The capacitance of a capacitor becomes \(\frac{7}{6}\) times its original value if a dielectric slab of thickness \(t=\frac{2}{3} d\) is introduced between the plates, where \(d\) is the separation between the plates. The dielectric constant of the slab is:

If the dielectric constant and dielectric strength be denoted by k and x respectively, then good capacitor must have :

The focal length of a converging lens is measured for violet, green, red and yellow colours. Arrange the focal length for different colours in increasing order.
(A) fv
(B) fg
(C) fr
(D) fy
Choose the correct answer from the options given below:

In an unbiased p-n junction, holes diffuse from the p-region to n-region because

A wire has a resistance of \( 3.0 \Omega \) at \( 30^{\circ}C \) and a resistance of \( 4.5 \Omega \) at \( 100^{\circ}C \). The temperature coefficient of resistance of the wire is

Match List-I with List-II

List-I (Optical instrument)	List-II (Magnifying power)
(A) Magnifying power m of a simple microscope	(I) \( m = 1 + (D/f) \)
(B) Magnifying power m of a simple microscope if the image is at infinity	(II) \( m = (L/f_0) \times (D/f_e) \)
(C) Magnifying power m of a compound microscope	(III) \( m = f_0 / f_e \)
(D) Magnifying power m of a telescope	(IV) \( m = D/f \)

Choose the correct answer from the options given below:

A source of electromagnetic wave of 400 W produces \(10^{20}\)photons per second. Identify the part of the electromagnetic spectrum to which these radiations belong:

Which of the following is correct for a parallel plate capacitor of separation 'd' when a slab of material of dielectric constant \(k\) has the same area as the plate of capacitor but has a thickness \(d / 2\) is inserted between the plates?
A. Its capacitance decreases
B. Its capacitance increases
C. \(C=C_0\left(\frac{2 k}{k+1}\right)\)
D. \(C=C_0\left(\frac{k+1}{2 k}\right)\)
E. Charge remains same.
Choose the correct answer from the options given below:

Match List I with List - II. -

List - l	List - II
(A) Mutualism	(l) Tiger and Deer
(B) Commensalism	(II) Cuscuta and hedge plant
(C) Parasitism	(III) Sucker fish and shark
(D) Predation	(IV) Crab and sea anemone

Choose the correct answer from the options given below:

Which of the following is not the salient feature of Human Genome Project (HGP)?

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichia coli RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

In agarose gel electrophoresis, the separated DNA fragments can be visualized with the help of compound known as:

The direction of transport of sperm in human is-
(A). Vas deferens
(B). Vasa efferentia
(C). Epididymis
(D). Ejaculatory duct
Choose the correct answer from the options given below:

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is: