List of top Questions asked in JEE Main- 2022

Let
\(A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}\)
and
\(B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}\)
Then \(A∩B\) is :

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is \(\frac{x}{15} \frac{ε_0A}{b}\), the value of \(x\) is ______?
A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b

The current density in a cylindrical wire of radius \(r = 4.0\) mm is \(1.0 \times 10^6\) \(A/m^2\). The current through the outer portion of the wire between radial distances \(\frac{r}{2}\) and \(r\) is \(xπ\) \(A\); where \(x\) is _________.

In the given circuit ‘a‘ is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be \(\frac{\sqrt x}{2}\).The value of x is________.
The cut-off voltage of the diodes (shown in figure) in forward bias is \(0.6\; V\). The current through the resistor of \(40\) \(Ω\) is____ mA.
The cut-off voltage of the diodes
A metallic rod of length \(20\) cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth’s magnetic field at that place is \(4 × 10^{–3}\) T and the angle of dip is \(45º\). The emf induced in the rod is __________mV.
A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If \(r_d\) and \(r_p\) are the radii of their circular paths respectively, then the ratio \(\frac{r_d}{r_p}\) will be \(\sqrt x:1\) where \(x\) is__________

\(\lim_{{x \to \frac{1}{\sqrt{2}}}} \frac{\sin(\cos^{-1}(x)) - x}{1 - \tan(\cos^{-1}(x))}\)
is equal to : 

g :R→R be two real valued functions defined as
\(f(x) = \begin{cases}        -|x + 3| &  x < 0 \\       e^x, & x \geq 0  \end{cases}\)
and
\(g(x) = \begin{cases}        x^2 + k_1x ,&  x < 0 \\       4x + k_2 ,&  x \geq 0  \end{cases}\)
where k1 and k2 are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) is
equal to:

If a point \(A(x, y)\) lies in the region bounded by the \(y\)-axis, straight lines  \(2y + x = 6\) and \(5x – 6y = 30\), then the probability that \(y < 1\) is
Let \(\overrightarrow a\) and \(\overrightarrow b\) be the vectors along the diagonals of a parallelogram having area \(2\sqrt2\). Let the angle between \(\overrightarrow a\) and \(\overrightarrow b\) be acute,\( |\overrightarrow a|=1\), and \(|\overrightarrow a⋅\overrightarrow b|=|\overrightarrow a×\overrightarrow b|\) If \(\overrightarrow c=2\sqrt2(\overrightarrow a×\overrightarrow b→)−2\overrightarrow b\) then an angle between\( \overrightarrow b\) and \(\overrightarrow c\) is
Let \(α, β\) be the roots of the equation \(x^2-\sqrt{2}x+\sqrt{6}=0\) and\( \frac{1}{α^2}+1\),\(\frac {1}{β^2}+1\) be the roots of the equation \(x^2 + ax + b = 0\) . Then the roots of the equation \(x^2 – (a + b – 2)x + (a + b + 2) = 0\) are
Let A and B be two \(3 × 3\) matrices such that AB = I and |A| =\(\frac{1}{8}\). Then |adj (B adj(2A))| is equal to
Let \(S=2+\frac{6}{7}+\frac{12}{7 ^2}+\frac{20}{7 ^3}+\frac{30}{7 ^4}+…\) Then \(4S\) is equal to
If m and n respectively are the number of local maximum and local minimum points of the function
\(f(x)=∫_0 ^{x^2} \frac{t^2–5t+4}{2+et}dt\), then the ordered pair (m, n) is equal to
A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is
The value of \(\cot\left(\sum_{n=1}^{50} \tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)\) is
\(\alpha = \sin 36^\circ\)  is a root of which of the following equation?
Let the normal at the point P on the parabola y2 = 6x pass through the point (5, –8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is

Let C be a circle passing through the points A(2, –1) and B (3, 4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle
\((x−5)^2+(y−1)^2=\frac{13}{2}\)
then r2 is equal to

If the two lines 
\(l1:\frac{(x−2)}{3}=\frac{(y+1)}{−2},z=2 \)
and
\( l2:\frac{(x−1)}{1}=\frac{(2y+3)}{α}=\frac{(z+5)}{2} \)
are perpendicular, then an angle between the lines l2 and 
\(l3:\frac{(1−x)}{3}=\frac{(2y−1)}{−4}=\frac{z}{4} \)
is

If the solution curve of the differential equation \(((tan−1y)−x)dy=(1+y^2)dx\) passes through the point \((1, 0)\), then the abscissa of the point on the curve whose ordinate is \(tan(1)\), is

Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x – 3y + 5z = 8. If the mirror image of the point 
\((2,−\frac{1}{2},2) \)
in the rotated plane is B( a, b, c),then

If \(\vec{a}⋅\vec{b}=1,\vec{b}⋅\vec{c}=2 and\) \(\vec{c}⋅\vec{a}=3,\)
then the value of
[\([\vec{a}×(\vec{b}×\vec{c}),\vec{b}×(\vec{c}×\vec{a}),\vec{c}×(\vec{b}×\vec{a})]\)
 is

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is