List of top Questions asked in JEE Main

20 mL of 0.1 M NH₄OH is mixed with 40 mL of 0.05 M HCl.The pH of the mixture is nearest to:(Given: K_b(NH₄OH) = 1 × 10^–5 ,log 2 = 0.30,log 3 = 0.48, log 5 = 0.69, log 7 = 0.84, log 11 =1.04)

The value of \(\int\limits_0^π \frac {e^{cos⁡\ x} sin⁡x}{(1+cos^2⁡x)(e^{cos⁡\ x}+e^{−cos⁡\ x})}dx\) is equal to :

Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal, respectively. The ratio of their respective ranges will be

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

A ball of mass \(0.15\) \(kg\) hits the wall with its initial speed of \(12\) \(ms^{–1}\) and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is \(100\) \(N\), calculate the time duration of the contact of ball with the wall.

The oscillating magnetic field in a plane electromagnetic wave is given by By = \(5 × 10^{–6}\) \(sin\;1000\;π(5x – 4 × 108\;t)T\). The amplitude of electric field will be:

Let \(\hat a\) and \(\hat b\) be two unit vectors such that \(| (a+b)+2(a × b)|\) =\( 2\). If \(θ ∈ (0, π)\) is the angle between a and b, then among the statements: \((S1)\): \(2|a×b|=|a-b|\) \((S2)\): The projection of a on \((\hat a+\hat b)\) is \(\frac{1}{2}\)

\(y=tan^{-1}(sec \;x^3 - tan\; x^3), \frac{π}{2} < x^3< \frac{3π}{2},\) then

Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is

Let \(E_1\) and \(E_2\) be two events such that the conditional probabilities \(P(E_1|E_2)=\frac 12\), \(P(E_2|E_1)=\frac 34\) and \(P(E_1∩E_2)=\frac 18\)⋅ Then:

Let \(λ^*\) be the largest value of \(λ\) for which the function \(f_λ(x) = 4λx^3 – 36λx^2 + 36x + 48\) is increasing for all \(x ∈ ℝ\). Then \(f_λ^* (1) + f_λ^* (– 1)\) is equal to :

If \(\frac{dy}{dx} + \frac{2x-y(2^y-1)}{2x-1} = 0, x,y > 0,y(1) = 1\), then \(y(2)\) is equal to:

If the solution of the differential equation
\(\frac{dy}{dx}\) \(+ e^x(x² - 2)y = (x^2 - 2x)(x^2 - 2)e^{2x}\)
satisfies y(0) = 0, then the value of y(2) is ______.

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is
(Take log₁₀1.88 = 0.274)

In Young’s double slit experiment, the fringe width is 12 mm. If the entire arrangement is placed in water of refractive index \(\frac 43\), then the fringe width becomes (in mm)

Light travels in two media \(M_1\) and \(M_2\) with speeds \(1.5 × 10^8ms^{–1 }\)and \(2.0 × 10^8ms^{–1}\), respectively. The critical angle between them is:

The magnetic field of a plane electromagnetic wave is given by:
\(\vec B=2×10^{−8}sin⁡(0.5×10^3x+1.5×10^{11}t)\hat jT\).
The amplitude of the electric field would be

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:

The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V, respectively. The percentage modulation index will be:

The compound(s) that is(are) removed as slag during the extraction of copper is 
(A) CaO 
(B) FeO 
(C) Al₂O₃ 
(D) ZnO 
(E) NiO 
Choose the correct answer from the options given below :

The enthalpy of combustion of propane, graphite and dihydrogen at 298 K are –2220.0 kJ mol^–1, –393.5 kJ mol^–1 and –285.8 kJ mol^–1, respectively.The magnitude of enthalpy of formation of propane (C₃H₈) is _____ kJ mol^–1. (Nearest integer)

A nucleus of mass M at rest splits into two parts having masses \(\frac{M′}{3}\) and \(\frac{2M′}{3}(M′<M).\)

An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 × 10^5\) \(J kg^{–1 }\)and thermal conducting of insulation wall is \(0.05\) \(Wm^{–1}\)°\(C^{–1})\)