A uniform electric field of 20 V m -1 exists in the vertically downward direction. What will be the increase in the electric potential as one goes up through a height of 60 cm?

A beam of light of wavelength 500 nm from a distant source falls on a single slit of width \( 10^{-4} \, \text{m} \), and the resulting diffraction pattern is observed on a screen 2 m away. The width of the central bright fringe is:

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:

Two identical capacitors are joined in parallel, charged to a potential V and then separated and connected in series, i.e., negative plate of first is connected to positive plate of second :

A message signal of peak voltage 20 V is used to modulate a carrier wave of amplitude 40 V in amplitude modulation. The ratio of maximum amplitude and minimum amplitude in amplitude modulated signal is:

Which of the following is true ?
(A) The equilibrium of a charged particle under the action of coulomb force alone can never be stable.
(B) A hollow metal sphere placed on an insulating stand is charged positively. The electric potential inside is same as on surface
(C) A free electron and a free proton are placed in a uniform field, both will experience same magnitude of the force
(D) A free electron and a free proton are placed in a uniform field, both will experience same acceleration
Choose the correct answer from the options given below :

The correct arrangment of colours in the descending order of their wavelength is
A. Green
B. Orange
C. Yellow
D. Violet
E. Red
Choose the correct answer from the options given below:

The two possible nuclei to complete the reactions given below are, respectively
(1) \({ }_7 N^{14}+{ }_2 He ^4={ }_8 O ^{17}+\)_______
(2) \({ }_8 O ^{16}+{ }_1 H ^2={ }_7 N^{14}+\)_____

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by r = k[CH₃OCH₃]^3/2. If the pressure is measured in bar and time in minutes, then the unit of rate constant will be

What is the product of the following reaction?
\(R-CN \frac{H_2 / Nl}{Na\left(H_{g}\right) / C_2 H_6 OH}\)
The options are:

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 :

Match List-I with List-II (Symbols have their usual meanings)

List-I (Physical Quantity)	List-II (Expression)
(A) Current density	(I) \( \frac{e E \tau}{m} \)
(B) Drift velocity	(II) \( \frac{n e^2 \tau}{m} \)
(C) Conductivity	(III) \( \frac{e \tau}{m} \)
(D) Mobility	(IV) \( n e v_d \)

Choose the correct answer from the options given below:

Match List-l with List-ll

List-l (Electronic configuration)	List-II (lon)
(A) \([ Ar ] 3 d^{10}\)	(I) \(Ce ^{4+}\)
(B) \(\left[ X _{ e }\right]\)	(II) \(Cu ^{+}\)
(C) \([ Rn ]\)	(III) \(Th ^{4+}\)
(D) \([ Xe ] 4 f^{11} 5 d^1\)	(IV) \(Lu ^{2+}\)

Choose the correct answer from the options given below: