The function $f:[0,3] \to [1,29]$ defined by $f(x) = 2x^3 - 15x^2 + 36x + 1$ is:
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
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A tourist visits four cities A, B, C and D in a random order.
What is the probability that he visits A before B?
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Three letters are dictated to three persons and an envelope is addressed to each of them.
The letters are inserted in…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1,2,6$, the other two ob…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Evaluate $\displaystyle \lim_{x\to 0}\frac{\sqrt{1-\cos 2x}}{x}$.
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Evaluate $\displaystyle \lim_{x\to 0}\left\lfloor \frac{\sin x}{x}\right\rfloor$, where $[;]$ denotes the greatest-inte…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If all words (with or without meaning) formed using letters of “JAMIA” are arranged in dictionary order, what is the 50…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The vertices of a parallelogram $ABCD$ are $A(3,-1,2)$, $B(1,2,-4)$ and $C(-1,1,2)$. The fourth vertex $D$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
A man running a race course notes that the sum of the distances from two flag posts
from him is always $10\,\text{m}$…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If the chord of contact of tangents from a point $P$ to the parabola $y^2 = 4 a x$
touches the parabola $x^2 = 4 b y$…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
From a point on the circle $x^2 + y^2 = a^2$, tangents are drawn to the circle $x^2 + y^2 = b^2$.
The chord of contac…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
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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
If the matrix $A$ is both symmetric and skew-symmetric, then:
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 $a,b,c$ 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 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
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
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
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
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
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
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