$\sin(\tan^{-1}x)$, where $|x| < 1$, is equal to

1

$\tan^{-1}!\left(\dfrac{1}{2}\right) + \tan^{-1}!\left(\dfrac{1}{3}\right) =$

Topic: JAMIA MILLIA ISLAMIA MCA 2024

2

Simplified form of $\cos^{-1}(4x^3 - 3x)$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

3

The coefficient of the middle term in the expansion of $(2 + 3x)^4$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

4

If $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ $(a \ne b)$ have exactly one common root, then what is the value of $(a + …

Topic: JAMIA MILLIA ISLAMIA MCA 2024

5

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = \dfrac{1}{x}$, $\forall x \in \mathbb{R}$. Then $f$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

6

A relation $R$ in a set $A$ is called ________, if $(a_1, a_2) \in R$ implies $(a_2, a_1) \in R$, for all $a_1, a_2 \in…

Topic: JAMIA MILLIA ISLAMIA MCA 2024

7

If $f : \mathbb{R} \to \mathbb{R}$ such that $f(x) = 3x$, then what type of function is $f$?

Topic: JAMIA MILLIA ISLAMIA MCA 2024

8

The maximum number of equivalence relations on the set $A = {1, 2, 3}$ are

Topic: JAMIA MILLIA ISLAMIA MCA 2024

9

A={1,2,3}. Which $f:A\to A$ does not have an inverse?

Topic: JAMIA MILLIA ISLAMIA MCA 2024

10

On A={1,2,3} let R={(1,2)}. Then R is&nbsp;

Topic: JAMIA MILLIA ISLAMIA MCA 2024

1

If $A$ is a square matrix such that $A^2 = A$, then $(I - A)^3 + A$ is equal to

Topic: JAMIA MILLIA ISLAMIA MCA 2024

2

A square matrix $A = [a_{ij}]{n \times n}$ is called a lower triangular matrix if $a{ij} = 0$ for

Topic: JAMIA MILLIA ISLAMIA MCA 2024

3

A matrix $A = [a_{ij}]_{m \times n}$ is said to be symmetric if

Topic: JAMIA MILLIA ISLAMIA MCA 2024

4

Let $A$ be a non-singular matrix of order $2 \times 2$. Then $|A^{-1}| =$

Topic: JAMIA MILLIA ISLAMIA MCA 2024

5

If $A$ and $B$ are symmetric matrices of the same order, then $(AB - BA)$ is a

Topic: JAMIA MILLIA ISLAMIA MCA 2024

6

What is $\displaystyle \lim_{x\to 0}\left(\frac{x\tan x}{\cot x}\right)$?

Topic: JAMIA MILLIA ISLAMIA MCA 2024

7

If $\sec!\left(\dfrac{x-y}{x+y}\right)=a$, then $\dfrac{dy}{dx}$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

8

If $x^{,y}y^{,x}=16$, then $\left.\dfrac{dy}{dx}\right|_{(2,2)}$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

9

The function $f(x)=x+\cos x$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2024

10

$\displaystyle \int x^{2}\sin(x^{3}),dx =$

Topic: JAMIA MILLIA ISLAMIA MCA 2024