BPSC TRE 1 PYQ Quiz – Higher Secondary Teacher Exam Subject Mathematics

#1. If A = {x : x + 1 5, x ∈ N}, then A ∩ B is

{2, 3, 4, 5}

{3, 4, 5, 6}

{1, 2, 4, 6}

More than one of the above

None of the above

Explanation: A = {1,2,3,4,5}, B = {3,4,5,…}, intersection is {3,4,5}.

#2. Let a relation R be defined over the set of non-zero rational numbers Q by aRb, if a = 1/b. Then over Q, this relation R is

reflexive, but not symmetric and transitive

symmetric, but not reflexive and transitive

transitive, but not reflexive and symmetric

More than one of the above

None of the above

Explanation: Symmetric if a=1/b then b=1/a, not reflexive as a≠1/a generally, not transitive.

#3. In how many ways can 5 rings of different types be worn in 4 fingers?

2⁵

3⁵

4⁵

More than one of the above

None of the above

Explanation: Each ring has 4 choices (fingers), so total ways = 4⁵.

#4. The nth roots of unity can be arranged in

an arithmetic progression

a geometric progression

a harmonic progression

More than one of the above

None of the above

Explanation: They are powers of e^(2πi/n), forming a GP.

#5. If (x + iy)¹/³ = a + ib, then x/a + y/b is equal to

4(a² - b²)

a² - b²

a² + b²

More than one of the above

None of the above

Explanation: Cubing and comparing real/imaginary parts gives x/a + y/b = 4(a² – b²).

#6. If the matrix [[5, 8, 6], [3, 2, 4], [1, 7, 9]] is expressed in the form A + B, where A is symmetric and B is skew-symmetric, then the value of B is

[[5, 11/2, 7/2], [11/2, 2, 11/2], [7/2, 11/2, 9]]

Sakshamta Exam 4&5

BPSC TRE 4.0

Karnataka TET 2025

CTET 2025

BPSC TRE Previous Question Paper Quiz

Results

#1. If A = {x : x + 1 5, x ∈ N}, then A ∩ B is

#2. Let a relation R be defined over the set of non-zero rational numbers Q by aRb, if a = 1/b. Then over Q, this relation R is

#3. In how many ways can 5 rings of different types be worn in 4 fingers?

#4. The nth roots of unity can be arranged in

#5. If (x + iy)¹/³ = a + ib, then x/a + y/b is equal to

#6. If the matrix [[5, 8, 6], [3, 2, 4], [1, 7, 9]] is expressed in the form A + B, where A is symmetric and B is skew-symmetric, then the value of B is

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#7. If x + 1/x = 1, then the value of x²⁰⁰⁰ + 1/x²⁰⁰⁰ is

#8. The equation of the circle described on the line joining the points (1, 2) and (1, 3) as diameter is

#9. If z₁ = 2 – i and z₂ = 1 + i, then the value of |(z₁ + z₂ + 1)/(z₁ – z₂ + i)|² is

#10. Which function is not discontinuous at x = 0?

#11. The solution of inequality (4x – 3)/(2x – 5) < 6 is

#12. A line lying in the yz-plane is inclined at an angle α with z-axis. Its direction cosines are

#13. If (2n)! / [3!(2n-3)!] and n! / [2!(n-2)!] are in the ratio 44 : 3, then n is

#14. Writing Lagrange’s mean value theorem as f(b) – f(a) = (b – a)f'(c), a < c < b the value of c, if f(x) = x(x – 1), a = 0, b = 1/2, is

#15. If ⁿPᵣ = ⁿPᵣ₊₁ and ⁿCᵣ = ⁿCᵣ₋₁, then the values of n and r are respectively

#16. The radius of an air bubble is increasing at the rate of 1/2 cm/second. At what rate is the volume of the bubble increasing when its radius is 1 cm?

#17. From 6 boys and 4 girls, 5 students are to be selected for admission to a course. In how many ways can this be done if there must be exactly 2 girls?

#18. Find the points on the curve x²/9 + y²/16 = 1, the tangents at which are parallel to x-axis.

#19. If C₀, C₁, C₂, …, Cₙ are the coefficients in the expansion of (1 + x)ⁿ, then C₁ + 2C₂ + 3C₃ + … + nCₙ is equal to

#20. The radius of the right circular cylinder of maximum curved surface inscribed in a right circular cone of radius r is

#21. For what value of n is (aⁿ⁺¹ + bⁿ⁺¹) / (aⁿ + bⁿ) the geometrical mean of a and b?

#22. The gradient of the normal to the curve y = 2x² + 3sin x at x = 0 is

#23. The sum of three numbers in AP is -3 and their product is 8. The numbers are

#24. An appropriate substitution for the integral ∫ [(1 + x¹/²) / (1 + x¹/³)] dx is

#25. The radius of a circular disc in which an arc of 12π cm subtends an angle of 36° at the centre is

#26. Integrate 1 / [x(xⁿ + 1)] with respect to x.

#27. The value of the determinant [[1, x, y], [0, cos x, sin y], [0, sin x, cos y]] is

#28. The general solution of the differential equation dy/dx = eˣ⁺ʸ + x²eʸ is

#29. The value of tan⁻¹(1/5) + tan⁻¹(1/3) + tan⁻¹(1/7) + tan⁻¹(1/8) is (Note: Image shows tan⁻¹ 1/5 + tan⁻¹ 1/3 + tan⁻¹ 1/7 + tan⁻¹ 1/9, checking common problem types)

#30. Find the differential equation representing the family of curves y = a sin(x + b), where a and b are arbitrary constants.

#31. If sin(π cos θ) = cos(π sin θ), then θ is

#32. The differential equation dy/dx + Py = Qyⁿ where P and Q are functions of x alone, can be reduced to linear form by dividing the equation by yⁿ and putting

#33. If the points (at₁², 2at₁) and (at₂², 2at₂) are the vertices of focal chord of parabola y² = 4ax, then

#34. The general solution of the differential equation sec² y dy/dx + 2x tan y = x³ is

#35. If e₁ and e₂ are eccentricities of the hyperbolas x²/a² – y²/b² = 1 and x²/a² – y²/b² = -1 respectively, then 1/e₁² + 1/e₂² is

#36. The value of î·(ĵ × k̂) + ĵ·(k̂ × î) + k̂·(î × ĵ) is

#37. The function f(x) = |cos x| is

#38. The condition, under which the roots of the cubic equation x³ – px² + qx – r = 0 are in a geometrical progression, is

#39. If the function f(x) = √(1 – √(1 – x²)), then f(x) is

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#40. What is the probability that a leap year, selected at random, will have 53 Sundays?

#41. If y = x³/3 − x⁵/5 + … , then dy/dx is equal to

#42. There are two children in a family. If it is known that at least one of the children is a boy, what is the probability that both the children are boys?

#43. The points A(1, 2, 3), B(1, 1, 1) and C(3, 5, 7) are

#44. Let A and B be independent events. If P(A)=0.3, P(B)=0.4, what is P(A ∩ B)?

#45. The differential coefficient of tan⁻¹(2x/(1−x²)) with respect to sin⁻¹(2x/(1−x²)) is

#46. Which term of the progression 5, √5, 1, … is 1/625?

#47. If y = e^{a cos⁻¹ x}, −1 < x < 1, then the value of (1−x²)d²y/dx² − x dy/dx is

#48. The sum of the roots of the equation x² − 4|x−2| + 4x − 8 = 0 is

#49. The angle between the lines (x−5)/3 = (y−3)/4 = (z−7)/1 and (x−1)/1 = (y−2)/2 = (z−6)/2 is

#50. If the mapping f : ℝ → ℝ is defined by f(x)=x²−6, then what is the value of f⁻¹(2)?

#51. xⁿ dx = xⁿ⁺¹/(n+1) + c is not true, if n is equal to

#52. The value of tan⁻¹√((1−sin x)/(1+sin x)) is

#53. ∫₀^{π/2} (√tan x)/(√tan x + √cot x) dx is

#54. The function sinᵖx cosᑫx has maximum value, when

#55. The differential equation of y = eˣ(Acos x + B sin x) is

#56. The equation of the normal to the ellipse x²/a² + y²/b² = 1 at the point (a cos θ, b sin θ) is

#57. The solution of x dy/dx = y − y² is

#58. If a⃗, b⃗, c⃗ are unit vectors such that a⃗·(b⃗×c⃗)=1/2 b⃗, then the angle which a⃗ makes with c⃗ is

#59. The vector in the direction of vector a⃗ = 3î + ĵ, whose resultant is 5 units, is

#60. A solution of the equation tan⁻¹(2x) − tan⁻¹(3x) = π/4 is

#61. The position vectors of two points A and B are î + ĵ and ĵ + k̂ respectively. If point C divides the line segment AB in the ratio 2:1, then the position vector of C is

#62. If A = [[cos x, sin x],[sin x, cos x]] and A² = I, then the value of x is

#63. If â and b̂ are unit vectors, and the angle between them is θ, then sin(θ/2) is

#64. Which of the following partially ordered sets is a chain?

#65. If a⃗ = 2î+5ĵ+3k̂, b⃗ = 3î+3ĵ+6k̂ and c⃗ = 2î+7ĵ+4k̂, then |(a⃗×b⃗)·(c⃗×a⃗)| is

#66. Three vectors a⃗, b⃗ and c⃗ are such that |a⃗|=3, |b⃗|=4, |c⃗|=5 and each of these is perpendicular to the sum of the other two. What is |a⃗+b⃗+c⃗|?

#67. The coordinates of the foot of the perpendicular drawn from point A(1,2,1) to the line joining the points B(1,4,6) and C(5,4,4) are

#68. The work done by two forces P⃗ = 3î+2ĵ+k̂ and Q⃗ = î+3ĵ+5k̂ in displacing a particle from point A(2î+5k̂) to point B(3î+7ĵ+2k̂) is