The value of \(\int \frac{1}{\sqrt{x^2+8 x+9}} d x\) is(Given \(C\) constant of integration):

The following statements are made on the basis of given graph.
(A) OB represents the cost function.
(B) MA represents the cost function.
(C) Loss occurs at x = 5.
(D) Loss occurs at x = 15.
(E) Profit occurs at x = 10.

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are :

If \(A=\left[\begin{array}{cc}-2 & 3 \\ k & 4\end{array}\right]\) is a singular matrix then value of \(k\) is :

The degree of the differential equation
\(\left[1+\left(\frac{d y}{d x}\right)\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is :

With reference to square matrices, which one of the following statement is NOT correct ?

Which of the following statements are correct?
(A) The mean and variance of the Poisson distribution are equal.
(B) The mean and variance of a Binomial distribution are equal.
(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is \(\frac{5}{108}\).
(D) If the variance of a Poisson distribution is 2 , then \(P(X=2)=2 e^{-2}\).
Choose the correct answer from the options given below :

Positive carbylamine test is shown by :

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
Faraday's laws of electrolysis are related to:

The thermostable DNA polymerase is isolated from the bacterium:

Rahul can run 34.4 m in the given time as Amit runs 50 m. By how much distance Rahul is away from Amit at the winning point, in a two km race?

The reaction in which an amide is treated with bromine in presence of ethanolic solution of sodium hydroxide is called

Identify the correct expression of Arrhenius equation :