The refractive index of the material of a prism is \( \sqrt{2} \) and angle of prism is \( 30^{\circ} \). One of the two refracting surface of the prism is made a mirror inwards, by silver coating at outer surface. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is:

A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor but has a thickness \( \frac{1}{4}d \), where d is the separation between the plates. If the slab is inserted between the plates, the potential difference becomes:
(Given: Potential difference across the capacitor without dielectric is \( V_0 \))

1. An electron of mass m is moving with kinetic energy k and momentum p. The de-Broglie wavelength associated will be :
(A) \( \lambda = \frac{\sqrt{2mk}}{p} \)
(B) \( \lambda = \frac{p}{h} \)
(C) \( \lambda = \frac{h}{p} \)
(D) \( \lambda = \frac{h}{\sqrt{2mk}} \)
Choose the correct answer from the options given below :

A TV tower has a height of 160 m. How much population is covered by the television broadcast, if the average population density around the tower is 1000 per km^2? Given radius of the earth is 6400 km.

At any instant t the values of voltage applied and the current through a series LCR circuit are given as : \( V = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ V}, I = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ A} \). The average power consumed in the circuit is given by :

Which of the following examples are based upon the total internal reflection of light?
(A) Optical fibre
(B) Twinkling of stars
(C) Mirage
(D) Sparkling of diamond
Choose the correct answer from the options given below:

What will be the time taken by light to travel 2 cm thickness of glass of refractive index 1.5?

Applying the Kirchhoff's rule to the loop (a) ABCA and (b) BCDEB, two correct equations are given

(A) \(8-4 I_2-2\left(I_2+I_3\right)-I_1=0\)
(B) \(4-2\left(I_2+I_3\right)-4\left(I_2+I_3-I_1\right)=0\)
(C) \(4+2\left(I_2-I_3\right)-4\left(I_2+I_3-I_1\right)=0\)
(D) \(8+4 I_2+2\left(I_2-I_3\right)-I_1=0\)
Choose the correct answer from the options given below:

The boiling point elevation constant \(K_b\) is also known as:

Select the statements which do not hold true for Cancer:
A. Cancerous cells show a property of contact inhibition.
B. Metastasis is the most feared property of malignant tumors.
C. Malignant tumor cells invade and damage the surrounding tissue.
D. Malignant tumor cells grows slowly
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Lines)	List-II (Direction Ratios)
(A) \(\frac{x-1}{2}=\frac{2-y}{1}=z\)	(I) \((1,3,-1)\)
(B) \(\frac{2 x-1}{2}=\frac{y+1}{3}=\frac{1-z}{1}\)	(II) \((2,-2,0)\)
(C) \(\frac{x+1}{2}=\frac{3-y}{2}=z=2\)	(III) \((2,-1,1)\)
(D) \(\frac{2 x-3}{4}=\frac{1-2 y}{2}=\frac{z}{5}\)	(IV) (2, -1, 5)

Choose the correct answer from the options given below:

The correct interpretation of Ohm's law is : (Here, \( \vec{J} \) is current density, '\( \sigma \)' is conductivity, \( \vec{E} \) is electric field and '\( \rho \)' is resistivity)

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
The product of complete hydrolysis of \(XeF _6\) in the following reaction is
\(XeF _6+ H _2 O \rightarrow ?+ HF\)