GATE|| Engineering Mathematics || Calculus || Pyqs (2010 to 2025 )

[ MCQ || GATE 2015 Set-1 || 2 Marks]

Let 𝐿, 𝑀, and 𝑁 be non-singular matrices of order 3 satisfying the equations 𝐿 ² = 𝐿 ⁻¹ , 𝑀 = 𝐿 ⁸ and 𝑁 = 𝐿 ² . Which ONE of the following is the value of the determinant of (𝑀 − 𝑁)? [ MCQ || GATE 2025 Set-2 || 1 Marks]

The value of 𝑥 such that 𝑥 > 1, satisfying the equation

[ MCQ || GATE 2025 Set-2 || 1 Marks]

Let f(x) be a continuous function from ℝ to ℝ such that

f(x) = 1 - f(2-x)

Which one of the following options is the CORRECT value of

[ MCQ || GATE 2024 Set-2 || 1 Marks]

The value of the definite integral

is ______. [ NAT || GATE 2023 || 1 Marks]

Let

f (x) = x³+ 15x² − 33x − 36

be a real-valued function.

Which of the following statements is/are TRUE? [ MSQ || GATE 2023 || 1 Marks]

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]? [ MCQ || GATE 2020 || 1 Marks]

Solve :

[ NAT || GATE 2015 Set-1 || 2 Marks]

Let f(x) = x^–1(1/3) and A denote the area of the region bounded by f(x) and the X-axis, when x varies from –1 to 1. Which of the following statements is/are TRUE?

      (I) f is continuous in [–1, 1]

      (II) f is not bounded in [–1, 1]

      (III) A is nonzero and finite

[ MCQ || GATE 2015 Set-2 || 2 Marks]