List of top Mathematics Questions asked in JEE Main

In a given data set mean of 40 observations is 50 and standard deviation is 12. Two readings which were 20 and 25, were mistakenly taken as 40 and 45. Find correct variance of data set

In the expansion of $(2^\frac{1}{4}+3^{-\frac{1}{4}})^n$, the ratio of $5^{th}$ term from start and $5^{th}$ term form end is $\sqrt 6 : 1$ , then find $3^{rd}$ term

$(2x^3-\frac{1}{3}x^8)^5$ → coefficient of $x^4$

The coefficient of $x^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is______

$\displaystyle\lim _{x \rightarrow 0} \frac{48}{x^4} \int_0^x \frac{ t ^3}{ t ^6+1} d t$ is equal to

The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to

Let y = y(x), y>0, be a solution curve of the differential equation (1 + x²) dy=y (x–y)dx. If y(0)=1 and y(2√2) , = b then

Let $f$ be a twice differentiable function on $R$.
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$
then $(2 a+1)^5 a^2$ is equal to ______.

Let $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

Find the number of integral values of x which satisfy the inequality x₂–10x+19<6.

A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :

Let $z_1=2+3 i$ and $z_2=3+4 i$ The set $S=\left\{z \in C:\left|z-z_1\right|^2-\left|z-z_2\right|^2=\left|z_1-z_2\right|^2\right\}$ represents a

The mean of coefficients of x, x², ....., x⁷ in the binomial expansion of (2 + x)⁹ is?

If [x+6]+[x+3] ≤ 7 and let call its solution as set A and set B is the solution of inequality 3^5x-8 < 3^-3x.

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-

If $x+y+z=17$ and x, y, z are non-negative integers, then find the number of integral solutions is

($\frac{2x^3-1}{3x^8}$)⁵$\rightarrow$coefficient of x⁴

Mean of first 15 numbers is 12 and variance is 14. Mean of next 15 numbers is 14 and variance is a. If variance of all 30 numbers is 13, then a is equal to

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x) = |[x] |+$\sqrt{x -[x] }$is discontinuous is _____.

Let be a sequence such that a₁ + a₂ +....+ a_n=$\frac{n^2+3n}{(n+1) (n+2)}$ If $28 ∑^{10}_{k=1} \frac{1}{a_k} = P _1 P_ 2 P _3 . . . P_ m$ , where p₁, p₂, …..p_mare the first m prime numbers, then m is equal to

Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then $r^2_1+r_2^2– r_1r_2$ is equal to_____.

If $∫^{0.15}_{-0.15 }|100x^2-1|dx=\frac{k}{3000,}$ then k is equal to____.

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___.

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

(S1): (p⇒q)∧(p∧((~q)) is a contradiction and
(S2): (p∧q)v((~q)v((~p)∧ q)v (p∧(~q))v((~p)∧ (~q)) is a tautology