The function \(f: R \rightarrow R, f(x)=x^2\) is :

Match List-I with List-II (Where R is the set of real numbers)

List-I	List-II
(A) \(sin\) \(x\) is continuous on :	(I) \(R -\{0\}\)
(B) \(tan\) \(x\) is continuous on :	(II) \(R\)
(C) \(\cot x\) is continuous on :	(III) \(R -\{n \pi: n \in Z \}\)
(D) \(x^{-n}, n \in N\) is continuous on:	(IV) \(R -\left\{(2 n+1) \frac{\pi}{2}: n \in Z \right\}\)

Choose the correct answer from the options given below :

The demand function (in Rs.) for a product is \(P=20-0.25 x\). where P is the price per unit and \(x\) is the number of units sold. Find the price of one unit when the revenue is maximized

A 50 Hz AC current of crest 1 A flows through a transformer primary. With mutual inductance \(0 . 5 ~ H\), the crest voltage induced in secondary is :

If \(X\) is normal distribution random variable with mean \(\mu=10\) and standard deviation \(\sigma=2, Z\) is standard normal variable and \(F(Z)\) is cumulative distribution function, then which of the following are true?
[Given that \(F(1.5)=0.9332, F(3)=0.9986, F(2.25)=0.9878\) and \(F(1)=0.8413\) ]
(A) \(P(X<13)=0.9332\)
(B) \(P(X>16)=0.9986\)
(C) \(P(12<X<14.5)=0.1465\)
(D) \(P(X>8)=0.8413\)
Choose the correct answer from the options given below:

Let \(A\) and \(B\) be \(3 \times 3\) matrices such that \(A \neq B\). If \(A^3=B^3\) and \(A^2 B=B^2 A\), then the determinant of \(A^2+B^2\) is :

Which of the following statements are correct ? (A) \(\sin ^{-1}(-x)=-\sin ^{-1} x, x \in[-1,1]\) (B) \(\tan ^{-1}(-x)=-\tan ^{-1} x,-1<x<1\) (C) \(\cos ^{-1}(-x)=\pi-\cos ^{-1} x,-1 \leq x \leq+1\) (D) \(\sec ^{-1}(-x)=\pi-\sec ^{-1} x,|x|>1\) (E) \(\cot ^{-1}(-x)=\pi-\cot ^{-1} x, x \in R\) Choose the correct answer from the options given below :

Which one of the following guides the entry of the pollen tube into the embryo sac?

If \(A=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\) and \(B=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\) then the matrix \(A B\) is equal to:

If \(\frac{3 x-5}{6}+8 \geq 4+\frac{2 x}{3}\), then

Verhulst-Pearl logistic growth equation can be represented by -

Match List I with List - II. -

List - I	List - II
(A) Linkage	(I) Trisomy of 21st chromosome
(B) Pleiotropy	(II) Multiple alleles
(C) Down's syndrome	(III) T.H. Morgan
(D) Blood group	(IV) Phenylketonuria

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom. Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidixing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
In polar C-O bond in carbonyl compounds, the nature of carbon and oxygen atom is