List of top Questions asked in JEE Main

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:

Let $λ ≠ 0$ be a real number. Let α, β be the roots of the equation $14x^2 – 31x + 3λ = 0$ and α, γ be the roots of the equation $35x^2 – 53x + 4λ = 0$. Then $\frac{3\alpha}{\beta}$ and $\frac{4\alpha}{\lambda}$ are the roots of the equation

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

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 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

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

The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent 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 $f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x$, $x∈R$ be a function which satisfies $f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy$. Then (a+b) equal to

Let $\Delta$ 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

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

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:

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

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

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

Reaction of propanamide with $Br_2/KOH(aq)$ produces :

Match List-I with List-II :

Choose the correct answer from the options given below :

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: [CoCl(NH₃)]^2– absorbs at lower wavelength of light with respect to [Co(NH₃)₅(H₂O) ^3–
Reason R: It is because the wavelength of the light absorbed depends on the oxidation state of the metal ion.
In the light of the above statements, choose the correct answer from the options given below:

The mismatched combinations are
A. Chlorophyll - Co
B. Water hardness - EDTA
C. Photography - [Ag(CN)₂]-
D. Wilkinson catalyst - [(Ph₃P)₃ RhCl]
E. Chelating ligand-D- Penicillamine

What is the correct order of acidity of the protons marked A-D in the given compounds?

	List I (Reagents Used)		List II (Compound with Functional group detected)
A	Alkaline solution of copper sulphate and sodium citrate	I
B	Neutral F_eCl₃solution	II
C	Alkaline chloroform solution	III
D	Potassium iodide and sodium hypochlorite	IV