List of top Mathematics Questions

The value of $ (1 + \omega - \omega^2)^7$ is

If $|\vec{a} | = 3, |\vec{b}| = 2, |\vec{c}| = 1$ then the value of $|\vec{a}. \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}| $ is (given that $\vec{a} + \vec{b} + \vec{c} = 0$)

In a culture the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present.

A tetrahedron has vertices at $O (0, 0, 0), A (1, 2, 1) B (2, 1, 3) $ and $C (-1, 1, 2)$. Then the angle between the faces $OAB$ and $ABC$ will be

If $ A$ and $B$ are matrices and $B = ABA^{-1}$ then the value of $(A + B) (A - B)$ is

What is the area of a loop of the curve $r = a \sin^3 \theta$ ?

If $e^x = y + \sqrt{ 1 + y^2}$ , then the value of y is

At an extreme point of a function $f (x)$, the tangent to the curve is

Let $f (x) = \frac{ax+ b}{cx + d} $ , then $fof(x) = x$, provided that :

All the words that can be formed using alphabets $A, H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

A ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The co-ordinates of the point $A$ is

The line joining $(5,0)$ to $((10 \cos \theta, 10 \sin \theta)$ is divided internally in the ratio $2: 3$ at $P$. If $q$ varies, then the locus of $P$ is

The number of integral values of $\lambda$ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0 $ is the equation of a circle whose radius cannot exceed $5$, is

The lengths of the tangent drawn from any point on the circle $15x^2 +15y^2 - 48x + 64y = 0$ to the two circles $5x^2 + 5y^2 - 24x + 32y + 75 = 0$ and $5x^2 + 5y^2 - 48x + 64y + 300 = 0$ are in the ratio of

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ I. $f(x)$ is increasing in $[-1,1]$ II. $f(x)$ has no root in $(-1,1)$. Which of the statements given above is/are correct?

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

The locus of the point of intersection of two tangents to the parabola $y^2 = 4ax$, which are at right angle to one another is

The differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ is

If $\omega$ is an imaginary cube root of unity, then the value of $\left(2-\omega\right)\left(2-\omega^{2}\right)+2\left(3-\omega\right)\left(3-\omega^{2}\right)+.....+\left(n-1\right)\left(n-\omega\right)\left(n-\omega^{2}\right)$

If $ X=\left\{-2, -1, 0, 1,2,3, 4, 5, 6, 7, 8\right\} $ and $ A=\left\{x : \left|x-2\right|\le3, x \, is\,an\, integer\right\}, $ then $ X-A= $

If $ y=tan^{-1}\left(\frac{2x}{1+3x^{2}}\right)+tan^{-1}\left(\frac{5+x}{1-5x}\right) $ , then $ \frac{dy}{dx}= $

Let $ A(a, 0) $ , $ B(0, b) $ and $ C (1, 1) $ be three points. If $ \frac{1}{a}+\frac{1}{b}=1 $ , then the three points are

The value of $ \displaystyle\lim_{x\to\infty} \left(\frac{x+5}{x+2}\right)^{x} $ is equal to

The coefficient of $ x^{2} $ in the expansion of $ (1 + x + x^{2} + x^{3})^{10} $ is

The mean of $ 100 $ items was $ 60 $ . Later it was found that two items were misread as $ 69 $ and $ 96 $ instead of $ 66 $ and $ 99 $ respectively. The correct mean of the $ 100 $ items is