Q1
MATHS
Unit 6: Sequence and Series
Let a1, a2, a3, ... be a G.P. of increasing positive terms. If a1a5 = 28 and a2 + a4 = 29, then a6 is equal to:
- A. 628
- B. 812
- C. 526
- D. 784
Correct answer & explanation hidden
Log in to view solution →
Q3
MATHS
Unit 13: Statistics and Probability
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is m/n, where gcd(m, n) = 1, then m + n is equal to:
- A. 14
- B. 13
- C. 11
- D. 4
Correct answer & explanation hidden
Log in to view solution →
Q4
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
The product of all solutions of the equation 5^(log_e x)^2 + 3^(log_e x)^2 = x^8, x > 0 is:
- A. e
- B. e^(8/5)
- C. e^(6/5)
- D. e^2
Correct answer & explanation hidden
Log in to view solution →
Q9
MATHS
Unit 7: Limit Continuity and Differentiability
Let f(x) be a real differentiable function such that f(0) = 1 and f(x + y) = f(x)f'(y) + f'(x)f(y) for all x, y in R. Then sum from n=1 to 100 of log_e f(n) is equal to:
- A. 2525
- B. 5220
- C. 2384
- D. 2406
Correct answer & explanation hidden
Log in to view solution →
Q13
MATHS
Unit 10: Co-ordinate Geometry
The area of the region, inside the circle (x - 2√3)^2 + y^2 = 12 and outside the parabola y^2 = 2√3x is:
- A. 3π + 8
- B. 6π - 16
- C. 3π - 8
- D. 6π - 8
Correct answer & explanation hidden
Log in to view solution →
Q16
MATHS
Unit 13: Statistics and Probability
A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ^2 denote the mean and variance of X, then the value of 64(μ + σ^2) is:
- A. 51
- B. 64
- C. 32
- D. 48
Correct answer & explanation hidden
Log in to view solution →
Q17
MATHS
Unit 1: Sets Relations and Functions
The number of non-empty equivalence relations on the set {1, 2, 3} is:
- A. 6
- B. 5
- C. 7
- D. 4
Correct answer & explanation hidden
Log in to view solution →
Q26
PHYSICS
Unit 11: Electrostatics
An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 10^6 m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron = 9.1 x 10^-31 kg and charge of electron = 1.6 x 10^-19 C)
- B. 1.6 x 10^6 m/s
- C. 1.6 x 10^4 m/s
- D. 1.6 x 10^5 m/s
Correct answer & explanation hidden
Log in to view solution →
Q27
PHYSICS
Unit 12: Current Electricity
Given below are two statements: Statement-I: The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II: The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below.
- A. Both Statement-I and Statement-II are false
- B. Statement-I is false but Statement-II is true
- C. Both Statement-I and Statement-II are true
- D. Statement-I is true but Statement-II is false
Correct answer & explanation hidden
Log in to view solution →
Q28
PHYSICS
Unit 5: Rotational Motion
A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
- A. 7/32 MR^2
- B. 9/32 MR^2
- C. 17/32 MR^2
- D. 13/32 MR^2
Correct answer & explanation hidden
Log in to view solution →
Q29
PHYSICS
Unit 8: Thermodynamics
An amount of ice of mass 10^-3 kg and temperature -10 °C is transformed to vapour of temperature 110 °C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = 2100 J/kg/K, specific heat of water = 4180 J/kg/K, specific heat of steam = 1920 J/kg/K, Latent heat of ice = 3.35 x 10^5 J/kg and Latent heat of steam = 2.25 x 10^6 J/kg)
- A. 3043 J
- B. 3024 J
- C. 3003 J
- D. 3022 J
Correct answer & explanation hidden
Log in to view solution →
Q30
PHYSICS
Unit 18: Atoms and Nuclei
An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 x 10^-11 m while that for the electron in third excited state is 8.48 x 10^-10 m. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is
- A. 3
- B. 16
- C. 9
- D. 4
Correct answer & explanation hidden
Log in to view solution →
Q31
PHYSICS
Unit 4: Work Energy and Power
A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity at the point A, the string becomes slack when the bob reaches at the point D. The ratio of the kinetic energy of the bob at the points A and D is ______.
- A. 1
- B. 2
- C. 4
- D. 3
Correct answer & explanation hidden
Log in to view solution →
Q32
PHYSICS
Unit 16: Optics
Given is a thin convex lens of glass (refractive index mu) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?
- A. R/mu
- B. R/(2mu-3)
- C. mu*R
- D. R/(2mu-1)
Correct answer & explanation hidden
Log in to view solution →
Q33
PHYSICS
Unit 19: Electronic Devices
Which of the following circuits represents a forward biased diode? Choose the correct answer from the options given below :
- A. (A) and (D) only
- B. (B), (D) and (E) only
- C. (C) and (E) only
- D. (B), (C) and (E) only
Correct answer & explanation hidden
Log in to view solution →
Q34
PHYSICS
Unit 12: Current Electricity
Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1 Ohm as shown in the figure. An external resistance of Re = 2 Ohm is connected via the sliding contact. The electric current in the circuit is :
- A. 0.9 A
- B. 1.35 A
- C. 0.3 A
- D. 1.0 A
Correct answer & explanation hidden
Log in to view solution →
Q35
PHYSICS
Unit 6: Gravitation
A small point mass m is placed at a distance 2R from the centre O of a big uniform solid sphere of mass M and radius R. The gravitational force on m due to M is F1. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to the remaining part of M is found to be F2. The value of ratio F1:F2 is:
- A. 12:11
- B. 11:10
- C. 12:9
- D. 16:9
Correct answer & explanation hidden
Log in to view solution →
Q36
PHYSICS
Unit 10: Oscillations and Waves
A closed organ pipe and an open organ pipe are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2, respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1:ρ2 = 1:16, then the length of the open tube is:
- A. 15/7 cm
- B. 20/7 cm
- C. 15/9 cm
- D. 20/9 cm
Correct answer & explanation hidden
Log in to view solution →
Q37
PHYSICS
Unit 13: Magnetic Effects of Current and Magnetism
If B is magnetic field and μ0 is permeability of free space, then the dimensions of (B/μ0) is:
- A. ML^2 T^-2 A^-1
- B. MT^-2 A^-1
- C. L^-1 A
- D. LT^-2 A^-1
Correct answer & explanation hidden
Log in to view solution →
Q39
PHYSICS
Unit 1: Units and Measurements
Given below are two statements: Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.
- A. Statement I is true but Statement II is false
- B. Statement I is false but Statement II is true
- C. Both Statement I and Statement II are false
- D. Both Statement I and Statement II are true
Correct answer & explanation hidden
Log in to view solution →
Q40
PHYSICS
Unit 17: Dual Nature of Matter and Radiation
The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of:
- A. Both Cs and Li
- B. Neither Cs nor Li
- C. Cs only
- D. Li only
Correct answer & explanation hidden
Log in to view solution →
Q41
PHYSICS
Unit 8: Thermodynamics
Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K. If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume effect of the surrounding temperature to be negligible):
- A. 16 E
- B. E
- C. 64 E
- D. 256 E
Correct answer & explanation hidden
Log in to view solution →
Q43
PHYSICS
Unit 16: Optics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason (R): The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below:
↻ Repeated question — also appeared in
2026 (1 set)
- A. Both A and R are true but R is not the correct explanation of A
- B. Both A and R are true and R is the correct explanation of A
- C. A is true but R is false
- D. A is false but R is true
Correct answer & explanation hidden
Log in to view solution →
Q44
PHYSICS
Unit 11: Electrostatics
A parallel-plate capacitor of capacitance 40 μF is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are
- A. 4 mC and 0.2 J
- B. 8 mC and 2.0 J
- C. 2 mC and 0.4 J
- D. 2 mC and 0.2 J
Correct answer & explanation hidden
Log in to view solution →
Q51
CHEMISTRY
Unit 2: Atomic Structure
Radius of the first excited state of Helium ion is given as x times radius of first stationary state of hydrogen atom. The value of x is:
- A. 1
- B. 2
- C. 3
- D. 4
Correct answer & explanation hidden
Log in to view solution →
Q52
CHEMISTRY
Unit 15: Hydrocarbons
The incorrect statements regarding geometrical isomerism are : (A) Propene shows geometrical isomerism. (B) Trans isomer has identical atoms/groups on the opposite sides of the double bond. (C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene. (D) 2-methylbut-2-ene shows two geometrical isomers. (E) Trans-isomer has lower melting point than cis isomer. Choose the correct answer from the options given below:
- A. (A) and (E) Only
- B. (A), (D) and (E) Only
- C. (B) and (C) Only
- D. (C), (D) and (E) Only
Correct answer & explanation hidden
Log in to view solution →
Q53
CHEMISTRY
Unit 4: Chemical Thermodynamics
A liquid when kept inside a thermally insulated closed vessel at 300K was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters?
↻ Repeated question — also appeared in
2026 (1 set)
- A. q = 0, delta U = 0, W = 0
- B. q = 0, delta U > 0, W < 0
- C. q > 0, delta U > 0, W > 0
- D. q < 0, delta U < 0, W > 0
Correct answer & explanation hidden
Log in to view solution →
Q54
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
Which of the following electronegativity order is incorrect?
↻ Repeated question — also appeared in
2026 (1 set)
- A. F > O > N
- B. C > B > Be
- C. P > S > Cl
- D. N > C > B
Correct answer & explanation hidden
Log in to view solution →
Q55
CHEMISTRY
Unit 11: d- and f-Block Elements
Lanthanoid ions with 4f7 configuration are : (A) Eu2+ (B) Gd3+ (C) Eu3+ (D) Tb3+ (E) Sm2+. Choose the correct answer from the options given below:
- A. (A) and (D) only
- B. (B) and (C) only
- C. (A) and (B) only
- D. (B) and (E) only
Correct answer & explanation hidden
Log in to view solution →
Q56
CHEMISTRY
Unit 15: Hydrocarbons
Given below are two statements : Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of hydrogen gas. Statement II : Four g of propyne reacts with sodium to liberate hydrogen gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below:
↻ Repeated question — also appeared in
2026 (1 set)
- A. Statement I is incorrect but Statement II is correct
- B. Both Statement I and Statement II are correct
- C. Statement I is correct but Statement II is incorrect
- D. Both Statement I and Statement II are incorrect
Correct answer & explanation hidden
Log in to view solution →
Q57
CHEMISTRY
Unit 17: Organic Compounds Containing Oxygen
The compounds which give positive Fehling's test are: (A) HOCH2-CO-(CHOH)3-CH2-OH ... [Other structures omitted in text]. Choose the correct answer from the options given below:
- A. (A), (D) and (E) Only
- B. (C), (D) and (E) Only
- C. (A), (C) and (D) Only
- D. (A), (B) and (C) Only
Correct answer & explanation hidden
Log in to view solution →
Q58
CHEMISTRY
Unit 7: Redox Reactions and Electrochemistry
Which of the following electrolyte can be used to obtain H2S2O8 by the process of electrolysis?
- A. Dilute solution of sodium sulphate.
- B. Acidified dilute solution of sodium sulphate.
- C. Dilute solution of sulphuric acid
- D. Concentrated solution of sulphuric acid
Correct answer & explanation hidden
Log in to view solution →
Q59
CHEMISTRY
Unit 16: Organic Compounds Containing Halogens
Given below are two statements: Statement I: CH3-O-CH2-Cl will undergo SN1 reaction though it is a primary halide. Statement II: CH3-O-CH2-Cl will not undergo SN2 reaction very easily though it is a primary halide. In the light of the above statements, choose the most appropriate answer from the options given below:
- A. Both Statement I and Statement II are incorrect
- B. Both Statement I and Statement II are correct
- C. Statement I is incorrect but Statement II is correct
- D. Statement I is correct but Statement II is incorrect
Correct answer & explanation hidden
Log in to view solution →
Q60
CHEMISTRY
Unit 19: Biomolecules
Which of the following acids is a vitamin?
- A. Adipic acid
- B. Ascorbic acid
- C. Saccharic acid
- D. Aspartic acid
Correct answer & explanation hidden
Log in to view solution →
Q61
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
Match List-I with List-II: (A) Al3+ < Mg2+ < Na+ < F- (I) Ionisation Enthalpy (B) B < C < O < N (II) Metallic character (C) B < Al < Mg < K (III) Electronegativity (D) Si < P < S < Cl (IV) Ionic radii
- A. (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
- B. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
- C. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
- D. (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
Correct answer & explanation hidden
Log in to view solution →
Q62
PHYSICS
Unit 18: Atoms and Nuclei
Which of the following statement is not true for radioactive decay?
- A. Decay constant increases with increase in temperature.
- B. Amount of radioactive substance remained after three half lives is 1/8th of original amount.
- C. Decay constant does not depend upon temperature.
- D. Half life is ln2 times of rate constant.
Correct answer & explanation hidden
Log in to view solution →
Q65
CHEMISTRY
Unit 6: Equilibrium
A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of CO2 is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm, then Kp is:
- A. 1.8 atm
- B. 0.3 atm
- C. 3 atm
- D. 0.18 atm
Correct answer & explanation hidden
Log in to view solution →
Q66
CHEMISTRY
Unit 7: Redox Reactions and Electrochemistry
A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A. The amount of the aluminium deposited at the cathode is [Given: molar mass of aluminium is 27 g mol^-1, Faraday constant = 96500 C mol^-1]
↻ Repeated question — also appeared in
2026 (1 set)
- A. 1.660 g
- B. 0.336 g
- C. 0.441 g
- D. 1.007 g
Correct answer & explanation hidden
Log in to view solution →
Q67
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
The IUPAC name of the following compound is:
↻ Repeated question — also appeared in
2026 (1 set)
- A. Methyl-6-carboxy-2,5-dimethylhexanoate
- B. 2-Carboxy-5-methoxycarbonylhexane
- C. 6-Methoxycarbonyl-2,5-dimethylhexanoic acid
- D. Methyl-5-carboxy-2-methylhexanoate
Correct answer & explanation hidden
Log in to view solution →
Q68
CHEMISTRY
Unit 12: Coordination Compounds
In which of the following complexes the CFSE will be equal to zero?
- A. [Fe(en)3]Cl3
- B. K4[Fe(CN)6]
- C. [Fe(NH3)6]Br2
- D. K3[Fe(SCN)6]
Correct answer & explanation hidden
Log in to view solution →
Q69
CHEMISTRY
Unit 5: Solutions
Arrange the following solutions in order of their increasing boiling points: (i) 10^-4 M NaCl (ii) Urea (iii) 10^-3 M NaCl (iv) 10^-2 M NaCl
- A. (i) < (ii) < (iii) < (iv)
- B. (iv) < (iii) < (i) < (ii)
- C. (ii) < (i) < (iii) < (iv)
- D. (ii) < (i) < (iii) < (iv)
Correct answer & explanation hidden
Log in to view solution →
Q70
CHEMISTRY
Unit 12: Coordination Compounds
From the magnetic behaviour of [NiCl4]2- (paramagnetic) and [Ni(CO)4] (diamagnetic), choose the correct geometry and oxidation state.
- A. [NiCl4]2-: tetrahedral, Ni(II); [Ni(CO)4]: square planar, Ni(0)
- B. [NiCl4]2-: square planar, Ni(II); [Ni(CO)4]: square planar, Ni(II)
- C. [NiCl4]2-: tetrahedral, Ni(II); [Ni(CO)4]: tetrahedral, Ni(0)
- D. [NiCl4]2-: tetrahedral, Ni(0); [Ni(CO)4]: square planar, Ni(0)
Correct answer & explanation hidden
Log in to view solution →