Choose the correct option from the following transitions in which the wavelength will be minimum

At one place on earth, the resultant magnetic field is 0.25 G and the angle of dip is 45°. The horizontal component of earth's magnetic field will be

A series LCR circuit with an inductor, a capacitor and a resistor of resistance 50 Ω is connected to an ac source of 24 V, 50 Hz. The impedance of the circuit is 56 Ω. The average power dissipated in the circuit is

Match List-l with List-II

LIST-I	LIST-II
A. Planck's constant	(I) \(\left[M L^2 T^{-2}\right]\)
B. Work function	(II) \([L]\)
C. Stopping potential	(III) \(\left[M L^2 T^{-3} A^{-1}\right]\)
D. de Broglie wavelength	(IV) \(\left[M L^2 T^{-1}\right]\)

Choose the correct answer from the options given below :

Three resistors, each of resistance R, are arranged in the following different combinations with a source of emf E. Arrange them in the decreasing order of power dissipation:
(A) Three resistors in series
(B) Three resistors in parallel
(C) One resistor in series with two resistors in parallel
(D) One resistor in parallel with two resistors in series
Choose the correct answer from the options given below:

The S.I unit of mutual inductance, the 'henry' can be written as

A plane electromagnetic wave of frequency 50 MHz travels in free space in the X- direction. At a particular point in space and time, the magnetic field is 0.003 G in the Z-direction. The magnitude and direction of the electric field is

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
The conversion of molecules \(X\) to \(Y\) follows second order kinetics. If the concentration of \(X\) is increased to four times, how does it affect the rate of formation of \(Y\) ?

Match List-l with List-ll

List-l (Abbreviation used in reproductive health)	List-II (Features)
(A) IVF	(I) Sperm is directly injected into the ovum
(B) ZIFT	(II) Transfer of ovum from a doner into the fallopian tube of recipient
(C) GIFT	(III) Embryos with more than 8 blastomers is transfered into the uterus
(D) ICSI	(IV) Fertilisation outside the body

Choose the correct answer from the options given below:

When benzene diazonium chloride reacts with phenol, it results in the formation of an orange colored compound (X); and when benzene diazonium chloride reacts with aniline, it results in the formation of a yellow colored compound ( Y ).
What are \(X\) and \(Y\) ?

The transition element having least number of unpaired electrons, is:

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.

Stanley Cohen and Herbert Boyer constructed the first recombinant DNA by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid of ____________ resistance. which was responsible for conferring antibiotic

A random variable X has the following probability distribution :

x	1	2	3	4	5
\(P ( X = x )\)	k	k	3k	\(2 k^2\)	\(4 k^2\)

Based on the above information, the value of ' \(K\) ' is :