A radioactive sample decays 7/8 times its initial quantity in 21 minutes. The half life of the sample will be

Which of the statements are true, If a convex lens is placed in water:
a. Its focal length increases.
b. Its focal length decreases.
c. Rays bend less when they move through lens.
d. There is no change in radius of curvature.
Choose the correct answer from the options given below :

A bar magnet held perpendicular to a uniform magnetic field experiences a torque \( T_1 \). By what angle should it be rotated to change the experienced torque to \( 0.5T_1 \)?

Three charges, +Q, q and +Q are placed with q at mid point of the line joining the other two charges. For the system of charges to be in equilibrium, the value of q is

An electron of mass \( 9.11 \times 10^{-31} \text{ kg} \) is moving with velocity \( 5.4 \times 10^6 \text{ m/s} \). Its momentum will be

An electron beam passes through a region of magnetic field of \( 2 \times 10^{-3} \text{ T} \) and an electric field of \( 3.2 \times 10^4 \text{ V m}^{-1} \), both acting perpendicular to each other. If the path of the electron remains undeviated calculate the speed of electron : [Mass of electron \( = 9.1 \times 10^{-31} \text{ kg} \)]

In transmission of power from generation plants to users, transformers are used. Identify the correct reason to choose appropriate transformers.
(A) A step-up transformer is used at the generation plant and high voltages are transmitted.
(B) A step-down transformer is used at the generation plant and low voltages are transmitted.
(C) A step-up transformer lowers the current and hence loss due to joule heating is less.
(D) A step-down transformer lowers the current and hence loss due to joule heating is less.
Choose the correct answer from the options given below:

When benzene diazonium chloride is treated with halogen acid in the presence of copper powder, the reaction is referred to as

The magnetic field in a travelling electromagnetic wave has a peak value of 30 nT. The peak value of electric field strength is : (speed of light in free space is \( 3 \times 10^8 \text{ m/s} \)).

Arrange the following complexes in decreasing order of absorption of wavelength of light in the visible region:
(A) \(\left[ Co ( CN )_6\right]^{3-}\)
(B) \(\left[ CoF _6\right]^{3-}\)
(C) \(\left[ Co \left( H _2 O \right)_6\right]^{3+}\)
(D) \(\left[ Co \left( NH _3\right)_6\right]^{3+}\)
Choose the correct option from below:

A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
The major product in the reaction of anisole with bromine in ethanoic acid, is :

A and B are two sets such that n(A) = 5 and n(B) = 7. The number of one-one functions from A to B is