What uniform magnetic field applied perpendicular to a beam of electrons moving at \( 1.3 \times 10^6 \text{ m/s} \) is required to make the electrons travel in a circular arc of radius 0.35 m?

The binding energy per nucleon is 1.1 MeV for \({ }_1^2 H\) and 7.0 MeV for \({ }_2^4 He\). The energy released in the given fusion reaction will be:
\({ }_1^2 H+{ }_1^2 H \rightarrow{ }_2^4 He\)

A body of mass 20 g and charge \( +50 \text{ }\mu\text{C} \) is suspended from the ceiling by a string. A horizontal electric field of 10 kV/m is applied.
The angle between the string and the vertical direction is :

9 cells each of emf e = 3 V and internal resistance r = 1 \( \Omega \) are connected in m = 3 rows, each having n = 3 cells in series. The current flowing in the external resistance of R = 5 \( \Omega \) connected across this arrangement of the cells is

A galvanometer having a resistance of \(7 \Omega\) is shunted by a resistance of \(3 \Omega\). If the total current is 1 A, the value of current passing through the shunt is

The half life of a radioactive nuclide is 20 hours. What fraction of original activity will remain after 80 hours ?

A series LCR circuit is connected to a variable frequency 230 V source. \( L = 5\text{H}, C = 80 \mu\text{F} \) & \( R = 40 \, \Omega \). The potential drop across R at resonating frequency is :

"The probability distribution of a random variable \(x\) is :
\(P(X=x)=\left\{\begin{array}{ll}k x^2, & \text { for } x=1,2,3 \\2 k x, & \text { for } x=4,5,6 \text { where } k \text { is a constant. } \\0, & \text { otherwise }\end{array}\right.\)
Match List-I with List-II

List I	List II
(A) k	(I) 7/22
(B) \(P(X \geq 4)\)	(II) 1/44
(C) \(P(X<4)\)	(III) 95/22
(D) E[X]	(IV) 15/22

Choose the correct answer from the options given below:

Probabilities to solve a specific problem by A, B and C are \(\frac{1}{2}, \frac{1}{3}\) and \(\frac{1}{4}\ respectively. Probability that at least one will solve the problem is:

The function \(f(x)=x^3+3 x^2+4 x+4, x \in R\) (set of real numbers):

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
Restriction enzymes are also known as

Amoebiasis in humans is caused by

Read the passage carefully and answer the questions
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
A reaction which is first order with respect to the reactant \(A\) has a rate constant of \(6 min^{-1}\). If the reaction is started with \([A]=5.0 mol L ^{-1}\) when would \([A]\) reach the value of \(0.05 mol L ^{-1}\)