A magnetic needle has magnetic moment of \( 5 \times 10^{-2} \, \text{Am}^2 \) and Moment of inertia \( 12 \times 10^{-6} \, \text{Kg m}^2 \). It performs 60 oscillations in 1 minute when suspended in a magnetic field. What is the magnitude of the magnetic field ?

The optical length of an astronomical telescope with magnifying power of 10 for normal adjustment is 55 cm. What is the focal length of the objective ?

What is the total energy of electron in the \( n^{th} \) stationary orbit of hydrogen atom ?

In Faraday's experiment on Electromagnetic Induction, in which of the following situations, more deflection will be shown by the galvanometer?

In a hydrogen atom an electron makes a transition from \( n_1 \rightarrow n_2 \), where \( n_1 \) and \( n_2 \) are the principal quantum numbers of the two states. Assuming Bohr's model to be valid, if the time period of the electron in the initial state is eight times that in the final state, the possible values of \( n_1 \) and \( n_2 \) are:

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

Match List-I with List-II

List-I	List-II
(A) Magnifying power of a simple microscope	(I) \( \frac{L}{f_o} \times \frac{D}{f_e} \)
(B) Magnifying power of a compound microscope	(II) \( \frac{f_o}{f_e} \left(1 + \frac{f_e}{D}\right) \)
(C) Magnifying power of a telescope (normal adjustment)	(III) \( 1 + \frac{D}{f_e} \)
(D) Magnifying power of a telescope when final image is formed at least distance of distinct vision	(IV) \( \frac{f_o}{f_e} \)

Choose the correct answer from the options given below:

Which of the following is not correct for an ac circuit ?

Which of the following statement about cry genes is NOT correct?

The formation of pomato is an example of:

Match the lanthanoid property given in List-I with lanthanoid ion given in List-II

LIST – I (Lanthanoid property)	LIST – II (lon)
(A) Strong oxidant	(I) \(Lu ^{3+}\)
(B) Strong reducing agent	(II) \(La ^{3+}\)
(C) \([ Xe ] f^{14}\) configuration	(III) \(Ce ^{4+}\)
(D) largest ionic radii	(IV) \(Eu ^{2+}\)

Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
Which one of the following is not associated with earthworm as 'farmer's friend'?

Match List - I with List - II.

LIST I	LIST II
A. Sea anemone and the clown fish	I. Competition
B. Tiger and the deer	II. Predation
C. Flamingoes and resident fishes in south American lakes	III. Commensalism
D. Mycorrhizae	IV. Amensalism
	V. Mutualism

Choose the correct answer from the options given below :