If \(f(x)=e^x g(x), g(0)=2, g^{\prime}(0)=1\) then \(f^{\prime}(0)\) is equal to:

If \(A\) and \(B\) are square matrices of the same order, then \((A+B)(A-B)\) is equal to

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. Find the probability of getting at least one green ball

If \(y=3^x+e^x+x^x+x^3\), then the value of \(\frac{d y}{d x}\) at \(x=3\) is:

If A and B are two events such that \(P(A) \neq 0\) and \(P(A / B)=1\) then :

Which of the following terms are associated with a linear programming problem?
(A) Constraints
(B) Independent events
(C) Feasible region
(D) Objective function
Choose the correct answer from the options given below :

The marginal cost (MC) and marginal revenue (MR) functions of a product are \(M C=20+\frac{x}{20}\) and \(M R=30\) respectively. If the fixed cost is 200 , then the maximum value of the profit is :

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
What will be the products formed in the following equation?

Read the passage carefully and answer the Questions
A homogeneous mixture of two or more than two components has uniform composition and properties. The binary solutions have two components, which may be solid, liquid or gas. The resultant solution has a larger amount of solvent and a smaller amount of solute. The amount of solute in a given amount of solvent decides the concentration of the resulting solution. The concentration can be expressed in various ways, like molarity, molality, normality and mole fraction.
Molarity of a solution containing 8 grams \(NaOH\) in one liter of water is:

A closely wound circular coil of radius 10 cm carries a current of 6.4 A. If the number of turns in the coil are 10 then magnetic moment of this coil is :

Boiling of Sucrose with water in the presence of acid \(H+\) will give :

The function \(f ( x )=\log (\sin x )\) is ___________

On heating n-type semiconductors -