A 0.5 m long solenoid has 500 turns and has a flux density of \( 2.52 \times 10^{-3} \text{ T} \) at its centre.
The current flowing in the solenoid would be (given, \( \mu_0 = 4\pi \times 10^{-7} \text{ Hm}^{-1} \))

Two slits are made 1 mm apart and the screen is placed 1 m away. What is the fringe width when a light used of wavelength 500 nm?

The refractive index of the material of a prism is \( \sqrt{2} \) and angle of prism is \( 30^{\circ} \). One of the two refracting surface of the prism is made a mirror inwards, by silver coating at outer surface. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is:

Which of the following statements are correct?
A. Electric field lines are always perpendicular to equipotential lines.
B. A zero electric field inside a conducting sphere does not mean that the potential gradient is also zero.
C. The resultant of two electric fields is determined by vector addition of the two field strengths.
D. If the field lines get closer together at any place, it means that the field strength is decreasing.
E. The resultant potential at a point is just the sum of the individual potentials.
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An electron is accelerated through a potential difference of \( V = 36 \text{ V} \). The de-Broglie wavelength associated with it will be

Two point charges, \( q_1 = 4\mu C \) and \( q_2 = -3\mu C \) (with no external field) are placed at (\(-6 \, cm, 0, 0\)) and (\(6 \, cm, 0, 0\)), respectively. The amount of work required to separate the two charges infinitely away from each other will be

\( P_1, P_2, P_3 \) are three Polaroid sheets; \( P_1 \) and \( P_3 \) are two crossed polaroids. What should be the angle between Polaroids \( P_1 \) and \( P_2 \), so that the value of \( I' = I_0/4 \)? (Where \( I' \) is intensity after \( P_2 \))

An ac source of variable angular frequency and constant amplitude is connected in series with a capacitance C and an electric bulb of resistance R. When angular frequency is increased then :

The finches found on Galapagos Islands were originally ___________ .

Which of the following statements are correct ?
(A) Determinant is a square matrix
(B) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{21}+a_{13} c_{31}\left(a_{i j}=\right.\) element, \(c_{i j}=\) cofactor \()\)
(C) Determinant is a number associated with a matrix
(D) Determinant is a number associated with a square matrix
(E) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{12}+a_{13} c_{13}\), where \(a_{i j}\) is the element, while \(c_{i j}\) is its corresponding cofactor
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Light of frequency \( \nu \) falls on a metal whose work function is \( h\nu_0 \). Choose the most appropriate condition from the following under which the photoelectric effect will take place.

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following molecule/ion is not expected to behave as a ligand?

Match List-I with List-II
An urn contains 4 white and 3 red balls. In a random draw of three balls, the probability of

List-I	List-II
(A) No red ball is	(I) \(\frac{12}{35}\)
(B) Only 1 red ball is	(II) \(\frac{1}{35}\)
(C) Exactly 2 red balls is	(III) \(\frac{4}{35}\)
(D) No white ball is	(IV) \(\frac{18}{35}\)

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