List of top Mathematics Questions asked in JEE Main

If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to:

$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?

Let f(x) = $x^2 - 5x$ and $g(x) = 7x - x^2$, then the area between the curves equals to:

When 4 dice are rolled, then the probability of 16 as a sum is:

A rectangle ABCD with ABCD with AB = 2 and BC = 4 is inscribed in rectangle PQRS such that vertices of ABCD lie on sides of PQRS then maximum possible area(in sq. unit) of rectangle PQRS is :

Two lines passing through (2, 3) parallel to coordinate axes. A circle of unit radius touches both the lines and lies on the origin side. Then the shortest distance of point (5,5) from the circle is:

$ \lim_{t \rightarrow x} \frac{t^2f(x) - x^2 f(t)}{t-x} = 1$, then 2f(2) + 3f(3) equals to:

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0

If a, b, c are in increasing A.P. and a + 1, b, c + 3 are in G.P. If A.M. of a, b, c is 8. Find cube of G.M. of a, b, c.

A parabola $y^2 = 12x$ has a chord PQ with mid-point (4, 1) then equation of PQ passes through

Team A plays 10 matches, probability of winning is $\frac1{3}$ and losing is $\frac2{3}$. They win x matches and lose y matches. Probability such that $|x – y| ≤ 2$ is P then find 3$^9P$.

For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2}=1, C_1$ is a circle touching hyperbola having centre at origin and $C_2$ is circle centred at four and touching hyperbola at vertices, if area of $C_1= 36π$ and area of $C_2 = 4π$. Find $a_2 + b_2 $= ?

Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

The radius of a circle is $\sqrt{10} .\,\, x + y = 4$ is the line intersecting the circle at P & Q. A chord MN is of length 2 m having slope –1. Find perpendicular distance between the two chords PQ and MN.

If $ f(x) =\begin{cases}\frac{(72)^x - 9^x -8^x+1}{\sqrt2-\sqrt{1+cosx}} &; x ≠0\\a\,log2\,log3 &  ; x=0\end{cases} $ is continuous at x = 0. Then $a^2$ equals to

If a, b, c are in A. P. and a + 1, b, c + 3 are in G. P., arithmetic mean of a, b, c is 8, then the value of cube of geometric mean of a, b, c is:

If (z)²+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α²+β²)

The coefficient of x⁷ in (1-x-x²+x³)⁶

\(f(x)=\frac{2x^2-3x+8}{2x^2+3x+8}\), Then sum of maximum and minimum values of f(x) is:

Find \(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{\sin^2x}{1+2^x} \;dx\)

Three urn A, B, C, A has 7 red and 5 black balls, B has 5 red and 7 black balls, C has 6 red and 6 black balls. One urn is selected and black ball is taken out. Find probability that the selected urn is A.

Find the number of rational numbers in the expansion of \((2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}\).

If \(f(x) =   \begin{cases}  x-2       & \quad 0\leq x\leq2\\     -2  & \quad -2\leq x\leq0   \end{cases}\) and \(h(x) = f(|x|) + |f(x)|, \int\limits^{k}_{0} h(x) dx\) is equal to _____.(k>0)