List of top Mathematics Questions asked in JEE Main

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

Let $S_1=\left\{z_1 \in C:\left|z_1-3\right|=\frac{1}{2}\right\}$ and $S _2=\left\{ z _2 \in C :\left| z _2-\right| z _2+1||=\left| z _2+\right| z _2-1||\right\}$ Then, for $z_1 \in S_1$ and $z_2 \in S_2$, the least value of $\left|z_2-z_1\right|$ is :

If the system of linear equations
2x + 3y – z = –2
x + y + z = 4
x – y + |λ|z = 4λ – 4
where λ ∈ R, has no solution, then

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 _______.

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 ________.

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 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 _______ .

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_______.

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 P be the plane containing the straight line$\frac{ x−3}{9}$=$\frac{y+4}{-1}$=$\frac{z-7}{-5}$and perpendicular to the plane containing the straight lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $\frac{x}{3}=\frac{y}{7}=\frac{z}{8}$.If d is the distance P from the point (2, –5, 11), then d² is equal to :

Let $f :R→R$ be a function defined by $f(x)=(2(1−\frac {x^{25}}{2})(2+x^{25}))^{\frac {1}{50}}$. If the function $g(x) = f (f (f (x))) + f (f (x))$, then the greatest integer less than or equal to $g(1)$ is _________.

Let the system of linear equations \[ x + 2y + z = 2, \quad \alpha x + 3y - z = \alpha, \quad -\alpha x + y + 2z = -\alpha \] be inconsistent. Then $\alpha$ is equal to:

If the system of linear equations

2x + y – z = 7

x – 3y + 2z = 1

x + 4y + δz = k, where δ, k ∈ R

has infinitely many solutions, then δ + k is equal to:

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is _______.

The area of the region enclosed by
$y≤4x^2, x2≤9y\ and\ y≤4,$
is equal to

Let
$β = \lim_{x →0} \frac{αx-(e^{3x}-1)}{αx(e^{3x}-1) }$for some$ α \in R.$
Then the value of α+β is

Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A₁ is twice the area A₂. Then the normal to the curve perpendicular to the line 2x – 12y = 15 does NOT pass through the point.

The domain of the function
$f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))$
where [t] is the greatest integer function, is

The area of the region given by $A =\left\{( x , y ): x ^2 \leq y \leq \min \{ x +2,4-3 x \}\right\}$ is :

If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a> 0 makes an angle 30° with the plane y – z + 2 = 0, then the direction cosines of the line are :

If $\displaystyle\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0 $ then $8(\alpha+\beta)$ is equal to :

The value of $\log_e2\frac{d}{dx}(\log_{cos⁡ x}\cosec x) $ at $x=\frac{\pi}{4}$ is