List of top Questions asked in JEE Main

Let $A=$ [$a_{ij}$]$_{2\times2}$ be a matrix and $A^2 = I$ where $a_{ij} \neq0$. If a sum of diagonal elements and b=det(A), then $3a^2+4b^2$ is

f domain of the function \[ f(x) = \log_e \left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) \] is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ 18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2) $ is equal to __________.

Number of moles of $AgCl$ formed in the following reaction is

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

The sum of roots of |x² - 8x + 15| - 2x + 7 = 0 is:

The number of following statements which are incorrect line emission

What is the ratio of σ and pi bonds in pyrophosphoric acid ?

Let A be a $n \times n$ matrix such that $| A |=2$ If the determinant of the matrix$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ is $2^{84}$, then $n$ is equal to ____

Match List I with List II

LIST I		LIST II
A	Cobalt catalyst	I	$(H_2+Cl_2)$ production
B	Syngas	II	Water gas production
C	Nickel catalyst	III	Coal gasification
D	Brine solution	IV	Methanol production

Choose the correct answer from the options given below:

The number of units, which are used to express concentration of solutions from the following is _______
Mass percent, Mole, Mole fraction, Molarity, ppm, Molality

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then

When vector $\overrightarrow A = 2\hat i+3\hat J+2\hat k$ is subtracted from vector $\overrightarrow B$ , it gives a vector equal to $2\hat j$ . Then the magnitude of vector $\overrightarrow B$ will be :

The degree of dissociation of monobasic acid is 0 3 By what percent is the observed depression in freezing point greater than the calculated depression in freezing point ?

If the function $f(x)=\begin{cases}(1+|\cos x|) \frac{\lambda}{|\cos x|} & , 0 < x < \frac{\pi}{2} \\\mu & , \quad x=\frac{\pi}{2} \\\frac{\cot 6 x}{e^{\cot 4 x}} & \frac{\pi}{2}< x< \pi\end{cases}$is continuous at $x=\frac{\pi}{2}, then 9 \lambda+6 \log _{ e } \mu+\mu^6- e ^{6 \lambda}$ is equal to

The relation $R =\{(a, b)$ : $\operatorname{gcd}(a, b)=1,2 a \neq b, a, b \in Z\}$ is :

Two solutions $A$ and $B$ are prepared by dissolving $1 g$ of non-volatile solutes $X$ and $Y$ respectively in $1 \,kg$ of water The ratio of depression in freezing points for $A$ and $B$ is found to be $1: 4$ The ratio of molar masses of $X$ and $Y$ is :

Match List-I with List-II :

Choose the correct answer from the options given below :

Let the number $(22)^{2022}$ + $(2022)^{22}$ leave the remainder $ \alpha $ when divided by 3 and $ \beta $ when divided by 7. Then $ (\alpha^2 + \beta^2) $ is equal to:}

If $ S_n = 4 + 11 + 21 + 34 + 50 + \dots $ to $ n $ terms, then $ \frac{1}{60} (S_{29} - S_9) $ is equal to:

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to

Let the system of linear equations $ x+y+ kz =2$ $ 2 x+3 y-z=1 $ $ 3 x+4 y +2 z= k$ have infinitely many solutions Then the system $ ( k +1) x+(2 k -1) y=7$ $ (2 k +1) x+( k +5) y=10$ has:

Electrons in a cathode ray tube have been emitted with a velocity of $1000\, m s ^{-1}$. The number of following statements which is/are true about the emitted radiation is _______ Given : $h =6 \times 10^{-34} J s , m _e=9 \times 10^{-31} kg$
(A) The deBroglie wavelength of the electron emitted is $66667 nm$
(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube
(C) The cathode rays start from cathode and move towards anode
(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube

Match List I with List II

List I		List II
A.	Angular momentum	I.	ML²T⁻²
B.	Torque	II.	ML⁻²T⁻²
C.	Stress	III.	ML²T⁻¹
D.	Pressure gradient	IV.	ML⁻¹T⁻²

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Match List I with List II

List I		List II
A	Physisorption	i	Single Layer Adsorption
B	Chemisorption	ii	20−40kJmol−1
C	N₂(g)+3H₂(g)—⇢^Fe(s)_^—⇢2NH₃(g)	iii	Chromatography
D	Analytical Application or Adsorption	iv	Heterogeneous catalysis

Choose the correct answer from the options given below:

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus $( K )$ and modulus of rigidity $(\eta)$ of a given solid object :

	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