At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\dfrac{dP}{dx}=100-12\sqrt{x}$. If the firm employs $25$ more workers, then the new level of production of items is :

1

$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :

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2

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of…

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3

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of AXB having 3 or mor…

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1

The area (in square units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis, and lying in the first quadrant is…

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2

Statement-1 : The value of the integral $\displaystyle \int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi…

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3

If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to

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4

If $x,y,z$ are in A.P. and $\tan^{-1}x,\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then :

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5

If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :

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6

The equation of the circle passing through the foci of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$, and having c…

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7

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)$, $(1,…

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8

A ray of light along $x+\sqrt{3}\,y=\sqrt{3}$ gets reflected upon reaching $X$-axis, the equation of the reflected ray …

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9

The term independent of $x$ in expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}\right)^{10}$ is

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10

Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{…

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