List of top Questions asked in JEE Main- 2023

Following tetrapeptide can be represented as

(F, L, D, Y, I, Q, P are one letter codes for amino acids)

Match List I and List II

List II	List II
A. van't Hoff factor, i	I. Cryoscopic constant
B. $k_f$	II. Isotonic solutions
C. Solution with same  with same osmotic pressure	III.  Normal molar mass /Abnormal molar mass
D. Azeotropes	IV. Solutions with same composition of  vapour above it

Choose the correct answer from the options given below :

A doctor prescribed the drug Equanil to a patient. The patient was likely to have symptoms of which disease?

Given below are two statements: 
Statement I: Nickel is being used as the catalyst for producing syn gas and edible fats. 
Statement II : Silicon forms both electron rich and electron deficient hydrides. 
In the light of the above statements, choose the most appropriate answer from the options given below:

The set of correct statements is :
(i) Manganese exhibits +7 oxidation state in its oxide. 
(ii) Ruthenium and Osmium exhibit +8 oxidation in their oxides. 
(iii) Sc shows +4 oxidation state which is oxidizing in nature. 
(iv) Cr shows oxidising nature in +6 oxidation state.

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

The statement B⇒((∼A) ∨ B) is equivalent to :

Consider a function f:N→R, satisfying
$ f(1)+2f(2)+3f(3)+⋯+xf(x)=x(x+1)f(x);x≥2 with f(1)=1.$
Then $\frac{1}{f(2022)} + \frac{1}{f(2028)}$ is equal to $

Let 𝐾 be the sum of the coefficients of the odd powers of 𝑥 in the expansion of $(1+𝑥)^{99}$. Let 𝑎 be the middle term in the expansion of \((2+\frac{1}{\sqrt 2} )^{200}\). If $\frac{⁡^{200}𝐶_{99} 𝐾}{𝑎} =\frac{2^𝑙 𝑚}{𝑛} $, where 𝑚 and 𝑛 are odd numbers, then the ordered pair (𝑙, 𝑛) is equal to

The shortest distance between the lines $\frac{x−1}2 =\frac{y−2}1 =\frac{z−6}{-3} $ and $\frac{x−1}2 =\frac{y+8}{-7} =\frac{z−4}{5} $ is

The value of the integral \(\int^2_1\bigg(\frac{t^4+1}{t^6+1}\bigg)\)dt is 

Let R be a relation defined on N as a ⁡R⁡b if 2a+3b is a multiple of 5 ,a , b∈N. Then R is

If the tangent at a point 𝑃 on the parabola \(𝑦^2=3𝑥\) is parallel to the line \(𝑥+2𝑦=1\) and the tangents at the points 𝑄 and 𝑅 on the ellipse \(\frac{𝑥^2}{ 4} +\frac{𝑦^2}{ 1} =1\) are perpendicular to the line 𝑥−𝑦=2, then the area of the triangle PQR is : 

If \(\overrightarrow a =\hat i+2\hat k,\overrightarrow b =\hat i+\hat j+\hat k,\overrightarrow c =7\hat i−3\hat j+4\hat k,r ×\hat b +\hat b ×\overrightarrow c =\overrightarrow0\) and \(\overrightarrow r .\overrightarrow a =0\). Then \(\overrightarrow r. \overrightarrow c\)  is equal to 

If the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}\)  and \(\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}\) intersect at the point 𝑃, then the distance of the point 𝑃 from the plane 𝑧=𝑎 is : 

The value of the integral \(∫_{\frac 12}^2 \frac{tan^{-1}x}{x}dx\) is equal to

The area of the region A = \({(x,y):|cos⁡x−sin⁡x|≤y≤sin⁡x,0≤x≤\frac{π}{ 2} }\) is

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is

Let \(\overrightarrow 𝑎 =4\hat 𝑖+3\hat 𝑗ˆ\) and \(\overrightarrow 𝑏 =3\hat 𝑖−4\hat 𝑗\)+\(5\hat 𝑘\). If \(\overrightarrow 𝑐\)  is a vector such that \(\overrightarrow 𝑐 ⋅(\overrightarrow 𝑎 ×\overrightarrow𝑏⃗ )+25=0\), \(\overrightarrow𝑐 ⋅(\hat𝑖+\hat𝑗+ \hat𝑘)=4\), and projection of \(\overrightarrow𝑐\)  on \(\overrightarrow𝑎\)  is \(1\) , then the projection of \(\overrightarrow 𝑐\)  on \(\overrightarrow 𝑏\) equals 

The set of all values of \(λ\) for which the equation \(cos^2⁡2x−2sin^4⁡x−2cos^2⁡x=λ\) has a real solution x, is 

The set of all values of \(t∈R\), for which the matrix \(\begin{bmatrix} e^t & e^{−t}(sin⁡\ t−2cos\ ⁡t) & e^{−t}(−2sin⁡\ t−cos\ ⁡t) \\[0.3em] e^t & e^{−t}(2sin\ ⁡t+cos\ ⁡t) & e^{−t}(sin\ ⁡t−2cos\ ⁡t) \\[0.3em] e^t & e^{−tcos\ ⁡t}& e^{−tsin\ ⁡t} \end{bmatrix}\) is invertible, is

In a part of a circuit shown: Find V_A – V_B in volts. It is given that current is decreasing at a rate of 1 ampere/s.

A particle undergoing SHM follows the position-time equation given as x = A sin \((\omega t+\frac{\pi}{3})\) . If the SHM motion has a time period of T, then velocity will be maximum at time \(t=\frac{T}{β}\) for first time after t = 0. Value of β is equal to

A block of mass 1 g is equilibrium with the help of a current carrying square loop which is partially lying in constant magnetic field (B) as shown. Resistance of the loop is 10 Ω. Find the voltage (V) (in volts) of the battery in the loop.

Initial volume of 1 mole of a monoatomic gas is 2 litres. It is expanded isothermally to a volume of 6 litres. Change in internal energy is xR. Find x.