A network of resistors is connected as shown in the figure. The potential drop across 4\(\Omega\) resistors is

Calculate the separation of two points on moon that can be resolved using 600 cm telescope. Given distance of moon from earth \(= 3.8 \times 10^{10}\) cm. The wavelength most sensitive to eye is \(5.5 \times 10^{-5}\) cm.

The work function of cesium is 2.27 eV. The cut off voltage which stops the emission of electron from cesium when irradiated with light of wavelength 400 nm is

In a single slit diffraction experiment, the aperture of the slit is 3 mm. A monochromatic light of wavelength 620 nm is normally incident on the slit. If the distance between the slit and the screen is 1.2 m, then the separation between the first order minima and the third order maxima on one side of the screen is

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm. Its refractive index is

Match List I with List II

LIST I	LIST II
A. Transducer	I. High frequency wave
B. Modulated Waves	II. Receiver
C. Band width	III. Provides output in electrical form
D. Demodulator	IV. Range of frequencies over which communication system works.

Choose the correct answer from the options given below:

A radioactive isotope phosphorous-32 has an initial activity \( 10 \mu \text{Ci} \) and has half life of \( 14 \text{ days} \). What is the activity of the source after \( 42 \text{ days} \) ?

Match List-I with List-II

List-I (Name of the test/Reaction)	List-II (Species)
(A) Tollen's Test	(I) \(Cu ^{2+} a n d OH ^{-}\)
(B) Fehling's Test	(II) \(Zn - Hg and HCl\)
(C) Clemmensen reduction	(III) \(2\left[ Ag \left(NH _3\right)_2\right]^{+} \) and \(OH ^{-}\)
(D) Wolff Kishner reduction	(IV) Hydrazine KOH /ethylene glycol

Choose the correct answer from the options given below :

If \(\operatorname{det}\left(\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right)=\operatorname{det}\left(\begin{array}{cc}6 & -2 \\ 1 & 1\end{array}\right)\), then the value of \(x\) is

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

A charge q is enclosed by a Gaussian spherical surface of radius R. If the radius is reduced to half of R, the outward electric flux will be

Select the appropriate reagent for the synthesis of tert-Butyl ethyl ether