Consider the following L.L.P.
Minimize \(z=30 x-30 y+1800\);
subject to \(x+y \leq 30, x \leq 15, y \leq 20, x+y \geq 15\) and \(x, y \geq 0\).
Then it attains its optimal value at the point

A machine costing ₹1,00,000 has a useful life of 5 years. The estimated scrap value is ₹20,000.
Using straight line method, the annual depreciation is:

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

What sum of money is needed to invest now so as to get Rs. 5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

Let R be the feasible region for a Linear Programming Problem and let \(z=a x+b y\) be the objective function. If R is bounded, then the objective function z has :

The product of order and degree of the differential equation \(\left(\frac{d^3 y}{d x^3}\right)^2+x^2 y\left(\frac{d^2 y}{d x^3}\right)^3=2 x^5\) is:

Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\).
Which of the following is true?

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases
with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\left(\Lambda_m^0\right)\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per
molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law
finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The unit of constant A is :

Derivative of \(2 x^2\) with respect to \(5 x^4\) is:

Identify the term (s) which is/are not associated with post transcriptional processing of RNA.
A. Termination factor
B. Splicing
C. Capping
D. Tailing
Choose the correct answer from the options given below:

The osmotic pressure of the equimolar solutions of the following at the same temperature will increase in the order:
(A) NaCl
(B) \(K_{2}SO_{4}\)
(C) \(K_{3}[Fe(CN)_{6}]\)
(D) \(NH_{2}CONH_{2}\)
Choose the correct answer from the options given below:

Apomixis is the -

Match List I with List II

LIST-I	LIST-II
A. \(\left[1 + \left(\frac{dy}{dx}\right)^2\right] = \frac{d^2y}{dx^2}\)	I. order 2, degree 3
B. \(\left(\frac{d^3y}{dx^3}\right)^2 - 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^4\)	II. order 2, degree 1
C. \(\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^3 = 0\)	III. order 1, degree 2
D. \(\left(\frac{dy}{dx}\right)^2 + 6y^3 = 0\)	IV. order 3, degree 2

Choose the correct answer from the options given below: