Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2023
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In how many ways can the following diagram be colored, subject to: (i) Each of the smaller triangles is to be painted w…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
A person writes letters to 6 friends and addresses the corresponding envelopes.
Let $x$ be the number of ways so that…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The 120 permutations of “MAHES” are arranged in dictionary order,
as if each were an ordinary 5-letter word.
The la…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The values of the parameter $a$ such that the roots $\alpha, \beta$ of
$2x^2 + 6x + a = 0$ satisfy the inequality $\d…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
Number of unimodular complex numbers which satisfy the locus
$\arg\!\left(\dfrac{z - 1}{z + i}\right) = \dfrac{\pi}{2…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The value of $\sin\dfrac{\pi}{16} \sin\dfrac{3\pi}{16} \sin\dfrac{5\pi}{16} \sin\dfrac{7\pi}{16}$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
Find the value of $ \dfrac{1}{\sin 10^\circ} - \dfrac{\sqrt{3}}{\cos 10^\circ} = ? $
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The number of students who take both the subjects’ mathematics and chemistry are 30. This represents 10% of the enrolme…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The domain of the real-valued function
$f(x) = \sqrt{x - 3} + \sqrt{x - 4}$
is the set of all values of $x$ satisfy…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The floor function $[x]$ is
Topic: JAMIA MILLIA ISLAMIA MCA 2023
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2023
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The middle term in the expansion of
$\left(1 + \dfrac{1}{x^2}\right)\!\left(1 + x^2\right)^n$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The sum of the infinite series
$\dfrac{2^2}{2!} + \dfrac{2^4}{4!} + \dfrac{2^6}{6!} + \dfrac{2^8}{8!} + \dots$ is equ…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
If ‘a’ is the arithmetic mean of ‘b’ and ‘c’, and $G_1$ and $G_2$ are the two geometric means between them,
then $G_1…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
For $x \in \mathbb{R}$, find $\displaystyle \lim_{x \to \infty} \left(\dfrac{x - 3}{x + 2}\right)^x = ?$
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The contrapositive of $p \to (\neg q \to \neg r)$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The mean of 100 observations is 50 and their standard deviation is 5.
The sum of squares of all observations is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
A card is drawn from a pack of 52 cards.
A gambler bets that it is a spade or an ace.
What are the odds against his…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
If $Z$ is an idempotent matrix, then $(I + Z)^n$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
If $A^2 - A = 3I$, then $A^{-1}$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The system of linear equations is:
$a + 2b + 3c = 7$
$2a + 4b + c = 12$
$3a + 6b + 4c = 20$
Topic: JAMIA MILLIA ISLAMIA MCA 2023
