For two matrices \(A=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]\) and \(B^T=\left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right], A-B\) equals

In a meeting, 70% of the members favour and 30% oppose a certain proposal.
A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour.
Then, E(X) is:

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

The solution of the differentiable equation \(2 x \frac{d y}{d x}+y=14 x^3, x>0\), is:

The nearest integral value of the shaded area shown below is :

Vector in the direction of \(\hat{i}+\hat{j}+\hat{k}\) with magnitude 5 units is :

The unit vector in the direction of \(\vec{a}+\vec{b}\) if \(\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k} \& \vec{b}=-\hat{i}+\hat{j}-\hat{k}\) is:

A resistance of \( 15\Omega \) is connected in series with an unknown resistance \( R_1 \). This combination is connected to one gap of a meter bridge, while a resistance \( R_2 \) is connected in the other gap. The balance point is at 50 cm. When \( 15\Omega \) is removed, the balance point shifts by 10 cm. The value of \( R_1 \) is

Primary Alkyl halide \(\text{C}_4\text{H}_9\text{Br}\) (X) reacts with alcoholic \(\text{KOH}\) to give the compound (Y). Compound (Y) is reacted with \(\text{HBr}\)
to give (Z) which is an isomer of (X). When (X) is reacted with \(\text{Na/dry ether}\), it gives a compound (T), \(\text{C}_8\text{H}_{18}\), which is
different from the compound formed when n-butyl bromide is reacted with \(\text{Na/dry ether}\). The correct IUPAC name of (T) is:

Match List I with List II

List I	List II
A. The triplet nature of genetic code	I. George Gamow
B. The technique of DNA fingerprinting	III. Alec Jefferys
C. lac operon	IV. Jacob and Monod
D. Central dogma	II. Francis Crick

Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Biofertilisers
Biofertilisers are organisms that enrich the nutrient quality of the soil and their main sources are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria can fix atmospheric nitrogen into organic forms. Other bacteria can also fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter). Fungi are also known to form symbiotic associations with plants (mycorrhiza). Many members of the genus Glomus form mycorrhiza. Plants having such associations show other benefits also, such as resistance to root-borne pathogens, tolerance to salinity and drought, and an overall increase in plant growth and development. Cyanobacteria are autotrophic microbes widely distributed in aquatic and terrestrial environments many of which can fix atmospheric nitrogen, e.g. Anabaena, Nostoc, Oscillatoria, etc. In paddy fields, cyanobacteria serve as an important biofertiliser. Blue green algae also add organic matter in to the soil and increase its fertility. Currently, in our country, a number of biofertilisers are available commercially in the market and farmers use these regularly in their fields to replenish soil nutrients and to reduce dependence on chemical fertilisers.
Choose the free living, nitrogen-fixing bacteria from the following.

If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are:

Which of the following frequencies will be suitable for beyond-the-horizon communication using sky waves?