For Z = 3x + 4y, subject to the constraints \(x+y \leq 5, x \geq 0, y \geq 0\), the shaded region shown in the figure as OAB is bounded and the coordinates of the corner points O, A, B are (0, 0), (5, 0) and (0, 5) respectively. The maximum value of Z is:

The values of ' \(a\) ' and ' \(b\) ' if the equation of straight line trend by least square method is given by \(y=a+b x\) such that \(\sum x=0, \sum y=84, \sum x y=108, \sum x^2=70\) for 6 observation as are :

The principal value of \(\operatorname{cosec}^{-1} \left(\frac{2}{\sqrt{3}}\right)\) is:

The value of \(\left|\begin{array}{ccc}1 & 1+p & 1+p+q \\ 2 & 3+2 p & 1+3 p+2 q \\ 3 & 6+3 p & 1+6 p+3 q\end{array}\right|\) is:

The interval where the function \(f(x)=2 x^3-9 x^2+12 x+15\) is decreasing, is :

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

The differential equation of the family of parabolas \(y^2=4 a x\) where \(a\) is an arbitrary constant is :

Identify the chiral molecule from the following,

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:

Haloalkanes can be represented by the formula

If \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]\), then \(A^{-1}\) is equal to :

Which of the following reactions are given by Phenols?
(A) Nitration
(B) Halogenation
(C) Oxidation
(D) Acetylation
Choose the correct answer from the options given above:

Which of the following have lowest value of pK, in their aqueous solution?