List of top Mathematics Questions

What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders are proportional ?

Rs 770 have been divided among A, B and C such that A receives 2/9th of what B and C together receive. Then A's share is

The sum of the interior angles of a polygon is 1620. The number of sides of the polygon must be

The radius of the circumcircle of an equilateral triangle of side 12 cm is

Acistern is filled in 5 hours and it takes 6 hours when thereis a leak in its bottom. If the cistern is full, in what time shall the leak empty it?

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is cm, then the area of the triangle is 12√2 cm, then the area of the triangle is

A and B together can do a piece of work in 6 days. A alone can doit in 10 days. What time will B require to do it alone ?

The sides of a rectangular field are in the ratio 3 : 4 with its area as 7500 sq m.The cost of fencing the field @ 25-paise per metre is

In a zoo, there are rabbits and pigeons. If their heads are counted, these are 90 while their legs are 224. Find the number of pigeons in the zoo.

If the difference between the simple and the compound interests on some principal amount at 20% for 3 years is Rs 48, then the principal amount must be

Walking at \(\frac{3}{4}\)  of his usual pace, a man reaches his office 20 minutes late. Find his usual time.

If $\overrightarrow{a}, \overrightarrow{b}$ and $ \overrightarrow{c}$ are unit vectors, then $|\overrightarrow{a}-\overrightarrow{b} |^2+| \overrightarrow{b}-\overrightarrow{c}|^2+| \overrightarrow{c}-\overrightarrow{a}|^2$ does not exceed

If $f (x) = xe^{x(1-x)}$ , then f (x) is

The value of $\int^{\pi}_{-\pi} \frac{ \cos^2 \, x }{ 1 + a^x } \, dx , a> 0 $ is

The complex numbers $z_1, z_2$ and $z_3$ satisfying $\frac{z_1-z_3}{z_2-z_3}=\frac{1-i \sqrt 3}{2}$ are the vertices of a triangle which is

The triangle formed by the tangent to the curve $f(x)=x^2+bx-b$ a t the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2 sq units, then the value of b is

If $\alpha+\beta=\frac{\pi}{2} and \beta+\gamma$, then $tan \alpha$ equals

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

If the positive numbers a,b,c,d are in AP. Then, $abc, abd, acd, bcd $ are

In the binomial expansion of $(a - b)^n , n \ge 5 $ the sum of the 5th and 6th terms is zero. Then, a /b equals

Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

Let $ \alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $y, \delta$ be the roots of $x^2 - 4x + q = 0$ if $ \alpha, \beta, y \delta$ are in GP, then the integer values of p and q respectively are

Let $f(x) = (1 + b^2)x^2 + 2bx + 1$ and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

For all $x\,\in\,(0,1)$