The number of all possible matrices of order 3 with each entry either 0 or 1 is :

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

Match List I with List II

LIST I	LIST II
A. If \(A^{-1}=\left[\begin{array}{ll}3 & 4 \\ 5 & 6\end{array}\right]\) then \(A\) is	I. \(\left[\begin{array}{ll}5 & 2 \\ 7 & 3\end{array}\right]\)
B. If \(A=\left[\begin{array}{cc}2 & -1 \\ 3 & 1\end{array}\right]\) then \(A A^T\) is	II. \(\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\)
C. If \(A^{-1}=\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right]\) then \(\left(A^T\right)^{-1}\) is	III. \(\left[\begin{array}{cc}-3 & 2 \\ \frac{5}{2} & -\frac{3}{2}\end{array}\right]\)
D. If \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j}=(i-j)^2\), then \(A\) is	IV. \(\left[\begin{array}{cc}5 & 5 \\ 5 & 10\end{array}\right]\)

The rise in prices before Christmas is an example of

For a random variable \(X, E(X)=3\) and \(E\left(X^2\right)=11\), then variance of \(X\) is :

A swimmer whose speed in still water is \(6 km / hr\), swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is \(3 km / hr\), then the distance between the two points is:

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 :

In a game, a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise, when a fair die is thrown.
The man decides to throw the die thrice but quits as soon as he gets a number greater than 4 .
The expected value of the amount (in Rs.) he wins or loses is :

The ammonia derivatives of carbonyl compounds obtained as colorless precipitate are
(A) Oxime
(B) Hydrazone
(C) Phenyl hydrazone
(D) Semicarbazone
Choose the correct answer from the options given below:

Which one of the following plants will have many ovules in their gynoecium?

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 oxidixing 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.
In polar C-O bond in carbonyl compounds, the nature of carbon and oxygen atom is

If \(\hat{a}, \hat{b}\) and \(\hat{c}\) are three units vectors and \(\hat{a}+\hat{b}+\hat{c}=\overrightarrow{0}\), then the angle between \(\hat{a}\) and ( \(-\hat{b}\) ) is

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a dior polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following is a chelate complex?