List of top Mathematics Questions asked in JEE Main

Area under the curve \(x^2 + y^2 = 169\) and below the line \(5x - y = 13\) is:

If \(f(x) =   \begin{cases}     2+2x  & ;x∈(-1,0)\\     1-\frac x3  & ;x∈[0,3)  \end{cases}\) and \(g(x) =   \begin{cases}     x  & ;x∈[0,1)\\     -x & ;x∈(-3,0)  \end{cases}\). Then range of \(fog(x)\) is

If the domain of the function \( f(x) = \log_e \left( \frac{2x + 3}{4x^2 + x - 3} \right) + \cos^{-1} \left( \frac{2x - 1}{x + 2} \right) \) is \( (\alpha, \beta] \), then the value of \( 5\beta - 4\alpha \) is equal to

Sum of the series \(\frac {1}{1-3.1^2+1^4}+\frac {2}{1-3.2^2+2^4}+\frac {3}{1-3.3^2+3^4}\) upto \(10\) terms is _____ .

If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)

Let \( a \) and \( b \) be two distinct positive real numbers. Let the 11^th term of a GP, whose first term is \( a \) and third term is \( b \), be equal to the \( p \)-th term of another GP, whose first term is \( a \) and fifth term is \( b \). Then \( p \) is equal to

If one of the diameters of the circle \(x^2+y^2-10x+4y+13=0\) is a chord of another circle and whose center is the point of intersection of the lines \(2x + 3y = 12\) and \(3x - 2y = 5 \) then the radius of the circle is

Evaluate the limit : \(\lim_{x \to \frac{\pi}{2}} \left( \frac{1}{\left( x - \frac{\pi}{2} \right)^3} \int_{\frac{\pi}{2}}^x \cos \left( \frac{1}{t^3} \right) \, dt \right)\)

Let \(\vec a =3î + ĵ -2k̂\), \(\vec b =4 î + ĵ +7 k̂\) and \(\vec c =î -3 ĵ +4 k̂\) be 3 vectors. If a vector \(\vec p\)  satisfies \(\vec p_x \vec b=\vec c_x\vec b\) and \(\vec p_x\vec a = 0\) then \(\vec p.( î - ĵ - k̂ )\) is equal to

If \(\frac {dy}{dx} - \frac {(sin2x)}{(1+cos^2x)}y = \frac {sinx}{1+cos^2x }\)and \(y(0) =0\) then \(y(\frac \pi2)\) is ………..

If the value of the integral

\[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{x^2 \cos x}{1 + \pi^x} + \frac{1 + \sin^2 x}{1 + e^{\sin^x 2023}} \right) dx = \frac{\pi}{4} (\pi + a) - 2, \]

then the value of \(a\) is:

In an increasing arithmetic progression \(a_1, a_2,..., a_n\) if \(a_6 = 2\) and product of \(a_1\), \(a_5\) and \(a_4\) is greatest, then the value of d is equal to

\(\lim\limits_{x→0} \frac {e^{|2sinx|}-2|sinx|-1}{x^2}\) is

In a paper there are 3 sections A, B and C which have 8, 6 and 6 questions each. A student have to attempt 15 questions such that they have to attempt at least 4 questions out of each sections. Then number of ways of attempting these questions are

An urn contains 15 red, 10 white, 60 orange balls, 15 green balls. 2 balls are taken with replacement. Find the probability 1 ball is red and the other ball is white.

If \(S_n=3+7+11....\) upto \(n\) terms and \(40<\frac {6}{n(n+1)}\displaystyle\sum_{k=1}^n S_k<45\). Then \(n\) is

If\(\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}\)is the solution of\( 4cos\theta+ 5sin\theta=1\)then the value of \(tan\alpha\) is

The area (in square units) of the part of the circle \(x^2 + y^2 = 169\) which is below the line \( 5x - y = 13 \) is\[\frac{\pi \alpha}{2 \beta} - \frac{65}{2} + \frac{\alpha}{\beta} \sin^{-1} \left( \frac{12}{13} \right)\]where \( \alpha \) and \( \beta \) are coprime numbers. Then \( \alpha + \beta \) is equal to

Let \( f(x) = 2^x - x^2, \, x \in \mathbb{R} \). If \( m \) and \( n \) are respectively the number of points at which the curves \( y = f(x) \) and \( y = f'(x) \) intersect the x-axis, then the value of \( m + n \) is

Let \( \alpha, \beta \) be the roots of the equation \( x^2 - x + 2 = 0 \) with \( \text{Im}(\alpha) > \text{Im}(\beta) \). Then \( \alpha^6 + \alpha^4 + \beta^4 - 5 \alpha^2 \) is equal to

The lines \[ \frac{x - 2}{2} = \frac{y + 2}{-2} = \frac{z - 7}{16} \] and \[ \frac{x + 3}{4} = \frac{y + 2}{3} = \frac{z + 2}{1} \] intersect at the point \( P \). If the distance of \( P \) from the line \[ \frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{1} \] is \( l \), then \( 14l^2 \) is equal to \ldots

If the solution curve \( y = y \, x \) of the differential equation \((1 + y^2) \left(1 + \log_e x\right) dx + x \, dy = 0, \quad x > 0\) passes through the point \( (1, 1) \) and\[y(e) = \frac{\alpha - \tan\left(\frac{3}{2}\right)}{\beta + \tan\left(\frac{3}{2}\right)},\]then \( \alpha + 2\beta \) is

A function \(y=f(x)\) satisfies\(f (x)sin2x+sinx-(1+cos^2x) f'(x)=0\) with condition\(f(0)=0\).Then\(f(\frac{\pi}{2})\) equals to

For \( x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \), if\[y(x) = \int \frac{\csc x + \sin x}{\csc x \sec x + \tan x \sin^2 x} \, dx\]and\[\lim_{x \to -\frac{\pi}{2}} y(x) = 0\]then \( y\left(\frac{\pi}{4}\right) \) is equal to