Match List-I with List-II

List-I (Equationof Lines)	List-II (Information)
(A) \(\vec{r}=(3 \hat{i}-2 \hat{j}+\hat{k})+\lambda(\hat{j}-2 \hat{k})\)	(I) Direction ratios are \(2,4,-1\)
(B) \(\frac{2-x}{1}=\frac{2 y+1}{4}, z=2\)	(II) Perpendicular to \(2 \hat{i}-\hat{j}+\hat{k}\)
(C) \(\frac{x}{1}=\frac{y-3}{2}=\frac{3-4 z}{2}\)	(III) Passing through the point \((3,-2,1)\)
(D) \(\vec{r}=(3 \hat{i}+2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\)	(IV) Direction ratios are \(-1,2,0\)

Choose the correct answer from the options given below :

Let \(P\) and \(Q\) be any two invertible matrices of the same order. Then Match List-I with List-II

List - I (Matrix)	List - II (Equivalent matrix)
(A) \((P Q)^{-1}\)	(I) \(Q^{-1} P\)
(B) \(\left(P^{-1} Q\right)^{-1}\)	(II) \(Q P^{-1}\)
(C) \(\left(P Q^{-1}\right)^{-1}\)	(III) \(Q^{-1} P^{-1}\)
(D) \(\left(P^{-1} Q^{-1}\right)^{-1}\)	(IV) \(Q P\)

Choose the Correct answer from the options given below :

The points on the curve \(\frac{x^2}{9}+\frac{y^2}{16}=1\) at which the tangents are parallel to \(x\) - axis are:

Match List-I with List-II

List - I	List - II
(A) Angle between \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}\)	(I) \(\pi\)
(B) Angle between \(\hat{i}-\hat{j}+\hat{k}\) and \(-\hat{i}+\hat{j}-\hat{k}\)	(II) \(\frac{3 \pi}{4}\)
(C) Angle between \(\hat{i}+\hat{j}\) and \(-\hat{i}\)	(III) \(\frac{\pi}{4}\)
(D) Angle between \(\hat{i}+\hat{k}\) and \(\hat{k}\)	(IV) \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

\(\int \frac{x+\sqrt{x}}{2 \sqrt{x}} d x=\)

The order of a null matrix is:

If \(f(x)=x^3 e^{-x}\), then the value of \(f^{\prime \prime}(1)\) is equal to

Which of the following statements are correct for dilute solutions?
(A) The elevation in boiling point is directly proportional to the molality of the solution.
(B) The elevation in boiling point is inversely proportional to the molality of the solution.
(C) The depression in freezing point is directly proportional to the molality of the solution.
(D) The depression in freezing point is inversely proportional to the molality of the solution.
Choose the correct answer from the options given below:

What amount of energy would be at the producer level if it is 50 KJ at third trophic level?

Which one of the following diseases is non-infectious?

Match List I with List II

List-I	List-II
A. Benzophenone \(\rightarrow\) Diphenylmethane	I. \(\text{LiAlH}_4\)
B. Benzaldehyde \(\rightarrow\) 1-phenylethanol	II. DIBAL-H
C. Cyclohexanone \(\rightarrow\) Cyclohexanol	III. \(\text{NH}_2\text{NH}_2\text{, KOH}\)
D. Methylbenzoate \(\rightarrow\) Benzaldehyde	IV. \(\text{CH}_3\text{MgBr, H}_2\text{O}\)

" 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 kingdon. 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.
Formalin which is used to preserve biological specimen is an aqueous solution of

Which one of the following is opposite part of micropylar end of ovule.