The domain of the function \(f(x)=\sin ^{-1}(2 x-3)\) is :

If \(\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0\) then the value of x is:

\(\int \frac{x}{x^2+x-12} d x\) is equal to

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with elements either 0 or 1 . Then the difference between the possible number of singular and non-singular matrices is

The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by \( C(x)=0.001 x^3+0.06 x^2+20 x+500\)
The marginal cost when 10 units are produced is:

A relation \(f: N \rightarrow N\) be defined by \(f(x)=x^2, x \in N\) (Set of Natural numbers), Then \(f(x)\) is

The value of the integral \(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x\) is:

Find the odd one out among the following structures?

Function \(f(x)=x^x, x>0\) decreases on the interval

The value of the integral \(I=\int \frac{(\log x)^3}{x} d x\) is :

A pendulum of length 'l' having a bob of mass 'm' carrying charge 'q' is suspended from a stationary rigid support in a region of uniform electric field 'E' as shown in the figure. If the system is in equilibrium, the nature and magnitude of 'q' will be :

Which of following reagents will furnish ambident nucleophile?
(A) AgCN
(B) KCN
(C) AgNO2
(D) KNO2
Choose the correct answer from the options given below :

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 stom 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.
The starting compound Y in the following reaction is
\(\text{Y}\) \(\xrightarrow{\text{oxidation}}\) \(\text{aldehyde}\) \(\xrightarrow{\text{oxidation}}\) \(\text{carboxylic acids}\)