GATE PYQ

Engineering Mathematics

Q31.
Which one of the following functions is continuous at x = 3?

Q32.
Consider the function f(x)=sin(x) in the interval x \in [\pi/4, 7\pi/4]. The number and location(s) of the local minima of this function are

Q33.
The weight of a sequence a_{0},a_{1},...,a_{n-1} of real numbers is defined as a_{0}+a_{1}/2+...+a_{n-1}/2^{n-1} A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of a_{0},a_{1},...,a_{n-1}. Then X is equal to

Q34.
What is the value of \lim_{n\rightarrow \infty }(1-\frac{1}{n})^{2n}?

Q35.
The formula \int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n-1} + y_n) - h/12 (\triangledown y_n - \triangle y_0) - h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) -19h/720 (\triangledown ^3 y_n - \triangle ^3 y_0) \dots is called

Q36.
x=a \cos(t), y=b \sin(t) is the parametric form of

Q37.
Given i=\sqrt{-1}, what will be the evaluation of the definite integral \int_{0}^{\pi /2}\frac{cosx + i sinx}{cosx -i sinx} dx?

Q38.
\int_{0}^{\pi /4}(1-tanx)/(1+tanx)dx evaluates to

Q39.
Which of the following statement is correct

Q40.
If f(x) is defined as follows, what is the minimum value of f(x) for x \in (0, 2] ? f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}