A coil having 'n' turns and resistance \( 'R' \, \Omega \) is connected with a galvanometer of resistance \( '4R' \, \Omega \). What is the induced current in the circuit when this combination (coil+galvanometer) is moved in time \( t \) from a magnetic flux \( \phi_1 \) to \( \phi_2 \) ?

A 50 Hz alternating current is flowing in a 28 mH coil. The reactance of the coil is

Which of the following statements are correct?
(A) The resistance of a conductor and its resistivity both depend on temperature.
(B) For a conductor of 1 m length and of \( 1 \text{ m}^2 \) cross-sectional area, the resistance is equal to its resistivity
(C) Resistance and resistivity both depend on cross-sectional area
(D) The resistivity of two wires made of same material but of different dimensions is the same.
Choose the correct answer from the options given below:

Which of the following is/are responsible for the formation of Rainbow ?
(A) Dispersion of light
(B) Interference of light
(C) Reflection of light
(D) Refraction of light
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A circular coil of radius 2.0 cm carries a current of 1.0 A. If the coil has 50 turns, the magnetic field at the centre of the coil will be:

Two polaroids \( P_1 \) and \( P_2 \) are set in crossed positions. A third polaroid \( P_3 \) is placed between the two making an angle \( \alpha \) with the axis passing from the first polaroid \( P_1 \). In what orientation will the transmitted intensity be maximum?

Match List-I with List-II:

List-I (Application)	List-II (Electromagnetic Waves)
(A) Used in radiography	(I) UV rays
(B) Detection by stimulating nerve endings of the human retina	(II) Microwaves
(C) Water purification	(III) Visible light
(D) Radar communication	(IV) X rays

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An ideal battery of 6 V and resistance R are connected in series in the primary circuit of a potentiometer of length 4 m and resistance \( 10 \Omega \). The value of R, to give a potential difference of 10 mV across 20 cm of potentiometer wire is:

For a long wire carrying a current of \( 10 \text{ A} \), the magnitude of magnetic field at a point \( 4 \text{ cm} \) away from it will be :

The function \(f(x)=x^2-4 x+6\) is
(A) Strictly decreasing on \((-\infty, 2) \cup(2, \infty)\)
(B) Strictly increasing on ( \(2, \infty\) )
(C) Strictly increasing on \((-\infty, \infty)\)
(D) Strictly decreasing on \((-\infty, 2)\)
Choose the correct answer from the options given below :

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.
Highest oxidation state of manganese in fluoride is \(+4\left( MnF _4\right)\) but highest oxidation state in oxides is \(+7\left( Mn _2 O _7\right)\) because:

If v is the frequency of ac mains, then the frequency of sonometer wire at resonance is :

If \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\) and \(|\vec{a}|=5,|\vec{b}|=3,|\vec{c}|=7\), then the acute angle between \(\vec{a}\) and \(\vec{b}\) is