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.

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

Two uniformly charged spherical conductors, A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at surface of the spheres A and B will be

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 a, b and c be the length of sides of a triangle ABC such that:
\(\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}\)
If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of \(\frac Rr\) is equal to :

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

The slope of normal at any point \((x, y), x > 0, y > 0\) on the curve \(y = y(x)\) is given by \(\frac{x^2}{xy-x^2y2^-1}\) If the curve passes through the point (1, 1), then \(e · y(e)\) is equal to

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 :

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)

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:

A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be

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)

A parallel beam of light of wavelength 900 nm and intensity 100 Wm^–2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm^–2 area perpendicular to the beam in one second is

The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x² + 2y² = 4 is an ellipse with eccentricity:

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: