The feasible region of the linear programming problem is represented below :

The constraints of this LPP are

The objective function of an LPP is \(z=a x+\beta y,(a, \beta>0)\) that has to be maximized/minimized subject to the constraints \(x+y \leq 2, x \geq 0, y \geq 0\).
Then \(\max (z)-\min (z)\) is equal to :

If \(C_{i j}\) represents the cofactor of element \(a_{i j}\) of the matrix \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5\end{array}\right]\), then the value of \(C_{23}+C_{31}-C_{22}\) is

The derivative of \(f(\cot x)\) with respect to \(g(cosec x)\) at \(x=\frac{\pi}{4}\) (where \(\left.f^{\prime}(1)=2, g^{\prime}(\sqrt{2})=4\right)\) is:

The equation of the normal to the curve \(y=\frac{x-7}{(x-2)(x-3)}\) at (7,0) is:

If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

A machine costing ₹ \(36000\) has an effective life of 5 years with scrap value of ₹ \( 5000\) following a linear method of depreciation. Which are correct?
(A) The value of the machine after 1 year is ₹ \(31000\)
(B) The value of the machine after 2 years is ₹ \(23600\)
(C) The value of the machine after 3 years is ₹ \(18400\)
(D) The value of the machine after 4 years is ₹ \(11200\)
Choose the correct answer from the options given below :

Which one of the following drinks are produced by distillation?
(A) Whisky
(B) Brandy
(C) Wine
(D) Beer
choose the correct answer from the option given below:

Which one of the following is not a cause of loss of biodiversity?

For an AC circuit, a phase diagram shows emf on X-axis, and current I is at angle \( \theta \) to emf. Angle \( \theta \) is phase angle between emf and current. Current I is resolved into two components, \( I \cos \theta \) is along emf on X-axis. \( I \sin \theta \) is along perpendicular direction to emf.
(A) Component \( I \cos \theta \) will draw the power from the source
(B) Component \( I \sin \theta \) will draw the power from the source
(C) \( I \cos \theta \) is called the powerless current
(D) \( I \sin \theta \) is called the powerless current
Choose the correct answer from the options given below:

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The measured potential for
\(A g ^{+}+ e ^{-} \rightarrow A g ( s )\)
does not change with

Consider the LPP, \(\operatorname{Min} Z=2 x-3 y\) subject to the conditions
\(x+y \leq 3\),
\(x \leq 3\),
\(x \geq 0, y \geq 0\)
then the minimum value of the objective function is at the point.

The shortest distance between the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{x-3}{4}\) and \(\frac{x-2}{4}=\frac{y-4}{6}=\frac{x-5}{8}\) is equal to: