If \(y=\log _2\left(\log _2 x\right)\), then \(\frac{d y}{d x}\) is equal to :

Let \(f: R \rightarrow R\) be defined as \(f(x)=5 x^2\). Choose the correct answer :

Let \(f: R \rightarrow R\) be defined as \(f(x)=10 x\). Then (Where R is the set of real numbers):

The area of the region bounded by the curve \(y=\sin x\) and the \(x\)-axis between \(x=\pi / 2\) and \(x=3 \pi / 2\) is :

The number of all possible matrices of order \(2 \times 3\) with entries \(-1\) or \(1\) is:

\(60 \%\) members of a committee favour a certain proposal and \(40 \%\) members oppose the proposal.
A member is selected and let the random variable \(X=0\) if he opposes and \(X=1\) if he is in favour.
Then the variance of the random variable \(X\) is

If \(y=5 e^{2 x}+4 e^{3 x}\), then \(\frac{d^2 y}{d x^2}\) equals:

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^2+\) and Mg\(^2+\)
Hardness of water can be estimated by titration with _________ .

The feasible region of a linear programming problem is bounded. The corresponding objective function is \(Z = 3x - 4y\). The objective function attains:

The historic convention on Biological Diversity ('The Earth Summit') held in 1992.

400 g of apple vinegar has \(40 \%\) apple juice in it. The amount of apple juice, which should be added to make it \(60 \%\) in apple vinegar, is :

An electric motor operating on a 50 V dc supply draws a current of 12 A. If the efficiency of the motor is 30%, the estimated resistance of the motor would be :

If \( \mu_0 \) is the permeability and \( \epsilon_0 \) is the permittivity of free space, then the velocity of light (c) is: