If \(A=\left[\begin{array}{ccc}-1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & -1 & 0\end{array}\right]\) is a symmetric matrix, then the value of 22 - y is:

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

The mean number of heads in two tosses of a coin is:

Match List-l with List-ll
Where \(R\) is set of real numbers

List-l	List-ll
(A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is	(I) one-one, Into
(B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(II) many-one, into
(C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is	(III) one-one, onto
(D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(IV) many-one, onto

Choose the correct answer from the options given below :

In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4, 18) and (6, 12). If objective function is Z = 30x + 20y then the sum of the maximum and the minimum values of Z is

The relationship between \(a\) and \(b\) making \(f(x)\) continuous at \(x=3\), where \(f(x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is:

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

The compound which produce turbidity immediately with Lucas reagent is

Answer the question on the basis of passage given below :
All transition elements display typical metallic properties like high melting point, boiling point, tensile strength, high malleability and ductility, luster, etc. Their metallic character increases down the group and elements of \(4 d\) and 5d series exhibit higher metallic characters. They show variable oxidation states and forms a number of coloured compounds due to the presence of unpaired electrons which shows d-d transitions and makes them paramagnetic.

\(\text{CH}_3-\text{CH}(\text{Br}) - \text{CH}_2 - \text{CH}_3 \xrightarrow{\text{alc. KOH}} \text{A} \xrightarrow{\text{Br}_2} \text{CH}_3-\text{CH}(\text{Br}) - \text{CH}(\text{Br}) - \text{CH}_3 \text{(B)}\)
\(\text{(B)} \xrightarrow{\text{alc. KOH}} \text{CH}_3-\text{C} = \text{C} – \text{CH}_3 \text{(C)}\)
\(\text{(C)} \xrightarrow{\text{Hg}^{2+}/\text{H}^+\atop \text{H}_2\text{O}} \text{D}\)
A and D respectively are :

The oxidation number of Co in the complex \(\left[ Co \left( H _2 NCH _2 CH _2 NH _2\right)_3\right]_2\left( SO _4\right)_3\) is:

\(\int \frac{d x}{2 \sin ^2 x+5 \cos ^2 x}\) is equal to