A 20 watt, 50 V lamp is to be connected to AC mains of 260 V, 50 Hz. Calculate the value of series capacitor to run the lamp.

The given graph shows the variation of terminal potential difference V, across the combination of three identical cells in series to an external resistor versus the current i in the circuit. The internal resistance of each cell is :

Displacement current exists only when

The refractive index of air with respect to glass 2/3. The refractive index of diamond with respect to air is 2.4. What will be the refractive index of glass with respect to diamond?

A wire carries a current of 2.0 A. The number of electrons crossing through its cross-section in 10 s will be

Electric field \(\vec{E}\) at the surface of charged conductor is:
A. \(|\vec{E}| = \frac{\sigma}{\epsilon_0}\)
B. \(\vec{E}\) has a tangential component
C. Electric field is zero everywhere inside the conductor.
D. Any excess charge must reside on the surface of the conductor.
Choose the correct answer from the options given below:

A heater boils \( x \) amount of water in time \( t_{1} \) and another heater boils the same water in time \( t_{2} \) having resistances \( R_{1} \) and \( R_{2} \) respectively. The ratio \( \frac{t_{1}}{t_{2}} \) will be:

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Arrange the following in the increasing order of their \(p K_{ a }\) values :
(A) \(CF _3- COOH\)
(B) \(O _2 N- CH _2- COOH\)
(C) \(NC - CH _2- COOH\)
(D) \(H - COOH\)
Choose the correct answer from the options given below :

Fe shows extra stability as \(\text{Fe}^{3+}\) due to :

The ability of some snails and fish to avoid summer related problems like heat and dessication is called

Which one of the given species has more numbers than the combined total number of rest of the other given species?

Given that at x = 1, the function \(x^4-62 x^2+a x+90\) attains its maximum value on the interval [0, 2], the value of a is:

If \(\mathbf{A}=\left[\begin{array}{ccc}0 & 0 & \sqrt{7} \\ 0 & \sqrt{7} & 0 \\ \sqrt{7} & 0 & 0\end{array}\right]\), then \(|\operatorname{adj} \mathbf{A}|\) is equal to