List of top Mathematics Questions

If $(1 - p)$ is a root of quadratic equation $x^2 + px + (1- p) = 0$, then its roots are

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is

The range of the function $f\left(x\right) = ^{7-x}P_{x-3}$ is

If $\displaystyle\lim_{x \to\infty} \left(1+ \frac{a}{x} + \frac{b}{x^{2}}\right)^{2x} = e^{2} $ , then the values of a and b, are

The coefficient of the middle term in the binomial expansion in powers of x of $(1+ \alpha x)^4$ and of $ (1 - \alpha x)^6$ is the same if $\alpha$ equals

The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is

Let $A=\begin{pmatrix} 1&-1 &1 \\[0.3em] 2 &1 &-3 \\[0.3em] 1 &1&1 \end{pmatrix}$ and $\,10\,B=\begin{pmatrix} 4&2 &2 \\[0.3em] -5 &0 & \alpha \\[0.3em] 1 &-2&3 \end{pmatrix} $. If B is the inverse of A , then $\alpha$ is

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^{\circ}$ and when he retires $40$ meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is

If $f: R \rightarrow S $ defined by $ f(x)=\sin x-\sqrt{3} \,\cos\,x+\,$ 1, is onto, function then S = ?

The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then

The unit vector which is orthogonal to the vector $3\widehat{i} + 2\widehat{j} + 6\widehat{k}$ and is coplanar with the vectors $ 2\widehat{i} + \widehat{j} + \widehat{k}$ and $\widehat{i} + \widehat{j} + \widehat{k}$ is

If three natural numbers from $1$ to $100$ are selected randomly then probability that all are divisible by both $2$ and $3$, is

Area of triangle formed by the lines $ x + y = 3$ and angle bisectors of the pair of straight lines $x^2 - y^2 + 2y = 1$ is

If the line $2x+\sqrt6y=2$ touches the hyperbola $x^2-2y^2=4$, then the point of contact is

If f(x) is differentiable and $\int_0^{t^2}x f(x) dx =\frac{2}{5}t^5,$ then $f\bigg(\frac{4}{25}\bigg)$ equals

The sides of a triangle are in the ratio $ 1 : \sqrt 3 : 2 $, then the angles of the triangle are in the ratio

If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is

If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre (2,1), then the radius of the circle is

If $^{n-1}C_r =(k^2 -3) \, ^nC_{r+1}$then k belongs to

Given both $\theta and \phi are acute angles and sin \theta=\frac{1}{2}, cos \phi=\frac{1}{3},$ then the value of $\theta+\phi $ belongs to

If one root is square of the other root of the equation $x^2+px+q=0,$ then the relation between p and q is

If $\omega (\ne 1)$ be a cube root of unity and $(1 + \omega^2)^n = (1 + \omega^4)^n,$ then the least positive value of n is

An infinite GP has first term x and sum 5, then x belongs to

Mr. X's salary is increased by 20\(\%\). On the increase, the tax rate is 10\(\%\) higher. The percentage increase in tax liability is

If 5 men take an hour to dig a ditch, then how long should 12 men take to dig a ditch of the same type?