List of practice Questions

A parallel plate capacitor made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s⁻¹.

What is the rms value of the conduction current?
Is the conduction current equal to the displacement current?
Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Find $(a + b)^4 - (a - b)^4$. Hence, evaluate $(\sqrt3 + \sqrt2)^4 - (\sqrt3 - \sqrt2)^4$.

∆ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm (Fig 9.17). The height AD from A to BC, is 6 cm. Find the area of ∆ABC. What will be the height from C to AB i.e., CE?

Molarity equation of a mixture of solutions of same substance is given by

If $t = \sin^{-1} 2^s$, then $\frac{ds}{dt}$ is equal to

Who were the people in Kezia’s family?

If $\left(1+ax\right)^{n} =1+6x+\frac{27}{2}x^{2}+\cdots+a^{n}\, x^{n}$, then the values of $a$ and $n$ are respectively

A hydrocarbon has molecular formula C2H6. Which of the class of hydrocarbons cannot have this formula?

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

If $|x - 3| < 2x + 9$ then $x$ lies in the interval

A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is

Find the inverse of each of the matrices(if it exists). $\begin{bmatrix}1&2&3\\0&2&4\\0&0&5\end{bmatrix}$

Define asexual reproduction. Describe two methods of asexual reproduction in animals.

If a gas absorbs

200 J

of heat and expands by

500

cm

^{3}

against a constant pressure of

2 \times 10^{5} N m^{- 2},

then the change in internal energy is:

Fig. 13.18 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)

What is genetic manipulation? How is it useful in agricultural practices?

Suppose $f: R \rightarrow(0, \infty)$ be a differentiable function such that $5 f(x+y)=f(x) \cdot f(y), \forall x, y \in R$ If $f(3)=320$, then $\displaystyle\sum_{n=0}^5 f( n )$ is equal to :

By now you may have concluded that Innisfree is a simple, natural place, full of beauty and peace. How does the poet contrast it with where he now stands? (Read stanza III.)

How Helmets Came To Be Used in Cricket
Nari Contractor was the Captain and an opening batsman for India in the 1960s. The Indian cricket team went on a tour to the West Indies in 1962. In a match against Barbados in Bridgetown, Nari Contractor (seriously injure and collapse). In those days helmets (not wear). Contractor (hit) on the head by a bouncer from Charlie Griffith. Contractor’s skull (fracture). The entire team (deeply concern). The West Indies players (worry). Contractor (rush ) to hospital. He (accompany) by Frank Worrell, the Captain of the West Indies Team. Blood (donate) by the West Indies players. Thanks to the timely help, Contractor (save). Nowadays helmets (routinely use) against bowlers.

If $sec\left(\frac{x^{2}-2x}{x^{2}+1}\right)=y$, then $\frac{dy}{dx}$ is equal to

Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

$PCl_5 (g) ⇋ PCl_3 (g) + Cl_2 (g)$
$CaO (s) + CO_2 (g) ⇋ CaCO_3 (s)$
$3Fe (s) + 4H_2O (g) ⇋ Fe_3O_4 (s) + 4H_2 (g)$

What is the story about the Kodavu people’s descent?

The oxygen molecule has a mass of 5.30 × 10^-26 kg and a moment of inertia of 1.94 ×10^-46 kg m² about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

Briefly explain the following statements from the text.
1.“You neither travelled to the past nor the future. You were in the present experiencing a different world.”
2. “You have passed through a fantastic experience: or more correctly, a catastrophic experience.”
3. Gangadharpant could not help comparing the country he knew with what he was witnessing around him.
4. “The lack of determinism in quantum theory!”
5. “You need some interaction to cause a transition.”

in the given figure , if AD=$7\sqrt3$, then find the length of BC.