An equiconvex lens has a focal length\(\frac{2}{3}\) times the radius of curvature of either surface. The refractive index of the material of the lens is :

A light with an energy flux of 25 \( W/cm^2 \) falls on a non-reflecting surface at normal incidence. If the surface has an area of 50 \( cm^2 \) and the total energy falling on the surface is \( 10 \times 10^5 \) J. The total duration of time of the incidence of light is

The resistance of a wire is \( R \, \Omega \). What will be its new resistance \( R_{new} \) if it is stretched to n times its original length?

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be :

In amplitude modulation, modulation index '\( \mu \)' should be:

Match List-I with List-II

List-I (Physical quantity)	List-II (Formula)
(A) Current sensitivity of galvanometer	(I) \( \frac{\mu_0 I}{2R} \)
(B) Magnetic field at the centre of a circular coil	(II) \( \frac{NAB}{kR} \)
(C) magnetic field due to a long straight wire carrying a current	(III) \( \frac{NAB}{k} \)
(D) Voltage sensitivity of galvanometer	(IV) \( \frac{\mu_0 I}{2\pi R} \)

Choose the correct answer from the options given below:

A heater boils \( x \) amount of water in time \( t_{1} \) and another heater boils the same water in time \( t_{2} \) having resistances \( R_{1} \) and \( R_{2} \) respectively. The ratio \( \frac{t_{1}}{t_{2}} \) will be:

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^2+\) and Mg\(^2+\)
Hardness of water can be estimated by titration with _________ .

In a kilometer race \(P\) runs at \(10 m / sec , Q\) runs at \(5 m / sec\) then which of the following statement \(( s )\) is \(/\) are correct?
(A) \(P\) wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below :

Match List-l with List-II

List-l (Structure)	List-II (Relation)
(A) Thalamus	(I) Seed
(B) Nucellus	(II) Fruit
(C) Ovule	(III) Germination
(D) Micropyle	(IV) Perisperm

Choose the correct answer from the options given below:

Match List I with List II

List - I (Disease)	List - II (Causal organism)
(A) Pneumonia	(I) Protozoan
(B) Common cold	(II) Roundworm
(C) Malaria	(III) Bacteria
(D) Ascariasis	(IV) Virus

Choose the correct answer from the options given below:

The particular solution of the differential equation \(\cos \left(\frac{d y}{d x}\right)=a,(a \in R ) ; y=2\) at \(x=0\) is given by

DNA fingerprinting works on the principle of