A charge q is moving with velocity \( \vec{v} \) in the presence of both electric field \( \vec{E} \) and magnetic field \( \vec{B} \). If velocity (\( \vec{v} \)), electric field (\( \vec{E} \)) and the magnetic field (\( \vec{B} \)) are mutually perpendicular. The charge will pass through the field undeflected if :

To remove an electron from the first orbit to infinity of hydrogen atom, the amount of energy required will be :

The critical angle for light ray going from medium-1 to medium-2 is \(i_c\). What will be the speed of light in medium-2, if its value in medium-1 is \(u\) ?

A proton accelerated through a potential difference of V volts has a de-Broglie wavelength \( \lambda \) associated with it. In order to get the same wavelength with an \( \alpha \)-particle, the required accelerating potential is

An electric dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by \(30^\circ\), then work done in rotating it by \(180^\circ\) is:

The forbidden energy gaps in conductors, semiconductors and insulators are \( (E_g)_c, (E_g)_s \) and \( (E_g)_I \) respectively. What is the relation among them ?

3 A double convex lens made of glass of refractive index has both radii of curvature of magnitude 20 cm. An object 3 cm high is placed at 10 cm from the lens. What is the nature and size of the image ?

The composition of starch in amylopectin is

Which of the following hormone is/are secreted by corpus luteum?
(A) Progesterone
(B) LH
(C) FSH
(D) Estrogen

A current element \(\Delta \vec{l}=\Delta x \hat{i}\) (where \(\Delta x=1 cm\) ) is placed at the origin and carries a current 10 A . The magnetic field on y -axis at a distance of 0.5 m is :

The fringe width in Young's double slit experiment is \( 2.4 \times 10^{-4} \, \text{m} \), when red light of wavelength 6400 \( \text{\AA} \) is used. The decrease in the fringe width, if light of wavelength 4000 \( \text{\AA} \) is used instead of red light, will be:

Read the passage carefully and answer the questions
Ethers with the general formula \(C _n H _{2 n+2} O\) and functional group C-O-C may be divided as symmetrical and unsymmetrical.
Lower symmetrical ether may be obtained by the dehydration of alcohols at low temperatures in the presence of protic acids,
such as \(H _2 SO _4\) and \(H _3 PO _4\) whereas at high temperature intramolecular dehydration takes place.
Formation of ether from primary alcohols is also accompanied by the formation of small amount of alkenes.
Due to the steric hinderance, secondary and tertiary alcohols undergo elimination reaction rather than substitution reaction yielding alkene as major product. Ethers can also be obtained by heating alkyl halides with sodium or potassium alkoxides.
Substituted Ethers (secondary & tertiary) can also be prepared using this method.
If primary halides are replaced with secondary and tertiary halides, alkenes are the major products.
The major product in the following reaction is

Rolle's theorem holds for the function \(x^3+b x^2+c x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), the respective values of \(b\) and \(c\) are :