List of top Mathematics Questions

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

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

I derive an annual income of Rs. 688.25 from Rs. 10,000 invested partly at 8% p.a. and partly at 5% p.a. simple interest. How much of my money is invested at 5%?

A worker is paid Rs. 56 for 35 hour week. Upto 40 hours, he is paid at the normal rate and on overtime, 1.5 times the normal. How many hours did he work to get Rs. 88?

X is what percent of \(\frac{4}{5}th\) of X?

The distance of the point $'\theta'$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ from a focus is

A bought 4 bottles of beer and B bought one bottle of lager, lager per bottle costing twice that of the beer. C bought nothing but paid Rs. 50 for his share of the drink which they mixed together and shared equally. If C's Rs. 50 covered his share, then what is the cost of the lager?

In a class, 20 opted for Physics, 17 for Maths, 5 for both and 10 for other subjects. The class contains how many students ?

Cube root of 658503 is

In a community of 175 persons, 40 read the Times, 50 read the Samachar and 100 do not read any. How many persons read both the papers ?

Two rockets approach each other, one at 42,000 mph and the other at 18,000 mph. They start 3256 miles apart. How far are they apart (in miles) 1 minute before impact?