The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then P\((0< x \leq 2\)) is equal to

The rise in prices before festivals is an example of

Consider the linear programming problem (LPP) :
Maximize \(Z=6 x+3 y\)
subject to the conditions
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\)
In reference to the above LPP, which of the following are correct?
(A) The feasible region is bounded.
(B) The corner points of the feasible region are (15,20), (40,15) and (0,75).
(C) The maximum value of the objective function is 285.
(D) The LPP does not have optimal solution.
Choose the correct answer from the options given below :

When data of the variable is collected at distinct time intervals for a specified period of time, it is called

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3\lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:

Area (in sq. units) of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is

The value of \(\frac{3}{2}(\hat{i} \cdot \hat{i})+\frac{1}{2}(\hat{j} \cdot \hat{j})+\frac{|\hat{i} \times \hat{i}|}{(\hat{k} \cdot \hat{k})}+\frac{(\hat{k} \cdot \hat{i})}{|\hat{i} \times \hat{j}|}\) is:

Let \(f(x)=\left\{\begin{array}{ll}|x|+3 & \text { if } x \leq-3 \\ -2 x & \text { if }-3 < x < 3, \text { then which of the following is true? } \\ 6 x+2 & \text { if } x \geq 3\end{array}\right.\)

Match List I with List II

\multicolumn1|c|\(LIST\)\(I\)	\multicolumn1|c|\( LIST\)\(II\)
A. \(Cu\)	I. \(+ 3\)
B. \(Sc\)	II. \(+ 7\)
C. \(Mn\)	III. \(+ 2\)
D.\(Fe\)	IV. \(+ 1\)

Choose the correct answer from the options given below:

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Which one of the following is not the cellular barrier of innate immunity?

Which one of the followings is an indirect measure of the organic matter present in water?

The unit of conductance(G) is

Maximize \(z=2 x-y\)
Subject to constraints
\(x+y \leq 4, \quad x+3 y \leq 6, \quad x \geq 0, \quad y \geq 0 .\)
The corner points of the feasible region are: