Monochromatic light of frequency \( 6 \times 10^{14} \text{ Hz} \) is produced by a laser source. The energy of photon of light is:

Two point charges \( 3 \text{ } \mu\text{C} \) and \( -3 \text{ } \mu\text{C} \) are located at points \( A: (3 \text{ cm}, 0, 0) \) and \( B: (-3 \text{ cm}, 0, 0) \), respectively. The electric field at the origin is

A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?

Two identical capacitors are joined in parallel, charged to a potential V and then separated and connected in series, i.e., negative plate of first is connected to positive plate of second :

Tritium has a half life of \(12.5\) years against beta decay. What fraction of a sample of pure tritium disintegrates in 25 years ?

A battery of emf 12 V and internal resistance \(3 \Omega\) is connected to a resistor. If the current in the circuit is 0.8 A, the terminal voltage of the battery, will be

According to Joule's law of heating, the rate of heat produced in a resistor is
(A) directly proportional to the current for the given resistance
(B) directly proportional to the square of the current for the given resistance
(C) directly proportional to the resistance for a given value of current
(D) inversely proportional to the resistance for a given voltage
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
Some strains of Bacillus thuringiensis produce proteins that do not kill certain arthropods, such as:

Mr. X wishes to purchase a flat for Rs. 44, 60, 800 with a down payment of Rs. 10,00,000 and the balance in equal monthly instalments (EMI) for 20 years. If the bank charges 7.5% per annum compounded monthly, then the EMI is :
[Given that \((1.00625)^{240}=4.4608\) ]

Consider the differential equation \(x d y=(x+y) d x\). Which of the following are true?
(A) It is a homogenous differential equation
(B) It is a differential equation of order 2
(C) The general solution of the differential equation contains 2 arbitrary constants
(D) Integrating factor of differential equation is \(\frac{1}{x}\)
(E) Degree of the differential equation is not defined
Choose the correct answer from the options given below:

Match List I with List II

List - I	List - II
(A) Aspergillus niger	(I) Statins
(B) Trichoderma polysporum	(II) Ethanol
(C) Monascus purpureus	(III) Citric acid
(D) Saccharomyces cerevisiae	(IV) Cyclosporin A

Choose the correct answer from the options given below:

Consider the LPP,
Maximize \(z=2 x+3 y\), subject to the conditions,
\(\begin{array}{l}x+y \leq 2 \\x \leq 2 \\x \geq 0, y \geq 0\end{array}\)
then maximum value of the objective function is:

Which of the following statements are correct?
(A) On dilution, conductivity of all the electrolytes decreases.
(B) On dilution, the number of ions per unit volume decreases.
(C) Molar conductivity increases with dilution.
(D) Limiting molar conductivity is the conductivity at a very high concentration.
Choose the correct answer from the options given below: