Consider \(z=x+3 y\) subject to the constraints \(2 x+3 y \geq 6,2 x+y \leq 8, x \geq 0, y \geq 0\). The minimum value of \(z\) is :

A man rows downstream 30 km and upstream 20 km. If he takes 5 hours to cover each distance, then the speed of stream is

Consider the following data

Year (X)	2014	2016	2018	2020	2022	2024
Profit(in Rs. Thousand) (Y)	7	9	10	12	14	14

Then for the above data the equation of straight line trend by method of least square is given by:

The principle value of \(\cos ^{-1}\left(-\frac{1}{2}\right)\) is :

If \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 0 & 0 & 1\end{array}\right]\), then \(\left|\operatorname{adj}\left(3 A^T\right)\right|^2\) is equal to

If A= \(\left[\begin{array}{cc}7 & 3 \\ 5 & -7\end{array}\right]\) be such that \(A^{-1}\) = kA, then k equals

The points on the curve \(\frac{x^2}{9}+\frac{y^2}{16}=1\) at which the tangents are parallel to \(x\) - axis are:

Which one is not correct about withdrawal syndrome?

Fehling solution gives red precipitate with.....

\(\int \frac{d x}{x^3 \sqrt{\left(1+x^4\right)}}=\)

Multiple additions of new genes or alleles to the new population and their loss from the old population of a particular place due to migration is known as:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
\[Itext\{Osmotic pressure\} ((Pi) \text\{of a solution does not depend upon\}\}]

The sensitivity of a potentiometer can be increased by: