$Q30.$ If the rank of the matrix \[ \begin{bmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{bmatrix} \] is $2$, then find the correct condition.

1

The system of linear equations is: $a + 2b + 3c = 7$ $2a + 4b + c = 12$ $3a + 6b + 4c = 20$

Topic: JAMIA MILLIA ISLAMIA MCA 2023

2

If $A^2 - A = 3I$, then $A^{-1}$ is —

Topic: JAMIA MILLIA ISLAMIA MCA 2023

3

If $Z$ is an idempotent matrix, then $(I + Z)^n$ is —

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4

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…

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5

The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all observations is —

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6

The contrapositive of $p \to (\neg q \to \neg r)$ is —

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7

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

8

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

9

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

10

The middle term in the expansion of $\left(1 + \dfrac{1}{x^2}\right)\!\left(1 + x^2\right)^n$ is —

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1

The general solution of differential equation $(\tan^{-1}y - x)dy = (1 + y^2)dx$ is:

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2

A pair of fair dice is thrown independently 3 times. The probability of getting a score of exactly 9 twice is

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3

Solution of the differential equation $\displaystyle \frac{dx}{dy}-\frac{x\log x}{1+\log x}=\frac{e^{y}}{1+\log x},\ \…

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4

Every gram of wheat provides $0.1$ gram of proteins and $0.25$ gram of carbohydrates. The corresponding values of ric…

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5

$Z = 7x + y$, 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

6

The point of inflection for $f(x) = 3x^4 - 4x^3$ are –

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7

$\displaystyle \int_{0}^{1000} e^{\,x-[x]}\,dx$ is –

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8

Let the equation of a curve passing through $(0,1)$ be $y=\displaystyle\int x^{2}e^{x^{3}}\,dx$. If the curve is writte…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

9

The value of $\displaystyle \int_{0}^{\pi/2}\sin^{4}x\,\cos^{4}x\,dx$ is –

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10

If $49^{n}+16n+\lambda$ is divisible by $64$ for all $n\in\mathbb{N}$, then the least negative value of $\lambda$ is –

Topic: JAMIA MILLIA ISLAMIA MCA 2023