List of top Mathematics Questions asked in JEE Main

The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is _________
Let A₁, A₂, A₃, … be squares such that for each n ≥ 1, the length of the side of $A_n$ equals the length of diagonal of $A_{n+1}$. If the length of $A_1$ is 12 cm, then the smallest value of n for which area of $A_n$ is less than one, is __________.
The number of points, at which the function f(x) = |2x + 1| - 3|x + 2| + |x² + x - 2|, x ∈ ℝ is not differentiable, is ________
Let \( f(x) \) be a polynomial of degree 6 in \( x \), in which the coefficient of \( x^6 \) is unity and it has extrema at \( x = -1 \) and \( x = 1 \). If \( \displaystyle \lim_{x \to 0} \frac{f(x)}{x^3} = 1 \), then \( 5 \cdot f(2) \) is equal to __________.
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A⁴ is equal to __________
The locus of the point of intersection of the lines (√3)kx + ky - 4√3 = 0 and √3 x - y - 4(√3)k = 0 is a conic, whose eccentricity is _________
Let $\vec{a} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a} = \vec{c} \times \vec{a}$ and $\vec{r} \cdot \vec{b} = 0$, then $\vec{r} \cdot \vec{a}$ is equal to __________.
Let \( f : \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = 2x - 1 \) and \( g : \mathbb{R} \setminus \{1\} \to \mathbb{R} \) be defined as \( g(x) = \dfrac{x - \frac{1}{2}}{x - 1} \). Then the composition function \( f(g(x)) \) is :
Let \( p \) and \( q \) be two positive numbers such that \( p + q = 2 \) and \( p^4 + q^4 = 272 \). Then \( p \) and \( q \) are roots of the equation :
The system of linear equations 3x - 2y - kz = 10, 2x - 4y - 2z = 6, x + 2y - z = 5m is inconsistent if :
The value of \( 2^{15}C_1 + 2^{15}C_2 - 3^{15}C_3 + \cdots - 15^{15}C_{15} + \binom{14}{1} + \binom{14}{3} + \binom{14}{5} + \cdots + \binom{14}{11} \) is :
If $e^{(\cos^2 x + \cos^4 x + \cos^6 x + .......) \log_e 2}$ satisfies $t^2 - 9t + 8 = 0$, then find $\frac{2 \sin x}{\sin x + \sqrt{3} \cos x}$ for $0<x<\pi/2$ :
\( \displaystyle \lim_{x \to 0} \frac{\int_{0}^{x^2} \sin(\sqrt{t}) \, dt}{x^3} \) is equal to :
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways is :
If \( f(x) = [x - 1]\cos\!\left( \frac{2x - 1}{2}\pi \right) \), then \( f \) is :
If $\int \frac{\cos x - \sin x}{\sqrt{8 - \sin 2x}} dx = a \sin^{-1} \left( \frac{\sin x + \cos x}{b} \right) + c$, find (a, b) :
The area (in sq. units) of the part of the circle $x^2 + y^2 = 36$, which is outside the parabola $y^2 = 9x$, is :
The tangent to the curve $y = x^3$ at the point $P(t, t^3)$ meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is :
The equation of the plane passing through the point (1, 2, -3) and perpendicular to the planes $3x + y - 2z = 5$ and $2x - 5y - z = 7$, is :
The distance of the point (1, 1, 9) from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x + y + z = 17$ is :
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is :
The statement among the following that is a tautology is :
If the least and the largest real values of \(\alpha\), for which the equation \(|z| + \alpha(z - 1) + 2i = 0\) (\(z \in C\) and \(i = \sqrt{-1}\)) has a solution, are \(p\) and \(q\) respectively; then \(4(p^2 + q^2)\) is equal to _________
Let \(B_i\) (\(i=1, 2, 3\)) be three independent events in a sample space. The probability that only \(B_1\) occurs is \(\alpha\), only \(B_2\) occurs is \(\beta\) and only \(B_3\) occurs is \(\gamma\). Let \(p\) be the probability that none of the events \(B_i\) occurs and these 4 probabilities satisfy the equations \((\alpha - 2\beta) p = \alpha\beta\) and \((\beta - 3\gamma) p = 2\beta\gamma\) (All the probabilities are assumed to lie in the interval (0, 1)). Then \(\frac{P(B_1)}{P(B_3)}\) is equal to __________.