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

1

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

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2

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

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3

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

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4

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

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5

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

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6

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

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7

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

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8

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

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9

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

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10

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 + …

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1

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

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2

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

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3

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

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4

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

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5

The objective function of a linear programming problem is

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6

If $|z_1| = 4,\ |z_2| = 3$, then what is the value of $|z_1 + z_2 + 3 + 4i|$ ?

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7

Region represented by $x \ge 0,\ y \ge 0$ is

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8

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. W…

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9

The absolute maximum value of $y = x^3 - 3x + 2$ in $0 \le x \le 2$ is

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10

$\displaystyle \int_{0}^{\pi} \sin^2 x,dx =$

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