If v is the frequency of ac mains, then the frequency of sonometer wire at resonance is :

Four diode connections are given below. Identify the diagram in which the diode is forward biased.
(A)

(B)

(C)

(D)

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Which of the following statements are correct?
(A) Total internal reflection occurs when a ray of light travels from a rarer transparent medium to a denser medium.
(B) In total internal reflection, the incident ray of light remains in the same medium after reflection.
(C) In total internal reflection, the angle of incidence inside the denser transparent medium is equal to the angle of reflection in the same medium.
(D) In total internal reflection inside a denser medium there is no angle of refraction
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One student cuts a magnet of magnetic moment M, into two identical parts perpendicular to its length. The magnetic moment of each part will be

If charge is moving perpendicular to uniform magnetic field then its time period of revolution is:

A closed surface in vacuum encloses charges \( - q \) and \( + 3q \). Another charge \( - 2q \) lies out side the surface. The total electric flux over the surface is :

The half life of a radioactive substance is 20 s. The decay constant is

Choose the correct match. '+' for beneficial interaction '-' for detrimental and 'O' for neutral effect.

LIst - I		LIst - II
Species A	Species B	Name of Interaction
(A) +	+	(I) Competition
(B) +	-	(II) Mutualism
(C) -	-	(III) Amensalism
(D) -	0	(IV) Predation

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Introduction of which of the following on Galopagos islands caused extinction of Abingdon tortoise ?

Select the brain capacity of Homo erectus from the following:

IUPAC name of the isomer of compound with molecular formula, \(FeCl _3 \cdot 6 H _2 O\) having \(i=3\) is :

Read the passage carefully and answer the questions
Biomolecules are the organic compounds present as an essential constituents of living organisms in different cells.The molecules are generally termed as macromolecules, which are carbohydrates, enzymes, nucleic acids, amino acids and proteins etc. Carbohydrates are classified as sugars and non-sugars include sucrose, glucose, fructose, starch and cellulose. Enzymes are coordinated with various chemical reactions in nucleic acid. Nucleic acids are found in living organisms made up of proteins and natural polymers. Two types that are generally found in biological systems are DNA and RNA nucleic acid. Amino acids are bifunctional groups of carboxyl and amino groups. Proteins are a class of biologically important compounds. They are crucial to virtually all processes in living systems. Some of them are hormones, which serve as chemical messengers that coordinatecertain biochemical activities.
Glucose when treated with Bromine water forms

Consider the following L.P.P.
Minimize \(z=400 x+300 y\), subject to \(100 x+200 y \geq 12000,300 x+400 y \geq 20000,200 x+100 y \geq 15000\) and \(x, y \geq 0\). Then