Interference of light obeys the Principle of conservation of:

The focal length of a thin lens in vacuum is f. If the material of the lens has refractive index \( \frac{3}{2} \), its focal length when immersed in water of refractive index \( \frac{4}{3} \) would be :

In the circuit shown in the figure, the ac source gives a voltage of V = 10 cos (500t). The ammeter reading will be :

In transmission of power from generation plants to users, transformers are used. Identify the correct reason to choose appropriate transformers.
(A) A step-up transformer is used at the generation plant and high voltages are transmitted.
(B) A step-down transformer is used at the generation plant and low voltages are transmitted.
(C) A step-up transformer lowers the current and hence loss due to joule heating is less.
(D) A step-down transformer lowers the current and hence loss due to joule heating is less.
Choose the correct answer from the options given below:

There is a small air bubble inside a glass sphere (\( \mu = 1.5 \)) of radius 10 cm. The bubble is 4.0 cm below the surface and is viewed normally from outside as shown. The apparent depth of the bubble will be

Two cells of emf 10 V and 6 V, each having internal resistances of \(2 \Omega\) are connected in parallel across points A and B. The equivalent emf of the cells is

Match List-I with List-II

List-I	List-II
(A) Electrical permittivity	(I) \(N m^2 C^{-1}\)
(B) Electric flux	(II) \(N^{-1} m^{-2} C^2\)
(C) Electric field	(III) \(Cm ^{-2}\)
(D) Surface charge density	(IV) \(N C^{-1}\)

Choose the correct answer from the options given below:

The integral \(I=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x\) is :

match List - I with List - II

List - I (function)	List - II (inceasing on the interval)
(A) f(x) = -\(x^2\) - 2x + 1	(I) \((-\infty,-1)\)
(B) f(x) = \(x^2\) + 1	(II) \((1, \infty)\)
(C) f(x) = \(x^2\) - 2x + 3	(III) \((-\infty, 0)\)
(D) f(x) = \(- x^2\)	(IV) \((0, \infty)\)

Choose the correct answert from the option given below :

A T.V. panel costing Rs 18000 has a useful life of 12 years. If the annual depreciation is Rs 1000, then its scrap value by linear method is :

Read the passage carefully and answer the questions
The transition metals and their compounds are known for their catalytic activity. This activity is ascribed to their ability to adopt multiple oxidation states and to form complexes. Vanadium(V) oxide (in Contact Process), finely divided iron, and nickel (in Catalytic Hydrogenation) are some of the examples. Catalysts at a solid surface involve the formation of bonds between reactant molecules and atoms of the surface of the catalyst (first row transition metals utilise 3d and 4s electrons for bonding). This has the effect of increasing the concentration of the reactants at the catalyst surface and also weakening of the bonds in the reacting molecules (the activation energy is lowering). Also because the transition metal ions can change their oxidation states, they become more effective as catalysts.
In the Wacker process the oxidation of ethene to ethanal is catalysed by _______

The greatest integer function \(f(x)=\lfloor x\rfloor\) is differentiable for all values of

An emf \( E = 200 \sin 300t \text{ volt} \) is applied across an inductor coil having a resistance of \( 1.0 \text{ } \Omega \). If the maximum current is found to be 10 A, then the value of inductance is approximately: