GATE EC || MATHEMATICS || PYQs (2000-2025)

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Question 1

What is the value of

em1

?

  • 0

  • e –2

  • e –1/2

  • 1

Question 2

Given i = √-1 what will be the evaluation of the definite integral

em2




  • 0

  • 2

  • -i

  • i

Question 3

Which one of the following functions is continuous at x = 3?



  • em3



  • em4



  • em5



  • em6


Question 4

If

em7


then the value of k is equal to _______.

  • 4

  • 5

  • 6

  • 7

Question 5

A non-zero polynomial f(x) of degree 3 has roots at x = 1, x = 2 and x = 3.  Which one of the following must be TRUE?


  • f(0)f(4) < 0


  • f(0)f(4) > 0

  • f(0) + f(4) > 0

  • f(0) + f(4) < 0

Question 6

The function f(x) = x sin x satisfies the following equation: f’’(x) + f(x) + t cos x = 0. The value of t is _________.

  • -2

Question 7

The value of

EM12


is ?

  • 0

  • ½

  • 1

  • ∞

Question 8

em13


__________.

  • 0.99

  •  1.00

  • 2.00

  •  3.00

Question 9

Consider the functions

I. e–x

II. x2 – sin x

III. √(X3 + 1)

Which of the above functions is/are increasing everywhere in [0, 1] ?

  •  II and III only

  • III only

  •  II only

  • I and III only

Question 10

Consider the following expression.

EM24


The value of the above expression (rounded to 2 decimal places) is______. 



  • 0.25

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