Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

If the elementary column transformation \(C_1 \rightarrow 2 C_1\) is carried out on the following matrix equation.
\(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}-1 & 2 \\ 5 & 0\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) Then the transformed equation will be:

The differential equation that represents the family of lines parallel to x + y = 2 is:

A steamer can row at the speed of 16 km/hr in still water. If the river is flowing at 8 km/hr and it takes 12 hours for a round trip, then the distance between the two places is :

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

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

The product of the order and degree of the following differential equation :
\(x \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + y^2 = 0\)

The pattern and behavior of the data in any time series are based on which of the following components:
(A) Secular trend component
(B) Seasonal component
(C) Cyclical component
(D) Irregular component
Choose the correct answer from the options given below :

Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:

The value of \(\int_{-1}^1 x^2[x] d x\) is:

Two closely related species can co-exist indefinitely and violate the Gause's 'Competitive Exclusion Principle' by:

Which of the following statements is correct for an electric dipole placed along the direction of a non-uniform electric field?

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Pyridinium chlorochromate is used for: