Given a linear programming problem max \(z=22 x+18 y\) subject to \(x+y \leq 20\), \(360 x+240 y \leq 5760\) and \(x \geq 0, y \geq 0\). Its corner points are:

The area of a triangle whose vertices are \(\left(x_1, y_1\right),\left(x_2, y_2\right)\) and \(\left(x_3, y_3\right)\) is given by the absolute value of

The matrix \(A = \begin{bmatrix} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{bmatrix}\) is a

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

If \(A\) and \(B\) are independent events such that \(P(A \mid B)=\frac{1}{3}\) and \(P(B)=\frac{1}{2}\), then the value of \(P(A \cap B)\) is equal to :

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

The original value of an asset minus the accumulated depreciation at a given date is known as:

A capacitor of \( 25 \mu \text{F} \) is connected in series with d.c Voltage of 5 V. The value of current in the circuit will be:

If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\) , then the possible values of x + y are:

Match List-l with List-II

List-l (Order of reaction)	List-II (Expressions/Unit)
(A) Unit of zero order	(I) \(k t=[ R ]_0-[ R ]_t\)
(B) Unit of First order	(II) \(mol L ^{-1} s^{-1}\)
(C) Integrated Rate Law for zero order	(III) \(s^{-1}\)
(D) Integrated Rate Law for First order	(IV) \([ R ]=[ R ]_0 e^{-k t}\)

Choose the correct answer from the options given below :

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol.
The discovery of penicillin was a chance discovery by Alexander Fleming while working on:

Bacillus thuringiensis produces Bt toxin crystals it does not kill the bacterium itself as the toxin is in the:

Certain Aldehydes, Retore and certain alcohol undergo iodoform test. Certain Aldehydes ketones undergo aldol condensation. While certain aldehydes undergo Cannizaro's reaction. Aldehydes responds to tollen reagent and fehling reagent test.
Which amongst the following will respond to both Tollens' reagent test and Fehling's reagent test?