List of top Mathematics Questions asked in JEE Main

If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x² at the point P and V is the vertex of the parabola, then the slope of the line through P and V is:

If
$0 < x< \frac{1}{\sqrt2}\ and\ \frac{\sin^{-1}x}{α} = \frac{\cos^{-1}x}{β} $
then a value of
$sin(\frac{2πα}{α+β}) $
is

The value of $cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})$ is equal to:

Let $S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}$ .
Then$n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)$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________.

The number of elements in the set S= {x∈R : 2cos⁡$(\frac{x_2+x}{6})$=$4^x+4^{-x}$}

Let z = a + ib, b≠ 0 be complex numbers satisfying

$\begin{array}{l} z^2=\overline{z}\cdot 2^{1-\left|z\right|}.\end{array}$

Then the least value of n∈ N, such that zⁿ= (z + 1)ⁿ, 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

$S=\left\{x∈[-6,3]-\left\{-2,2 \right\} :\frac{|x+3|-1}{|x|-2}>=0 \right\} \space and \space \left\{T={x∈Z:x^2-7|x|+9<=0}\right\}$

Then the number of elements in S ⋂ T is

Let $\frac{dy}{dx} = \frac{ax-by+a}{bx+cy+a}$, where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is

Let p and p + 2 be prime numbers and let
$Δ=\begin{vmatrix} p! & (p+1)! & (p+2)! \\ (p+1)! & (p+2)! & (p+3)! \\ (p+2)! & (p+3)! & (p+4)! \\ \end{vmatrix}$
Then the sum of the maximum values of α and β, such that p^α and (p + 2)^β divide Δ, is _______.

If
$f(x) = \begin{cases} x + a, & x \leq 0 \\ |x - 4|, & x > 0 \end{cases}$ and $g(x) = \begin{cases} x + 1, & x < 0 \\ (x - 4)^2 + b, & x \geq 0 \end{cases}$
are continuous on R, then (gof) (2) + (fog) (–2) 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 _______.

Let a, b ∈ R be such that the equation ax² – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x² – 2bx + 21 = 0, then α² + β² is equal to

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

If [t] denotes the greatest integer ≤ t, then the number of points, at which the function
$f(x) = 4|2x + 3| + 9\lfloor x + \frac{1}{2} \rfloor - 12\lfloor x + 20 \rfloor$
is not differentiable in the open interval (–20, 20), is ____ .

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 f(x)=$\left\{\begin{matrix} |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\ |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.$ where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is

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 $\alpha, \beta$ 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 _______.