List of top Mathematics Questions asked in JEE Main

Let the number of matrices of order 3 x 3 are possible using the digits [0, 1, 2, 3, … , 10) is mn, then (m + n) is ___. (where m is a prime number)
If \(y = max \{ {\sqrt{x}, x^2-4, x^3+2}\}\), then the number of solution(s) of y=1 is/are____?

Matrix A is 2×2 matrix and A2=I, no elements of the matrix are zero, let the sum of diagonal elements is a and det(A)=b, then the value of 3a2+b2 is?

Maximum value n such that (66)! is divisible by 3n

Sum of first 20 terms: 5, 11, 19, 29, 41

Maximum value n such that (66)! is divisible by 3n
Let 
\(S=\left\{x∈[-6,3]-\left\{-2,2 \right\} :\frac{|x+3|-1}{|x|-2}>=0 \right\} \space and \space \left\{T={x∈Z:x^2-7|x|+9<=0}\right\}\)
Then the number of elements in S ⋂ T is
\(\int_{0}^{2} \left( |2x^2 - 3x| + \left[x - \frac{1}{2}\right] \right) \, dx,\)
where [t] is the greatest integer function, is equal to
Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the first 21 terms of an AP, whose first term is 10ar, nth term is an and the common difference is 10ar2, is equal to
If \(\lim_{n\rightarrow \infty}\)(\(\sqrt{n^2-n-1}\) + nα+β)=0 then 8(α + β) is equal to

Let f: ℝ → ℝ be defined as
\(f(x) = \left\{   \begin{array}{ll}     [e^x] &  x < 0 \\     [a e^x + [x-1]] & 0 \leq x < 1 \\     [b + [\sin(\pi x)]] &  1 \leq x < 2 \\     [[e^{-x}] - c] &  x \geq 2 \\   \end{array} \right.\)
Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t. 
Then, which of the following statements is true?

The sum of all real value of \(x\) for which \(\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}\)  is equal to________.

If
\(\sum_{k=1}^{10} \frac{k}{k^4 + k^2 + 1} = \frac{m}{n}\)
where m and n are co-prime, then m + n is equal to

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = _______.

The curve y(x) = ax3 + bx2 + cx + 5 touches the x-axis at the point P(–2, 0) and cuts the y-axis at the point Q, where y′ is equal to 3. Then the local maximum value of y(x) is

The Integral
\(\int \frac{(1 - \frac{1}{\sqrt{3}})(\cos x - \sin x)}{1 + \frac{2}{\sqrt{3}}\sin2 x} \,dx\)
is equal to

Let \(\alpha, \beta\) be the roots of the equation \(x^2 - 4\lambda x + 5 = 0\) and α, γ be the roots of the equation \(x^2 - (3\sqrt{2} + 2\sqrt{3})x + 7 + 3\lambda\sqrt{3} = 0\). If \(\beta + \gamma = 3\sqrt{2}\) then \((\alpha + 2\beta + \gamma)^2\) is equal to _______.
A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2, 1) is 14. Let f(x, y) = 0 be the locus of P, which intersects the x-axis at the points A, B and the y-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to
\(\begin{array}{l}\displaystyle \lim_{ x\to 0}\left(\frac{(x+2\cos x)^3 + 2(x+2\cos x)^2 + 3 \sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} \end{array}\)
is equal to _________.
If \(\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}\), where \(\alpha, \beta, \gamma \in \mathbb{R}\) then which of the following is NOT correct?

The number of functions f, from the set
\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)
such that
\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)
is ______.

Let the minimum value v0 of
v = |z|2+|z-3|2+|z-6i|2,z∈C
is attained at z = z0. Then
\(|2z^2_0-\overline{z}^3_0+3|^2+v^2_0\)
is equal to

Let S = {1, 2, 3, …, 2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is
If\(\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}\)is equal to 2n. m, where m is odd, then n + m is equal to ______.
A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is \(\frac{\sqrt{29}}{3}\) then B also lies on the line :