List of top Mathematics Questions asked in JEE Main

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

Let $\overrightarrow 𝑎 =4\hat 𝑖+3\hat 𝑗ˆ$ and $\overrightarrow 𝑏 =3\hat 𝑖−4\hat 𝑗$+$5\hat 𝑘$. If $\overrightarrow 𝑐$ is a vector such that $\overrightarrow 𝑐 ⋅(\overrightarrow 𝑎 ×\overrightarrow𝑏⃗ )+25=0$, $\overrightarrow𝑐 ⋅(\hat𝑖+\hat𝑗+ \hat𝑘)=4$, and projection of $\overrightarrow𝑐$ on $\overrightarrow𝑎$ is $1$ , then the projection of $\overrightarrow 𝑐$ on $\overrightarrow 𝑏$ equals

Let $f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)$ and $S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}$. If $4\beta \sum_{\theta∈S}\theta$, then $f(\beta)$ is equal to

Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ Then $S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$ :

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse $x^2 + 4y^2 = 36$ is r, then $12r^2$ is equal to

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

Let $𝑎_1=𝑏_1=1$and $𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)$, $𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}$, $∀𝑛≥2$. If $𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}$ and $𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}$, then $2^7(2𝑆−𝑇)$ is equal to ____ .

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors Then which one of the following statements is TRUE ?

The domain of $f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}$, $x∈R$ is

The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

If the x-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___.

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is $(α,β,\frac{6}{7}),$ then 98(α + β)² is equal to___.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

If the mean deviation about median for the number $3,5,7,2 k , 12,16,21,24$ arranged in the ascending order, is 6 then the median is

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

Let $ R = \{a, b, c, d, e\} $ and $ S = \{1, 2, 3, 4\} $. Total number of onto functions $ f: R \to S $ such that $ f(a) \neq 1 $, is equal to:

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.