It is observed that only 25% of a given radioactive sample is left undecayed after 16 days. What is the decay constant of the sample in \(\text{day}^{-1}\)?

An inductor of reactance 100 \( \Omega \) and resistor of resistance 100 \( \Omega \) are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is:

In a moving coil galvanometer, the coil is wound over a metallic frame in order to

The ratio of the radius of the third orbit to that of the second orbit in a hydrogen atom is

In a potentiometer arrangement for comparing emf of two cells, it was found that a cell of emf 1.25 V gives a balance point at 0.35 m length of the wire. On replacing the cell by another cell, the balance point shifted to 0.63 m. The emf of the second cell is :

A slit of width 'd' is illuminated by red light of wavelength 650 nm. What should be the value of slit width 'd' so that first minimum fall at an angle of diffraction of \(\frac{\pi}{6}\) ?

The core of a transformer is laminated to:

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

The purest form of commercial iron is

Read the Passage carefully and answer the Questions:
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^{ a }[B]^{ y }\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The unit of rate constant for first order reaction is:

Mercury is the only liquid metal at room temperature due to:

Which of the following is not a sexually transmitted disease?

Find the drift velocity of electrons in a metal conductor having density of conduction electrons \(9 \times 10^{28} m^{-3}\) of cross sectional area \(2 \times 10^{-7} m^2\) carrying 2 A current :