GATE Engineering Mathematics & Analytical Skills 1

Question 1

What is the derivative of sin(x)?

Accepted Answer

cos(x)

Answer

-sin(x)

Answer

-cos(x)

Answer

sin(x)

Question 2

Which matrix operation results in a change in the determinant's sign?

Accepted Answer

Swapping two rows

Answer

Scaling a row

Answer

Adding a row to another

Answer

Multiplying a row by 0

Question 3

What is the Laplace transform of 1?

Accepted Answer

1/s

Answer

s

Answer

s^2

Answer

s+1

Question 4

If A is an invertible matrix, what is the determinant of A inverse?

Accepted Answer

1/det(A)

Answer

det(A)

Answer

det(A)^2

Answer

-det(A)

Question 5

Which of the following is a second-order differential equation?

Accepted Answer

d²y/dx² = 3x

Answer

dy/dx = x^2

Answer

y = mx + c

Answer

∫x dx

Question 6

What is the probability of getting a sum of 7 when two dice are thrown?

Accepted Answer

1/6

Answer

1/12

Answer

1/8

Answer

1/10

Question 7

Which numerical method is used for solving ordinary differential equations?

Accepted Answer

Runge-Kutta method

Answer

Gaussian Elimination

Answer

Newton-Raphson method

Answer

Simpson’s Rule

Question 8

What is the general solution of a homogeneous linear differential equation?

Accepted Answer

Sum of complementary function and particular solution

Answer

Only particular solution

Answer

Only complementary function

Answer

Zero always

Question 9

In probability, what does a cumulative distribution function (CDF) represent?

Accepted Answer

Cumulative probability up to a value

Answer

Probability mass

Answer

Probability density

Answer

Mean of a distribution