GATE 2026 ST – Question 11
Let p(t)=t(t−1)(t−2) and $F(x)=\int_{1/2}^x1/p(t)dt$,1/2≤x<1. Which holds?
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Correct answer: (B) F is strictly increasing.
Explanation
For 1/2≤t<1, t>0,t−1<0,t−2<0, so p(t)>0 and F′(t)=1/p(t)>0. Hence **B**. Near 1, p(t) behaves as 1−t and the integral diverges to +∞, so C is false under the finite-limit convention. Also p(3/4)=15/64, giving F′=64/15 rather than 1.