Mathematics Mechanical previous year questions with answer

Ques 11 Gate 2023

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The value of k that makes the complex valued function. f(z) = e^–kx [cos2y – i sin2y] analytic:

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Ques 12 Gate 2022 Set-2

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If f(x) = 2ln(√e), what is the area bounded by f(x) for the interval [0, 2] on the x-axis?

A

1/2

B

1

C

2

D

4

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Ques 13 GATE 2022 SET-2

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Consider the following functions for non-zero positive integers, p and q.

Which one of the following options is correct based on the above?

A

f(2,2) = g(2,2)

B

f(g(2,2), 2) < f(2, g(2,2))

C

g(2,1) ≠ f(2,1)

D

f(3,2) > g(3,2)

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Ques 14 GATE 2022 SET-2

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F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?

A

1

B

2

C

3

D

4

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Ques 15 GATE 2022 SET-2

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Consider a cube of unit edge length and sides parallel to coordinate axes, with its centroid at the point (1, 2, 3). The surface integral ∫_A 𝑭⃗ ⋅𝑑𝑨⃗ of a vector field 𝑭⃗ = 3xi + 5yj + 6zk over the entire surface A of the cube is ______.

A

14

B

27

C

28

D

31

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Ques 16 GATE 2022 SET-2

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Consider the definite integral

Let I_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is I_s. The percentage error is defined as e = 100 × (I_e − I_s)/I_e. The value of e is

A

2.5

B

3.5

C

1.2

D

0

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Ques 17 GATE 2022 SET-2

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Given If a and b are positive integers, the value of is ________.

A

√πa

B

(π/a)

C

b√πa

D

b√(π/a)

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Ques 18 GATE 2022 SET-2

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A polynomial φ(s) = a_nsⁿ + a_n-1s^n-1 + ... + a₁s + a₀ of degree n > 3 with constant real coefficients a_n, a_n-1, ... a₀ has triple roots at s = -σ. Which one of the following conditions must be satisfied?

A

φ(s) = 0 at all the three values of s satisfying s² + σ² = 0

B

C

D

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Ques 19 GATE 2022 SET-2

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For the exact differential equation,

, which one of the following is the solution?

A

u² + 2x² = constant

B

xu² + u = constant

C

1/2 x²u²+ 2u = constant

D

1/2 u x² + 2x = constant

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Ques 20 Gate 2022 Set-1

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The average of the monthly salaries of M, N and S is ₹ 4000. The average of the monthly salaries of N, S and P is ₹ 5000. The monthly salary of P is ₹ 6000.What is the monthly salary of M as a percentage of the monthly salary of P?

A

50

B

75%

C

100%

D

125%

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