List of top Mathematics Questions

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?

A circular grassy plot of land, 42 m in diameter, has a path 3.5 m wide running around it outside.The cost of gravelling the path at Rs 4 per square metre is

A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is

A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm that the level may be raised 20 cm in 5 hours?

An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe is