List of top Questions asked in JEE Main- 2023

For α, β, z ∈ C and λ > 1, if \(\sqrt{λ - 1}\) is the radius of the circle |z - α|² + |z - β|² = 2λ, then |α - β| is equal to _____.

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)ⁿ⁺², which are in the ratio 1 : 3 : 5, is equal to

For \(a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}\) and \(B = {z∈C : Re (a + z ) < Im ( a + z)}.\) Then among the two statements: 
(S₁) : If \(Re (a), Im (a) > 0\), then the set A contains all the real numbers 
(S₂): If \(Re (a), Im (a) < 0,\) then the set B contains all the real numbers

Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal to

If four distinct points with position vectors \(\overrightarrow a,\overrightarrow b,\overrightarrow c\)  and \(\overrightarrow d\)  are coplanar, then \([\overrightarrow a \overrightarrow b \overrightarrow c]\) is equal to

If the system of linear equations
7x +11y + αz = 13
5x + 4y + 7z = β
175x + 194y + 57z = 361
has infinitely many solutions, then α + β + 2 is equal to:

If the \(1011^{th}\) term from the end in the binominal expansion of \((\frac{4x}{5}-\frac{5}{2x})^{2022}\) is 1024 times \(1011^{th}\) term from the beginning, then |x| is equal to

Let the tangent to the parabola \(y^2 = 12x\) at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola \(α^2 x^2 – 9y^2 = 9α^2\) at its point (α– 1, α + 2) is equal to__

The number of points, where the curve \(f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1\), \(x ∈ R\) cuts x-axis, is equal to

For \(k ∈ N\), if the sum of the series \(1 + \frac{4}{k}+\frac{8}{k^2}+\frac{13}{k^3}+\frac{19}{k^4}+..\)..  is 10, then the value of k is___

If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

Let S = \(\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}\) if \(\alpha-\frac{13}{11}i\in S, a \in R-{0}\), then  \(242\alpha^2\) is equal to ____.

Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.

Let the probability of getting head for a biased coin be \(\frac{1}{4}\) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation \(64x² + 5Nx + 1 = 0\) has no real root is \(\frac{p}{q}\) , where p and q are co-prime, then q – p is equal to _______.

Let \(\overrightarrow a=\overrightarrow i+2\overrightarrow j+3 \overrightarrow k\) and \(\overrightarrow b= \overrightarrow i+ \overrightarrow j - \overrightarrow k\) . If \(\overrightarrow c\) is a vector such that \(\overrightarrow a. \overrightarrow c=11,\overrightarrow b.(\overrightarrow a.\overrightarrow c)=27\) and \(\overrightarrow b. \overrightarrow c=-\sqrt{3}|b|,\)  then \(|\overrightarrow a \times \overrightarrow c|^2\) is equal to _______ .

If the line \(l_1 : 3y - 2x = 3\) is the angular bisector of the lines \(l_2 : x - y + 1 = 0\) and \(l_3\) : \(αx + βy + 17 = 0\), then \(α^2 + β^2  - α - β\) is equal to__

A car P travelling at 20 \(ms^{–1}\) sounds its horn at a frequency of 400 Hz. Another car Q is travelling being the first car in the same direction with a velocity 40 \(ms^{–1}\) . The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound = 360 \(ms^{–1}\) ]

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, \(\overrightarrow E =6.6 \;\hat jV/m  .\)What is \(\overrightarrow B\) at this point ?

The energy of \(He^+\) ion in its first excited state is, (The ground state energy for the Hydrogen atom is – 13.6 eV) :

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid. 
B. The electron will not experience magnetic force. 
C. The electron will continue to move along the axis of the solenoid. 
D. The electron will be accelerated along the axis of the solenoid. 
E. The electron will follow parabolic path-inside the solenoid. 
Choose the correct answer from the options given below :

The root mean square speed of molecules of nitrogen gas at 27°C is approximately : (Given mass of a nitrogen molecule = \(4.6 × 10^{–26}\) kg and take Boltzmann constant KB = \(1.4 × 10^{–23}\) JK–1 )

The current flowing through \(R_2\) is