If \(3\left[\begin{array}{cc}x & y \\ z & w\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 w\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+w & 3\end{array}\right]\), then the values of \(x, y, z\) and \(w\) are

The area (in sq. units) bounded by the parabola \(y^2=4 a x\), its latus rectum and the \(x\)-axis in the first quadrant is:

The degree of the differential equation \(\left(2+\left(\frac{d y}{d x}\right)^2\right)^{\frac{3}{2}}=a^2 \frac{d^2 y}{d x^2}\) is :

If A speaks truth in \(75\%\) cases and B speaks truth in \(80\%\) cases, then the probability that they contradict each other in a statement, is :

Which of the following are normal equations to fit a straight line trend \(y=a+b x\) by the method of least squares?

The standard deviation of the number of tails in three tosses of a coin is :

Choose the wrong statement.

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
During denaturation process of protein which structure(s) remain intact ?

The order of the following reaction will be :
\(2FeCl_3 + SnCl_2 \rightarrow 2FeCl_2 + SnCl_4\)

Androgens are synthesised and secreted by which of the following?

A parallel plate capacitor whose capacitance C is 13.0 pF is charged by a battery to a potential difference V = 13.0 V between its plates. What is the potential energy of the capacitor ?

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.
Among below given carbohydrates, which one is not a polysaccharides ?

The average emf induced in a coil is 2 V when current is changed in 0.4 s.
(A) from 5 A to 2 A and the self-inductance of the coil is 0.266 mH
(B) from 4 A to 4 A in the opposite direction, the self-inductance of the coil is 0.10 mH