List of top Mathematics Questions

An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are \(60^\circ\) and \(45^\circ\), respectively. Then the height of the lower plane from the ground, in metres, 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 metres away from the tree, the angle of elevation becomes \(30^\circ\). The breadth of the river is

A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from \(30^\circ\) to \(45^\circ\), then how soon, after this, will the car reach the tower?

What is the least value of k such that the function x$^2$ + kx + 1 is strictly increasing on (1,2)

In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ?

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

The volume of the tetrahedron with vertices P (-1, 2, 0), Q ( 2, 1, -3), R (1, 0, 1) and S (3, -2, 3) is

$If \, \, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}, \, \vec{b}= \, -\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c} \, = \, 3\hat{i}+\hat{j}$ then t such that $\vec{a}+t\vec{b}$ is at right angle to $\vec{c}$ will be equal to

On the set $Q$ of all rational numbers the operation $\star$ which is both associative and commutative is given by $a \star b$, is:

If $\sec \theta=m$ and $\tan \theta=n$ , then $\frac{1}{m}\left[(m+n)+\frac{1}{(m+n)}\right] $ is :

If $A = \begin{bmatrix} {1}&{-3}\\ {2}&{K} \\ \end{bmatrix}$ and $A^2-14A+10I=A$,then $K$ = is equal to :

If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is

An equilateral triangle is inscribed in the parabola y$^2$ = 4x one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and passing through (1, 1, 1) is

The length of the shortest distance between the lines $\vec{r}=3\hat{i}+5\hat{j}+7\hat{k}+\lambda(\hat{i}-2\hat{j}+\hat{k})$ and $\vec{r} = -\hat{i}-\hat{j}-\hat{k}+\mu (7\hat{i}-6\hat{j}+\hat{k})$ is

If x = -9 is a root of A = $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{vmatrix}$ = 0, then other two root are

The values of $\alpha$ for which the system of equation x + y + z = 1, x + 2y + 4z = $\alpha$, x + 4y + 10z = $\alpha^2$ is consistent are given by

Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist

The value of the integral $\int\limits_{0}^{\frac{\pi}{2}} log \left(tan\,x\right)dx=$

The particular integral of $\frac{d^2y}{dx^2}+2y=x^2$is

The distance between the pair of parallel lines $ x^2 + 2xy + y^2 - 8ax - 8ay - 9a^2 = 0$ is :

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.

A well 22.5 deep and of diameter 7m has to be dug out. Find the cost of plastering its inner curved surface at Rs 3 per sq metre.

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cyclindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?