Q1
MATHS
Unit 10: Co-ordinate Geometry
Let the domain of the function f(x) = log_5(log_7(log_2(9x - x^2 - 13))) be the interval (m, n). Let the hyperbola x^2/a^2 - y^2/b^2 = 1 have eccentricity n/3 and the length of the latus rectum 8m/3. Then b^2 - a^2 is equal to :
- A. 5
- B. 11
- C. 9
- D. 7
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Q2
MATHS
Unit 8: Integral Calculus
Let f(x) = integral of (e^x / (1+x)^(3/2)) * (1 + (2x/(1-x^2))) dx. If f(0) = 0, then f(1/2) is equal to :
- A. 3e - 1
- B. 2e + 1
- C. 2e - 1
- D. 3e + 1
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Q3
MATHS
Unit 12: Vector Algebra
Let a = i - 2j + k, b = 3j - k, c = a x b, and d = c x a. Then (a - b) . d is equal to :
- A. 4
- B. -4
- C. -2
- D. 2
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Q4
MATHS
Unit 10: Co-ordinate Geometry
A rectangle is formed by the lines x=0, y=0, x=3 and y=4. Let the line L be perpendicular to 3x + y + 6 = 0 and divide the area of the rectangle into two equal parts. Then the distance of the point (-1/2, 5) from the line L is equal to :
- A. 2/5
- B. 3/sqrt(10)
- C. 1/sqrt(10)
- D. 2/sqrt(10)
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Q5
MATHS
Unit 10: Co-ordinate Geometry
Let the line y = x - 1 intersect the ellipse x^2/2 + y^2 = 1 at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :
- A. tan^-1(1/4) - pi
- B. tan^-1(2/4) - pi
- C. 2tan^-1(2/4) + pi
- D. tan^-1(2/4) - pi
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Q6
MATHS
Unit 1: Sets Relations and Functions
Let A = {-2, -1, 0, 1, 2, 3, 4}. Let R be a relation on A defined by xRy if and only if |2x + y| <= 2. Let lambda be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric respectively. Then m + n + lambda is equal to :
- A. 32
- B. 34
- C. 33
- D. 35
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Q7
MATHS
Unit 9: Differential Equations
Let y = f(x) be the solution of the differential equation (x^4 + 3)dy + 4x^3 y dx = 2sin(x)dx, x > 0, y(0) = pi/2. Then f(pi^(1/4)) is equal to :
- A. 81
- B. 92
- C. 64
- D. 72
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Q8
MATHS
Unit 2: Complex Numbers and Quadratic Equations
If alpha and beta (alpha < beta) are the roots of the equation |x-3|^2 - 3|x-3| + 2 = 0, x >= 0, then beta + alpha/beta is equal to :
↻ Repeated question — also appeared in
2026 (1 set)
- A. 8
- B. 9
- C. 10
- D. 11
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Q9
MATHS
Unit 7: Limit Continuity and Differentiability
Let f(x) be defined as (ax^2 + 2ax - 3)/(4x^2 + 4x - 3) for x != -3/2 and (31b)/2 for x = -3/2. If f(x) is continuous at x = -3/2 and f(f(7/5)) = 7/5, then x is equal to:
- A. 2
- B. 1
- D. 1.4
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Q10
MATHS
Unit 8: Integral Calculus
The value of the integral from pi/24 to 5pi/24 of dx / (1 + tan(2x)) is :
- A. pi/12
- B. pi/18
- C. pi/6
- D. pi/3
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Q11
MATHS
Unit 3: Matrices and Determinants
Among the statements: I: If det(M) = 0 where M is a specific 3x3 determinant involving cos terms, then cos^2(alpha) + cos^2(beta) + cos^2(gamma) = 3/2. II: If a given matrix equation holds, then p^2 = 196q. Which is true?
- A. both are false
- B. only II is true
- C. both are true
- D. only I is true
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Q12
MATHS
Unit 4: Permutations and Combinations
The value of 100C50 + 100C51 + ... + 100C100 is:
- A. (101/2) * 2^100
- B. (100/2) * 2^100
- C. (101/2) * 2^101
- D. (1/2) * 2^100
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Q13
MATHS
Unit 13: Statistics and Probability
The mean and variance of 8 numbers: 10, 7, 1, x, y, 9, 2, 16 are 7 and 29/4 respectively. The mean of 4 numbers x, y, x+y+1, x+y-1 is:
- A. 11
- B. 9
- C. 10
- D. 12
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Q14
MATHS
Unit 5: Binomial Theorem and its Simple Applications
The sum of all possible values of n in N such that the coefficients of x, x^2, and x^3 in the expansion of (1+x)^n * (1+x)^n are in arithmetic progression is:
- A. 3
- B. 7
- C. 12
- D. 9
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Q14
MATHS
Unit 5: Binomial Theorem and its Simple Applications
The sum of all possible values of n ∈ N, so that the coefficients of x^2, x^3 and x^4 in the expansion of (1+x)^n(1+x)^n(1+x)^n? No, (1+x)^n * (1+x)^n? Let's clarify the text: (1+x)^n * (1+x)^n. Actually, the text reads (1+x)^n(1+x)^n. Correction based on context: expansion of (1+x)^n * (1+x)^n (often written (1+x)^2n). The text says (1+x)^n * (1+x)^n or similar. Re-reading: 'expansion of (1+x)^n(1+x)^n'. Coefficients of x^2, x^3, x^4 are in A.P.
- A. 3
- B. 7
- C. 12
- D. 9
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Q15
MATHS PAPER 2B
Unit 10: Co-ordinate Geometry
The vertices B and C of a triangle ABC lie on the line (x-1)/1 = (y-z)/2 = (z-2)/3. The coordinates of A and B are (1,6,3) and (4,9,α) respectively and C is at a distance of 10 units from B. The area (in sq. units) of ΔABC is:
- A. 5√13
- B. 15√13
- C. 20√13
- D. 10√13
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Q16
MATHS PAPER 2B
Unit 14: Trigonometry
Number of solutions of 3cos²θ + 8cosθ + 3 = 0, θ ∈ [-π, 2π] is:
- B. 5
- C. 3
- D. 4
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Q17
MATHS
Unit 2: Complex Numbers and Quadratic Equations
Let S = {z : |3z - 3 + i| ≤ 7} be a set of complex numbers. Then min |z + 5 + 3i| is equal to:
- A. 1/2
- B. 3/2
- C. 2
- D. 5/2
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Q18
MATHS PAPER 2B
Unit 7: Limit Continuity and Differentiability
Let α and β respectively be the maximum and minimum values of the function f(θ) = 4(sin⁴(π/4 - θ) + sin⁴(π/4 + θ)) - 6(sin⁶(π/4 - θ) + sin⁶(π/4 + θ)) for θ ∈ R. Then α² + β² is equal to:
- A. 4
- B. 5
- C. 3
- D. 6
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Q19
MATHS
Unit 9: Differential Equations
A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in:
- A. 24 days
- B. 42 days
- C. 30 days
- D. 36 days
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Q20
MATHS
Unit 12: Vector Algebra
Let the direction cosines of two lines satisfy the equations: 4λ + m - n = 0 and 2mn + 10nλ + 3mλ = 0. Then the cosine of the acute angle between these lines is:
- A. 10/38
- B. 20/3√38
- C. 10/7√38
- D. 10/3√38
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Q21
MATHS
Unit 3: Matrices and Determinants
Let |A| = 6, where A is a 3x3 matrix. If (adj(adj(3adj(A)))) = (adj(2A))^n * m, where m, n ∈ N, then m + n is equal to ____.
- A. 60
- B. 62
- C. 64
- D. 66
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Q22
MATHS
Unit 8: Integral Calculus
Let the area of the region bounded by the curve y = max(sin x, cos x), lines x = 0, x = 2π, and the x-axis be A. Then 2A + A is equal to:
- A. 8
- B. 10
- C. 12
- D. 14
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Q24
MATHS
Unit 13: Statistics and Probability
From the first 100 natural numbers, two numbers, first a and then b, are selected randomly without replacement. If the probability that |a - b| ≥ 10 is m/n, where gcd(m, n) = 1, then m + n is equal to ____.
- A. 311
- B. 315
- C. 320
- D. 325
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Q25
MATHS
Unit 4: Permutations and Combinations
The number of 4-letter words, with or without meaning, which can be formed using the letters of the word PQRPQRSTUVP, is ____.
- A. 1422
- B. 1428
- C. 1432
- D. 1438
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Q26
PHYSICS
Unit 16: Optics
A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of the second prism is ____.
- A. 4.5°
- B. 6°
- C. 4°
- D. 5°
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Q27
PHYSICS
Unit 4: Work Energy and Power
A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with vertical. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R. If bob B just manages to complete the circular path of radius R up to a point Q after being hit elastically by bob A, then radius R is:
- A. 3/5
- B. 1/5
- C. (2+√3)/5
- D. (2-√3)/5
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Q28
PHYSICS
Unit 14: Electromagnetic Induction and Alternating Currents
Match List-I with List-II regarding electromagnetic equations and their corresponding laws.
- A. A-II, B-III, C-I, D-IV
- B. A-II, B-III, C-IV, D-I
- C. A-I, B-IV, C-III, D-II
- D. A-IV, B-I, C-II, D-III
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Q29
PHYSICS
Unit 1: Units and Measurements
Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is:
- A. 0.24
- B. 0.18
- C. 0.06
- D. 0.08
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Q30
PHYSICS
Unit 17: Dual Nature of Matter and Radiation
The de Broglie wavelength of an oxygen molecule at 27°C is λ = x * 10^-12 m. The value of x is (Given h = 6.63*10^-34, k = 1.38*10^-23, m = 5.31*10^-26 kg):
- A. 26
- B. 24
- C. 30
- D. 20
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Q31
PHYSICS
Unit 10: Oscillations and Waves
A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is:
- A. 120
- B. 0.75
- C. 7.5
- D. 15
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Q32
PHYSICS
Unit 4: Work Energy and Power
Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B. The energy stored in A is E. The energy stored in B, when spring constants satisfy kA = 4/3 * kB, is:
- A. 4E
- B. 2E
- C. 3E
- D. 4/3 E
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Q33
PHYSICS
Unit 5: Rotational Motion
The moment of inertia of a square loop made of four uniform solid cylinders (radius R, length L) about an axis passing through the mid points of opposite sides (total mass M) is:
- A. 3/8 MR^2 + 7/12 ML^2
- B. 3/4 MR^2 + 1/6 ML^2
- C. 3/4 MR^2 + 7/12 ML^2
- D. 3/8 MR^2 + 1/6 ML^2
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Q34
PHYSICS
Unit 12: Current Electricity
A wire of uniform resistance λ Ω/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (diameter). The equivalent resistance between points A and B is:
↻ Repeated question — also appeared in
2026 (1 set)
- A. 3rλ/8
- B. (π+1)2rλ
- C. 6rλ(π+3) / (16+3π)
- D. 2rπλ
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Q35
PHYSICS
Unit 7: Properties of Solids and Liquids
The strain-stress plot for materials A, B, C, and D is shown in the figure. Which material has the largest Young's modulus?
- A. C
- B. D
- C. A
- D. B
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Q36
PHYSICS
Unit 16: Optics
Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are 2.4 × 10^8 m/s and 2.7 × 10^8 m/s respectively, then the value of critical angle is:
- A. cot^-1(3/13)
- B. sin^-1(9/8)
- C. tan^-1(8/17)
- D. cos^-1(8/9)
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Q38
PHYSICS
Unit 18: Atoms and Nuclei
In hydrogen atom spectrum (R is Rydberg's constant): A. The maximum wavelength of the radiation of Lyman series is 4/(3R). B. The Balmer series lies in the visible region of the spectrum. C. The minimum wavelength of the radiation of Paschen series is 9/R. D. The minimum wavelength of Lyman series is 5/(4R). Choose the correct answer from the options given below:
- A. B, D Only
- B. A, B and C Only
- C. A, B and D Only
- D. A, B Only
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Q40
PHYSICS
Unit 11: Electrostatics
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is:
- A. 3q/ε0
- B. q/ε0
- C. 3q/(2ε0)
- D. 3q/(4ε0)
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Q41
PHYSICS
Unit 14: Electromagnetic Induction and Alternating Currents
A 20 m long uniform copper wire held horizontally is allowed to fall under gravity (g = 10 m/s^2) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire as it travels a vertical distance of 200 m is ______ mV.
↻ Repeated question — also appeared in
2026 (1 set)
- A. 0.2 × 10
- B. 20 × 10
- C. 2 × 10
- D. 200 × 10
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Q42
PHYSICS
Unit 5: Rotational Motion
Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod, then angular velocity of the system about A is:
↻ Repeated question — also appeared in
2026 (1 set)
- A. 2L / (3md^2)
- B. 2L / (md^2)
- C. 4L / (3md^2)
- D. 2L / (5md^2)
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Q43
PHYSICS
Unit 4: Work Energy and Power
In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in °C), if all the heat produced during the collision is retained by these spheres, is: (specific heat of sphere material = 31 cal/kg·°C and 1 cal = 4.2 J)
- A. 1.75
- B. 1.44
- C. 1.15
- D. 1.95
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Q44
PHYSICS
Unit 1: Units and Measurements
In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51, then the correct thickness of the sheet is ____ mm. [Assume least count is 0.01 mm]
- A. 1.50
- B. 1.48
- C. 1.54
- D. 1.51
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Q45
PHYSICS
Unit 13: Magnetic Effects of Current and Magnetism
Given below are two statements: Assertion (A): The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains. Reason (R): At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
- A. (A) is true but (R) is false
- B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
- C. Both (A) and (R) are true and (R) is the correct explanation of (A)
- D. (A) is false but (R) is true
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Q47
PHYSICS
Unit 15: Electromagnetic Waves
The equation of the electric field of an electromagnetic wave propagating through free space is given by E = 377 sin(6.27 * 10^8 t - 2.09 * 10^0 x) N/C. The average power of the electromagnetic wave is 1/α W/m^2. The value of α is ____. (Take ε0μ0 = 1/c^2 in SI units)
- A. 1
- B. 2
- C. 4
- D. 8
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Q48
PHYSICS
Unit 12: Current Electricity
Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for V = 5 sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ____ μF.
- A. 25
- B. 50
- C. 75
- D. 100
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Q49
PHYSICS
Unit 16: Optics
In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are 2 : 1 and 1 : 2 respectively. The corresponding ratio of the distances between the slits and the respective screens (D1 / D2) is ____.
- A. 1
- B. 2
- C. 4
- D. 8
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Q51
CHEMISTRY
Unit 2: Atomic Structure
Which of the following statements regarding the energy of the stationary state is true in the following one-electron system?
- A. -1.09 * 10^-18 J for second orbit of H atom
- B. +2.18 * 10^-18 J for second orbit of He+ ion
- C. +8.72 * 10^-18 J for first orbit of He+ ion
- D. -2.18 * 10^-18 J for third orbit of Li 2+ ion
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Q53
CHEMISTRY
Unit 9: Classification of Elements and Periodicity in Properties
The correct trend in the first ionization enthalpies of the elements in the 3rd period of periodic table is:
- A. Al < Si < S < P < Cl
- B. Al < S < P < Si < Cl
- C. Si < S < Al < P < Cl
- D. S < Si < Al < P < Cl
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Q55
CHEMISTRY
Unit 7: Redox Reactions and Electrochemistry
In the given electrochemical cell, Ag(s) | AgCl(s) | FeCl2(aq), FeCl3(aq) | Pt(s) at 298 K, the cell potential (Ecell) will increase when:
- A. Concentration of Fe2+ is increased.
- B. Concentration of Fe3+ is decreased.
- C. Concentration of Fe2+ is decreased.
- D. Concentration of Cl- is increased.
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Q58
CHEMISTRY
Unit 4: Chemical Thermodynamics
A cup of water at 5°C (system) is placed in a microwave oven and the oven is turned on for one minute during which, the water begins to boil. Which of the following option is true?
- A. q > 0, w = 0, ΔU > 0
- B. q > 0, w < 0, ΔU > 0
- C. q < 0, w < 0, ΔU < 0
- D. q > 0, w < 0, ΔU < 0
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Q59
CHEMISTRY
Unit 12: Coordination Compounds
Given below are two statements: Statement I: [CoBr4]2- ion will absorb light of lower energy than [CoCl4]2- ion. Statement II: In [CoI4]2- ion, the energy separation between the two set of d-orbitals is more than [CoCl4]2- ion. In the light of the above statements, choose the correct answer:
- A. Both Statement I and Statement II are false
- B. Statement I is true but Statement II is false
- C. Statement I is false but Statement II is true
- D. Both Statement I and Statement II are true
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Q60
CHEMISTRY
Unit 15: Hydrocarbons
But-2-yne and hydrogen (one mole each) are separately treated with (i) Pd / C and (ii) Na / liq. NH3 to give the products X and Y respectively. Identify the incorrect statements.
A. X and Y are stereoisomers.
B. Dipole moment of X is zero.
C. Boiling point of X is higher than Y.
D. X and Y react with O3 / Zn, H2O to give different products.
- A. B and C only
- B. B and D only
- C. A and B only
- D. A and C only
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Q61
CHEMISTRY
Unit 2: Atomic Structure
Given: (A) n=5, m=1; (B) n=3, l=2, m=1, s=+1/2. The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are:
↻ Repeated question — also appeared in
2026 (1 set)
- A. 26 and 1
- B. 4 and 1
- C. 2 and 4
- D. 8 and 1
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Q63
CHEMISTRY
Unit 12: Coordination Compounds
The statements that are incorrect about the nickel (II) complex of dimethylglyoxime are:
A. It is red in colour
B. It has a high solubility in water at pH 9
C. The Ni ion has two unpaired d-electrons
D. The N-Ni-N bond angle is almost close to 90 degrees
E. The complex contains four five-membered metallacycles (metal containing rings)
- A. C and E only
- B. A, D and B only
- C. B, C and E only
- D. C and D only
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Q65
CHEMISTRY
Unit 3: Chemical Bonding and Molecular Structure
Identify the molecule (X) with maximum number of lone pairs of electrons (obtained using Lewis dot structure) among HNO3, H2SO4, NF3 and O3. Choose the correct bond angle made by the central atom of the molecule (X).
- A. 120 degrees
- B. 107 degrees
- C. 102 degrees
- D. 116 degrees
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Q66
CHEMISTRY
Unit 13: Purification and Characterisation of Organic Compounds
Match List-I with List-II.
List-I: A. Unsaturation (Baeyer's test), B. Alcoholic group (Ceric ammonium nitrate test), C. Aldehyde group (Tollen's reagent), D. Phenolic group (FeCl3 test)
List-II: I. Red colour appears, II. Silver mirror appears, III. Violet colour appears, IV. Discharge of pink colour
- A. A-III, B-IV, C-II, D-I
- B. A-III, B-IV, C-I, D-II
- C. A-IV, B-I, C-II, D-III
- D. A-IV, B-III, C-II, D-I
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Q67
CHEMISTRY
Unit 20: Principles Related to Practical Chemistry
Given below are two statements:
Statement-I: Sublimation is used for the separation and purification of compounds with low melting point.
Statement-II: The boiling point of a liquid increases as the external pressure is reduced.
In the light of the above statements, choose the correct answer from the options given below:
- A. Statement-I is false but Statement-II is true.
- B. Statement-I is true but Statement-II is false.
- C. Both Statement-I and Statement-II are true.
- D. Both Statement-I and Statement-II are false.
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Q67
CHEMISTRY
Unit 14: Some Basic Principles of Organic Chemistry
Given below are two statements:
Statement-I : Sublimation is used for the separation and purification of compounds with low melting point.
Statement-II : The boiling point of a liquid increases as the external pressure is reduced.
In the light of the above statements, choose the correct answer from the options given below:
- A. Statement-I is false but Statement-II is true.
- B. Statement-I is true but Statement-II is false.
- C. Both Statement-I and Statement-II are true.
- D. Both Statement-I and Statement-II are false.
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Q69
CHEMISTRY
Unit 10: p-Block Elements
The correct statements from the following are:
(A) Ionic radii of trivalent cations of group 13 elements decreases down the group.
(B) Electronegativity of group 13 elements decreases down the group.
(C) Among the group 13 elements, Boron has highest first ionisation enthalpy.
(D) The trichloride and triiodide of group 13 elements are covalent in nature.
Choose the correct answer from the options given below:
- A. A and C only
- B. A and D only
- C. C and D only
- D. B and D only
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Q70
CHEMISTRY
Unit 6: Equilibrium
Consider the general reaction given below at 400 K: xA(g) ⇌ yB(g). The values of Kp and Kc are studied under the same condition of temperature but variation in x and y.
(i) Kp = 85.87 and Kc = 2.586 (appropriate units)
(ii) Kp = 0.862 and Kc = 28.62 (appropriate units)
The value of x and y in (i) and (ii) respectively are:
- A. (i) 3,1 ; (ii) 3,1
- B. (i) 4, 1 ; (ii) 4, 1
- C. (i) 1,3 ; (ii) 2,1
- D. (i) 1, 2 ; (ii) 2, 1
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Q71
CHEMISTRY
Unit 8: Chemical Kinetics
For the thermal decomposition of reaction AB(g) → A(g) + B(g), the following is constructed (graph of [AB] vs time). The half life of the reaction is 'x' min. x = ____ min. (Nearest integer)
- A. 5
- B. 10
- C. 15
- D. 20
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Q73
CHEMISTRY
Unit 1: Some Basic Concepts in Chemistry
x mg of pure HCl was used to make an aqueous solution. 25.0 mL of 0.1M Ba(OH)2 solution is used when the HCl solution was titrated against it. The numerical value of x is ____ x 10^-1. (Nearest integer) Given: Molar mass of HCl and Ba(OH)2 are 36.5 and 171.0 g/mol respectively.
- A. 1825
- B. 182
- C. 365
- D. 912
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Q75
CHEMISTRY
Unit 12: Coordination Compounds
The crystal field splitting energy of [Co(oxalate)3]^-3 complex is 'n' times that of the [Cr(oxalate)3]^-3 complex. Here 'n' is ____. [Assume ΔP = 0]
- A. 1
- B. 2
- C. 3
- D. 4
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