A wire has a resistance of \( 3 \text{ } \Omega \) at 20°C and \( 5 \text{ } \Omega \) at 100°C. The temperature coefficient of resistance of the wire is:

Match List-I with List-II

List-I (Formula)	List-II (Physical quantity)
(A) \( neAv_d \)	(I) Mobility
(B) \(\frac{v_d}{E}\)	(II) Current
(C) \(\frac{n e^2 \tau}{m}\)	(III) Conductivity
(D) \(\frac{m}{n e^2 \tau}\)	(IV) Resistivity

Choose the correct answer from the options given below:

Three parallel plates (each of area A) are separated by distances \( d_1 \) and \( d_2 \) respectively. The in-between spaces are filled with dielectrics of relative permittivity \( \epsilon_1 \) and \( \epsilon_2 \). The permittivity of free space is \( \epsilon_0 \). The capacitance of the combination is:

An ammeter and a Voltmeter are to be connected in a circuit. Which of the following statements are correct?
(A) Ammeter has negligible resistance.
(B) Ammeter is always connected in series in the circuit.
(C) Voltmeter should have negligible resistance.
(D) Voltmeter should be connected in parallel so that the whole current may pass through it.
Choose the correct answer from the options given below:

The capacities of two capacitors are \( C_1 \) and \( C_2 \) and their respective potentials are \( V_1 \) and \( V_2 \). If they are connected with a wire, then the loss of energy is given by :

A tiny spherical oil drop of mass 8 mg is kept suspended by applying a potential difference of 100 V between two metallic plates kept separated by a distance 1 cm. The number of electrons on the oil drop are : (Take \( g = 10 \text{ ms}^{-2} \))

Resolving power of a telescope can be increased by increasing :

Wings of an insect and wings of a bird are :

Which of the following correctly expresses the equation for species- area relationships? Where( S=Species richness, A=Area, Z=slope of line (regression coefficient), C=Y- intercept

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), 4d series (Y to Cd), \(5 d\) series ( La and Hf to Hg ) and 6 d series which has \(A c\) and elements from \(R f\) to \(C n\). The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and \(p\)-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
Which of the following is not regarded as transition metal?

For a medium with permittivity \( (\epsilon) \) and permeability \( (\mu) \), the speed of light \( (v) \) is given by :

In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is \( \frac{\pi}{3} \). If capacitor is removed from the circuit instead of inductor, the phase difference is again \( \frac{\pi}{3} \). What is the power factor of the circuit?

Bt toxin produced by Bacillus thuringiensis is resistant to :