List of top Questions asked in JEE Main- 2022

Let f be a differentiable function in \((0, \frac{π}{2})\). If \(∫_{cosx} ^1 t^2f(t)dt=sin^3x+cosx\), then \(\frac{1}{\sqrt3}f'(\frac{1}{\sqrt3})\) is equal to
Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal requires a bandwidth of 8 kHz, how many channels can be accommodated for transmission?
A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be
(Given cos135°= –0.7)
The number of N atoms in \(681\ g\) of \(C_7H_5N_3O_6\) is \(x × 10^{21}\). The value of \(x\) is ______ . (\(N_A\) = \(6.02 × 10^{23}\ mol^{–1}\)) (Nearest Integer)

Let S be the set of all the natural numbers, for which the line 
\(\frac{x}{a}+\frac{y}{b}=2 \)
is a tangent to the curve
\((\frac{x}{a})^n+(\frac{y}{b})^n=2 \)
at the point (a, b), ab ≠ 0. Then :

Match List-I with List-II.

 List - I List - II
  A.    Moment of inertia of solid sphere of Radius R about any tangent           i.\(\frac{5}{3}MR^2\)  
B.Moment of inertia of hollow sphere of radius (R) about any tangentii.\(\frac{7}{5}MR^2\)
C.Moment of inertia of circular ring of radius (R) about its diameteriii.\(\frac{1}{4}MR^2\)
D.Moment of inertia of circular disc of radius (R) about any diameteriv.\(\frac{1}{2}MR^2\)

Choose the correct answer from the options given below.

 

 

 

 



 

Let P and Q be any points on the curves (x – 1)2 + (y + 1)2 = 1 and y = x2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

In the given conversion the compound A is:

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m

Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms–2. The value of F is
(Take g = 10 ms–2)
A weightless and frictionless pulleys with three masses
The force required to stretch a wire of cross-section $1 cm ^2$ to double its length will be: (Given Yong's modulus of the wire $=2 \times 10^{11} N / m ^2$ )

Let the solution curve y = y(x) of the differential equation (4 + x2)dy – 2x(x2 + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _______.

If the function
\(f(x) =   \begin{cases}    \frac {log_e(1−x+x^2)+log_e(1+x+x_2)}{sec⁡\ x−cos⁡\ x},      & \quad x∈(−\frac \pi2,\frac \pi2)−{0}\\     k,  & \quad x=0   \end{cases}\)
is continuous at \(x = 0\), then k is equal to
 NCC parade is going at a uniform speed of $9\, km / h$ under a mango tree on which a monkey is sitting at a height of $196\, m$ At any particular instant, the monkey drops a mango A cadet will receive the mango whose distance from the tree at time of drop is : (Given g= 9.8 m/s2)
A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is____.(Nearest integer) 
Given : 1. The vapour pressure of water of 280 K is 14.2 mm Hg. 
            2. R = 0.082 L atm K–1 mol–1
If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :
A vessel contains \(14 g\) of nitrogen gas at a temperature of \(27°C\). The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be: 
Take \(R=8.32 J-mol^{-1}K^{-1}\)
Hydrolysis of which compound will give carbolic acid?
The sum of all real value of \(x\) for which \(\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}\)  is equal to________.
While estimating the nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.25g of the compound neutralized 2.5mL of 2M H2SO4. The percentage of nitrogen present in organic compound is ________

\(\lim_{{x \to 0}} \limits\) \(\frac{cos(sin x)  -  cos x }{x^4}\) is equal to :

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ mol–1 is ________. [nearest integer]
[Assume steam to be an ideal gas. Given ΔvapHΘ for water at 373 K and 1 bar is 41.1 kJ mol–1; R = 8.31 J K–1 mol–1]
A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15\sqrt2\) \(kmh^{–1}\), the rain drops hit herhead vertically. The speed of rain drops with respect to the moving girl is

Let
A =\(\begin{pmatrix}     4 & -2 \\     \alpha & \beta \\ \end{pmatrix}\)
If A2 + γA + 18I = 0, then det (A) is equal to ______.

Let A be a \(2×2\) matrix with \(det (A) = –1\) and \(det((A + I) (Adj (A) + I)) = 4\). Then the sum of the diagonal elements of A can be