List of top Mathematics Questions

If the parabola $x^2=4ay$ passes through the point $(2, 1)$, then the length of the latus rectum is

The probability of solving a problem by three persons $A, B$ and $C$ independently is $\frac{1}{2}$, $\frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability of the problem is solved by any two of them is

If A = {1,2,3,4,5,6}, then the number of subsets of A which contain at least two elements is

The value of $\sin^2 51^\circ + \sin^2 39^\circ$ is

If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

The area bounded by the curves $\text{y} = \left(\text{x} - 1\right)^{2} \text{, } \text{y} = \left(\text{x} + 1\right)^{2}$ and $\text{y} = \frac{1}{4}$ is

Suppose that the side lengths of a triangle are three consecutive integers and one of the angles is twice another. The number of such triangles is/are

The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman, is

The number of discontinuity of the greatest integer function $f\left(x\right)=\left[x\right], \, x\in \left(- \frac{7}{2} , \, 100\right)$ is equal to

If $y=4x-5$ is tangent to the curve $y^{2}=px^{3}+q$ at $\left(\right.2, \, 3\left.\right)$ then $\left(\right.p,q\left.\right)$ is

If $5^{97}$ is divided by $52$ $,$ then the remainder obtained is

The two lines $l x+my=n$ and $l'x+m'y=n'$ are perpendicular if

$\displaystyle \lim_{x\to0}\left(\frac{\tan \,x}{\sqrt{2x +4} - 2}\right)$ is equal to

If some three consecutive in the binomial expansion of $(x + 1)^n$ is powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficient is :-

If $\sum^\limits{25}_{r=0} \left\{^{50}C_{r} . ^{50-r}C_{25-r}\right\}=K\left(^{50}C_{25}\right) $ , then $K$ is equal to :

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to :

Let $(x + 10)^{50} + (x - 10)^{50} = a_0 + a_1 x + a_2x^2 + ..... + a_{50} \; x^{50} , $ for all $x \in R , $ the $\frac{a_2}{a_0} $ is equal to :-

The term independent of x in the expansion of $\bigg(\frac{1}{60} - \frac{x^8}{81}\bigg). \bigg(2x^2 - \frac{3}{x^2}\bigg)^6$ is equal to:

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is $90^{\circ}$, then the length (in cm) of their common chord is :

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If 'S'BS is a right angled triangle with right angle at B and area ($\Delta$S'BS) = 8 s units, then the length of a latus rectum of the ellipse is :

Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, -1)$. The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ is :

If a circle $C$ passing through the point $(4,0)$ touches the circle $x^2 + y^2 + 4x - 6y = 12$ externally at the point $(1, -1)$, then the radius of $C$ is :

If one end of a focal chord of the parabola, $y^2 = 16x$ is at $(1, 4),$ then the length of this focal chord is

Let \( f \) be the function defined by \[ f(x) = \begin{cases} x^2 - 1, & x \neq 1 \\ x^2 - 2|x-1|^{-1}, & x = 1 \end{cases} \] The function is continuous at: