If the matrix \(\left[\begin{array}{ccc}-3 & x-y & 5 \\ 1 & 0 & z \\ x+y & 4 & 7\end{array}\right]\) is symmetric, then the correct option of the following, is :

Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :

In a Linear Programming problem, the objective function is always :

The volume of parallelepiped whose co-terminous edges are given by \(-3 \hat{i}+7 \hat{j}+5 \hat{k},-5 \hat{i}+7 \hat{j}-3 \hat{k}\) and \(7 \hat{i}-5 \hat{j}-3 \hat{k}\) is :

On which of the following components, the pattern and behavior of the data in any time series is based?
(A). Secular trend component
(B). Seasonal component
(C). Cyclical component
(D). Regular component
Choose the correct answer from the options given below :

The value of integral \(\int \sqrt{4 x^2+9} d x\) is

In reference to the Inferential Statistics, which of the following is NOT correct?

When monochromatic orange light is used instead of violet light in a convex lens, its focal length will :

A closely wound solenoid of 1000 turns and area of cross section \( 1.2 \text{ cm}^2 \) carries a current of 5 A. It is suspended horizontally in uniform magnetic field of \( 5 \times 10^{-2} \text{ T} \) making an angle of \( 30^\circ \) with the axis of solenoid. The torque acting on the solenoid is:

Read the passage carefully and answer the questions
Carbohydrates such as cane sugar, glucose, starch etc. belong to a class of naturally occurring organic compounds. Structurally these are polyhydroxy aldehydes or ketones or the compounds which produce such units on hydrolysis. Carbohydrates which are sweet in taste are called sugars. Theses sugars can be reducing or non-reducing. Monosaccharides cannot be hydrolyzed to simpler units whereas Oligosaccharides yield two to ten monosaccharide units on hydrolysis. Polysaccharides yield large number of monosaccharide units on hydrolysis. This class of biomolecules is essential for living systems as they serve as storage molecules in plants and animals. In addition, they provide raw materials for important industries like furniture, textiles, paper, lacquers and breweries. Two aldopentose form important constituents of nucleic acids. Carbohydrates are also called saccharides (Greek: sakcharon which means sugar). Sugar which is used in household and in milk also comes under this class of biomolecules.
Reducing sugars respond to

In a coil of self inductance 10 H, the rate of change of current is \( 4 \text{ A s}^{-1} \). The electromotive force (emf) induced in the coil will be

Interstitial compounds are formed when small atoms like H, C, or N are trapped in the crystal lattice of metal. Which of the following statements are true about the interstitial compounds?
(A) Interstitial compounds have higher melting points than the pure metals.
(B) Interstitial compounds are very soft.
(C) Interstitial compounds are very reactive.
(D) Interstitial compounds retain metallic conductivity.
Choose the correct answer from the options given below:

Among the following statements on the nitration of aromatic compounds, the false one is: