List of top Mathematics Questions asked in JEE Main

Let $\alpha, \beta$ be the roots of the equation $x^2 - 4\lambda x + 5 = 0$ and α, γ be the roots of the equation $x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0$. If $\beta + \gamma = 3\sqrt{2}$ then $(\alpha + 2\beta + \gamma)^2$ is equal to _______.

If the sum of all the roots of the equation $e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0$
is log_eP, then p is equal to _____.

The line y = x + 1 meets the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$ at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)² is equal to

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of $7α + 3β$ is equal to ________ .

If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x + y – 29 = 0$, is $x^2 + ay^2 + bxy + cx + dy + k = 0$, then $a + b + c + d + k$ is equal to

If the circle
x²+y²-2gx+6y-19c = 0,g,c∈R
passes through the point (6, 1) and its centre lies on the line x – 2cy = 8, then the length of intercept made by the circle on x-axis is

The number of real solutions of the equation e^4x + 4e^3x - 58e^2x + 4ex + 1 = 0 is _____.

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

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

Let S={z=x+iy:|z–1+i|≥|z|,|z|<2,|z+i|=|z–1|}.
Then the set of all values of x, for which w = 2x + iy ∈ S for some y ∈ R is

If the sum of the first ten terms of the series
$\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501}$+… is $\frac{m}{n}$,
where m and n are co-prime numbers, then m + n is equal to __________.

The number of points of intersection of $|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, $z \in \mathbb{C}$, is

Let $S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}$ and
let $T_n = {A ∈ S : A^{n(n + 1)} = I}. $
Then the number of elements in $\bigcap_{n=1}^{100}$ $T_n $ is

The value of the integral
$\frac{48}{\pi^4} \int_{0}^{\pi}(\frac{3\pi x^2}{2} - x^3) \frac{ \sin(x)}{1 + \cos^2x} \, dx$
is equal to ________

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of $A∩B$ is ___________

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 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 ______.

If the sum of solutions of the system of equations 2sin²θ – cos2θ = 0 and 2cos²θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Let
$A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}$
and
$B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}$
Then $A∩B$ is :

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
$\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}$
Then which of the following statements are true?
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f
R : f ′ is increasing for x > √2

If $\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$ then which of the following is NOT correct?

$\begin{array}{l} I_n\left(x\right)=\int_0^x\frac{1}{\left(t^2+5\right)^n}dt, n=1, 2, 3,\cdots\end{array}$

Then

Let the abscissae of the two points P and Q on a circle be the roots of x² – 4x – 6 = 0 and the ordinates of P and Q be the roots of y² + 2y – 7 = 0. If PQ is a diameter of the circle x² + y² + 2ax + 2by + c = 0, then the value of (a + b – c) is

Let $x(t)=2\sqrt2costsin\sqrt2t $ and $y(t)=2\sqrt2sintsin\sqrt2t$ ,$t ∈(0,\frac{π}{2})$

Then $\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}$ at $t=\frac{π}{4}$ is equal to