List of top Mathematics Questions asked in JEE Main

Consider two sets A and B. Set A has 5 elements whose mean & variance are 5 and 8 respectively. Set B has also 5 elements whose mean & variance are 12 & 20 respectively. A new set C is formed by subtracting 3 from each element of set A and by adding 2 to each element of set B. The sum of mean & variance of the set C is

The mean and variance of 7 observations are 8 and 16 respectively If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observation, then $a+3 b-5$ is equal to ______

The mean of coefficients of \(x, x^2, ....., x^7\) in the binomial expansion of \((2 + x)^9\) is?

Let $S=\{1,2,3,4,5,6\}$ Then the number of one-one functions $f: S \rightarrow P ( S )$, where $P ( S )$ denote the power set of $S$, such that $f(m) \subset f(m)$ where $n < m$ is _______
Area bounded by the curve 2y2 = 3x and the line x+y = 3 outside the circle (x-3)2 + y2 = 2 and above the x-axis is A. The value of 4(π +4A) is?
$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$is equal to
5 boys with allotted roll numbers and seat numbers are seated in such a way that no one sits on the allotted seat. The number of such seating arrangements is?
If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
Let the number of matrices of order 3 x 3 are possible using the digits [0, 1, 2, 3, … , 10) is mn, then (m + n) is ___. (where m is a prime number)
If \(y = max \{ {\sqrt{x}, x^2-4, x^3+2}\}\), then the number of solution(s) of y=1 is/are____?

Matrix A is 2×2 matrix and A2=I, no elements of the matrix are zero, let the sum of diagonal elements is a and det(A)=b, then the value of 3a2+b2 is?

Maximum value n such that (66)! is divisible by 3n

Sum of first 20 terms: 5, 11, 19, 29, 41

Maximum value n such that (66)! is divisible by 3n
Let A = {1, a1, a2…a18, 77} be a set of integers with 1 <a1<a2<….<a18< 77. Let the set A + A = {x + y :x, y∈A} contain exactly 39 elements. Then, the value of a1 + a2 +…+a18 is equal to _____.
Let r ∈ {p, q, ~p, ~q} be such that the logical statement r ∨ (~p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :
The number of positive integers k such that the constant term in the binomial expansion of \(( 2x^3 + \frac {3}{x^k} )^{12}, x ≠ 0\) is \(2^8\) . l, where l is an odd integer, is______.
The number of elements in the set { \(z = a + ib ∈ C : a,b ∈ Z\) and \(1 < | z - 3 + 2i | < 4\) } is _______ .
Let the lines
\(y + 2x = \sqrt {11} + 7\sqrt 7\) and \(2y + x = 2\sqrt {11} + 6\sqrt 7\)
be normal to a circle \(C : (x – h)^2 + (y – k)^2 = r^2\). If the line
\(\sqrt {11}y - 3x =\frac { 5\sqrt {17}}{3} + 11\)
is tangent to the circle C, then the value of \((5h – 8k)^2 + 5r^2\) is equal to _______.
Let R1 and R2 be relations on the set {1, 2, ….., 50} such that R1 ={(p, pn) : p is a prime and n≥ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 – R2 is ______.
The number of real solutions of the equation e4x + 4e3x - 58e2x + 4ex + 1 = 0 is _____.
The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.
If \(\vec a= 2\hat i +\hat j + 3\hat k\), \(\vec b = 3\hat i + 3\hat j + \hat k\) and \(\vec c = c_1\hat i + c_2\hat j + c_3\hat k\) are coplanar vectors and \(\vec a.\vec c = 5\), \(\vec b⊥\vec c\)  then \(122( c_1 + c_2 + c_3 )\) is equal to _____ .
Let \(p, q, r \)be three logical statements. Consider the compound statements
\(S_1 : ((~p) ∨q) ∨ ((~p) ∨r)\) and
\(S_2 :p→ (q∨r)\)
Then, which of the following is NOT true?
Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let \(\frac \pi 8\) and \(θ\) be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then \(tan^2θ\) is equal to