List of top Mathematics Questions asked in JEE Main

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to
The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)
If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).
If \(f(x) = (x - 2)^2 (x - 3)^3\) and \(x ∈ [1, 4]\) and If \(M\) and \(m\) denotes maximum and minimum values respectively, then \(M - m\) is
A = {1, 2, 3, 4} , R = {(1, 2), (2, 3), (2, 4)} R ⊆ S and S is an equivalence relation then the minimum number of elements to be added to R is n, then the value of n is?
An equation of a plane parallel to the plane \(x-2y+2z-5=0\) and at a unit distance from the origin is?
Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).
The value of integral \(∫_0^{\frac \pi4} \frac {xdx}{cos^42x+sin^42x}\).
\(3, 7, 1,......., 404\) and \(4, 7, 10,......, 403\). Find sum of common terms.
Number of ways of arranging 5 officers in 4 rooms.
If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
Let be a sequence such that a1 + a2 +....+ an=\(\frac{n^2+3n}{(n+1) (n+2)}\) If  \(28 ∑^{10}_{k=1} \frac{1}{a_k} =  P _1 P_ 2 P _3 . . . P_ m\) , where p1, p2, …..pm are the first m prime numbers, then m is equal to
Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______
The range of f(x) = \(4\sin^{-1}(\frac{x^2}{x^2+1})\) is 
Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L _1: 3 x -4 y +12=0$, and $L _2: 8 x +6 y +11=0$ If $P$ lies below $L _1$ and above $L _2$, then $100(\alpha+\beta)$ is equal to
Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{T _{\subseteq} A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is _______ .
Let the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) represent three coterminous edges of a parallelepiped of volume \(V\). Then the volume of the parallelepiped, whose coterminous edges are represented by \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) and \(\mathbf{a} + 2\mathbf{b} + 3\mathbf{c}\), is equal to:

The integral \(\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx\) is equal to:

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___
Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to
The converse of ((~ p) ∧ q) ⇒ r 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:

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to
The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is