The integral \(I=\int \frac{e^{5 \log _0 x}-e^{4 \log _0 x}}{e^{3 \log _0 x}-e^{2 \log _0 x}} d x\) is equal to:

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}\) equals

Let \(f:[-2,2] \rightarrow[-2,2]\) be a function defined by \(f(x)=x|x|\), then \(f\) is:

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

The corner points of the bounded feasible region determined by the system of linear constraints are \((0,8),(4,4)\), \((12,12),(0,20)\). Let \(z=p x+q y\), where \(p, q>0\). Condition on \(p\) and \(q\) so that the maximum of \(z\) occurs at both the points \((12,12)\), \((0,20)\) is

In what ratio must pulses at ₹72 per kg be mixed with pulses ₹90 per kg so that the mixture be worth ₹80 per kg?

There are 4 bulbs out of which 2 are defective. Each bulb is tested in random order till both the defective bulbs are identified. The probability that only two tests are required to identify the defective bulbs is:

During bromination of phenol, Lewis acid is not necessary required because of :

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc. Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN , NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.
Which of the following is most reactive towards nucleophilic addition reaction ?

A square loop is placed near a long straight current carrying wire as shown in figure. If the loop is moved away from the wire

If 2000 electric field lines enter a given volume of closed space and 4000 field lines diverge from it, then the total charge within the volume is (Given \( \epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{m}^{-2}\text{N} \))

Select the correct name for the following reaction:
\(\text { Acetone } \xrightarrow{NH_2 NH_3} \text { Hydrazone } \xrightarrow{KOH / \text { ethylenes syreol, Heet }} \text { Propane }+N_2\)

Arrange the following steps of genetically engineered insulin production.
(A) Isolation and purification of the insulin gene from beta cells of the
pancreatic islets
(B) Expression of gene in host cell
(C) Joining the two polypeptides by disulfide bonds
(D) Cloning of insulin gene in Escherichia coli cloning host cell
Choose the correct answer from the options given below: