List of top Questions asked in JEE Main

Let M be a $3 \times 3$ matrix such that $M \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, M \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}$ and $M \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}$. If $M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}$, then $x+y+z$ equals :

If $f: \mathbb{N} \to \mathbb{Z}$ is defined by \[ f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}, k \in \mathbb{N}, \] and $\sum_{n=1}^k f(n) = 98$, then $k$ is equal to :

First order gas phase reaction \(A \to B + C\). \(p_i = \text{initial pressure of gas A}\), \(P_t = \text{total pressure of the reaction mixture at time t}\). Expression of rate constant (k) is

The square of the distance of the point P(5, 6, 7) from the line $\frac{x-2}{2} = \frac{y-5}{3} = \frac{z-2}{4}$ is equal to:

Consider the system of linear equations in x, y, z:
x+2y+tz = 0,
6x + y + 5t z = 0,
3x + y + f(t) z = 0,
where f: R$\rightarrow$ R is a differentiable function. If this system has infinitely many solutions for all t $\in$ R, then f

The shortest distance between the lines
\(\vec{r} = (\frac{1}{3}\hat{i} + \frac{8}{3}\hat{j} - \frac{1}{3}\hat{k}) + \lambda(2\hat{i} - 5\hat{j} + 6\hat{k})\)
and \(\vec{r} = (-\frac{2}{3}\hat{i} - \frac{1}{3}\hat{k}) + \mu(\hat{j} - \hat{k}), \lambda, \mu \in \mathbb{R}\), is:

If the system of equations:
\(x + y + z = 5\)
\(x + 2y + 3z = 9\)
\(x + 3y + \lambda z = \mu\)
has infinitely many solutions, then the value of \(\lambda + \mu\) is:

Consider the matrices} \[ A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}, \quad B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}. \] If matrices \( P \) and \( Q \) are such that \( PA = B \) and \( AQ = B \), then the absolute value of the sum of the diagonal elements of \( 2(P + Q) \) is _______.}

A \(1\,\mu\text{C}\) charge moving with velocity} \[ \vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k}) \, \text{m/s} \] in the region of magnetic field} \[ \vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k}) \, \text{T} \] The magnitude of force acting on it is \( \sqrt{\alpha} \times 10^{-6} \) N. The value of \(\alpha\) is ____.}

Let a line \(L\) passing through the point \((1,1,1)\) be perpendicular to both the vectors \(2\hat{i}+2\hat{j}+\hat{k}\) and \(\hat{i}+2\hat{j}+2\hat{k}\). If \((a,b,c)\) is the foot of perpendicular from the origin on the line \(L\), then the value of \(34(a+b+c)\) is:

Let \[ A= \begin{bmatrix} 1 & 2\\ 1 & \alpha \end{bmatrix} \quad \text{and} \quad B= \begin{bmatrix} 3 & 3\\ \beta & 2 \end{bmatrix}. \] If \(A^2-4A+I=O\) and \(B^2-5B-6I=O\), then among the following statements: (S1): \[ [(B-A)(B+A)]^T= \begin{bmatrix} 13 & 15\\ 7 & 10 \end{bmatrix} \] (S2): \[ \det(\operatorname{adj}(A+B))=-5 \] Choose the correct option:

Let \( \alpha, \beta \in \mathbb{R} \) be such that the system of linear equations} \[ x + 2y + z = 5 \] \[ 2x + y + \alpha z = 5 \] \[ 8x + 4y + \beta z = 18 \] has no solution. Then \( \frac{\beta}{\alpha} \) is equal to:

For a reaction $A \to P$ at $T$ K, the half life ($t_{1/2}$) is plotted as a function of initial concentration $[A]_o$ of A as given below. The value of $x$ in the given figure is ______ s (Nearest integer)}

At 298 K, the molar conductivity of $x% \ (w/w)$ MX solution (aqueous) is 123.5 S cm$^2$ mol$^{-1}$. The conductance of same solution is $1.9 \times 10^{-3}$ S. The value of $x$ is ______ $\times 10^{-2}$.
(Given : cell constant $= 1.3 \text{ cm}^{-1}$; molar mass of MX is 75 g mol$^{-1}$, density of aqueous solution of MX at 298 K is 1.0 g mL$^{-1}$)}

20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be 80.0 mm higher than the tube dipped in water. The molar mass of hemoglobin is ______ kg mol$^{-1}$. (Nearest integer)
(Given : $g=10 \text{ m s}^{-2}$, $R=8.3 \text{ kPa dm}^3 \text{ K}^{-1}\text{mol}^{-1}$, density of solution $= 1000 \text{ kg m}^{-3}$)}

RMgI when treated with ice cold water liberated a gas which occupied 1.4 dm$^3$/g at STP. The gas produced is further reacted with iodine in presence of $HIO_3$ to give compound (X). Compound (X) in presence of Na and dry ether produced compound (Y). Molar mass of compound (Y) is ______ g mol$^{-1}$. (Nearest integer)}

The total number of unpaired electrons present in the $d^3$, $d^4$ (low spin), $d^5$ (high spin), $d^6$ (high spin) and $d^7$ (low spin) octahedral complex systems is ______.

A paper dipped in a dil. $H_2SO_4$ solution of 'X' upon treatment with $SO_2$ gas turns into green. The compound 'X' is :

Given below are two statements :
Statement I :

$\alpha$ and $\beta$ D-(+)-glucose are two anomers of D-(+)-glucose.
Statement II : The open chain forms of D-glucose and D-fructose contain three similar chiral carbons at $C_3, C_4$ and $C_5$.
In the light of the above statements, choose the correct answer from the options given below :}

Identify the incorrect statement about tertiary structure of proteins.

Given below are two statements :
Statement I : Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will give benzylamine.
Statement II : Nitration of aniline with $HNO_3/H_2SO_4$ at 288 K produces m-nitroaniline in higher amount than o-nitroaniline (pH adjusted).
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :
Statement I : The condensation reaction between $CH_3-CH=O$ and

under optimum pH will produce

.
Statement II : The molecule,

will generate $Ph-CH=O$ in the presence of dilute acid.
In the light of the above statements, choose the correct answer from the options given below :

Complete the following reaction sequence and give the name of major product 'P'.

Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass 72 g mol$^{-1}$.

Identify the correct statements from the following
A. $[Fe(C_2O_4)_3]^{3-}$ is the most stable complex among $[Fe(OH)_6]^{3-}$, $[Fe(C_2O_4)_3]^{3-}$ and $[Fe(SCN)_6]^{3-}$
B. The stability of $[Cu(NH_3)_4]^{2+}$ is greater than that of $[Cu(en)_2]^{2+}$
C. The hybridization of Fe in $K_4[Fe(CN)_6]$ is $d^2sp^3$
D. $[Fe(NO_2)_3Cl_3]^{3-}$ exhibits linkage isomerism
E. $NO_2^-$ and $SCN^-$ ligands are NOT ambidentate ligands
Choose the correct answer from the options given below :