The general solution of the differential equation \(x d y+\left(y-e^x\right) d x=0\) is :
where C is constant of integration

A machine costing ₹1,00,000 has a useful life of 5 years. The estimated scrap value is ₹20,000.
Using straight line method, the annual depreciation is:

If \(A\) and \(B\) are matrices of same order, then ( \(A B^{ T }-B A^{ T }\) ) is always:

The value of \(\lambda\), so that the vector \(\vec{a}=2 \hat{i}+\lambda \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}\) are perpendicular to each other, is :

If \(\left[\begin{array}{ccc}x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0\end{array}\right]\) is a skew symmetric matrix, then the value of \(x+y+z\) is

Which of the following statements are correct?
(A) Direction ratios of the line \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}\) are 2, 3, 4
(B) Direction ratios of the line \(\frac{x-1}{2}=\frac{2-y}{7}=\frac{2 z-1}{6}\) are 2, -7, 3
(C) Direction cosines of z axis are 0, 1, 0
(D) Direction ratios of the line joining the point (1, 2, -3) and (4, 5, 6) are 1, 1, 3
(E) Direction cosines of a line which makes equal angles with the coordinate axes are \(\frac{1}{3}, \frac{-1}{3}, \frac{1}{3}\)
Choose the correct answer from the options given below:

A cell of emf 1.1 V and internal resistance \(0.5 \Omega\) is connected to a \(0.5 \Omega\) wire. Another cell of same emf is added in series, but current remains unchanged. The second cell's internal resistance is :

Observe the given figure and answer the following questions:

Which of the following is a cytokine barrier?

The cell \(emf\) depends on:

The capacity of a parallel plate capacitor does not depend on :

Let \(R\) be a relation on the set of integers \(Z\) such that \(R=\left\{(a, b), a=2^k b, a, b, k \in Z\right\}\), then \(R\) is :

If the following data is obtained from a simple random sample : 6, 7, 9, 10, 11, 17
Then the point estimate of population standard deviation 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.
The starting compound (Y) in the following reaction is
\(Y \xrightarrow{\text { axidation }} \text { aldehyde } \xrightarrow{\text { oxidation }} \text { carboxylic acids }\)