List of top Mathematics Questions asked in JEE Main

Let the solution curve y = y(x) of the differential equation (4 + x²)dy – 2x(x² + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _______.

Let P be the plane passing through the intersection of the planes

r→.(i+3k−k)=5 and r→ .(2i−j+k)=3,

and the point (2, 1, –2). Let the position vectors of the points X and Y be

i−2j+4k and 5i−j+2k

respectively. Then the points

If the absolute maximum value of the function
f(x)=(x²–2x+7)e(4x³−12x²−180x+31) in the interval [–3, 0] is f(α), then

If a₁ (> 0), a₂, a₃, a₄, a₅ are in a G.P., a₂ + a₄ = 2a₃ + 1 and 3a₂ + a₃ = 2a₄, then a₂ + a₄ + 2a₅ is equal to _______.

$y=tan^{-1}(sec \;x^3 - tan\; x^3), \frac{π}{2} < x^3< \frac{3π}{2},$ then

Let $\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\vec{a} \times \vec{b}$ on the vector $-\hat{ i }+2 \hat{ j }-2 \hat{ k }$ is $30$, then $\alpha$ is equal to

For the hyperbola $H: x^2 – y^2 = 1$ and the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b>0$, let the
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line $y= \sqrt\frac{5}{2} x+k$ be a common tangent of E and H.
Then $4(a^2 + b^2)$ is equal to _______.

The plane passing through the line L :lx – y + 3(1 – l) z = 1, x + 2y – z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x – 8y + 7z = 4. If θ is the acute angle between the line L and the y-axis, then 415 cos²θ is equal to ________.

Let f : [0, 1] → R be a twice differentiable function in (0, 1) such that f(0) = 3 and f(1) = 5.
If the line y = 2x + 3 intersects the graph of f at only two distinct points in (0, 1) then the least number of points x ∈ (0, 1) at which f”(x) = 0, is ___________.

The system of equations

–kx + 3y – 14z = 25

–15x + 4y – kz = 3

–4x + y + 3z = 4

is consistent for all k in the set

For real number a, b (a > b > 0), let
$\text{{Area}} \left\{ (x, y) : x^2 + y^2 \leq a^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1 \right\} = 30\pi$
and
$\text{{Area}} \left\{ (x, y) : x^2 + y^2 \geq b^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \right\} = 18\pi$
Then the value of (a – b)² is equal to _____.

If $a_1, a_2, a_3$ ….. and $b_1, b_2, b_3$ ….. are A.P., and $a_1 = 2, a_{10} = 3, a_1b_1 = 1 = a_{10}b_{10}$, then $a_4b_4$ is equal to

If $\begin{array}{l} \frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\cdots +\frac{10240}{3}=2^n\cdot m, \end{array}$where m is odd, then m⋅n is equal to ________.

The value of $\cot\left(\sum_{n=1}^{50} \tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is

The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x² + 2y² = 4 is an ellipse with eccentricity:

The value of the integral $∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx$ is equal to:

Let f : R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If
$l_1 = \int_{0}^{4nk} f(x) \, dx$ and $l_2 = \int_{-k}^{3k} f(x) \, dx$, then

Let for n = 1, 2, …, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is
$\frac{1}{(n+1)^2}$ . Then the value of
$\frac{1}{26} + \sum_{n=1}^{50} \left(S_n+\frac{2}{n+1}-n-1 \right)$
is equal to ________.

The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

Let R₁ = {(a, b) ∈ N × N : |a – b| ≤ 13} and R₂ = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

If A =$\sum_{n=1}^{\infty}$$\frac{1}{( 3 + (-1)^n)^n}$ and B = $\sum_{n=1}^{\infty}$$\frac{(-1)^n}{( 3 + (-1)^n)^n}$ ,
then A/B is equal to :

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\frac{5}{4}$. If the equation of the normal at the point $(\frac{8}{√5}, \frac{12}{5})$ on the hyperbola is 8√5 x + β y = λ, then λ – β is equal to ____.

If the lines
$\stackrel{→}{r}= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )$
and
$\stackrel{→}{r} = ( \alpha \hat{i} - \hat{j} ) + μ( \hat{2j} - \hat{3k} )$
are co-planer , then the distance of the plane containing these two lines from the point $( α , 0 , 0 )$ is :