List of top Mathematics Questions asked in JEE Main

Consider a set \( S = \{ a, b, c, d \} \). Then the number of reflexive as well as symmetric relations from \( S \to S \) are

The number of solution(s) of the equation \[ x |x + 4| + 3 |x + 2| = 0 \] is/are equal to:

If domain of \(f(x) = \sin^{-1}\left(\frac{5-x}{2x+3}\right) + \frac{1}{\log_{e}(10-x)}\) is \((-\infty, \alpha] \cup (\beta, \gamma) - \{\delta\}\) then value of \(6(\alpha + \beta + \gamma + \delta)\) is equal to :

If the domain of the function \[ \cos^{-1} \left( \frac{2x - 5}{11x - 7} \right) + \sin^{-1} \left( 2x^2 - 3x + 1 \right) \] is \[ [0, a] \cup [12/13, b] \] then \( \frac{1}{ab} \) is equal to}

If the domain of the function \[ f(x) = \frac{1}{\ln(10-x)} + \sin^{-1} \left( \frac{x+2}{2x+3} \right) \] is \( (-\infty, -1) \cup (-1, b) \cup (b, c) \cup (c, \infty) \), then \( (b + c + 3a) \) is equal to:

The sum of roots of the equation \[ |x - 1|^2 - 5 |x - 1| + 6 = 0 \] is

\( y = \log_5 \log_3 \log_7 (9x - x^2 - 13) \), If its domain is \( (m, n) \) and \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] is a hyperbola having eccentricity \( \frac{n}{3} \) and length of the latus rectum is \( \frac{8m}{3} \), find \( b^2 - a^2 \):

If two numbers \( a \) and \( b \) are selected from \( S = \{1, 2, 3, \dots, 100\} \), then the probability that \( |a - b| \geq 10 \) is:

If probability distribution is given by \[ P(x) = \begin{array}{c|c|c|c|c|c|c|c} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(x) & k & 2k^2 & 6k^2 & 2k^2 + k & 4k & k & k \\ \end{array} \] Then, the value of \( P(3<x \leq 6) \) is:

There are 10 defective and 90 non-defective balls in a bag. 8 balls are taken one by one with replacement. Find the probability that at least 7 defective balls are selected.

Bag \( A \) contains 9 white and 8 black balls and bag \( B \) contains 6 white and 4 black balls. A ball is randomly transferred from bag \( B \) to bag \( A \), then a ball is drawn from bag \( A \). If the probability that the drawn ball is white is \( \dfrac{p}{q} \) (where \( p \) and \( q \) are coprime), then find \( p + q \):

Let $S$ has 5 elements and $P(S)$ is the power set of $S$. Let an ordered pair $(A,B)$ is selected at random from $P(S)\times P(S)$. If the probability that $A\cap B=\varnothing$ is $\dfrac{3^m}{2^n}$, then the value of $(m+n)$ is

If a line \(ax + y = 1\) does not intersect the hyperbola \(x^2 - 9y^2 = 9\) then a possible value of \(\alpha\) is :

Given \[ f(t)=\left|\frac{t+1}{t^2}\right|,\ (t<0) \] is strictly decreasing in the interval $(2\alpha,\alpha)$, then the maximum value of \[ g(x)=2\log_e(x-2)+\alpha x^2+4x-\alpha \] is:

Let $f(x)$ be a differentiable function satisfying the equations $\lim_{t \to x} \dfrac{t^2 f(x)-x^2 f(t)}{t-x} = 3$ and $f(1)=2$. Find the value of $2f(2)$.

The solution of the differential equation \[ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx \] is (where \( c \) is the integration constant):

If \( y = y(x) \) and \[ (1 + x^2)\,dy + (1 - \tan^{-1}x)\,dx = 0 \] and \( y(0) = 1 \), then \( y(1) \) is equal to:

If \( x^4 \, dy + (4x^3 y + 2 \sin x) \, dx = 0 \) and \( f\left( \frac{\pi}{2} \right) = 0 \), then find the value of \( \pi^4 f\left( \frac{\pi}{3} \right) \) (where \( y = f(x) \)):

The minimum value of \( \cos^2\theta + 6\sin\theta\cos\theta + 3\sin^2\theta \) is:

Let \(O\) be the vertex of the parabola \(y^{2}=16x\). The locus of the centroid of \(\triangle OPA\), when point \(P\) lies on the parabola and point \(A\) lies on the \(x\)-axis such that \(\angle OPA = 90^\circ\), is:

Ellipse \( E:\; \dfrac{x^2}{36} + \dfrac{y^2}{16} = 1 \). A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to \(5\). If the principal axis of the hyperbola is the \(x\)-axis, then the length of the latus rectum of the hyperbola is:

The area enclosed by \[ x^2 + 4y^2 \le 4,\qquad y \le |x| - 1,\qquad y \ge 1 - |x| \] is equal to:

Image of point P (1, 2, a) with respect to line mirror \(\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2}\) is point Q (5, b, c), then value of \((a^2 + b^2 + c^2)\) is :

Given triangle $OAB$ where $O$ is the origin, $A=(0,-\sqrt{3}a)$ and $B=(-\sqrt{2}b,0)$. Let the circumradius of $\triangle OAB$ be $4$ units. If the locus of the centroid of $\triangle OAB$ is a circle, then its radius is: