The maximum value of \(\left(\frac{1}{x}\right)^x\) for \(x>0\) is

If \(\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi\) then the value of \(\alpha^2 \beta^2 \gamma^2+3(\alpha+\beta+\gamma)\) is:

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than \(9\) , given that the black resulted in a \(5\) is:

For an objective function \(z=a x+b y\) where \(a, b>0\).
The corner points of feasible region determined by a set of constraints are \((0,20),(10,10),(30,30),(0,40)\).
The condition on \(a\) and \(b\) such that max \(z\) occurs at both the points \((30,30)\) and \((0,40)\) is:

If \(A = \mathbb{R} - \left\{\frac{3}{2}\right\}\) and function \(f: A \rightarrow A\) is defined by \(f(x) = \frac{3x-2}{2x-3}\), then

If the vectors \(\vec{a}=3 \hat{i}-p \hat{j}+5 \hat{k}\) and \(\vec{b}=-6 \hat{i}+14 \hat{j}+q \hat{k}\) are collinear, then the value of \(p\) and \(q\) are :

The sum of the order and degree of the differential equation having \(y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B\) where A and B are arbitrary constants, as its general solution is:

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
What is the SI unit of conductivity?

Clarias gariepinus, the African catfish is an example of

Which of the following country has the highest biodiversity?

The armature coil of a generator has 20 turns and its area is \( 0.127 \, \text{m}^2 \). How fast approximately should it be rotated in a magnetic field of \( 0.2 \, \text{Wb m}^{-2} \) so that the peak value of induced emf is 160 V?

Mr. X wishes to purchase a flat for Rs. 44, 60, 800 with a down payment of Rs. 10,00,000 and the balance in equal monthly instalments (EMI) for 20 years. If the bank charges 7.5% per annum compounded monthly, then the EMI is :
[Given that \((1.00625)^{240}=4.4608\) ]

For transistor action, which of the following statements are correct
A. Both the emitter junction as well as the collector junction are forward biased.
B. The base region must be very thin and lightly dopped.
C. Base, emitter and collector should have same doping concentration.
D. The emitter junction is forward and collector junction is reverse bias.
Choose the correct answer from the options given below: