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Question 1
[ MCQ || GATE 2015 Set-1 || 2 Marks]
h(x) / g(x)
–1/x
g(x) / h(x)
x/(1–x)2
Question 2
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]
0
1
2
3
Question 3
The value of 𝑥 such that 𝑥 > 1, satisfying the equation
[ MCQ || GATE 2025 Set-2 || 1 Marks]
√e
e
𝑒2
𝑒 − 1
Question 4
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]
0
1
2
−1
Question 5
The value of the definite integral
is ______. [ NAT || GATE 2023 || 1 Marks]
0
Question 6
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]
f(x) does not have a local maximum.
f(x) has a local maximum
f(x) does not have a local minimum.
f(x) has a local minimum.
Question 8
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]
II and III only
III only
II only
I and III only
Question 10
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]
II only
III only
II and III only
I, II and III
There are 22 questions to complete.
