List of top Mathematics Questions

Let $PQR$ be a right angled isosceles triangle, right angled at $P (2,1)$. If the equation of the line $QR$ is $2x + y = 3$, then the equation representing the pair of lines PQ and PR is

For a positive integer n let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ...+ \frac{1}{(2^n)-1},$ then

The harmonic mean of the roots of the equation $ (5+\sqrt 2)\, x^2 - (4+\sqrt 5)\, x + 8 + 2\sqrt5 = 0 $ is

For a positive integer n, let $f_n(\theta)=\Bigg(tan\frac{\theta}{2}\Bigg)(1+sec \theta)(1+sec 2\theta)(1+ sec 2^2 \theta)... (1+sec 2^n \theta), then$

Let $a_1,a_2,...,a_{10}$ be in AP and $h_1, h_2$ equal to .....,$h_{10}$ be in HP. If $a_1 = h_1 = 2$ and $ a_{10} = h_{10} = 3,$ then $a_4 h_7$ is

If in the expansion of $(1 + x)^m (1 - x)^n$, the coefficients of $x$ and $x^2$ are 3 and - 6 respectively, then m is euqal to

$ lim_{ n \to \infty} \frac{1}{n} \displaystyle \sum_{r = 1}^ {2n} \frac{r}{ \sqrt{ n^2 + r^2}} $ equals

Let $ S_1, S_2,...$ be squares such that for each $ n \ge 1 $ the length of a side of $ S_n $ equals the length of a diagonal of $ S_{n+1}$. If the length of a side of $ S_1 $ is 10 cm, then for which of the following values of n is the area of $S_n$ less than 1 sq cm?

If two distinct chords, drawn from the point (p, q) on the circle $x^2 + y^2 = px + qy$ (where, $ pq \ne 0$) are bisected by the X-axis, then

$\displaystyle\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos\,x}$ is equal to

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible, is

Let $f(x) = x - [x] $, for every real number x, where [x] is the integral part of x Then, $ \int^1_{-1} \, f ( x ) \, dx$ is

The value of $\displaystyle \sum_{k=1}^6 \bigg(\sin\frac{2\pi k}{7}-i \cos \frac{2\pi k}{7}\bigg)$ is

If in a $\triangle$ PQR, sin P, sin Q, sin R are in AP, then

Let f (x) = min { x, $x^2$ } for every real number of x, then

In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals:

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is

If $T_r$ is the $r$th term of an AP, for $r = 1,2,3,.... $ .If for some positive integers m and n, we have $T_m=\frac{1}{n}$ and $T_m=\frac{1}{m}$ then $T_{mn} $ equals

If $P = (x, y),F_1 = (3,0), F_2 = ( 3, 0)$ and $ 16x^2 + 25y^2 = 400,$ then $PF_1 + PF_2$ equals

If $P (1,2), Q (4,6), R (5, 7)$ and $S (a,b)$ are the vertices of a parallelogram $PQRS$, then

If $x > 1, y > 1, z > 1$ are in GP, then $\frac{1}{1+In\, x}, \frac{1}{1+In\, y},\frac{1}{1+In\, z},$ are in

Number of divisors of the form $(4n + 2), n\ge 0$ of the integer 240 is

If $\omega$ is an imaginary cube root of unity, then (1 + $\omega$ - $\omega^2)^7$ is equal to