Two point charges, +2 \( \mu \text{C} \) and -3 \( \mu \text{C} \), are separated by a distance of 20 cm in the air. At what point between the two charges and on the line joining the two charges is the electric potential zero?
(Take the potential at infinity to be zero)

Choose the correct option from the following transitions in which the wavelength will be minimum

A moving coil galvanometer has a resistance of 40 \( \Omega \). It gives a full scale deflection with a current of 2 mA. How is to be modified to convert it to a voltmeter of 5 V range?

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm, coming from a distant object, the limit of resolution of the telescope is close to :

Which of the following atoms/ions have a ground state energy of -54.4 eV ?

Arrange the following electromagnetic waves in their increasing order of energy.
(A) Gamma rays
(B) X- rays
(C) Microwaves
(D) Infrared waves
(E) Ultraviolet rays
Choose the correct answer from the options given below:

Two nuclei have their mass numbers in the ratio of \(1: 3\). The ratio of their nuclear densities would be :

Match List-l with List-ll

List-l (Rate expression)	List-II (Overall order of reaction)
(A) \(r=k[A]^{0.2}[B]^{0.3}[C]\)	(I) \(\frac{3}{10}\)
(B) \(r=k[A]^{0.2}[B]^{-0.3}[C]\)	(II) 1
(C) \(r=k[A][B]^{0.8}[C]^{-1}\)	(III) \(3 / 2\)
(D)\(r=k[A]^{0.2}[B]^{0.3}[C]^{0.5}\)	(IV) \(9 / 10\)

Choose the correct answer from the options given below:

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^x[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
Which of the following statements are correct?
(A) Catalysts increase the rate of a chemical reaction.
(B) Catalysts can catalyze both spontaneous and non-spontaneous reactions.
(C) Higher the activation energy for a chemical reaction, lower is the rate of the reaction.
(D) Catalyst increases the potential energy barrier.
Choose the correct answer from the options given below:

The correct structure representing N,N-dimethylethanamine is

The maximum value of \(\sin x \cdot \cos x\) is :

Area of a rectangle having vertices A, B, C, D with position vectors \(-\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) and \(-\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) respectively is:

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is : [Given \(e^{-2}=0.135\)]