Two positive numbers \(x\) and \(y\) such that \(x+y=60\) and \(x y^3\) is maximum are :

The value of \(|\text{adj}(2A)|\), if \(A = [a_{ij}]_{3 \times 3}\) and \(|A| = 2\) is:

The straight line \(\frac{x+2}{3} = \frac{z-3}{-2}, y=2\) is

The system of equations
\(\begin{aligned} & x-3 y-8 z=-10 \\ & 2 x+5 y+\lambda z=13 \\ & 3 x+y-4 z=0\end{aligned}\)
has infinite number of solutions if the value of \(\lambda\) is equal to:

If \(\vec{a}=2 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\vec{c}=-\hat{i}+\hat{k}\) are three vectors, then the area (in sq, units) of the parallelogram whose diagonals are \((\vec{b}+\vec{c})\) and \((\vec{a}+\vec{c})\) is

Which of the following is correct about the compound annual growth rate (CAGR)?

If A and B are symmetric matrices, then \(A B-B A\) is

Read the given passage and answer the following questions:
Secondary treatment or biological treatment: The primary effluent is passed into large tanks where air is pumped into it. This allows vigorous growth of aerobic microbes. While growing, these microbes consume the major part of the organic matter in the effluent. This significantly change the BOD (biochemical oxygen demand) of the effluent. The effluent in then passed into a tank a small part of the sludge is pumped back into the aeration tank to serve as the inoculum. The remaining major part of the sludge is pumped into large tanks called sludge digesters. Here, other kinds of bacteria grow anaerobically in the sludge. The biogas produced can be used source of energy as it is inflammable. The effluent from the secondary treatment plant is generally released into natural water bodies like rivers and streams.
Which of the following gas is not produced in anaerobic digestion?

The polluting potential of waste water is determined by:

The demand function for a certain product is represented by the equation: p = 20 + 5x - \(3 x^2\), where \(x\) is the number of units demanded and p is the price per unit (in Rs.), then the marginal revenue when 2 units are sold, is:

Curd is at \(80^{\circ} F\),five minutes later it came down at \(60^{\circ} F\).
After another 5 minutes, its temperature became \(50^{\circ} F\).
Given that the rate of change of temperature is proportional to (T - S).
where S is temperature of surroundings and T is temperature of the curd at any time t.
Then the temperature of the surroundings is :

Arrange the following compounds in order of their increasing boiling points.
(A) Pentan-1-ol
(B) n-Butane
(C)PentanalChoose the correct answer from the options given below:

The area (in sq. units) of the region bounded by \(y=2 x+3\), the \(x\)-axis, and the ordinates \(x=-2, x=2\) is equal to