List of top Mathematics Questions asked in JEE Main

Let a function f: ℝ → ℝ be defined as :
$\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}$
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?

Let the function
$f(x)$=$\begin{cases} \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\ \space 10 & \text;{if } x = 0 \\ \end{cases}$
be continuous at x = 0. Then α 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

Let A=$\begin{pmatrix} 2 &-1 &-1 \\ 1&0 &-1 \\ 1&-1 &0 \end{pmatrix}$ and B=A–I. If ω=$\frac{\sqrt3 i-1}{2}$, then the number of elements in the set {n∈{1,2,⋯,100}:$A^n+(ωB)^n$=A+B} is equal to _______.

The ordered pair (a, b), for which the system of linear equations
3x – 2y + z = b
5x – 8y + 9z = 3
2x + y + az = –1
has no solution, is :

Let
$A = \begin{pmatrix} 1+i & 1 \\ -i & 0 \end{pmatrix}$ where $i=\sqrt{−1}.$
Then, the number of elements in the set
$\left\{n∈\left\{1,2,…,100\right\}:A^n=A\right\}$
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, n^th term is a_n and the common difference is 10ar², is equal to

Let A = {1, a₁, a₂…a₁₈, 77} be a set of integers with 1 <a₁<a₂<….<a₁₈< 77. Let the set A + A = {x + y :x, y∈A} contain exactly 39 elements. Then, the value of a₁ + a₂ +…+a₁₈ 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

Let α, β(α > β) be the roots of the quadratic equation x² – x – 4 = 0.
If $P_n=α^n–β^n, n∈N$ then $\frac{P_{15}P_{16}–P_{14}P_{16}–P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}$
is equal to _______.

Let the function f(x) = 2x² – log_ex, x> 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y² = 4ax at a point P on it passes through the point (8a, 8a –1) but does not pass through the point (-1/a, 0). If the equation of the normal at P is
$\frac{x}{α}+\frac{y}{β}=1$
then α + β is equal to _______ .

Consider the sequence $a_1, a_2, a_3, \ldots \ldots$ such that $a_1=1, a_2=2$ and $a_{n+2}=\frac{2}{a_{n+1}}+a_n$ for $n =1,2,3, \ldots$ If $\left(\frac{a_1+\frac{1}{a_2}}{a_3}\right) \cdot\left(\frac{a_2+\frac{1}{a_3}}{a_4}\right) \cdot\left(\frac{a_3+\frac{1}{a_4}}{a_5}\right) ... \left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^a\left({ }^{61} C_{31}\right)$, then $\alpha$ is equal to :

If $z = 2 + 3i$, then $z^5 + (\overline{z})^5$ is equal to:

If
$\lim_{{x \to 1}} \frac{{\sin(3x^2 - 4x + 1) - x^2 + 1}}{{2x^3 - 7x^2 + ax + b}} = -2$
, then the value of (a – b) is equal to_______.

If
$\sum\limits_{k=1}^{31}$ $(^{31}C_k) (^{31}C_{k-1})$ $-\sum\limits_{k=1}^{30}$ $(^{30}C_k) (^{30}C_{k-1})$ $= \frac{α (60!)} {(30!) (31!)}$
where $α ∈ R$, then the value of 16α is equal to

Let the tangents at two points A and B on the circle$ x^2 + y^2 – 4x + 3 = 0$ meet at origin O(0, 0). Then the area of the triangle OAB is

If $\lim_{n\rightarrow \infty}$($\sqrt{n^2-n-1}$ + nα+β)=0 then 8(α + β) is equal to

Let $S=\left\{(x,y)∈\N×\N:9(x−3)^2+16(y−4)^2≤144\right\}$
and $T=\left\{(x,y)∈\R×\R:(x−7)^2+(y−4)^2≤36\right\}.$
Then n(S ⋂ T) is equal to ____ .

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Let $α, β$ be the roots of the equation $x^2-\sqrt{2}x+\sqrt{6}=0$ and$ \frac{1}{α^2}+1$,$\frac {1}{β^2}+1$ be the roots of the equation $x^2 + ax + b = 0$ . Then the roots of the equation $x^2 – (a + b – 2)x + (a + b + 2) = 0$ are

Let a function ƒ : N →N be defined by
$f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.$
then, ƒ is

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers Let $f ( x )=\alpha x ^5+\beta x ^3+\gamma x , x \in R$ and $g: R \rightarrow R$ be such that $g(f(x))=x$ for all $x \in R$ If $a_1, a_2, a_3, \ldots, a_n$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac{1}{n} \displaystyle\sum_{i=1}^n f\left(a_i\right)\right)\right)$is equal to :

Let A and B be two $3 × 3$ non-zero real matrices such that AB is a zero matrix. Then