The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all observations is —
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2023
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The contrapositive of $p \to (\neg q \to \neg r)$ is —
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
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
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
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 tens digit of $1! + 2! + 3! + 4! + \dots + 49!$ is —
Topic: JAMIA MILLIA ISLAMIA MCA 2023
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
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2023
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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
$Q30.$ If the rank of the matrix
\[
\begin{bmatrix}
a & 0 & 0 \\
0 & b & 0 \\
0 & 0 & c
\end{bmatrix}
\]
is $2$, then …
Topic: JAMIA MILLIA ISLAMIA MCA 2023
The general solution of differential equation $(\tan^{-1}y - x)dy = (1 + y^2)dx$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2023
A pair of fair dice is thrown independently 3 times. The probability of getting a score of exactly 9 twice is
Topic: JAMIA MILLIA ISLAMIA MCA 2023
Solution of the differential equation
$\displaystyle \frac{dx}{dy}-\frac{x\log x}{1+\log x}=\frac{e^{y}}{1+\log x},\ \…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
Every gram of wheat provides $0.1$ gram of proteins and $0.25$ gram of carbohydrates.
The corresponding values of ric…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
$Z = 7x + y$, subject to constraints:
$5x + y \ge 5,\ x + y \ge 3,\ x \ge 0,\ y \ge 0.$
Then minimum value of $Z$ o…
Topic: JAMIA MILLIA ISLAMIA MCA 2023
