For the given \(5\) values, \(15, 18, 21, 27, 39;\) the three year moving averages are:

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
The coordinates of the points where the line through the points \(A \backslash \& B\) crosses the \(X Y\) plane is:

If \(\theta\) is the angle between any two vectors \(\vec{a}\) and \(\vec{b}\), then \(|\vec{a} \cdot \vec{b}|=|\vec{a} \times \vec{b}|\) for \(\theta\) equal to __________.

If \(y=e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)}\), then \(\frac{d^2 y}{d x^2}\) is equal to :

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table:

Date	1	2	3	4	5	6	7
Number of cases	2	0	5	12	20	27	46

The 3-day moving averages are:

Consider the matrices \(A=\left[\begin{array}{ccc}9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 / 5 & 0 & 0 \\ 0 & 1 / 4 & 0 \\ 0 & 0 & 1 / 3\end{array}\right]\). The value of \(\left|(A B)^{-1}\right|\) is

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
The sugar having ẞ-glycosidic linkage is

An individual is suffering from an inborn error of metabolism which is inherited as the autosomal recessive trait. Identify the disorder.

If a man with blood group A marries a woman with blood group AB. Which of the following blood group will never be found in their children?

The maximum distance between the transmitting and receiving antenna for a satisfactory communication in LOS mode is 48 Km . If the height of the receiving antenna is 8 (Given radius of earth \(R_e=6400 km\) )

The relation \(R\) on the set \(N \times N\) defined by \((a, b) R(c, d) \Longleftrightarrow a+d=b+c\), \(\forall(a, b),(c, d) \in N \times N\), where N is the set of natural numbers, is:

Read the passage below and answer the question:
The accumulation of molecular species at the surface rather than in the bulk of a solid or liquid is termed as adsorption. There are two types of adsorption. In physisorption, attractive forces are mainly Van der Waals while in chemical adsorption adsorbate is held with chemical bonds adsorbent. Adsorption increases with increase in pressure and decreases as temperature is increased.
Which of the following is not characteristic of chemical adsorption?