The solution of the differential equation xdy - ydx = 0 represents

The values of \(b\) for which \(y=2 x^2-b x+2\) touches the \(x\)-axis are:

\(\int_0^2 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{2-x}} d x\) is equal to:

The area enclosed by the ellipse \(\frac{x^2}{9^2}+\frac{y^2}{6^2}=1\) is :

A person has invested Rs. 20,000 in 2020 for 5 years.
If the CAGR for his investment is 11.84%, the end balance of his investment is [Given \((1.1184)^5=1.7498\) ]

The non-negative remainder when 7³⁶ is divided by 5 is:

If \(f(x)=a \log _e|x|+b x^2+x\) has critical points at \(x=-2\) and \(x=1\), then

If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is :

H-bond does not exist in:

The function \(f(x)=|x-1|, x \in R\) is:

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Propionibacterium sharmanii is used for the production of-

The standard electrode potential for a Daniell cell is 1.1 V. Calculate the standard Gibbs energy for the reactiction
\(Zn ( s )+ Cu ^{2+}( aq ) \rightarrow Zn ^{2Solution+}( aq )+ Cu ( s )\)

If the maximum value of the function \(f(x)=\frac{\log _e x}{x}, x>0\) occurs at \(x=a\), then \(a^2 f^{\prime \prime}(a)\) is equal to: