List of top Mathematics Questions asked in JEE Main

Let the tangent to the circle C₁: x² + y² = 2 at the point M(–1, 1) intersect the circle C₂: (x – 3)² + (y – 2)² = 5, at two distinct points A and B. If the tangents to C₂ at the points A and B intersect at N, then the area of the triangle ANB is equal to

Let a circle C : (x – h)² + (y – k)² = r², k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

If \(y(x) = (x^x)^x, \quad x > 0\), then \(\frac{d^2x}{dy^2} + 20\) at \(x = 1\) is equal to __________.

Let f and g be twice differentiable even functions on (–2, 2) such that
\(ƒ(\frac{1}{4})=0, ƒ(\frac{1}{2})=0, ƒ(1) =1\) and \(g(\frac{3}{4}) = 0 , g(1)=2\)
.Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is :

The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line x + y = 4 is _______.

Let

\(a→=α\^{i}+3\^{j}−\^{k}, \overrightarrow{b}=3\^{i}−β\^{j}+4\^{k} and \overrightarrow{c}=\^{i}+2\^{j}−2\^{k }\)

where α,β∈R, be three vectors. If the projection of

\(\overrightarrow{a} on \overrightarrow{c} is \frac{10}{3} and \overrightarrow{b}×\overrightarrow{c}=−6\^{i}+10\^{j}+7\^{k}, \)

then the value of α+β is equal to

Let the area of the triangle with vertices \(A(1, α), B(α, 0)\) and \(C(0, α)\) be \(4\) sq. units. If the points \((α, –α), (–α, α)\) and \((α^2, β)\) are collinear, then \(β\) is equal to

If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky – 5z = 1 and 3kx – ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

Let for the 9^th term in the binomial expansion of (3 + 6x)ⁿ, in the increasing powers of 6x, to be the greatest for x = 3/2, the least value of n is n₀. If k is the ratio of the coefficient of x⁶ to the coefficient of x³, then k + n₀ is equal to :

The remainder on dividing 1 + 3 + 3² + 3³ + … + 3²⁰²¹ by 50 ____ is

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Let \((a_n)^∞_{n=0}\) be a sequence such that a₀=a₁=0 and \(a_{n+2}=2a_{n+1}−a_n+1\) for all n⩾0. Then, \(∑^∞_{n=2} \frac{a_n}{7^n}\) is equal to

If \(\frac{1}{(20-a)(40-a)} + \frac{1}{(40-a)(60-a)} + \ldots + \frac{1}{(180-a)(200-a)} = \frac{1}{256}\), then the maximum value of a is :

Let a set A = A₁⋃ A₂⋃ …⋃ A_k, where A_i⋂ A_j = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y) : y ∈ A_i if and only if x ∈ A_i, 1 ≤ i ≤ k}. Then, R is

\(\begin{array}{l} \frac{2^3-1^3}{1\times7}+\frac{4^3-3^3+2^2-1^3}{2\times 11}+\frac{6^3-5^3+4^3-3^3+2^3-1^3}{3\times 15}+\cdots+\frac{30^3-29^3+28^3-27^3+\cdots+2^3-1^3}{15\times63}\end{array}\)

is equal to _______.

If
\(cot α=1\) and \(sec β=−\frac{5}{3}\) where \(π<α<\frac{3π}{2} and \frac{π}{2}<β<π\)
, then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :

If \(\begin{array}{l}\int_{0}^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2 + \sqrt{(1+x^2)^3}}}dx = \alpha \sqrt{2}+\beta\sqrt{3},\end{array}\)where \(α, β\) are integers, then \(α + β\) is equal to

If the constant term in the expansion of\( (3x^3−2x^2+\frac{5}{x^5})^{10}\) is 2^k·l, where l is an odd integer, then the value of k is equal to

The total number of functions, f : {1, 2, 3, 4} \(\rightarrow\) {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to

The slope of the tangent to a curve C: y = y(x) at any point (x, y) on it is \(\frac{2e^{2x}-6e^{-x}+9}{2+9e^{-2x}}\).If C passes through the points (0,\(\frac{1}{2}\)+\(\frac{\pi}{2\sqrt2}\)) and (α,\(\frac{1}{2e^{2\alpha}}\)), then e^α is equal to

The general solution of the differential equation (x – y²)dx + y(5x + y²)dy = 0 is:

The sum of diameters of the circles that touch (i) the parabola 75x² = 64(5y – 3) at the point (\(\frac{8}{5},\frac{6}{5}\)) and (ii) the y-axis is equal to _______.

For any real number x, let [x] denote the largest integer less than equal to x. Let f be a real-valued function defined on the interval [–10, 10] by \(f(x)=\left\{\begin{matrix} x=[x] & if \,[x]\, is \,odd\\ 1+[x]-x\,& if\,[x] \,is\,even \end{matrix}\right.\), if [x] is even, the value of \(\frac{\pi^2}{10}\int_{-10}^{10}f(x)cos\pi x dx\) is