The points of extremum of the function $f(x) = \displaystyle \int_0^x e^{t^2} (1 - t^2)\,dt$ are:
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
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Let $f(x) = (x^3 + a x^2 + b x + 5\sin^3 x)$ be increasing for all $x \in \mathbb{R}$.
Then $a$ and $b$ satisfy:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $m$ is the slope of tangent at any point on the curve $e^y = 1 + x^x$, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $\displaystyle \lim_{x \to \infty} \left(1 + \frac{a}{x} + \frac{b}{x^2}\right)^{2x} = e^2$,
then values of $a$ an…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Number of points at which the function $f(x) = \min(|x|, |x+1|, |x-4|)$
is not differentiable is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Consider two functions $f(x)$ and $g(x)$ such that
$f(x) = |x| + [x]$ and $g(x) = |x|[x]$,
where $[x]$ denotes the …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If a determinant of order $3\times3$ is formed using numbers $1$ or $-1$,
then the minimum value of the determinant i…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $a,b,c$ are in A.P., then the value of determinant
$\begin{vmatrix}
x+2 & x+3 & x+2a \\
x+3 & x+4 & x+2b \\
x+4 & …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $A = \begin{bmatrix} 3 & -9 \\ -12 & 6 \end{bmatrix}$,
then $\operatorname{adj}(3A + 12A^2)$ is equal to:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If the matrix $A$ is both symmetric and skew-symmetric, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $f:\mathbb{R}\to\mathbb{R}$ is given by $f(x) = (3 - x^3)^{1/3}$,
then $f(f(f(f(x))))$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
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Value of $\displaystyle \int e^{x^2} \left( \frac{1}{x} - \frac{1}{2x^2} \right) dx$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Value of $\displaystyle \int_{0}^{\frac{\pi}{2}} (x^3 + x\cos x + \tan^3 x + 1) dx$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
$\displaystyle \int \frac{d\theta}{1 - \tan\theta}$ equals:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Distance between the two planes
$2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
A man known to speak truth $3$ out of $4$ times throws a die and reports that it is a six.
The probability that it is…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The probability of shooter hitting a target is $\dfrac{3}{4}$.
Find the minimum number of shots required so that the …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $A$ and $B$ are independent events such that $P(A) = 0.3$, $P(B) = 0.6$,
then $P(\text{neither A nor B})$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Period of the function $f(x) = \cos\left(\dfrac{2x}{3}\right) - \sin\left(\dfrac{4x}{5}\right)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Which of the following is not an indeterminate form?
Topic: JAMIA MILLIA ISLAMIA MCA 2019
