List of top Questions asked in JEE Main- 2023

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

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 :

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

Choose the correct answer from the options given below.

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 :

A current carrying rectangular loop $P Q R S$ is made of uniform wire The length $P R=Q S=5 \,cm$ and $P Q=R S=100\, cm$ If ammeter current reading changes from $I$ to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_{P Q}^{2 I}\right)$ is:

Formulae for Nessler's reagent is:

Decreasing order of the hydrogen bonding in following forms of water is correctly represented by
A. Liquid water
B. Ice
C. Impure water
Choose the correct answer from the options given below:

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :

A current of $15 \,mA$ flows in the circuit asshown in figure The value of potentialdifference between the points $A$ and $B$ will be

The water quality of a pond was analysed and its BOD was found to be 4. The pond has

Some drugs bind to a site other than, theactive site of an enzyme This site is knownas

Given below are two statements :

Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable

Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed

In the light of the above statements, choose the correct answer from the options given below:

If an object cools down from 80°C to 60°C in 5 min in a surrounding of temperature 20°C. The time taken to cool from 60°C to 40°C will be (Assume Newton’s law of cooling to be valid)