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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&1&1&0&1&1&1&0&0.8&1
\\\hline\textbf{2 Marks Count}&0&0&1&0&0&0&0&0.2&1
\\\hline\textbf{Total Marks}&1&1&2&1&1&1&\bf{1}&\bf{1.2}&\bf{2}\\\hline
\end{array}}}$$

Recent questions in Calculus

26 votes
1 answer
1
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where a $a \neq b \text{ then } \int_1^2 f(x)dx$ is $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
asked Feb 16, 2015 in Calculus jothee 3.8k views
23 votes
5 answers
2
The value of $\lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
asked Feb 14, 2015 in Calculus jothee 6k views
16 votes
2 answers
3
Compute the value of: $\large \int_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
asked Feb 13, 2015 in Calculus makhdoom ghaya 3.6k views
35 votes
7 answers
4
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
asked Feb 12, 2015 in Calculus jothee 7.7k views
23 votes
4 answers
5
Consider a function $f(x) = 1- |x| \text{ on } -1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, -1$ $-1, 0$ $0, 1$ $-1, 2$
asked Feb 12, 2015 in Calculus jothee 3k views
16 votes
5 answers
6
$\lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is $\infty $ 0 1 Not defined
asked Feb 11, 2015 in Calculus makhdoom ghaya 3.9k views
1 vote
2 answers
7
A. 1 B. 2 C. 3 D. 4
asked Feb 4, 2015 in Calculus Vikrant Singh 547 views
0 votes
1 answer
8
If $\int \limits_0^{2 \pi} |x \: \sin x| dx=k\pi$, then the value of $k$ is equal to ______.
asked Feb 3, 2015 in Calculus eppshankar 111 views
0 votes
1 answer
9
Evaluate
asked Jan 30, 2015 in Calculus Nisha kumari 176 views
0 votes
1 answer
10
The order and degree of the differential equation (A) 3 and 2 (B) 2 and 3 (C) 3 and 3 (D) 3 and 1
asked Jan 30, 2015 in Calculus Nisha kumari 605 views
12 votes
4 answers
11
What is the value of $\int_{0}^{2\pi}(x-\pi)^2 (\sin x) dx$ $-1$ $0$ $1$ $\pi$
asked Nov 3, 2014 in Calculus Ishrat Jahan 2.8k views
16 votes
3 answers
12
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} \text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} \text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
asked Oct 29, 2014 in Calculus Ishrat Jahan 3.6k views
18 votes
2 answers
13
Let $f$ be a function defined by $f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$ Find the values for the constants $a$, $b$, $c$ and $d$ so that $f$ is continuous and differentiable everywhere on the real line.
asked Oct 9, 2014 in Calculus Kathleen 2.2k views
15 votes
3 answers
14
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h) - f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 – h)}{h^2}$
asked Oct 9, 2014 in Calculus Kathleen 3.1k views
11 votes
1 answer
15
Find the minimum value of $3-4x+2x^2$.
asked Oct 8, 2014 in Calculus Kathleen 1.3k views
1 vote
1 answer
16
The solution of differential equation $y''+3y'+2y=0$ is of the form $C_1e^x+C_2e^{2x}$ $C_1e^{-x}+C_2e^{3x}$ $C_1e^{-x}+C_2e^{-2x}$ $C_1e^{-2x}+C_2e^{-x}$
asked Oct 8, 2014 in Calculus Kathleen 482 views
18 votes
2 answers
17
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solution Exactly one solution Exactly two solutions An infinite number of solutions
asked Oct 8, 2014 in Calculus Kathleen 2.5k views
7 votes
4 answers
18
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
asked Sep 29, 2014 in Calculus Kathleen 2.9k views
18 votes
5 answers
19
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
asked Sep 29, 2014 in Calculus jothee 4.2k views
23 votes
4 answers
20
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $-2\pi$ $\pi$ $-\pi$ $2\pi$
asked Sep 28, 2014 in Calculus jothee 3.3k views
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