List of top Mathematics Questions

Find the value of $ \sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1 $

Solve $ {{\sin }^{-1}}\,2x+{{\cos }^{-1}}\,2x+2\,{{\tan }^{-1}}\,x=\pi $

Find $ \frac{dy}{dx}, $ if $ y={{\sin }^{2}}x+{{\cos }^{4}}x $

Find the value of $ \cos \,\,(29\pi /3)? $

Find the area of the triangle with vertices $ (2,3), $ $ (0,\,\,1) $ and $ (1,\,\,2) $ .

Solve for $ x,\,\,{{\tan }^{-1}}(1/x)=\pi +{{\tan }^{-1}}x,\,\,0 < x < 1 $

Find the intersection of the spheres $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13 $ and $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8 $

Find the derivative of $ \sqrt{2}x+2\sqrt{x}-\frac{1}{x} $ ?

Integrate $ \frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}} $

Given two vectors are $ \hat{i}-\hat{j} $ and $ \hat{i}+2\hat{j}, $ the unit vector is coplanar with the two vectors and perpendicular to the first. Find the vector?

For what values of $x$, the numbers $ -1,\,x,-3/4 $ are in $GP$ ?

Differentiate $ \sin \,\,(\sin \,\,2x). $

Let $ A=\{1,\,\,2\,\{a,\,\,b\},\,\,3,\,\,4\}, $ which among the following statements is incorrect?

Find the range of the function $ f:[0,\,1]\to R,\,\,f(x)={{x}^{3}}-{{x}^{2}}+4x+2{{\sin }^{-1}}x $ ?

There are $7$ horses in a race, Mr. X selected $2$ horses at random and bet on them. The probability that Mr. X selected the winning horse, is

If $0< x< \pi$, then $\frac{\sin 8 x+7 \sin 6 x+18 \sin 4 x+12 \sin 2 x}{\sin 7 x+6 \sin 5 x+12 \sin 3 x}$ equal to

Solve $ \frac{dy}{dx}+\frac{y}{x}={{x}^{3}} $

Equation of the plane perpendicular to the line $\frac {x}{1} = \frac {y}{2} = \frac {z}{3}$ and Passing through the point $(2, 3, 4)$ is

A gardener is digging a plot of land. As he gets tired, he works more slowly. After $' t '$ minutes he is digging at a rate of $\frac {2} {\sqrt {t}} $square metres per minute. How long will it take him to dig an area of $40$ square metres ?

The general solution of the differential equation $\frac {dy}{dx}+\frac {y}{x}=3x$ is

If $x+y\leq2,x \geq 0,y \geq 0$ the point at which maximum value of $3x + 2y$ attained will be

If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to

Given $0 \leq x \leq \frac {1}{2}$ then the value of $\tan \left[\sin^{-1}\left\{\frac{x}{\sqrt {2}}+\frac {\sqrt {1-x^2}} {\sqrt {2}}\right\}-\sin^{-1}x\right]$ is

The subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is

A spherical balloon is being inflated at the rate of $35\, cc$ per minute, When its radius is $7\, cm$, its surface area increases at the rate of