An inductor of reactance 100 \( \Omega \) and resistor of resistance 100 \( \Omega \) are joined in series and connected by AC source of emf 220 V. Power dissipated in the circuit is:

A series LCR circuit is connected to a 230 V, 50 rad/s source. Given L = 5 H, C = 80 \( \mu \)F and R = 40 \( \Omega \). Impedance of the circuit is

In the given figure, the potentiometer wire, AB has a resistance of 5 \( \Omega \) and length 10 m. The balancing length AJ for 0.4 V is nearly:

Three charges \(+4 q, Q\) and \(q\) are placed along \(x\)-axis at points, \(x=0, I / 2\) and I respectively. The value of Q to make the net force on \(q\) to be zero :

Two antennas A and B have maximum line of sight range R = 45.5 km. If the height of antenna A is 32 m then the height of antenna B is : (Given radius of earth is = 6400 km)

Match List I with List II

LIST I	LIST II
A. Cyclotron frequency	I. \(\frac{N A B}{K R}\)
B. Magnetic field due to a circular coil	II. \(\frac{q B}{2 \pi m}\)
C. Magnetic field inside a toroid	III. \(\frac{\mu_0 N I}{2 \pi R}\)
D. Voltage sensitivity	IV.\(\frac{\mu_0 I}{2 R}\)

Choose the correct answer from the options given below:

A wire of resistance 20 Ω is bent to form a complete circle. What will be its resistance between two diametrically opposite points?

Two large plane parallel sheets with equal but opposite surface charge densities \(+\sigma\) and \(-\sigma\). A point charge q placed at points P1, P2, and P3 experiences forces F1, F2, and F3 respectively. Then :

The Differential Equation representing the family of tangents to the circle \(x^2+y^2=r^2\)is:

Two similar coils of radius R are lying concentrically with their planes perpendicular to each other and carrying current I and 2I respectively. What is the resultant magnetic field at the center?

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of C X bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
What is chiral carbon ?

Which of the following statements are correct?
(A) \(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y<1\)
(B) \(\tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y>1\)
(C) \(\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in(-1,1)\)
(D) \(\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}, x \in R\)
(E) \(\cos ^{-1}(-x)=-\cos ^{-1} x, x \in[-1,1]\)
Choose the correct answer from the options given below:

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 \( g = 10 \text{ ms}^{-2} \))