Q1
PHYSICS
Unit 1: Units and Measurements
Find the dimensions of 1/μ₀ε₀.
- A. [AL]
- B. [AL⁻¹]
- C. [MAL]
- D. [MALT⁻¹]
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Q1
CHEMISTRY
Unit 12: Coordination Compounds
For complex ion [NiCl4]2– what is the charge on metal and shape of complex respectively?
- A. +2, Tetrahedral
- B. +2, Square planar
- C. +4, Tetrahedral
- D. +4, Square Planar
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Q1
MATHS
Unit 11: Three Dimensional Geometry
The shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-1)/4 and (x-2)/7 = (y-8)/8 = (z-1)/2 is
- A. 88/sqrt(1277)
- B. 78/sqrt(1277)
- C. 66/sqrt(1277)
- D. 55/sqrt(1277)
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Q2
PHYSICS
Unit 6: Gravitation
A solid sphere of mass M and radius R exerts a gravitational force F on a point mass. Now a concentric spherical mass M/7 is removed. What is the new force?
- A. F/7
- B. 6F/7
- C. 5F/7
- D. 3F/7
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Q2
CHEMISTRY
Unit 5: Solutions
Compare boiling point of given solutions: (i) 10–4 M NaCl, (ii) 10–3 M NaCl, (iii) 10–2 M NaCl, (iv) 10–4 M urea.
- A. I > II > III > IV
- B. III > II > I > IV
- C. II > I > III > IV
- D. III > I > II > IV
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Q2
MATHS
Unit 13: Statistics and Probability
In a bag there are 6 white and 4 black balls. If two balls are drawn at random, then the probability that both balls are white is
- A. 1/2
- B. 1/3
- C. 2/3
- D. 1/4
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Q3
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
The correct decreasing order of electronegativity is:
- A. F > Cl > I > Br
- B. Cl > F > Br > I
- C. F > Cl > Br > I
- D. Br > F > I > Cl
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Q3
MATHS
Unit 1: Sets Relations and Functions
Let A = {1, 2, 3}. The number of non-empty equivalence relations on A is
- A. 4
- B. 5
- C. 6
- D. 8
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Q4
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
Which of the following has maximum size out of Al3+, Mg2+, F–, Na+?
- A. Al3+
- B. Mg2+
- C. F–
- D. Na+
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Q4
MATHS
Unit 7: Limit Continuity and Differentiability
If f(x) = (4sec x)^(-2) + (cosec x)^(-2), then the maximum and minimum value of f(x) is
- A. (22π^2/33 + 1001/9)
- B. (22π^2/68 + 1105/17)
- C. (22π^2/59 + 1117/19)
- D. (22π^2/27 + 1268/16)
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Q5
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
The IUPAC name of the given species is:
- A. 2, 3-dimethyl methyl carboxy butanoic acid
- B. 4-methoxy carbonyl-2, 3-dimethyl propanoic acid
- C. 3-methoxycarbonyl-2-methyl butanoic acid
- D. 1-carboxy-2, 3-dimethyl methyl butanoate
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Q5
MATHS
Unit 6: Sequence and Series
If (p/4)^2 + (p/4)^4 + (p/4)^6 + ... + (3/4)^2 + (3/4)^4 + (3/4)^6 + ... = 11/8, then the value of p is
- A. 14/5
- B. 16/5
- C. 3/5
- D. 4/5
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Q6
MATHS
Unit 9: Differential Equations
If (dx/dy) + (x/y) = (y^2/x^3), with x(1) = 1, then x(1/2) equals
- A. 2 - e
- B. 3 - e
- C. 5 - e
- D. 7 - e
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Q7
PHYSICS
Unit 18: Atoms and Nuclei
The radius of an electron in the ground state of hydrogen is a₀. What is the radius of an electron in a He⁺ ion in the 3rd excited state?
- A. 8a₀
- B. 4a₀
- C. 16a₀
- D. 8a₀
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Q7
CHEMISTRY
Unit 6: Equilibrium
Consider the equilibrium reaction CO2(g) + C(s) ⇌ 2CO(g). If initial pressure of CO2 is 0.6 atm and after equilibrium is established, total pressure is 0.8 atm. Then, find Kp.
- A. 0.4
- B. 0.2
- C. 0.6
- D. 0.8
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Q7
MATHS
Unit 6: Sequence and Series
Let Tr = (64)/((2r-1)(2r+1)(2r+3)(2r+5)). Then the limit of sum of Tr as n approaches infinity is equal to
- A. 22/45
- B. 32/35
- C. 27/45
- D. 32/45
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Q7
MATHS
Unit 6: Sequence and Series
Let Tr = (2r-1)(2r+1)(2r+3)(2r+5) / 64, then lim(n->∞) Σ_{r=1}^n (1 / Tr) is equal to
- A. 22/45
- B. 32/35
- C. 27/45
- D. 32/45
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Q8
PHYSICS
Unit 8: Thermodynamics
Ice at –10°C is to be converted into steam at 110°C. Mass of ice is 10⁻³ kg (1g). What amount of heat is required?
- A. ΔQ = 730 cal
- B. ΔQ = 900 cal
- C. ΔQ = 1210 cal
- D. ΔQ = 870 cal
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Q8
CHEMISTRY
Unit 16: Organic Compounds Containing Halogens
Statement-I: CH3–O–CH2–Cl will show nucleophilic substitution by SN1 mechanism in protic medium. Statement-II: CH3–O–CH2–Cl will not undergo nucleophilic substitution via SN2 mechanism easily.
- A. Statement-I and statement-II both are correct
- B. Statement-I and statement-II both are incorrect
- C. Statement-I is correct but statement-II is incorrect
- D. Statement-I is incorrect but statement-II is correct
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Q8
MATHS
Unit 5: Binomial Theorem and its Simple Applications
The coefficient of x^2012 in (1-x)^2008 (1+x+x^2)^2007 is
↻ Repeated question — also appeared in
2025 (1 set)
- B. 1
- C. 2
- D. 3
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Q9
PHYSICS
Unit 11: Electrostatics
A charge of value q is placed at the edge of an imaginary cube of side a. Find the net flux through the cube.
- A. q / (epsilon_0)
- B. q / (8 * epsilon_0)
- C. q / (4 * epsilon_0)
- D. q / (6 * epsilon_0)
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Q9
CHEMISTRY
Unit 19: Biomolecules
Which of the following acids is also known as vitamin C?
- A. Adipic acid
- B. Ascorbic acid
- C. Saccharic acid
- D. Aspartic acid
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Q9
MATHS PAPER 2A
Unit 10: Co-ordinate Geometry
If the images of the points A(1, 3), B(3, 1) and C(2, 4) in the line x + 2y = 4 are D, E and F respectively, then the centroid of the triangle DEF is
- A. (3, -1)
- B. (2/5, -1/5)
- C. (2/5, 1/5)
- D. (1/5, 2/5)
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Q10
PHYSICS
Unit 10: Oscillations and Waves
A closed organ pipe in the 9th harmonic resonates with the 4th harmonic of an open organ pipe (l_closed = 10 cm). Find the length of the open organ pipe.
↻ Repeated question — also appeared in
2025 (1 set)
- A. 80/9 cm
- B. 110/9 cm
- C. 100/9 cm
- D. 15 cm
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Q10
CHEMISTRY
Unit 2: Atomic Structure
An electron of He+ is present in 3rd excited state. Find its de-Broglie wavelength.
- A. 6.64 Å
- B. 1.66 Å
- C. 3.32 Å
- D. 13.28 Å
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Q10
MATHS
Unit 1: Sets Relations and Functions
If A = {1, 2, 3, ..., 10}, B = {(m, n) | m, n ∈ A, m < n and gcd(m, n) = 1}. Then the number of elements in set B is
- A. 30
- B. 31
- C. 28
- D. 29
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Q11
MATHS
Unit 4: Permutations and Combinations
How many ways are there to pick 5 letters from English alphabets such that M is the middle of the letters (repetition not allowed).
- A. 26C5 * 5!
- B. 25C4 * 4!
- C. 26C4 * 4!
- D. 25C5 * 5!
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Q12
PHYSICS
Unit 12: Current Electricity
Which of the following graphs correctly represents the variation of resistivity (ρ) with temperature (T) for a conductor?
- A. Non-linear increase
- B. Linear decrease
- C. Constant
- D. Exponential decrease
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Q12
CHEMISTRY
Unit 11: d- and f-Block Elements
4f7 configuration is possible for: (a) Eu3+, (b) Eu2+, (c) Gd3+, (d) Tb3+, (e) Sm2+
- A. (a) and (c)
- B. (b) and (c)
- C. (d) and (e)
- D. Only (c)
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Q12
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let |Zi| = 1 for i = 1, 2, 3 satisfying Z1Z2^2 + Z2Z3^2 + Z3Z1^2 = a + b√2, where a, b are rational numbers such that arg(Z1/Z2) = π/4, arg(Z2/Z3) = π/4 and arg(Z3/Z1) = -π/2. Find (a, b).
- A. (5, 2)
- B. (-5, -2)
- C. (5, -2)
- D. (-5, 2)
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Q13
PHYSICS
Unit 16: Optics
If the whole YDSE apparatus is immersed in a liquid of refractive index mu, then what is the effect on fringe width?
- A. Fringe width increases
- B. Fringe width decreases
- C. Fringe width remains unchanged
- D. It may increase on one side and decrease on other side
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Q13
MATHS
Unit 13: Statistics and Probability
Let a coin be tossed thrice. Let the random variable x be defined as 'tail follows head'. Let the mean of x be μ and variance be σ^2. Find 64(μ + σ^2).
- A. 48
- B. 64
- C. 132
- D. 128
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Q14
PHYSICS
Unit 8: Thermodynamics
Two spherical black bodies of radius 0.8 m and 0.2 m are at temperatures of 400 K and 800 K respectively. Find the ratio of rate of heat loss (P1/P2).
- A. 8
- B. 4
- C. 2
- D. 1
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Q14
MATHS
Unit 7: Limit Continuity and Differentiability
Let g(x) = f(x/3) + f(3 - x/3) for all x ∈ (0, 3) and f''(x) > 0 for all x ∈ (0, 3), then g(x) decreases in the interval (0, α), then α is
↻ Repeated question — also appeared in
2025 (1 set)
- A. 7/4
- B. 2/3
- C. 9/4
- D. 7/3
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Q15
MATHS
Unit 12: Vector Algebra
Let b_vec = λ*i_cap + 4*j_cap, λ > 0 and the projection vector of b_vec on a_vec = 2*i_cap + j_cap is c_vec. If |a_vec + c_vec| = 7, then the area of the parallelogram formed by vector b_vec and c_vec is (in square units)
- A. 8
- B. 16
- C. 32
- D. 64
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Q15
MATHS
Unit 12: Vector Algebra
Let vector b = λi + 4j + k, λ > 0 and the projection vector of b on vector a = 2i + j - k is c. If |a + c| = 7, then the area of the parallelogram formed by vector b and c is (in square units)
- A. 8
- B. 16
- C. 32
- D. 64
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Q16
PHYSICS
Unit 17: Dual Nature of Matter and Radiation
Light of wavelength 550 nm is incident on surfaces of cerium and lithium. Work functions are 1.9 eV and 2.5 eV respectively. Electron will be ejected from:
- A. Cerium only
- B. Lithium only
- C. From both of them
- D. None of them
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Q16
MATHS
Unit 10: Co-ordinate Geometry
Let the parabola y = x^2 + px - 3 cuts the coordinate axes at P, Q and R. A circle with centre (-1, -1) passes through P, Q and R, then the area of triangle PQR.
- A. 5/2
- B. 3/2
- C. 3
- D. 5
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Q17
PHYSICS
Unit 11: Electrostatics
An electron enters a parallel plate capacitor (length 10 cm, field E = 9.1 N/C) with velocity vx = 10^6 m/s. Find the transverse velocity vy when it exits.
- A. 1.6 * 10^4 m/s
- B. 1.6 * 10^5 m/s
- C. 1.6 * 10^7 m/s
- D. 1.6 * 10^3 m/s
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Q18
MATHS
Unit 10: Co-ordinate Geometry
A hyperbola with foci (1, 14) and (1, -12) passes through the point (1, 6). The length of the latus rectum of the hyperbola is
- A. 144/5
- B. 50
- C. 288/5
- D. 100
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Q21
MATHS
Unit 3: Matrices and Determinants
If A be a 3 × 3 square matrix such that det(A) = -2. If det(3 adj(-6 adj(3A))) = 2^n * 3^m, where m >= n, then 4m + 2n is equal to
- A. 104
- B. null
- C. null
- D. null
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Q22
MATHS
Unit 6: Sequence and Series
If a1, a2, a3..., an are in geometric progression such that a1a5 = 28, a2 + a4 = 29, then the value of a6 is
- A. 635
- B. 784
- C. 872
- D. 898
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