CUET 2026 Mathematics Mock Test 1

Questions in this Mathematics paper

Preview all 10 questions below. Attempt the test to check your answers, see your score and review the solution for each question.

1. If y(x) = det([[sin x, cos x, sin x + cos x + 1], [27, 28, 27], [1, 1, 1]]) for x ∈ R, then d²y/dx² + y equals:

   • A-1
   • B0
   • C1
   • D2

2. Let y = f(x) satisfy dy/dx + (xy)/(x² − 1) = (x⁶ + 4x)√(1 − x²), −1 < x < 1, with f(0) = 0. If 6∫[-1/2 to 1/2] f(x)dx = 2π − α, then α² equals:

   • A25
   • B26
   • C27
   • D28

3. If the system 2x + λy + 3z = 5, 3x + 2y − z = 7, 4x + 5y + μz = 9 has infinitely many solutions, then λ² + μ² equals:

   • A20
   • B24
   • C26
   • D28

4. Let f : R → R be a thrice differentiable odd function satisfying f′(x) ≥ 0, f″(x) = f(x), f(0) = 0, f′(0) = 3. Then 9f(ln 3) equals:

   • A24
   • B30
   • C36
   • D42

5. Let y = y(x) satisfy cos x(log(cos x))² dy + (sin x − 3y sin x log(cos x))dx = 0, x ∈ (0, π/2). If y(π/4) = −1/log 2, then y(π/6) equals:

   • A1/(log 3 − log 4)
   • B1/log 2
   • C1/log 3
   • D1/log 4

6. If f(x) = ∫ dx/[x^(1/4)(1 + x^(1/4))] and f(0) = −6, then f(1) equals:

   • A4(ln 2 − 2)
   • B4(ln 2 − 1)
   • C2(ln 2 − 1)
   • D6(ln 2 − 2)

7. The number of relations on A = {1, 2, 3} containing at most 6 elements including (1,2), that are reflexive and transitive but not symmetric is:

   • A4
   • B5
   • C6
   • D7

8. The number of singular matrices of order 2, whose elements are from the set {2, 3, 6, 9}, is:

   • A32
   • B36
   • C40
   • D44

9. Let a ∈ R and A be a matrix of order 3×3 such that det(A) = −4 and A + I = [[1, a, 1], [2, 1, 0], [a, 1, 2]]. If det((a + 1) adj((a − 1)A)) is 2^m 3^n, then m + n equals:

   • A14
   • B07
   • C18
   • D20

10. Let A = [[log₅128, log₄5], [log₅8, log₄25]]. If Aᵢⱼ is the cofactor of aᵢⱼ, Cᵢⱼ = Σ(aᵢₖAⱼₖ), and C = [Cᵢⱼ], then 8|C| equals:

    • A2³⁸
    • B2⁴⁰
    • C2⁴²
    • D2⁴⁴