The capacitance of a parallel capacitor plate, when a slab of material of dielectric constant \(k\) having same area as the plates of a parallel plate capacitor but thickness \(\frac{d}{2}\) (where 'd' is the separation of the plates) is inserted between the plates, will be :
(Given \(C _0=\) capacitance of capacitor with air as medium between plates)

The work done in moving a 1 C charge over an equipotential surface in X direction through a distance of 20 cm is :

Polaroids A and B are placed with their axes perpendicular to each other. Unpolarised light of intensity \(I_0\) is incident on A. A third polaroid C is kept between A and B such that its axis makes an angle of \(30^\circ\) with that of B. The Intensity of transmitted light through B is:

Two point charges of 1 C each are separated from each other by a distance of 1 m in vacuum.
The force of interaction between them is:

A charged particle is moving in a cyclotron. What is the effect on time for one revolution of this charged particle, when its radius of the orbit is doubled?

A straight wire of mass 500 g and length 7 m carries a current of 1.4 A. It is suspended in mid air by a uniform horizontal magnetic field B perpendicular to the length of the wire. The magnitude of magnetic field is:

The self inductance of a coil is 200 \( \mu \)H, current changes by 1 A in 0.05 sec. What is the emf produced?

If \(f(x) = \begin{cases} \frac{\sqrt{4+x}-2}{x}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}\) is continuous at \(x = 0\), then the value of k is:

The density of a population in a given habitat during a given period, fluctuates due to changes in -
(A) Natality
(B) Immigration
(C) Emigration
(D) Mortality
Choose the correct answer from the options given below:

Which of the following are NOT correct about "Sinking Fund"?
(A) It does not have any specific purpose.
(B) It can be used in any emergency.
(C) Any amount, any time can be deposited in it.
(D) It is set up for a particular upcoming expense.
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
The major product in the reaction of anisole with bromine in ethanoic acid, is :

Match List-I with List-II

List - I (Differential Equations)	List - II (Degree/Order)
(A) Degree of the differential equation \(\frac{d^3 y}{d x^3}+2 \log x \cdot y=0\)	(I) 3
(B) Order of the differential equation \(\frac{d^4 y}{d x^4}+\left(\frac{d y}{d x}\right)^4+x y=0\)	(II) 2
(C) Degree of the differential equation \(\left(\frac{d^4 y}{d x^4}\right)^2+\left(\frac{d y}{d x}\right)^3+x^2 y=0\)	(III) 1
(D) Order of the differential equation \(\frac{d^3 y}{d x^3}+y\left(\frac{d y}{d x}\right)^3=0\)	(IV) 4

Choose the correct answer from the options given below:

Amniocentesis should not be used for: