The area of the region bounded by the curves \(x^2 = 4y\), the line \(x = 3\) and x axis is:

Determine the value of k for which the function \(f(x)=\left\{\begin{array}{ll}\frac{x^2-9}{x-3}, & x \neq 3 \\ k, & x=3\end{array}\right.\) is continuous at x = 3

Which of the following functions has a local minima at \(x=0\) ?
(A) \(f(x)=x^3\)
(B) \(f(x)=|x|\)
(C) \(f(x)=x^2\)
(D) \(f(x)=x^{-2}\)
Choose the correct answer from the options given below :

If a random variable \(X\) has the following probability distribution :

X	0	1	2	3
P(X)	K	\(\frac{K}{2}\)	\(\frac{K}{4}\)	\(\frac{K}{8}\)

then,
Match List-I with List-II

List-I	List-II
(A) The value of \(K\) is	(I) \(2 / 15\)
(B) \(P(0<X<2)\) is	(II) \(1 / 15\)
(C) \(P(1<X<3)\) is	(III) \(8 / 15\)
(D) \(P(X>2)\) is	(IV) \(4 / 15\)

Choose the correct answer from the options given below :

The differential equation of the family of curves \(y=A e^{3 x}+B e^{-3 x}\) where A and B are arbitrary constants, is

Let \(x\) denote the number of heads in a simultaneous toss of three coins, then \(P(0 < x \leq 3)\)

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

A zener diode is :

The current in a solenoid changes from 0.0A to 10.0A in 0.1 sec. If an average emf of 2V is induced in the circuit, the value of self-inductance is:

What is the shape of a wavefront when light emerging out of a convex lens when a parallel beam of light incident over it ?

Read the passage carefully and answer the Questions
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups.
Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The compound having the highest boiling point is

\(\text{R-Br} \xrightarrow{\text{Mg, dry Ether}} \text{P} \xrightarrow{\text{EtOH}} \text{Q}\)
What is Q?

Which of the following is always upright in an ecosystem?