GUJCET 2024 Mathematics Question Paper (Available)- Download Solution PDF with Answer Key

Global maximum value of function f(x) = sin x + cos x, x∈ [0, π] is:

• (1) 1
• (2) 2
• (3) √2
• (4) 0

If x = a(1 − cos θ), y = a(0 + sin 0), then dy/dx is:

• (1) tan θ/2
• (2) cos θ/2
• (3) cot θ/2
• (4) sin θ/2

Evaluate ∫ e^2x/(e^2x+1) dx.

• (1) log(e^2x) + C
• (2) log(e^2x + 1) + C
• (3) log(e^2x + 1) - x + C
• (4) x - log(e^2x + 1) + C

Evaluate the integral ∫ e^x * (1+sin(x)) / (1-sin(x)) dx.

• (1) e^x tan (x) + C
• (2) e^x tan (x/2) + C
• (3) e^x sin (x/2) + C
• (4) 2e^x tan (x/2) + C

Evaluate the integral ∫ 1/√(4x - x²) dx.

• (1) sin^-1 (x) + C
• (2) sin^-1 (x/2) + C
• (3) cos^-1 (x/2) + C
• (4) sin^-1 ((x-2)/2) + C

If |2017 2018| + |2021 2022| = 2k, find k³. |2019 2020| |2023 2024|

• (1) 4
• (2) -4
• (3) 8
• (4) -8

If the area of △PQR with vertices P(k, 1), Q(2, 4), R(1, 1) is 3 square units, find k.

• (1) -1
• (2) 3
• (3) -1,3
• (4) 1,3

If A = |0 0 -1|, |0 -1 0|, |-1 0 0|, find I + A², where I is the identity matrix.

• (1) I
• (2) A
• (3) 2I
• (4) 0

If the value of cos α is √3/2 , then A + A' = I, where A = |sin α -cos α|, |cos α sin α|

• (1) √3/2
• (2) 1/2
• (3) 1
• (4) 0

If A is a square matrix such that A² = A, then (I – A)³ – (I + A)² =

• (1) A - I
• (2) I - 2A
• (3) 2(I - 2A)
• (4) 2(I - A)

Find sin⁻¹(sin(23π/6)).

• (1) 23π/6
• (2) -π/6
• (3) π/6
• (4) 11π/6

The value of tan⁻¹(-1) + sec⁻¹(-2) + sin⁻¹(1/√2) is:

• (1) 3π/4
• (2) 5π/12
• (3) 3π/2
• (4) 2π/3

If y = tan⁻¹ x, then

• (1) 0 ≤ y ≤ π
• (2) -π/2 < y < π/2
• (3) 0 < y < π
• (4) -π/2 ≤ y ≤ π/2

If f : Z → Z, defined by f(x) = x³ + 2, then the function f is

• (1) one-to-one
• (2) onto
• (3) both one-to-one and onto
• (4) neither one-to-one nor onto

The relation R = {(a, a), (b, b), (c, c), (a, c)} defined on the set {a, b, c} is

• (1) Reflexive
• (2) Symmetric
• (3) Transitive
• (4) spontaneous, traditional, but not conformist.

If P(B) ≠ 0 and P(A|B) = 1 for two events A and B, then

• (1) A ⊂ B
• (2) A = B
• (3) B ⊂ A
• (4) A ∩ B = φ

If a pair of dice is thrown, the probability of getting an even prime number on each die is

• (1) 1/6
• (2) 1/36
• (3) 1/12
• (4) 1/3

Given events A and B are absolute and P(A) = p, P(B) = ½, and P(AUB) = ⅗, the value of p is

• (1) 1/10
• (2) 1/5
• (3) 6/10
• (4) 1/6

If x + y < 55 and x + y ≥ 10, with x ≥ 0, y ≥ 0, then the minimum value of the objective function z = 7x + 3y is:

• (1) 0
• (2) 30
• (3) 55
• (4) Solution region is not feasible, so not found.

If the vertices of the finite feasible solution region are (0, 6), (3, 3), (9, 9), (0, 12), then the maximum value of the objective function z = 6x + 12y is

• (1) 72
• (2) 54
• (3) 144
• (4) 162