List of top Mathematics Questions asked in JEE Main

let D_k=$\begin{vmatrix} 1 & 2k& 2k-1\\ n & n^2+n+2 & n^2\\ n & n^2+n & n^2+n+2 \end{vmatrix}$ if $∑^n_{ k=1}$ D_k=96, Then n 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?

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 _____.

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

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___.

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____

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________.

$\lim_{{x \to 0}} \limits$ $\frac{cos(sin x) - cos x }{x^4}$ is equal to :

Let
A =$\begin{pmatrix} 4 & -2 \\ \alpha & \beta \\ \end{pmatrix}$
If A² + γA + 18I = 0, then det (A) is equal to ______.

Let A be a $2×2$ matrix with $det (A) = –1$ and $det((A + I) (Adj (A) + I)) = 4$. Then the sum of the diagonal elements of A can be

If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p² + q²)x² – 2q(p + r)x + q² + r² = 0 is also a root of the equation x² + 2x – 8 = 0, then (q² + r²)/p² is equal to _______ .

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

If $\lim_{n\rightarrow \infty}$ $\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]$
then the integral value of k is equal to _______.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X≤ 2) is equal to

$\sum_{r=1}^{20}$(r²+1)(r!) is equal to

If for p ≠ q ≠ 0, the function
$f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}$
is continuous at x = 0, then

Let f(x) = [2x² + 1] and $g(x)=\left\{\begin{matrix} 2x-3,\,x<0&\\2x+3, x≥0 &\end{matrix}\right.$where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

If α, β are the roots of the equation
$x^2-(5+3^{\sqrt{log_35}}-5^{\sqrt{log_53}})+3(3^{(log_35)^{\frac{1}{3}}}-5^{(log_53)^{\frac{2}{3}}}-1) = 0$
then the equation, whose roots are α + 1/β and β + 1/α , is

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
$(2, a),−\frac{1}{2}<a<2 $
then p is equal to _______.

If the system of linear equations.
$8x + y + 4z = –2$
$x + y + z = 0$
$λx–3y=μ$
has infinitely many solutions, then the distance of the point $(λ, μ, -1/2)$ from the plane $8x + y + 4z + 2 = 0$ is