List of top Mathematics Questions asked in JEE Main

A tangent to the hyperbola $\frac{x^{4}}{4}-\frac{y^{2}}{2}=1$ meets x-axis at $P$ and y-axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on :
The ellipse $E_1 : \frac{x^2}{9} + \frac{y^2}{4}$ = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse $E_2$ is
Let $a_1, a_2, a_3,...$ be an $A.P$, such that $\frac{a_{1}+a_{2}+\ldots+a_{p}}{a_{1}+a_{2}+a_{3}+\ldots+a_{q}} = \frac{p^{3}}{q^{3}} ; p\ne q$ Then $\frac{a_{6}}{a_{21}}$ is equal to:
The cost of running a bus from $A$ to $B$ , is $Rs.\left(av+\frac{b}{v}\right)$ where $v$ km/h is the average speed of the bus. When the bus travels at $30\, km/h$, the cost comes out to be $Rs.\, 75$ while at $40\, km/h$, it is $Rs. \,65$. Then the most economical speed (in $km/ h$) of the bus is :
The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at (0, 3) is
Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .
Let R be the set of real numbers A = {(x, y) $\in$ R $\times$ R : y - x is an integer} is an equivalence relation on R. B = {(x, y) $\in$ R $\times$ R : x = $\alpha$y for some rational number $\alpha$} is an equivalence relation on R.
If $ {{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x, $ then $ x $ is equal to
The variance of first n even natural numbers is $\frac{n^2 - 1}{4}$. The sum of first n natural numbers is $\frac{n(n + 1)}{2}$ and the sum of squares of first n natural numbers is $\frac{n(n + 1)(2n +1)}{6}$.
Which of the following statements is true?
The vector sum of two forces is perpendicular to their vector differences. In that case the forces
Probability of four sons to a couple is
Let \(S=x: x∈R\) and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to
If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.
If 4log10⁡[x+1]−6log10⁡x−2⋅3log10⁡[x2+2]=0 then the value of 120x is
Find the equation of normal to the curvey=(1+x)y+sin−1⁡(sin2⁡x) at x=0

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1$.Then $6 y^2( e )$ is equal to

Given \(f(x) =   \begin{cases}     \frac{tan((a+1)x)+tanx\cdot b}{x}       & \quad x\lt 0\\     3  & \quad x=0\\ \frac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{\sqrt{a}bx\sqrt{x}}  & \quad x\gt 0\end{cases}\) It is a continuous function at x=0, then find \(\frac{b}{a}\)
If ax2+bx+c=0 and cx2+bx+a=0 (a,b,c∈R) have a common non - real root, then
Find the range of \(\frac{1}{7}-\sin5x\)
Tetrahedral dice having outcomes (1, 2, 3, 4) has 3 outcomes a, b, c (which are visible). Probability that ax2 + bx + c = 0 has real roots is m/n (m, n are coprime), then m + n =?
The 50th word in the dictionary using the letters B, B, H, J, O is:
A circle passes through (0, 0) and (1, 0) and touches the circle x2 + y2 = 9. Then the locus of the centre of the circle is:
If f(x) = 3ax3 + bx2 + cx + 1 and f(1) = 41, f'(1) = 2 and f''(2)= 4, then find (a2 + b2 + c2).

Let \(S=\left\{0∈(0,\frac{π}{2}) : \sum^{9}_{m=1} \sec(θ+(m-1)\frac{π}{6})\sec(θ+\frac{mπ}{6}) = -\frac{8}{\sqrt3}\right\}\)
Then,