List of top Mathematics Questions asked in JEE Main

The area of the region {(x,y): x² ≤ y ≤8-x², y≤7} is

Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____

Let $I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx$, x>0. If $\lim\limits_{x\rightarrow\infin}I(x)=0$, then I(1) is equal to

Let the point (p, p+1) lie inside the region $E = \{(x,y):3-x≤y≤\sqrt{9-x^2}, 0 ≤ x ≤ 3\} $If the set of all values of p is the interval (a,b). then b2 + b - a2 is equal to_____

Let S_K = $\frac{1+2+...+ K}{K}$ and $\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)$, where A,B,C,D∈N and A has least value. Then

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

Let P = $\left[\begin{matrix} \frac{\sqrt3}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{matrix}\right]$ A = $\left[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right]$ and Q = PAP^T. If P^TQ²⁰⁰⁷P = $\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]$, then 2a+b-3c-4d equal to

Let α, β, γ be the three roots of the equation x³+bx+c=0. If βγ =1=-α, then b³+2c³-3α³-6β³-8γ³ is equal to

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

If 5f(x) + 4f ($\frac{1}{x}$) = $\frac{1}{x}$+ 3, then $18\int_{1}^{2}$ f(x)dx is:

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

The remainder on dividing $5^{99}$ by 11 is

Statement (P $\Rightarrow$ Q) $\land$ (R $\Rightarrow$ Q) is logically equivalent to :

Let $\theta$ be the angle between the planes $P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$ and $P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15$ Let $L$ be the line that meets $P_2$ at the point $(4,-2,5)$ and makes an angle $\theta$ with the normal of $P_4$ If $\alpha$ is the angle between $L$ and $P_2$, then $\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)$ is equal to

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} $

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15$^\circ$ and 60$^\circ$ respectively. B and Q are on the same horizontal level. If C is a point on AB such that CB = 15 m, then the area (in m$^2$) of the quadrilateral BCPQ is equal to :

If the variance of the frequency distribution

x_i	Frequency f_t
2	3
3	6
4	16
5	$\alpha$
6	9
7	5
8	6

is 3 , then $\alpha$ is equal to

The number of real roots of the equation $\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}$, is:

The value of tan 9°-tan27°-tan63°+tan81° is____.

Let A be the point (1, 2) and B be any point on the curve $ x^2 + y^2 = 16 $. If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C ($ \alpha, \beta $), then the length of the line segment AC is:

If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line $\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}$ is ax by+cz+6=0. then a + b + c is equal to

Let the mean and variance of the frequency distribution

x_i	2	4	6	8	10	12	14	16
f_i	4	4	α	15	8	β	4	5

are 9 and 15.08 respectively, then the value of α²+β²-αβ is ____.

If the lines $\frac{x−1}{2}=\frac{2−y }{−3} =\frac{ z−3 }{α}$ and $ \frac{x−4 }{5} =\frac{y−1}{ 2}= \frac{z}{ β}$ intersect, then the magnitude of the minimum value of 8αβ is ___.