List of top Mathematics Questions asked in JEE Main

If $z = 2 + 3i$, then $z^5 + (\overline{z})^5$ is equal to:

If
$0 < x< \frac{1}{\sqrt2}\ and\ \frac{\sin^{-1}x}{α} = \frac{\cos^{-1}x}{β} $
then a value of
$sin(\frac{2πα}{α+β}) $
is

If $\lim_{n\rightarrow \infty}$ $\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]$
then the integral value of k is equal to _______.

If
$\lim_{{x \to 1}} \frac{{\sin(3x^2 - 4x + 1) - x^2 + 1}}{{2x^3 - 7x^2 + ax + b}} = -2$
, then the value of (a – b) is equal to_______.

If the function
$f(x) = \begin{cases} \frac {log_e(1−x+x^2)+log_e(1+x+x_2)}{sec⁡\ x−cos⁡\ x}, & \quad x∈(−\frac \pi2,\frac \pi2)−{0}\\ k, & \quad x=0 \end{cases}$
is continuous at $x = 0$, then k is equal to

Let $S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}$ and $S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}$ Then, for $z_1 \in S_1$ and $z_2 \in S_2$, the least value of $\left|z_2-z_1\right|$ is :

If
$\sum\limits_{k=1}^{31}$ $(^{31}C_k) (^{31}C_{k-1})$ $-\sum\limits_{k=1}^{30}$ $(^{30}C_k) (^{30}C_{k-1})$ $= \frac{α (60!)} {(30!) (31!)}$
where $α ∈ R$, then the value of 16α is equal to

The sum of all real value of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}$ is equal to________.

Let the tangents at two points A and B on the circle$ x^2 + y^2 – 4x + 3 = 0$ meet at origin O(0, 0). Then the area of the triangle OAB is

If $\lim_{n\rightarrow \infty}$($\sqrt{n^2-n-1}$ + nα+β)=0 then 8(α + β) is equal to

Let A be a $2×2$ matrix with $det (A) = –1$ and $det((A + I) (Adj (A) + I)) = 4$. Then the sum of the diagonal elements of A can be

2sin($\frac{\pi}{22}$)sin($\frac{3\pi}{22}$)sin($\frac{5\pi}{22}$)sin($\frac{7\pi}{22}$)sin($\frac{9\pi}{22}$) is equal to

The number of functions f, from the set
$A = {x∈N: x^2-10x+9≤0} $to the set $B = {n62:n∈N}$
such that
$f(x)≤(x-3)^2+1$, for every $x∈A,$
is ______.

Let $S=\left\{(x,y)∈\N×\N:9(x−3)^2+16(y−4)^2≤144\right\}$
and $T=\left\{(x,y)∈\R×\R:(x−7)^2+(y−4)^2≤36\right\}.$
Then n(S ⋂ T) is equal to ____ .

The Integral
$\int \frac{(1 - \frac{1}{\sqrt{3}})(\cos x - \sin x)}{1 + \frac{2}{\sqrt{3}}\sin2 x} \,dx$
is equal to

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Let $α, β$ be the roots of the equation $x^2-\sqrt{2}x+\sqrt{6}=0$ and$ \frac{1}{α^2}+1$,$\frac {1}{β^2}+1$ be the roots of the equation $x^2 + ax + b = 0$ . Then the roots of the equation $x^2 – (a + b – 2)x + (a + b + 2) = 0$ are

The number of matrices
$A=\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}$, where a,b,c,d ∈−1,0,1,2,3,…..,10
such that A = A^-1, is ______.

Let a, b ∈ R be such that the equation ax² – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x² – 2bx + 21 = 0, then α² + β² is equal to

Let a function ƒ : N →N be defined by
$f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.$
then, ƒ is

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers Let $f ( x )=\alpha x ^5+\beta x ^3+\gamma x , x \in R$ and $g: R \rightarrow R$ be such that $g(f(x))=x$ for all $x \in R$ If $a_1, a_2, a_3, \ldots, a_n$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac{1}{n} \displaystyle\sum_{i=1}^n f\left(a_i\right)\right)\right)$is equal to :

Let $S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}$ .
Then$n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)$is equal to :

Choose the correct answer:

1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?

Let A and B be two $3 × 3$ non-zero real matrices such that AB is a zero matrix. Then