List of top Mathematics Questions asked in JEE Main

Let two vertices of triangle ABC be (2, 4, 6) and (0, –2, –5), and its centroid be (2, 1, –1). If the image of third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to

A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ. Then the locus of the point, that divides the line segment AB in the ratio 2 : 3, is a circle of radius

Let the ellipse $E : x^2 + 9y^2 = 9$ intersect the positive x- and y-axes at the points A and B respectively Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle which vertices A, P and the origin O is m/n , where m and n are coprime, then m – n is equal to

The slope of tangent at any point (x, y) on a curve y = y(x) is $\frac{x^2+y^2}{2xy},x>0$ If y(2) = 0, then a value of y(8) is

Let f be a differentiable function such that x² f(x) - x = $4 \int^x_0tf(t)dt,f(1)=\frac{2}{3}. \;\text{Then 18f(3)is equal to}$

If I(x) = $\int e^{sin^2x}$$(cos \;x \;sin \;2x - sin \;x)dx$ and I (0) = 1, then $I(π/3)$ is equal to

From a square of side 30 cm the squares of side x cm is cut off to make a cuboid of maximum volume. The surface area of cuboid with open top is?

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

If the coefficient of x⁷ in expansion of $(ax- \frac{1}{bx^2})^{13}$ is equal to the coefficient of x^-5 in expansion of $(ax + \frac{1}{bx^2})13$, then a⁴b⁴ is ______

Let the complex number $ z = x + iy $ be such that $\frac{2z - 3i}{2z + i}$ is purely imaginary. If $ x + y^2 = 0 $, then $ y^4 + y^2 - y $ is equal to

The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is __

Let the sixth term in the binomial expansion of $({\sqrt{2}^{log_{2}}(10-3^{x})+\sqrt[5]{2^{(x-2)log_{2}{3}}}})^{m}$, in the increasing powers of $2^{(x-2)log_{2}3}$, be 21 If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an AP, then the sum of the squares of all possible values of x is

Let $\alpha x+\beta y+y z=1$ be the equation of a plane passing through the point$(3,-2,5)$and perpendicular to the line joining the points $(1,2,3)$ and $(-2,3,5)$ Then the value of $\alpha \beta y$is equal to ____

If the term without $x$ in the expansion of $\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}$is 7315 , then $|\alpha|$ is equal to ___

The sum of the common terms of the following three arithmetic progressions$3,7,11,15, \ldots , 399$, $2,5,8,11, \ldots , 359$and $2,7,12,17, \ldots , 197,$ is equal to _____

Number of integral solutions to the equation $x+y+z=21$, where $x \geq 1$, $y \geq 3$, $z \geq 4$, is equal to ___

If the x-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

The point of intersection $C$ of the plane $8 x+y+2 z=0$ and the line joining the points $A (-3,-6,1)$ and $B (2,4,-3)$divides the line segment $AB$ internally in the ratio$k : 1 \ If a , b , c (| a |,| b |, | c |$are coprime) are the direction ratios of the perpendicular from the point $C$on the line $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$, then $| a + b + c |$is equal to ___

The number of integral values of $k$, for which one root of the equation \[2x^2 - 8x + k = 0\] lies in the interval $(1, 2)$ and its other root lies in the interval $(2, 3)$, is:

A triangle is formed by $X$-axis, $Y$-axis and the line $3 x+4 y=60$ Then the number of points $P ( n , b )$ which lie strictly inside the triangle, where a is an integer and $b$ is a multiple of a, is ____

$25 \%$ of the population are smokers A smoker has 27 times more chances to develop lung cancer than a non smoker A person is diagnosed with lung cancer and the probability that this person is a smoker is $\frac{k}{10}$, Then the value of $k$ is____

If $m$ and $n$ respectively are the numbers of positive and negative values of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{99}{2}$, then $m n$ is equal to__

Points $P(-3,2), Q(9,10)$ and $R(\alpha, 4)$ lie on a circle $C$ with $P R$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2 x-k y-1$, then $k$ is equal to_____

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can ofter 5 fruits to Anil is______

If $\int\limits_{\frac{1}{3}}^{3}\left|\log _e x\right| d x=\frac{m}{n} \log e\left(\frac{n^2}{v}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^2+n^2-5$ is equal to _____