List of top Mathematics Questions asked in JEE Advanced

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

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

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

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

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

The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has

The parameter on which the value of the determinant $\Rightarrow \Delta=\begin{vmatrix}1& a & a^2\\ \cos(p-d)x& \cos\ px & \cos(p+d)x\\ \sin(p-d)x& \sin\ px& \sin(p+d)x\\ \end{vmatrix}$ does not depend upon, is

The function $f(x) = [x] \cos \left(\frac{2x-1}{2}\right) \pi$, [.] denotes the greatest integer function, is discontinuous at

The function $f(x) = max \{(1 - x), (1 + x), 2\}, x \in (- \infty, \infty)$ is