List of practice Questions

The volume charge density of a sphere of radius 6 m is 2μC cm^-3. The number of lines of force per unit surface area coming out from the surface of the sphere is _______ × 10¹⁰ NC^-1.

In the given figure, the value of V₀ will be ______ V.

Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length 2l have the same resistance (R) then its diameter will be ________ d.

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is

The intermediate X, in the reaction is:

In the following reaction:

The compound A and B respectively are:

The reaction of
 
with bromine and \(KOH\) gives \(RNH_2\) as the end product. Which one of the following is the intermediate product formed in this reaction?

Which of the following sets of quantum numbers is not allowed?

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

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 :

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:

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)