GATE ES area:engineering-mathematics PYQs & Answers — Page 3

Questions 21–30 of 57. Imported answers require independent review unless marked reviewed.

Topic practice 57 questionsPage 3 of 6

The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one boy?

Your answerChoose one option.

3/8

1/8

1/4

1/2

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Ten cards in a pack are numbered as 1, 2, 3, . . .10. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is ______.

Your answerChoose one option.

4/10

6/10

2/10

3/10

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The eigen values of the matrix

are

Your answerSelect all correct options. You can choose more than one.

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If X is a vector, and A and B are linear operators, then the correct mathematical relation(s) is/are

Your answerSelect all correct options. You can choose more than one.

(A+B)X = AX + BX

(λA)X = λ(AX)

(AB)X = A(BX)

(A+B)X = AᵀX+BᵀX

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has a local maximum at x = ______ (an integer value) in the range x = −2 to +2.

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Consider the equation

; with y = 1 at x = 0.

The value of y at x = 1 is ______ (rounded off to 2 decimal places).

Take the value of e (base of natural logarithm) as 2.7.

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A population (with mean

) follows normal distribution. Ten samples (N) are drawn at random with a mean value of “x” and standard deviation of “S”. Following table provides the confidence limits, C(t) of the cumulative probability function for Student’s t – distribution two-tailed test with degree of freedom D.

Which one of the following expression is correct for testing the null hypothesis H₀:

at 10% significance level?

D	C(t)=0.9	C(t)=0.95	C(t)=0.975
9	1.38	1.83	2.26
10	1.37	1.81	2.23
11	1.36	1.80	2.20

Your answerChoose one option.

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Which one is the solution y(x) for the following ordinary differential equation and the specified boundary conditions?

Your answerChoose one option.

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Consider the function

Expand f(x+h) using Taylor’s series. In this context, the correct statement(s) is/are

Your answerSelect all correct options. You can choose more than one.

Second term in the Taylor’s series i.e., the term which includes h is:

First term is

Third term in the Taylor’s series i.e., the term which includes

is:

Third term in the Taylor’s series i.e., the term which includes

is:

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Consider the equation for a curve,

The area enclosed by the curve, the

-axis (

line); the vertical lines passing through

and

is ______ (rounded off to 2 decimal places)

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GATE ES area:engineering-mathematics PYQs

Question 7

Question 11

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Question 32

Question 33

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Question 37

Question 42

Question 49