List of top Mathematics Questions asked in JEE Main

Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b

If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.

A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.

If \(r = |z|,\ θ = arg(z)\) and \( z = 2 – 2\ tan (\frac {5\pi}{8})\) then find \((r, θ)\).

The number of ways to distribute 8 identical books into 4 distinct bookshelf is (where any bookshelf can be empty)

The remainder when \(64^{{32}^{32}}\) is divided by 9 is.

Let \((\alpha, \beta, y)\) be the foot of perpendicular form the point \((1,2,3)\) on the line \(\bigg(\frac{x + 3}{5}\) = \(\frac{y - 1}{2}\) = \(\frac{z + 4}{3}\) \(\bigg)\)then \(19 (\alpha + \beta + y)\)

Area bounded by \(0 ≤ y ≤ \text {min}(x^2+ 2, 2x + 2)\), \(x∈[0, 3]\), then \(12A\) is

\((α, β)\) lie on the parabola \(y^2 = 4x\) and \((α, β)\) also lie on chord with midpoint \((1,\frac 54)\) of another parabola \(x^2 = 8y\), then value of \(|(8 – β)(α – 28)|\) is

There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is.

A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

In which interval the function \(f(x) = \frac {x}{(x^2-6x-16)}\) is increasing?

The mean of 5 observations is \(\frac {24}{5}\) and variance is \(\frac {194}{25}\) . If the mean of first four observations is \(\frac 72\) , then the variance of first four observations is

If A(l, –1, 2), B(5, 7, –6), C(3, 4, –10) and D(–l, –4, –2) are the vertices of a quadrilateral ABCD, then its area is :

The integral \(\int_{0}^{\pi/4} \frac{136 \sin x}{3 \sin x + 5 \cos x} \, dx\) is equal to

Let \[ a = 1 + \frac{{^2C_2}}{3!} + \frac{{^3C_2}}{4!} + \frac{{^4C_2}}{5!} + \dots,\]
\[ b = 1 + \frac{{^1C_0 + ^1C_1}}{1!} + \frac{{^2C_0 + ^2C_1 + ^2C_2}}{2!} + \frac{{^3C_0 + ^3C_1 + ^3C_2 + ^3C_3}}{3!} + \dots \]Then \( \frac{2b}{a^2} \) is equal to _____

Suppose \( \theta \in \left[ 0, \frac{\pi}{4} \right] \) is a solution of \( 4 \cos \theta - 3 \sin \theta = 1 \). Then \( \cos \theta \) is equal to:

Let \( f(x) = x^5 + 2x^3 + 3x + 1 \), \( x \in \mathbb{R} \), and \( g(x) \) be a function such that \( g(f(x)) = x \) for all \( x \in \mathbb{R} \). Then \( \frac{g(7)}{g'(7)} \) is equal to:

If \[\int_{0}^{\pi/4} \frac{\sin^2 x}{1 + \sin x \cos x} \, dx = \frac{1}{a} \log_e \left( \frac{a}{3} \right) + \frac{\pi}{b\sqrt{3}},\]where \( a, b \in \mathbb{N} \), then \( a + b \) is equal to _____

If the line \(\frac{2 - x}{3} = \frac{3y - 2}{4\lambda + 1} = 4 - z\) makes a right angle with the line  \(\frac{x + 3}{3\mu} = \frac{1 - 2y}{6} = \frac{5 - z}{7},\) then \( 4\lambda + 9\mu \) is equal to:

The coefficients a, b, c in the quadratic equation ax² + bx + c = 0 are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}. The probability of this equation having repeated roots is :

The value of \(\int_{-\pi}^{\pi} \frac{2y(1 + \sin y)}{1 + \cos^2 y} \, dy\)

Consider the following two statements:
Statement I: For any two non-zero complex numbers \( z_1, z_2 \),
\((|z_1| + |z_2|) \left| \frac{z_1}{|z_1|} + \frac{z_2}{|z_2|} \right| \leq 2 (|z_1| + |z_2|)\)
Statement II: If \( x, y, z \) are three distinct complex numbers and \( a, b, c \) are three positive real numbers such that  
\(\frac{a}{|y - z|} = \frac{b}{|z - x|} = \frac{c}{|x - y|},\)
then  
\(\frac{a^2}{y - z} + \frac{b^2}{z - x} + \frac{c^2}{x - y} = 1.\)
Between the above two statements,

For the function \(f(x) = \sin x + 3x - \frac{2}{\pi}(x^2 + x), \quad x \in \left[0, \frac{\pi}{2}\right],\)consider the following two statements:  
1. \( f \) is increasing in \( \left(0, \frac{\pi}{2}\right) \).  
2. \( f' \) is decreasing in \( \left(0, \frac{\pi}{2}\right) \).  
Between the above two statements