List of top Mathematics Questions asked in JEE Main

Let A =$\left[\begin{matrix} 2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2 \end{matrix} \right]$. If |adj(adj(adj 2A)) | = (16)ⁿ, then n is equal to

Let (a+bx+cx²)¹⁰ = $ \sum_{i=0}^{20} $ p_ixⁱ, a,b,c∈N. If p₁=20 and P₂ = 210, then 2(a+b+c) is equal to

If $ A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix} $, $ A^{-1} = \alpha A + \beta I $ and $ \alpha + \beta = -2 $, then $ 4\alpha^2 + \beta^2 + \lambda^2 $ is equal to:

If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is

Let the plane P : 4x – y + z = 10 be rotated by an angle $\frac{π}{2}$ about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

Let C be the circle in the complex plane with centre z₀ =$\frac{1}{2}$ (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|₂ is equal to

Let$ |\vec{a}|=2, |\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{π}{4}$. Then $|(\vec{a}+2\vec{b})×(2\vec{a}-3\vec{b})|^2$ is equal to

The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to

Let $\Delta$ be the area of the region $\{(x,y)∈R^2:x^2+y^2≤21,y^2≤4x,x≥1\}$. Then $\frac{1}{2}(\Delta-21\text{ sin}^{-1} (\frac{2}{\sqrt7}))$ is equal to

The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is

Let be a sequence such that a₁ + a₂ +....+ a_n=$\frac{n^2+3n}{(n+1) (n+2)}$ If $28 ∑^{10}_{k=1} \frac{1}{a_k} = P _1 P_ 2 P _3 . . . P_ m$ , where p₁, p₂, …..p_mare the first m prime numbers, then m is equal to

Let $f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x$, $x∈R$ be a function which satisfies $f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy$. Then (a+b) equal to

Let $𝑦=𝑦(𝑥)$ be the solution of the differential equation $𝑥\;𝑙𝑜𝑔_𝑒⁡𝑥\frac{𝑑𝑦}{ 𝑑𝑥} +𝑦=𝑥^2𝑙𝑜𝑔_𝑒⁡𝑥,(𝑥>1)$. If $𝑦(2)=2$, then $𝑦(𝑒)$ is equal to

Let s={$z=x+ry:\frac{2z-3i}{4z+2i}$ is a real number}. Then which of the following is not correct?

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non-zero vectors and $\hat{\mathbf{n}}$ is a unit vector perpendicular to $\mathbf{c}$ such that: $\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)$ and $ \mathbf{b} \cdot \mathbf{c} = 12 $, then $ \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) $ is equal to:

If the coefficient of x⁷ in ($ax^2 +\frac{ 1}{2bx}^{11}$) and x^-7 in ($ax - \frac{1}{3bx^2}^{11}$), are euual then

Let the line L pass through the point (0, 1, 2), intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

Let x = x(y) be the solution of the differential equation 2(y+2) log_e (y+2)dx+(x+4-2log_e(y+2))dy = 0, y >-1 with x (e⁴-2)=1. Then x(e⁹-2) is equal to

The statement ~[p v (~(p ∧ q))] is equivalent to

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

The value of $\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0$ such that $y(1)=1$ Then $\left|(y(2))^3-12 y(2)\right|$ is equal to :

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\vec{c}$ such that $\vec{a}$=$\alpha \vec{b}$-$\hat{n}$, $\alpha \neq 0$ and $\vec{b}$ .$ \vec{c}$=12, then |$\vec{c} \times(\vec{a} \times \vec{b})$| is equal to: