A radioactive sample has \(4.0 \times 10^{18}\) active nuclei at a certain instant. How many of these nuclei will still be in the same active state after three half lives ?

For an ac source rated at 220 V, 50 Hz, which of the following statements is correct?

A long solenoid with 25 turns per cm has a small loop of area \( 2.0 \text{ cm}^2 \) placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 3.0 A to 5.0 A in 0.1 s. The induced emf in the loop due to change in the current is

An electric dipole with dipole moment \( 3 \times 10^{-9} \, \text{C m} \) is aligned at \( 30^\circ \) with the direction of uniform electric field of magnitude \( 6 \times 10^4 \, \text{N C}^{-1} \). What will be the magnitude of torque?

A wire has a resistance of \( 2.1 \, \Omega \) at \( 25^\circ \text{C} \) and a resistance of \( 2.8 \, \Omega \) at \( 100^\circ \text{C} \). The temperature coefficient of the resistance is :

Match List-I with List-II

List-I	List-II
(A) The current lags behind the emf by \( \pi/4 \) in phase	(I) A.C. circuit containing only an inductor
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase	(II) A.C. circuit with resistance and inductances in series
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \)	(III) A.C. circuit containing only as capacitor
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \)	(IV) A.C. circuit with resistance and capacitor in series

Choose the correct answer from the options given below :

How much energy will be carried out by electromagnetic radiation of wavelength \( 3 \times 10^{-6} \text{ m} \)?

Read the given passage and answer the question given below.
The sex linked recessive disease, which shows its transmission from unaffected carrier female to some of the male progeny has been widely studied. In this disease, a single protein that is a part of the cascade of proteins involved in the clotting of blood is affected. Due to this in an affected individual a simple cut will result in non-stop bleeding. The heterozygous female (carrier) for the disease may transmit it to sons. The possibility of a female becoming a sufferer of disease is extremely rare because mother of such a female has to be at least carrier and the father should be sufferer. The family pedigree of Queen Victoria shows a number of suffering descendents as she was a carrier of the disease.
Man who is sufferer of the disease marries a woman who is a carrier of this disease. What percentage of children born as carrier of this disease?

Number of coulombs required for the reduction of \(1\) mol of \(MnO_4^-\ \text{to}\ Mn^{2+}\) is:

Read the passage carefully and answer the Questions
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The reaction is an example of

What will be the number of genotypes and phenotypes obtained in \(F _2\) generation when male parent RRyy is crossed with female parent rrYY?

Which of the following equation correctly describes 'Net primary productivity'?

To find the focal length of a convex lens, a student obtains the real, inverted and magnified image on the screen as shown in the figure below.

Now the whole set up is immersed in water without disturbing the object and position of the screen. What will be student's observation on the screen?