List of top Mathematics Questions

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?

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

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

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

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

If the circle $x^2+y^2+2\,gx+2fy+=0,$ and $x^2+y^2+2g'x+2f'y$ touch each other, then

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

The value of $\sin \left[\cot^{-1}\{{\cos(tan^{-1}\,x)\}}\right]$ is

If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then

Which of the following is an empty set?

The number of proper subsets of a set having $n + 1$ elements is

The interval I such that $\int^1_0\frac{dx}{\sqrt{1+x^4}}\in \,I$ is given by

A card is picked at random from a pack of cards. Given that the picked card is a Queen, what is the probability that it is a spade ?

The curve $x^2 - xy + y^2 =27$ has tangents parallel to $x-axis$ at

Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =