Let \(f(x)=4 x^3-18 x^2+27 x-5, x \in \mathbb{R}\). Then which of the following statements are TRUE?
(A) \(f^{\prime \prime}(x)=24 x-36\)
(B) \(f\) has local maxima at \(x=\frac{3}{2}\) but no minima
(C) \(f\) has neither maxima nor minima
(D) \(f\) has both maxima and minima
Choose the correct answer from the options given below:

In a Linear Programming problem, the objective function is always :

Let \(f(x)=|x|\) and \(g(x)=[x]\), then the value of \(f \circ g\left(-\frac{9}{2}\right)-g \circ f\left(-\frac{9}{2}\right)\) is :

If the points \((2,1),(-1,4)\) and \((a, 3)\) are collinear then the value/(s) of a is/(are) :

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

The angle between the line \(\vec{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})\) and the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4\) is :

Let \(|\vec{a}|=5,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=6\), then the value of \(|\vec{a} \times \vec{b}|\) is equal to

If a 99% confidence interval states that the population mean is greater than 100 and less than 400, then the sample mean and margin of error respectively are:

The sun maintains its shine because of the

Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively.
Both the pipes are opened together for some time and then pipe P is closed.
If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

Which of the following vitamins are water soluble ?
(A) Thiamine
(B) Riboflavin
(C) Pyridoxine
(D) Ascorbic acid
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions.
Amines are considered to be derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. They are usually prepared from nitro compounds, halides, amides, imides etc. The presence of hydrogen bonding influences its physical properties. In alkylamines, a combination of electron releasing steric and hydrogen bonding factors influences the stability of substituted ammonium cations in protic polar solvents and thus affects the basic nature of amines. Alkyl amines are found to be stronger bases than ammonia which is more basic than water. Primary and secondary amines are engaged in intermolecular association due to hydrogen bonding. This intermolecular association is more in primary amines than in secondary amines. Tertiary amines do not have intermoleulcar association due to the absenceof hydrogen atom available for hydrogen bonding. Thus, the boiling point of amines depends on hydrogen bonding. In aromatic amines, electron releasing and withdrawing groups increase and decrease their basic character. Aryl diazonium salts usually obtained from arylamine undergo replacement of the diazonium group with a variety of nucleophile. Their coupling reaction of aryl diazonium salts with phenol or arylamine results in formation of dyes.
The most basic species in the following is

If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is