List of top Mathematics Questions asked in JEE Main

For k ∈ R, let the solution of the equation
$\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}$
Inverse trigonometric functions take only principal values. If the solutions of the equation x² – bx – 5 = 0 are
$\frac{1}{α^2}+\frac{1}{β^2} $and $\frac{α}{β}$
, then b/k2 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 _____.

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 p and q be two real numbers such that p + q = 3 and p⁴ + q⁴ = 369. Then
$(\frac{1}{p} + \frac{1}{q} )^{-2}$
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 _________.

The value of the integral $∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}$ is equal to

The length of the perpendicular from the point (1, –2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y – z = 0 = x – 2y + 3z – 5 is

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 :

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 _______ .

The domain of the function
$f(x) = \sin^{-1}\left(\frac{x^2 - 3x + 2}{x^2 + 2x + 7}\right)$
is :

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 A and B be any two 3 × 3 symmetric and skew symmetric matrices, respectively. Then Which of the following is NOT true?

If the system of equations
$ x + y + z = 6 $,
$ 2x + 5y + \alpha z = \beta $,
$ x + 2y + 3z = 14 $
has infinitely many solutions, then $ \alpha + \beta $ is equal to:

Let the normal at the point P on the parabola y² = 6x pass through the point (5, –8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is

Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. Define $f : S → S$ as
$f(n) = \begin{cases} 2n, & \text{if } n \in \{1,2,3,4,5\} \\ 2n-11, & \text{if } n \in \{6,7,8,9,10\} \end{cases}$
Let $g : S → S$ be a function such that.
$(f \circ g)(n) = \begin{cases} n + 1, & \text{if } n \text{ is odd} \\ n - 1, & \text{if } n \text{ is even} \end{cases}$
Then $g(10) \cdot (g(1) + g(2) + g(3) + g(4) + g(5))$ is equal to __________.

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:

Let
A = $\begin{pmatrix}1 & 2\\ -2 & -5 \end{pmatrix}$
Let $ \alpha, \beta \in \mathbb{R} $ be such that $ \alpha A^2 + \beta A = 2I $. Then $ \alpha + \beta $ is equal to

The number of points of intersection of $|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, $z \in \mathbb{C}$, is

The number of distinct real roots of the equation x⁵(x³ – x² – x + 1) + x (3x³ – 4x² – 2x + 4) – 1 = 0 is ______ .

Let,
$\vec{a}=a\hat{i}+2\hat{j}−\hat{k}$ and $\vec{b}=−2\hat{i}+α\hat{j}+\hat{k}$
, where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors
$\vec{a}$ and $\vec{b}$ is $\sqrt{15(α^2+4)}$ , then the value of $2|\vec{a}|^2+(\vec{a}⋅\vec{b})|\vec{b}|^2 $
is equal to :

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

Let f,g : R → R be functions defined by*
$f(x) = \begin{cases} [x], & x < 0 \\ |1 - x|, & x \geq 0 \end{cases}$
and $g(x) = \begin{cases} e^x - x, & x < 0 \\ {(x - 1)^2 - 1}, & x \geq 0 \end{cases}$
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

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?

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:

Let
$x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}$
For k ∈ N, if X’A^kX = 33, then k is equal to ____ .