In a compound microscope, the distance between objective lens and eye lens is always:

A resistor connected to a battery is heated due to the current. The quantity which does not change is

At what distance should an object be placed from a convex lens of focal length 15 cm to obtain a real image three times the size of the object?

The electric field E associated with an electromagnetic wave is given by \( E = E_0 \sin(kx - \omega t) \). The speed of the wave is

Arrange the following electromagnetic waves in the ascending order of their wavelengths.
(A) Radio waves
(B) Gamma rays
(C) Infrared rays
(D) Ultraviolet rays
Choose the correct answer from the options given below:

In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is :

Which of the following statement is not true for the electromagnetic waves?

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.
mRNA silencing through RNA interference (RNAi) refers to the:

About ______ the first cellular forms of life appeared on earth.

If the cost function of a product is given by \(C(x)=\frac{3}{4} x^2-5 x+21\), then the marginal cost when \(x=10\) is

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

A convex lens of focal length 10 cm is placed in front of a convex mirror of radius of curvature 14 cm. An object is placed at a distance of 20 cm from convex lens. The distance between the lens and the mirror so that the final image formed by the combination coincides with the object itself will be:

Match List I with List II.

LIST I	LIST II
A. Endemism	I. Ex-situ conservation
B. Alien species	II. Variations in Rauwolfia vomitoriea
C. Cryopreservation	III. Species confined to a particular region
D. Genetic diversity	IV. Parthenium

Choose the correct answer from the options given below: