List of top Mathematics Questions asked in JEE Main

Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\neq0$. Then the locus of the centroid of $\triangle OAB$ is a circle of radius

Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to

Let $\alpha,\beta\in\mathbb{R}$ be such that the function \[ f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x<1 \\ (\alpha+3)x+(\alpha-\beta), & x\ge1 \end{cases} \] is differentiable at all $x\in\mathbb{R}$. Then $34(\alpha+\beta)$ is equal to}

The value of $\dfrac{\sqrt{3}\cosec 20^\circ - \sec 20^\circ}{\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ}$ is equal to

Let $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is

From a lot containing $10$ defective and $90$ non-defective bulbs, $8$ bulbs are selected one by one with replacement. Then the probability of getting at least $7$ defective bulbs is

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become $10.1$ and $1.99$, respectively. Then $\alpha+\beta$ equals

Let $ \dfrac{\pi}{2} < \theta < \pi $ and $ \cot \theta = -\dfrac{1}{2\sqrt{2}} $. Then the value of \[ \sin\!\left(\frac{15\theta}{2}\right)(\cos 8\theta + \sin 8\theta) + \cos\!\left(\frac{15\theta}{2}\right)(\cos 8\theta - \sin 8\theta) \] is equal to

If the mean and the variance of the data

are $\mu$ and 19 respectively, then the value of $\lambda + \mu$ is

Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to $7x-y=14$. Find $|\alpha+\beta+\gamma+\delta|$.

Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions $ f : A \to B $ is equal to

If $ z = \dfrac{\sqrt{3}}{2} + \dfrac{i}{2} $, $ i = \sqrt{-1} $, then \[ \left(z^{201} - i\right)^8 \] is equal to

The number of elements in the set \[ S = \left\{ x : x \in [0,100] \text{ and } \int_{0}^{x} t^2 \sin(x - t)\,dt = x^2 \right\} \] is

The number of ways 16 oranges distributed to 4 children, each gets at least one.

Let $ A = \{0,1,2,\ldots,9\} $. Let $ R $ be a relation on $ A $ defined by $(x,y) \in R$ if and only if $ |x - y| $ is a multiple of $3$. Given below are two statements:
Statement I: $ n(R) = 36 $.
Statement II: $ R $ is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.

Let \[ \sum_{k=1}^{n} a_k = \alpha n^2 + \beta n. \] If $ a_{10} = 59 $ and $ a_6 = 7a_1 $, then $ \alpha + \beta $ is equal to

Let \[ I(x) = \int \frac{3\,dx}{(4x+6)\sqrt{4x^2 + 8x + 3}} \] and \[ I(0) = \frac{\sqrt{3}}{4} + 20. \] If \[ I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b} + c, \] where $a, b, c \in \mathbb{N}$ and $\gcd(a,b)=1$, then find the value of \[ a + b + c. \]

Let $ \vec{a} = \hat{i} - 2\hat{j} + 3\hat{k} $, $ \vec{b} = 2\hat{i} + \hat{j} - \hat{k} $, $ \vec{c} = \lambda \hat{i} + \hat{j} + \hat{k} $ and $ \vec{v} = \vec{a} \times \vec{b} $. If $ \vec{v} \cdot \vec{c} = 11 $ and the length of the projection of $ \vec{b} $ on $ \vec{c} $ is $ p $, then find the value of $ 9p^2 $.

The least value of $(\cos^2 \theta - 6\sin \theta \cos \theta + 3\sin^2 \theta + 2)$ is

The area of the region enclosed between the circles $x^2 + y^2 = 4$ and $x^2 + (y - 2)^2 = 4$ is:

Let $ \vec{a}, \vec{b}, \vec{c} $ be three vectors such that \[ \vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c}). \] If $ |\vec{a}| = 1 $, $ |\vec{b}| = 4 $, $ |\vec{c}| = 2 $, and the angle between $ \vec{b} $ and $ \vec{c} $ is $60^\circ$, then $ |\vec{a} \cdot \vec{c}| $ is equal to.

If \[ f(x) = \begin{cases} \dfrac{a|x| + x^2 - 2(\sin|x|)(\cos|x|)}{x}, & x \ne 0, \\ b, & x = 0, \end{cases} \] is continuous at $ x = 0 $, then $ a + b $ is equal to.

Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S) + n(P)$ is equal to ___

Points of intersection of ellipses $x^2 + 2y^2 - 6x - 12y + 23 = 0$ and $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ lie on a circle. Value of $ab + 18r^2$ is

Let \[ A = \begin{bmatrix} 0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0 \end{bmatrix} \] and $ B $ be a matrix such that \[ B(I - A) = I + A. \] Then the sum of the diagonal elements of $ B^{T}B $ is equal to