At any instant t the values of voltage applied and the current through a series LCR circuit are given as : \( V = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ V}, I = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ A} \). The average power consumed in the circuit is given by :

A 10 pF capacitor is connected to a 24 V battery. The electrostatic energy stored in the capacitor is:

Which of the following phenomenon can be explained by the wave picture of light
A. Photo-electric effect
B. Compton effect
C. Polarisation
D. Diffraction
Choose the correct answer from the options given below:

The correct relation between the transistor parameters \(\alpha\) and \(\beta\) is -

The wavelength will be minimum in the transitions of electrons from:

When white light consisting of wavelengths ranging from 400 nm to 700 nm passes through water (u = 4/3), then the wavelength range in water will be :

Which of the following is NOT correct in the case of the output obtained from a full wave rectifier?

Neutral or weakly alkaline \(KMnO_4\) solution will oxidise iodide ion into :

The work function for Aluminium surface is 4.2 eV. Find the threshold wavelength for the photoelectric emission.

Which of the following statements are true regarding Lanthanoid elements?
i. \(\text{La}(\text{OH})_3\) is the basic hydroxide of Lanthanoids.
ii. \(\text{Zr}^{4+}\) and \(\text{Hf}^{4+}\) ions have almost similar ionic sizes.
iii. \(\text{Ce}^{4+}\) acts as an oxidising agent.
iv. Trivalent Lanthanoid ions are not coloured.
Choose the correct answer from the options given below:

The equivalent resistance of the network shown in figure between the points a and b will be

Read the passage carefully and answer the questions:
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their
molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, are

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.
Which one of the following statements is not true with respect to microbes?