  'r' alone

image_available: no

question_subject: physics


question: Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is

answer: D

image_available: no

question_subject: chemistry


question: Among the following metal carbonyls, the C-O bond order is lowest in

answer: D

image_available: no

question_subject: chemistry


question: A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

answer: B

image_available: no

question_subject: chemistry


question: Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is

response_choices: (A) CHO, (B) CHO, (C) COOH, (D) CO2H, CO2H

answer: A

image_available: yes

question_subject: chemistry


question: The number of stereoisomers obtained by bromination of trans-2-butene is

answer: A

image_available: no

question_subject: chemistry


question: Among the following, the least stable resonance structure is

response_choices: (A) [Resonance structure A], (B) [Resonance structure B], (C) [Resonance structure C], (D) [Resonance structure D]

answer: A

image_available: yes

question_subject: chemistry


question: A positron is emitted from 2311Na. The ratio of the atomic mass and atomic number of the resulting nuclide is

answer: C

image_available: no

question_subject: chemistry


question: For the process H2O(l) (1 bar, 373 K) → H2O(g) (1 bar, 373 K), the correct set of thermodynamic parameters is

response_choices: A) ΔG = 0, ΔS = +ve, B) ΔG = 0, ΔS = -ve, C) ΔG = +ve, ΔS = 0, D) ΔG = -ve, ΔS = +ve

answer: A

image_available: no

question_subject: chemistry


question: Consider a reaction aG + bH → Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is

answer: D

image_available: no

question_subject: chemistry


question: STATEMENT-1 : Alkali metals dissolve in liquid ammonia to give blue solutions. because STATEMENT-2 : Alkali metals in liquid ammonia give solvated species of the type [M(NH3)x]+ (M = alkali metals).

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True; Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: B

image_available: no

question_subject: chemistry


question: STATEMENT-1 : Glucose gives a reddish-brown precipitate with Fehling's solution. because STATEMENT-2 : Reaction of glucose with Fehling's solution gives CuO and gluconic acid.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: C

image_available: no

question_subject: chemistry


question: STATEMENT-1 : Molecules that are not superimposable on their mirror images are chiral. because STATEMENT-2 : All chiral molecules have chiral centres.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: C

image_available: no

question_subject: chemistry


question: STATEMENT-1 : Band gap in germanium is small. because STATEMENT-2 : The energy spread of each germanium atomic energy level is infinitesimally small.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: B

image_available: no

question_subject: physics


question: Among the following, identify the correct statement.

response_choices: (A) Chloride ion is oxidised by O₂ (B) Fe²⁺ is oxidised by iodine (C) Iodide ion is oxidised by chlorine (D) Mn²⁺ is oxidised by chlorine

answer: C

image_available: no

question_subject: chemistry


question: While Fe³⁺ is stable, Mn³⁺ is not stable in acid solution because

response_choices: (A) O₂ oxidises Mn²⁺ to Mn³⁺ (B) O₂ oxidises both Mn²⁺ to Mn³⁺ and Fe²⁺ to Fe³⁺ (C) Fe³⁺ oxidises H₂O to O₂ (D) Mn³⁺ oxidises H₂O to O₂

answer: D

image_available: no

question_subject: chemistry


question: Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and H₂SO₄ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of

response_choices: (A) Fe₄[Fe(CN)₆]₃ (B) Fe₃[Fe(CN)₆]₂ (C) Fe₂[Fe(CN)₆]₂ (D) Fe₃[Fe(CN)₆]₃

answer: A

image_available: no

question_subject: chemistry


question: Which one of the following reagents is used in the above reaction?

response_choices: (A) aq.NaOH + CH₃Cl (B) aq.NaOH + CH₂Cl₂ (C) aq.NaOH + CHCl₃ (D) aq.NaOH + CCl₄

answer: C

image_available: no

question_subject: chemistry


question: The electrophile in this reaction is

response_choices: (A) :CHCl  (B) +CHCl₂  (C) :CCl₂  (D) -CCl₃

answer: C

image_available: no

question_subject: chemistry


question: The structure of the intermediate I is

response_choices: (A) [Structure A]  (B) [Structure B]  (C) [Structure C]  (D) [Structure D]

answer: B

image_available: yes

question_subject: chemistry


question: Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) O₃ → O₂ + O₂, (B) CrO₄²⁻ + H⁺ →, (C) MnO₄⁻ +NO₂ + H⁺ →, (D) NO₂ + H₂SO₄ + Fe²⁺ →
Column II: (p) redox reaction, (q) one of the products has trigonal planar structure, (r) dimeric bridged tetrahedral metal ion, (s) disproportionation

answer: (A, p), (B, r), (C, r), (D, s)

image_available: yes

question_subject: chemistry


question: Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) C₆H₅CHO, (B) CH₃C≡CH, (C) CN⁻, (D) I⁻
Column II: (p) gives precipitate with 2,4-dinitrophenylhydrazine, (q) gives precipitate with AgNO₃, (r) is a nucleophile, (s) is involved in cyanohydrin formation

answer: (A, p), (B, q), (C, r), (D, s)

image_available: yes

question_subject: chemistry


question: Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices: (A) simple cubic and face-centred cubic, (B) cubic and rhombohedral, (C) cubic and tetragonal, (D) hexagonal and monoclinic, (p) have these cell parameters a =b=c and α = β = γ, (q) are two crystal systems, (r) have only two crystallographic angles of 90°, (s) belong to same crystal system

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

image_available: yes

question_subject: chemistry


question: Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

answer: C

image_available: no

question_subject: mathematics


question: If |z|=1 and z ≠ ±1, then all the values of z/(1-z^2) lie on

response_choices:
(A) a line not passing through the origin
(B) |z|=√2
(C) the x-axis
(D) the y-axis

answer: D

image_available: no

question_subject: mathematics


question: Let E^c denote the complement of an event E. Let E, F, G be pairwise independent events with P(G)>0 and P(E ∩ F ∩ G)=0. Then P[E^c ∩ F^c | G] equals

answer: C

image_available: no

question_subject: mathematics


question: (d^2x)/(dy^2) equals

answer: D

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question_subject: mathematics


question: The differential equation dy/dx = √(1-y^2)/y determines a family of circles with

response_choices: (A) variable radii and a fixed centre at (0, 1) (B) variable radii and a fixed centre at (0, -1) (C) fixed radius 1 and variable centres along the x-axis (D) fixed radius 1 and variable centres along the y-axis

answer: C

image_available: yes

question_subject: mathematics


question: Let a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?

response_choices: (A) a × b = b × c = c × a = 0 (B) a × b = b × c = c × a ≠ 0 (C) a × b = b × c = a × c ≠ 0 (D) a × b, b × c, c × a are mutually perpendicular

answer: B

image_available: no

question_subject: mathematics


question: Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2 CD . Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

answer: B

image_available: no

question_subject: mathematics


question: Let f(x) = (x)/(1 + x^n)^(n) for n >= 2 and g(x) = (f ∘ f ∘ ... ∘ f) (x). Then [x^(-2)g(x) dx] equals

answer: A

image_available: no

question_subject: mathematics


question: The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

answer: C

image_available: no

question_subject: mathematics


question: Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5. STATEMENT-1 : The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t. because STATEMENT-2 : The vector 14i + 2j + 15k is parallel to the line of intersection of given planes.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, (C) Statement-1 is True, Statement-2 is False, (D) Statement-1 is False, Statement-2 is True

answer: D

image_available: no

question_subject: mathematics


question: STATEMENT-1 : The curve y = -x^2/2 + x + 1 is symmetric with respect to the line x = 1. because STATEMENT-2 : A parabola is symmetric about its axis.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: A

image_available: no

question_subject: mathematics


question: Let f(x) = 2 + cos x for all real x. STATEMENT-1 : For each real t, there exists a point c in [t, t + π] such that f'(c) = 0. because STATEMENT-2 : f(t) = f(t + 2π) for each real t.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: B

image_available: no

question_subject: mathematics


question: Lines L1: y - x = 0 and L2: 2x + y = 0 intersect the line L3: y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R. STATEMENT-1: The ratio PR: RQ equals 2√2: √5. because STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: C

image_available: no

question_subject: mathematics


question: Which one of the following statements is correct? (A) G1 > G2 > G3 > ... (B) G1 < G2 < G3 < ... (C) G2 = G1 = G3 = ... (D) G1 < G3 < G5 < ... and G2 > G4 > G6 > ...

answer: C

image_available: no

question_subject: mathematics


question: Which one of the following statements is correct? (A) A1 > A2 > A3 > ... (B) A1 < A2 < A3 < ... (C) A1 > A3 > A5 > ... and A2 < A4 < A6 < ... (D) A1 < A3 < A5 < ... and A2 > A4 > A6 > ...

answer: A

image_available: no

question_subject: mathematics


question: Which one of the following statements is correct?

response_choices:
(A) H₁ > H₂ > H₃ > ⋯
(B) H₁ < H₂ < H₃ < ⋯
(C) H₁ > H₂ > H₃ > ⋯ and H₃ < H₄ < H₆ < ⋯
(D) H₁ < H₃ < H₅ < ⋯ and H₂ > H₄ > H₆ > ⋯

answer: B

image_available: no

question_subject: physics


question: The line y = x meets y = ke^x for k ≤ 0 at

response_choices:
(A) no point
(B) one point
(C) two points
(D) more than two points

answer: B

image_available: no

question_subject: mathematics


question: The positive value of k for which ke^x - x = 0 has only one root is

answer: A

image_available: no

question_subject: mathematics


question: For k > 0, the set of all values of k for which ke^x - x = 0 has two distinct roots is

answer: A

image_available: no

question_subject: mathematics


question: Let f(x) = (x^2 - 6x + 5) / (x^3 - 5x + 6). Match the expressions/statements in Column I with expressions/statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) If -1 < x < 1, then f(x) satisfies (B) If 1 < x < 2, then f(x) satisfies (C) If 3 < x < 5, then f(x) satisfies (D) If x > 5, then f(x) satisfies
Column II: (p) 0 < f(x) < 1 (q) f(x) < 0 (r) f(x) > 0 (s) f(x) < 1

answer: p: not selected, q: A, r: C and D, s: A and D

image_available: yes

question_subject: mathematics


question: Let (x, y) be such that sin⁻¹(a x) + cos⁻¹(y) + cos⁻¹(b x y) = π/2. Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) If a = 1 and b = 0, then (x, y), (B) If a = 1 and b = 1, then (x, y), (C) If a = 1 and b = 2, then (x, y), (D) If a = 2 and b = 2, then (x, y)
 Column II: (p) lies on the circle x² + y² = 1, (q) lies on (x² - 1)(y² - 1) = 0, (r) lies on y = x, (s) lies on (4x² - 1)(y² - 1) = 0

answer: p, q, r, s

image_available: no

question_subject: mathematics


question: Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

response_choices: (A) Two intersecting circles, (B) Two mutually external circles, (C) Two circles, one strictly inside the other, (D) Two branches of a hyperbola, (p) have a common tangent, (q) have a common normal, (r) do not have a common tangent, (s) do not have a common normal

answer: A: pq, B: pq, C: rs, D: rs

image_available: yes

question_subject: mathematics