Q1
PHYSICS
Unit 16: Optics
An equiconvex lens of focal length f, is cut into four parts as shown in the diagram. The focal length of each part is
- A. f
- B. 2f
- C. f/2
- D. 4f
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Q2
MATHS PAPER 2B
Unit 14: Trigonometry
If θ ∈ [0, 2π] satisfying the system of equations 2sin^2 θ = cos 2θ and 2cos^2 θ = 3sin θ. Then the sum of all real values of θ is
- A. π/2
- B. π
- C. 3π/2
- D. 2π
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Q2
PHYSICS
Unit 7: Properties of Solids and Liquids
Radius of a tube decreases from 2R to R in which ideal liquid is flowing at same level. Speed at one end is 2 m/s as shown, find speed v at other end.
- A. 4 m/s
- B. 1 m/s
- C. 2 m/s
- D. 8 m/s
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Q2
CHEMISTRY
Unit 5: Solutions
Density of 3 M NaOH is 1.25 g/ml. Molality of solution is
- A. 2.65
- B. 2.5
- C. 2.8
- D. 3
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Q3
MATHS
Unit 1: Sets Relations and Functions
Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16}. If f : A → B, the number of many-one functions from A to B is
- A. 24
- B. 232
- C. 256
- D. 252
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Q3
PHYSICS
Unit 11: Electrostatics
The dimensional formula of capacitance is
- A. [M^-1L^2T^2A^-3]
- B. [M^-1L^-2T^4A^3]
- C. [M^-1L^-2T^4A^2]
- D. [M^-1L^-2T^2A^2]
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Q3
CHEMISTRY
Unit 12: Coordination Compounds
Arrange according to CFSE:
(i) [Co(NH3)4]2+
(ii) [Co(NH3)6]3+
(iii) [Co(NH3)6]2+
(iv) [Co(en)3]3+
- A. (iv) > (ii) > (iii) > (i)
- B. (iv) > (iii) > (ii) > (i)
- C. (i) > (iii) > (ii) > (iv)
- D. (i) > (ii) > (iii) > (iv)
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Q4
MATHS
Unit 4: Permutations and Combinations
4 boys and 3 girls are to be seated in a row such that all girls seat together and two particular boys B1 and B2 are not adjacent to each other. Then the number of ways in which this arrangement can be done.
- A. 432
- B. 430
- C. 516
- D. 1002
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Q6
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
Compare dipole moment of (I) NF3, (II) CHCl3, (III) H2S, (IV) HBr
- A. I > II > III > IV
- B. II > III > I > IV
- C. II > III > IV > I
- D. III > I > IV > II
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Q7
CHEMISTRY
Unit 20: Principles Related to Practical Chemistry
Given below are two statements:
S-I: Lassaigne test is used for detection of Nitrogen, phosphorous, sulphur and Halogens.
S-II: Lassaigne extract is made with magnesium metal.
- A. Both S-I and S-II are correct.
- B. Both S-I and S-II are incorrect.
- C. S-I is correct but S-II is incorrect.
- D. S-I is incorrect but S-II is correct.
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Q8
MATHS
Unit 6: Sequence and Series
Number of terms in an arithmetic progression is 2n. Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then n equals
- A. 3
- B. 5
- C. 7
- D. 4
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Q8
PHYSICS
Unit 16: Optics
Statement-I : Fringe width of red light is more than fringe width of violet light. Statement-II : Fringe width is directly proportional to the wavelength of light used. Choose the correct option.
- A. Statement-I is correct and statement-II is incorrect
- B. Both statement-I and statement-II are correct
- C. Statement-I is incorrect and statement-II is correct
- D. Both statement-I and statement-II are incorrect
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Q8
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
Which one has two secondary Hydrogen atoms?
- A. 2, 2, 4, 4-tetramethylheptane
- B. 2, 2, 3, 4-tetramethylheptane
- C. 2, 2, 3, 3-tetramethyloctane
- D. 3-ethyl-2, 2-dimethylpentane
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Q9
PHYSICS
Unit 9: Kinetic Theory of Gases
For non-vibrating diatomic gas has adiabatic constant of γ1 & for vibrating diatomic gas has adiabatic constant of γ2 then
- A. γ1 > γ2
- B. γ1 < γ2
- C. γ1 = γ2
- D. None of these
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Q10
MATHS
Unit 5: Binomial Theorem and its Simple Applications
In the expansion of (x^5 + x^3 - 1)^5, let alpha, beta, gamma, and delta be the coefficients of x, x^3, x^5, and x^7 respectively. If alpha*u - beta*v = 18 and gamma*u + delta*v = 20, then u + v is equal to:
- A. 1/3
- B. 2/3
- C. 1
- D. 4/3
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Q10
CHEMISTRY
Unit 1: Some Basic Concepts in Chemistry
200 mL of 0.2 M solution of NaOH is mixed with 400 mL of 0.5 M NaOH solution. Molarity of mixture is
- A. 0.4
- B. 0.6
- C. 4 M
- D. 0.8 M
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Q11
MATHS PAPER 2B
Unit 10: Co-ordinate Geometry
Let A(6, 8), B(10*cos(alpha), -10*sin(alpha)) and C(-10*sin(alpha), -10*cos(alpha)) be 3 points. If the orthocentre of triangle ABC is (0, 9), then 100*sin^2(alpha) is equal to:
- A. 25
- B. 100
- C. 50
- D. 75
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Q12
PHYSICS
Unit 6: Gravitation
Statement I: A pendulum is taken from Earth to another planet having mass four times and radius double than earth, then time period of pendulum remain same as on earth. Statement II: The time period of pendulum only depends on the gravity of the planet.
- A. Statement I is true but statement II is false.
- B. Statement II is true but statement I is false.
- C. Both statements are false.
- D. Both statements are true.
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Q12
CHEMISTRY
Unit 4: Chemical Thermodynamics
Identify the extensive and intensive property.
- A. Mass, volume, conductivity – Intensive property
- B. Mass, temperature, heat, volume – Extensive property
- C. Mass, volume, internal energy – Extensive property
- D. Density, temperature, moles, internal energy – Intensive property
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Q13
MATHS
Unit 1: Sets Relations and Functions
A relation R is defined on set A = {1, 2, 3} and R = {(1, 2), (2, 3)}. Elements are added such that R becomes reflexive and transitive but not symmetric. Find the number of such relations.
- A. 3
- B. 4
- C. 2
- D. 9
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Q13
CHEMISTRY
Unit 10: p-Block Elements
Among Group-15 elements, what is the maximum covalency of an element having weakest E–E bond (E = element)?
↻ Repeated question — also appeared in
2022 (1 set)
- A. 4
- B. 3
- C. 5
- D. 2
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Q16
CHEMISTRY
Unit 7: Redox Reactions and Electrochemistry
Consider the following statements S-1 and S-2 and choose the correct option.
S-1 : During corrosion, pure metal acts as anode and impure metal acts as cathode.
S-2 : Rate of corrosion is more in alkaline medium than in acidic medium.
- A. Both S-1 and S-2 are correct
- B. Both S-1 and S-2 are incorrect
- C. S-1 is correct but S-2 is incorrect
- D. S-1 is incorrect but S-2 is correct
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Q21
CHEMISTRY
Unit 11: d- and f-Block Elements
In Ru (Ruthenium) and Nb (Niobium), if in Ru, 4d electrons are x and in Nb, 4d electrons are y, then find the sum of x and y.
- A. 10
- B. 11
- C. 12
- D. 9
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Q22
MATHS
Unit 3: Matrices and Determinants
If A is a 3x3 matrix such that det(A) = 1, tr(A) = 10, and B is a matrix defined as B = adj(adj(2A)), then det(B) + tr(B) is equal to:
- A. 336
- B. 256
- C. 80
- D. 160
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Q24
MATHS PAPER 2B
Unit 10: Co-ordinate Geometry
The number of maximum number of common tangents to the curves y = (x - 2)^2 and y^2 = 16 - 8x is
- A. 1
- B. 2
- C. 3
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Q25
CHEMISTRY
Unit 2: Atomic Structure
Calculate the radius of the first excited state of the He⁺ ion (in Å).
- A. 1.058
- B. 0.529
- C. 2.116
- D. 0.264
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Q25
MATHS PAPER 2B
Unit 11: Three Dimensional Geometry
Let P(10, -2, -1) and Q be the point of perpendicular drawn from point R(1, 7, 6) on the line joining the points (2, -5, 11) and (-6, 7, -5). Then the length PQ is
- A. 13
- B. 12
- C. 14
- D. 11
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