The solution of a LPP with basic feasible solutions (0,0), (10,0), (0,20), (10, 15) and objective function Max Z = 2x + 3y is:

If y = - 4 a root of \(\left|\begin{array}{lll}y & 2 & 3 \\ 1 & y & 1 \\ 3 & 2 & y\end{array}\right|=0\), then the product of the other two roots is

A random variable X has the following probability distribution :

X	1	2	3	4	5	6	7
\(P(X)\)	C	2C	2C	3C	\(C^2\)	\(2 C^2\)	\(7 C^2+C\)

Then the value of C is :

The order and degree of the differential equation \(\left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^3 + x^3 \left(\frac{dy}{dx}\right)^5 - \sqrt{x^2+1}\) are respectively:

Let E and F are events associated with an experiment. If \(P(E)=0.4, P(F)=0.8\) and \(P(F \mid E)=0.6\) then \(P(E \mid F)\) is:

If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is :

Let \(x\) denote the number of heads in a simultaneous toss of three coins, then \(P(0 < x \leq 3)\)

The polluting potential of waste water is determined by:

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
Identify the product Y in the following reaction
\(\text{CH}_3\text{-CH = CH – CH}_2\text{OH}\) \(\xrightarrow{\text{Pyridinium Chlorochromate}}\) \(\rightarrow\text{Y}\)

An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true ?

The DNA fingerprinting technique is based on -

Which of the following is NOT correct about the Central Limit Theorem?

Which one of the following is a result of convergent evolution?