Which of the following are correct?
(A) If \(A\) and \(B\) are symmetric matrices such that \(A B=B A\), then \(A B\) is symmetric.
(B) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A+B)\) is a symmetric matrix.
(C) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B-B A)\) is a symmetric matrix.
(D) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B+B A)\) is a skew-symmetric matrix.
Choose the correct answer from the options given below :

The value of \(\int_{-3}^2 x^2|2 x| d x\) is:

A person can row a boat in still water at the rate of \(5 km / hr\). It takes him \(4\) times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is:

For \(x \in[-1,1]\), if \(4 \sin ^{-1} x+\cos ^{-1} x=\pi\) then \(x\) is equal to :

For predicting the straight line trend in the sales of cars (in thousands) on the basis of 5 consecutive years' data, the company uses a 3-year moving averages method.
If the sales of cars for respective years are 15, 24, 18, 33 and 42, then which of the following averages will not be computed?

There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1, then the probability that all the lines are busy?

The function \(f(x)=\tan x-x\) for \(x \in\left(0, \frac{\pi}{2}\right)\) is :

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
The downstream processing does not include -

From a container full of orange juice, 7.5 liters was drawn out and replaced by soda water.
This process is repeated 5 more time.
The ratio of quantity of orange juice and soda water left in the container is 4:5.
How much liter of orange juice did the container originally had?
(Use \((0.44)^{1 / 6}\) = 0.802)

In a given habitat during a given period of time, population density increases if :-

With reference to D-glucose, which of the following cannot be explained by its open chain structure?
(A) D-Glucose does not give Schiff's test.
(B) The pentaacetate of D-glucose does not react with hydroxylamine.
(C) Glucose is found to exist in two different crystalline forms.
(D) D-glucose reacts with mild oxidizing agents like Br2-H2O and forms gluconic acid.
Choose the correct answer from the options given below:

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:

If \( n_h \) is the number of holes per unit volume and \( n_e \) is the number of conduction electrons per unit volume in an extrinsic semiconductor. The relation between \( n_h, n_e \) and \( n_i \) is (\( n_i \) is intrinsic carrier concentration):