List of top Mathematics Questions

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

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

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?

The vector sum of two forces is perpendicular to their vector differences. In that case the forces

A train can travel 20\(\%\) faster than a car. Both start from the point A at the same time and reach point B 75 km away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hr. The faster train passes the slower train in 36 sec. The length of each train is

In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race?

The length of the longest rod that can be placed in a room which is 12 m long 9 m broad and 8 m high is

The remainder when 784 is divided by 342 is