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
If the integral $\int \frac{cos 8x+1}{cot 2x-tan 2x} dx=A cos 8x+k,$ where $k$ is an arbitrary constant, then $A$ is equal to:
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.
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 $\frac{n(n + 1)(2n +1)}{6}$.
If $ {{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x, $ then $ x $ is equal to
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 A=(02qrpq−rp−qr). If AAT=I3, then |p| is:

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,

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0
Let A = [1, 2, 3, 4, 5], m be the number of relations such as 4x ≤ 5y XRY and n be the minimum number of elements to be added from A × A to make a symmetric relation. Then the value of n + m.
Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is
If an be the nth  term of the GP of positive numbers. Let ∑n=100100a2n=α and ∑n=1100a2n−1=β such that α≠β then the common ratio is:
If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;

The angle θ between the vectors \(\rm \vec{a} = 5\hat{i} - \hat{j} +  \hat{k}\) and \(\rm \vec{b} = \hat{i} + \hat{j} -  \hat{k}\) equals to

If a→,b→,c→ are non-coplanar vectors and λ is a real number, then[λ(a→+b→)λ2b→λc→]=[a→b→+c→b→] for

For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has 

If 4x2 + py2 = 45 and x2 - 4y2 = 5 cut orthogonally, then the value of p is:
If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha, \beta)$, then the quadratic equation whose roots are $\alpha+4 \beta$ and $4 \alpha+\beta$, is