GATE Calculus: Single Variable Calculus – Previous Year Questions
11 GATE previous year questions on Single Variable Calculus (Calculus, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q36 – Define f:ℝ→ℝ by f(x)=x³sin x if x=0 or x is irrational,and f(p/q)=1/q³ for nonzero reduced rational p/q,q∈ℕ. Which holds?
- GATE 2021 ST Q37 – For f:[0,∞)→ℝ,which statement is true?
- GATE 2021 ST Q38 – A differentiable f:ℝ→ℝ satisfies f(0)=0 and f′(x)+2f(x)>0 for all x. Which holds?
- GATE 2022 ST Q50 – Which real functions are uniformly continuous on [0,∞)?
- GATE 2023 ST Q43 – Let g(x)=f(x)+f(2−x) on [0,2],where f is continuous on [0,2] and twice differentiable inside. Which statement is NOT true?
- GATE 2024 ST Q47 – Continuous f:[−2,2]→ℝ satisfies which statements?
- GATE 2025 ST Q11 – Differentiable f:[0,∞)→[0,∞) has f(0)=0,f(x)>0 for x>0, and f(x)2= 0x[f(t)2+f(t)]dt. Which range contains f(2)?
- GATE 2025 ST Q36 – Let F be all real functions continuous on [a,b] and differentiable on (a,b). Which is correct?
- GATE 2026 ST Q11 – Let p(t)=t(t−1)(t−2) and F(x)= 1/2x1/p(t)dt,1/2≤x<1. Which holds?
- GATE 2026 ST Q12 – Differentiable f:(−1,1)→ℝ satisfies: I:if f(0)≥0 and f′(x)>0 at every nonnegative zero, then f(x)>0 for x>0. II:if f(0)≤0 and f′(x)>0 at every…
- GATE 2026 ST Q24 – Evaluate nn 1-1/(2n)1+1/(2n)et2-1dt (integer).