List of top Mathematics Questions

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?

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

The length of the chord $x + y = 3$ intercepted by the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ is

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

If $\sum\limits^{n}_{r=0} \frac{r+2}{r+1} \,^{n}C_{r} = \frac{2^{8}-1}{6} $, then $n =$

If $\log a, \log b$, and $\log c$ are in A.P. and also $\log a-\log 2 b, \log 2 b-\log 3 c, \log 3 c-\log a$ are in A.P., then

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 parabola having its focus at $(3, 2)$ and directrix along the $y$-axis has its vertex at

If $\sin^{-1} \left(\frac{2a}{1+a^{2}}\right) -\cos^{-1} \left(\frac{1-b^{2}}{1+b^{2}}\right) = \tan^{-1} \left(\frac{2x}{1-x^{2}}\right) , $ then what is the value of x?

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

The curve $y = xe^x$ has minimum value equal to

The number of values of $r$ satisfying the equation $^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r} $ 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 equation $x^2 - 2 \sqrt{3} xy + 3y^2 - 3x + 3 \sqrt{3} y - 4 = 0 $ represents

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

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :

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

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

Let $p = \displaystyle\lim_{x \to 0^+ } ( 1 + \tan^2 \sqrt{x} )^{\frac{1}{2x}}$ then $log \,p$ is equal to

If $\frac{^{n+2}C_6}{^{n-2}P_2} = 11$, then $n$ satisfies the equation :

If the four letter words (need not be meaningful ) are to be formed using the letters from the word $"MEDITERRANEAN"$ such that the first letter is $R$ and the fourth letter is $E$, then the total number of all such words is :

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is