An electric dipole of moment P is placed along the direction of electric field E. The work done in deflecting the dipole through 180° is equal to

A 12 pF capacitor is connected to a 50 V battery. The electrostatic energy stored in the capacitor is

The wavelength of the first spectral line of an element is 5893 Å. The first excitation energy is :

The half life of a radioactive substance is 30 s. Calculate the time taken for the sample to decay to \( \frac{3}{4} \) th its initial value.

For a normal human eye, rearrange the parts of the eye as they are situated in the path of the light entering the eye:
(A) Vitreous Humor
(B) Cornea
(C) Ciliary muscles
(D) Aqueous Humor
(E) Retina
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When two capacitors charged to different potential are connected in parallel the statement which is not true about it is :

The storage battery of a car has an emf of 10 V. If the internal resistance of the battery is \( 0.2 \Omega \), then the maximum current that can be drawn from the battery is

The type of isomerism exhibited by the complex \([\text{CoCl}_2 (\text{en})_2]\) is:

If \(y=\log _e\left(\frac{e^2}{x^2}\right)\) for \(x \neq 0\), then \(\frac{d^2 y}{d x^2}\) equals

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.
In Williamson synthesis, the alkoxide ion attacks the alkyl halide via which pathway?

For the set of all straight lines in a plane, the relation of "perpendicularity" is:
(A) reflexive but neither symmetric nor transitive.
(B) symmetric but neither reflexive nor transitive.
(C) transitive but neither reflexive nor symmetric.
(D) neither reflexive nor symmetric nor transitive.
(E) reflexive, symmetric but not transitive.
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A battery of emf 4 V and internal resistance \(1 \, \Omega\) is connected across a wire of resistance \(9.0 \, \Omega\). The number of electrons passing through the cross-section of the wire in 4 s is:

Match List-I with List-II
Consider two vectors \(\vec{a}=\hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=-3 \hat{i}-6 \hat{j}+3 \hat{k}\).

List-I	List-II
(A) Angle between \(\vec{a}\) and \(\vec{b}\)	(I) \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\)
(B) Angle between \(\vec{a}\) and \(x\)-axis	(II) \(\cos ^{-1}\left(\frac{2}{\sqrt{6}}\right)\)
(C) Angle between \(\vec{b}\) and \(x\)-axis	(III) \(\pi\)
(D) Angle between \(\vec{a}\) and \(y\)-axis	(IV) \(\cos ^{-1}\left(-\frac{1}{\sqrt{6}}\right)\)

Choose the correct answer from the options given below: