List of top Questions asked in JEE Main- 2023

The major product formed in the following reaction is
the major product A and B from the the following reaction are
Let D be the domain of the function f(x)=sin−1(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α 2 +\(\frac{ 5}{ β}\) is equal to 
Let α,β be the roots of the quadratic equation  x2+√6x+3=0. Then  \(\frac{α^23+β^23 + α ^14 + β ^14 }{α ^15 + β ^15 + α 160 + β ^{10}}\)  is equal to
let \(A=\begin{bmatrix} 1 & \frac{1}{51} \\ 0& 1 \end{bmatrix}\) if \(B=\begin{bmatrix} 1 &2\\ -1& -1 \end{bmatrix} A=\begin{bmatrix} -1 &2\\ 1& 1 \end{bmatrix}\) then the sum of all the elements of the matrix \(∑ ^{50}_{n=1}\) Bn is Equal to 
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 be a sequence such that a1+a2+....+ an=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P1P2P3 . . . Pm ,  where p1, p2, …..pm are the first m prime numbers, then m is equal to
If the local maximum value of the function f x)=\((\frac{√3e}{2 sin x} ) sin^2x ,\) \(x∈(0 ,\frac{π}{2}) \), is k/e , then  ( \(\frac{k}{ e}\) ) 8 + \(\frac{k^8}{e^ 5}\) + k 8  is equal to
Let \(P(\frac{2√3}{√7} ,\frac{ 6}{√7} ), \)Q,R and S be four points on the ellipse 9x2 + 4y2 = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If  \(\frac{1}{( P Q ) ^2} + \frac{1}{( R S ) ^2} = \frac{P}{q }\),   where p and q are coprime, then p + q is equal to
If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) )  between the coordinates axes, then α is equal to 
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
Let the lines l1: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l2: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to
Let a, b, c be three distinct real numbers, none equal to one. If the vectors \(a\^i+\^j+\^k , \^i+b\^j+\^k\) and \( \^i+\^j+c\^k \) are coplanar, then  \(\frac{1}{ 1 − a }+ \frac{1}{ 1 − b} + \frac{1 }{1 − c }\) is equal to 
Let  \(λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈\)  and \(\overrightarrow{ b} = 3 \^i− \^j + 2 \^k\) . be a vector such that  ( \(\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}\) ) × \(\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}\) and  \(\overrightarrow{ b}.\overrightarrow{ C}=-20\)  Then \( | \overrightarrow{c} + ( λ \^i + \^j + \^k ) |  ^2 \) is equal to
Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to
Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and  
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology 
Match List I with List II List I List II A. Spring constant I. (T-1) B. Angular speed II. (MT-2) C. Angular momentum III. (ML2) D. Moment of Inertia IV. (ML2T-1)
 List I   List II 
ASpring constant I(T-1) 
BAngular speedII (MT-2) 
CAngular momentumIII(ML2) 
DMoment of InertiaIV(ML2T-1)
Choose the correct answer from the options given below:
Given below are two statements:
Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. 
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. 
In the light of given statements, choose the most appropriate answer from the options given below.  
The amplitude of 15sin(1000πt) is modulated by 10sin(4πt) signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz 
(B) 2 Hz  
(C) 250 Hz  
(D) 498 Hz  
(E) 502 Hz 
Choose the correct answer from the options given below: 
Given below are two statements :  
Statement I : When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.  
Statement II : In a series LCR circuit, the value of power factor at resonance is one. 
In the light of given statements, choose the most appropriate answer from the options given below:

An engine operating between the boiling and freezing points of water will have 
A. efficiency more than 27%  
B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.  
C. efficiency equal to 27%  
D. efficiency less than 27% 

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If an electric dipole of dipole moment 30 x 10-5 Cm is enclosed by a closed surface, the net flux coming out of the surface will by zero.
Reason R : Electric dipole consists of two equal and opposite charges.
In the light of above, statements, choose the correct answer from the options given below:
A wire of resistance 160 Ω is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be

Given below are two statements:  
Statement I : The diamagnetic property depends on temperature.  
Statement II : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.  
In the light of given statement, choose the correct answer from the options given below: