Let functions \(f:\{1,3,4\} \rightarrow\{1,2,5\}\) and \(g:\{1,2,5\} \rightarrow\{1,3\}\) be defined as \(f=\{(1,2),(3,5),(4,1)\}\) and \(g=\{(1,3),(2,3),(5,1)\}\) respectively. Then, which one of the following is correct statement for \(g \circ f\)?

In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :

If area of the triangle with vertices \(A(2, k), B(1,1), C(10,8)\) is \(\frac{47}{2}\) sq. units, then one of the values of \(k\) is:

For the given five values 18, 25, 20, 36, 49, the three years moving averages are

If \(\left[\begin{array}{ccc}x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0\end{array}\right]\) is a skew symmetric matrix, then the value of \(x+y+z\) is

It is currently 9:40 AM. What will be the time in next 610 hours?

The corner points of the feasible region determined by the system of linear constraints are \((0,0),(0,40),(20,40),(60,20),(60,0)\).
The objective function is \(z=4 x+3 y\).
Compare the quantity in Column - A and Column - B.

Column - A	Column - B
Maximum value of z	350

A box contains 2 black and 4 red balls and another box contains 4 black and 3 red balls. If a ball is drawn at random from one of the two boxes, then the probability of getting a black ball is

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
"Maltose" disaccharide is composed of

Which of the following is used as a biological control agent for insects and other arthropods ?

Which of the following statements are true with reference to homology or homologous organs?
(A) Homology indicates common ancestry.
(B) Whale and Cheetah share similarities in the pattern of the bones of the forelimbs.
(C) Vertebrate heart is an example of homologous organs.
(D) Thorn of Bougainvillea and tendrils of cucurbita represent homology.
Choose the correct answer from the options given below:

Match List-l with List-II:

List-I (Products)	List-II (Organisms)
(A) Statin	(I) Streptococcus
(B) Clot buster	(II) Trichoderma
(C) Swiss cheese	(III) Monascus
(D) Cyclosporin-A	(IV) Propionibacterium

Choose the correct answer from the options given below:

Write down the number of \(3 d\) electrons in \(Co ^{2+}\) ion: