Let \(A=\{a, b, c\}\). Then number of relations containing \((a, b)\) and \((b, c)\) which are reflexive and transitive but not symmetric is :

Let \(f(x)=x^2+\frac{250}{x}\) be any function defined on \(R -\{0\}\), where \(R\) is the set of real numbers. Then which of the following are FALSE?

The area included between \(y^2=4 x, y=x+1\) and x-axis is :

A function \(f: R \rightarrow\{x \in R:-1< x<1\}\) is defined as \(f(x)=\frac{x}{1+|x|}\), then \(f\) is :

The function \(f: Z \rightarrow Z\) defined by \(f(x)=x^2+x\), where \(Z\) is the set of integers, is:

In a kilometer race \(P\) runs at \(10 m / sec , Q\) runs at \(5 m / sec\) then which of the following statement \(( s )\) is \(/\) are correct?
(A) \(P\) wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below :

If the integral \(I=\int \frac{x^2}{\sqrt{1+x}} d x=\frac{1}{\alpha}(1+x)^\alpha-\frac{8 \alpha}{15}(1+x)^{\alpha-1}+2(1+x)^{\alpha-2}+C\), where \(C\) is the constant of integration, then the value of \(\alpha\) is :

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? 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.
A boy wants to set curd from milk. Suggest which of the following microbes can be useful for him?

Shyam invested ₹ 2, 00, 000 in 2019 for 5 years.
If the compound annual growth rate (CAGR) for his investment is \(10 \%\), then the end balance of his investment is :

Acetaldehyde on treatment with Fehling's solution gives a precipitate of

p-aminoazobenzene is produced from:

Baculoviruses are pathogen that attack :

The first instance of construction of an artificial recombinant DNA molecule was carried out on the plasmid of: