As astronomical telescope of ten fold angular magnification has a length of 44 cm. The focal length of the objective is:

Choose the correct statements :
(A) A nuclide is represented as \( ^A_Z X \)
(B) Nuclids with same number of protons are called isotopes
(C) \( \alpha \)-ray scattering experiments allow determination of the nuclear radius
(D) Nuclids with same number of neutrons are called isotones
(E) The nuclear force distinguishes between neutron and proton
Choose the correct answer from the options given below :

An electron moves with a velocity of \( 1200 \, \text{m s}^{-1} \) in a magnetic field of 0.4 T at an angle of 30\(^\circ\). What will be the approximate radius of its path? (Take \( e/m \) of electron \( = 1.76 \times 10^{11} \, \text{C kg}^{-1} \))

Two long current carrying conductors separated by a distance 'r' carrying equal currents in the same direction exert a force 'F' per unit length on each other. Now current in one of them is reversed, and distance between them is made twice the original distance. The force per unit length will become:

If charge is moving parallel to uniform magnetic field, its path will be:

Identify the correct statement among the following in the context of a nuclear reactor.

The current and power dissipation in an inductor coil are 2 A and 200 W, respectively.
When connected to an alternating source of 220 V, 50 Hz. The resistance and inductance of the coil are (take \( \pi^2 = 10 \)):

A proton is accelerated by a potential V and the de-Broglie wavelength associated with it is \(\lambda\). By how much potential a deuteron should be accelerated to acquire the same de-Broglie wavelength as that of a proton?

The vapour pressure of a solution is 2985 \(\text{Nm}^{-2}\) when 5 g of a non-electrolyte is added to 100 g of water at a particular temperature.
The vapour pressure of pure water at this temperature is 3000 \(\text{Nm}^{-2}\).
The molecular mass of the solute is

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
In context of the Lanthanoids, which of the following statements is/are NOT correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. Availability of \(4f\) electrons results in the formation of compounds in \(+4\) oxidation state for all the members of the series
C. Because of similar properties, the separation of lanthanoids is not easy
D. \(La(OH)_3\) is least basic among hydroxides of lanthanoids
E. Ce can act as an oxidising agent
Choose the correct answer from the options given below:

A proton accelerated through potential difference V has de Broglie wavelength \(\lambda\). On doubling the potential, the de Broglie wavelength of the proton :

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

Match List-I with List-II

List-I (Series)	List-II (Values of \( n_1 \) and \( n_2 \) in Bohr's formula)
(A) Lyman	(I) \( n_1=4, n_2 \geq 5 \)
(B) Balmer	(II) \( n_1=3, n_2 \geq 4 \)
(C) Paschen	(III) \( n_1=2, n_2 \geq 3 \)
(D) Brackett	(IV) \( n_1=1, n_2 \geq 2 \)

Choose the correct answer from the options given below: