A random variable X has the following probability distribution

X	0	1	2
\(P ( X )\)	\(1 / 4\)	\(1 / 2\)	\(1 / 4\)

then, which of the following is correct?

The maximum value of Z = 3x + y subject to the constraints
x + y \(\le\) 7,
x \(\le\) 5,
y \(\le\) 4,
x \(\ge\) 0, y \(\ge\) 0 is:

If \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ -4 & 2 & 4\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -2 \\ 3 & -4 \\ 2 & 4\end{array}\right]\) then product \(A B\) is :

Consider a random sample of 10 students having 116 cm as mean height and standard deviation as 9.798 cm .
If the suggested mean height of the students population is 110 cm , then the \(t\)-test statistic of the sample is :
Given: \(\frac{\sqrt{10}}{9.798}=0.3227\)

The probability distribution of a discrete random variable x is given below:

\(x\)	\(2\)	\(3\)	\(4\)	\(5\)
\(p(x)\)	\(\frac{5}{k}\)	\(\frac{7}{k}\)	\(\frac{9}{k}\)	\(\frac{10}{k}\)

The value of \(k\) is

Lower half of a convex lens is opaque. The image of an object placed in front will :

If \(\left[\begin{array}{c}x+y+z+w \\ x+y \\ x+z \\ x+w\end{array}\right]=\left[\begin{array}{c}10 \\ 6 \\ 5 \\ 3\end{array}\right]\), find the value of \(x^2+y^2-(w+z)^2\).

Select the correct statements from the options given below:-
A. Parthenium is an endemic species of India
B. Eicchornia is an invasive alien species in India
C. Lantana is also known as carrot grass
D. African catfish is a threat to indigenous catfish
Choose the correct answer from the options given below:

The solubility of the gas in a liquid :
(A) Increases with increase in pressure
(B) Decreases with increase in pressure
(C) Increases with increase in temperature
(D) Decreases with increase in temperature
Choose the correct answer from the options given below :

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction. The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(= \text{k}[\text{A}]^x [\text{B}]^y\)
Here k is the rate constant
\(x + y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants A and B, respectively.
If the temperature is raised by \(10^\circ\text{C}\), then the rate of the reaction increases approximately by:

If \(A=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), and \(A^2=3 A+k I\), then the value of \(k\) is:

The electric field vector associated with electromagnetic wave in free space is given by \(E=40 \cos \left(6 \times 10^8 t-k x\right) V m ^{-1}\). The value of \(k\) in SI unit is :

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are :