According to Bohr's Model :
(A) The radius of the orbiting electron is directly proportional to \({'n'. } \)
(B) The speedof the orbiting electron is directly proportional to \(\frac{1}{n} \)
(C) The magnitude of the total energy of the orbiting electron is directly proportional to \(\frac{1}{n^2} \)
(D) The radius of the orbiting electron is directly proportional to \( =n^2 \)
Correct options :

Let \(e^y(x+1)=1\). Then which of the following are TRUE
(A) \(\frac{d^2 y}{d x^2}=-\frac{1}{(x+1)^2}\)
(B) \(\frac{d^2 y}{d x^2}=\left(\frac{d y}{d x}\right)^2\)
(C) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=-1\)
(D) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=1\)
(E) \(\left.\frac{d^2 y}{d x^2}\right|_{x=1}=\frac{1}{4}\)
Choose the correct answer from the options given below :

A tub contains \(60\) litres of milk. From this tub, \(6\) litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

A player participates in 3 matches against three teams \(T_1, T_2\) and \(T_3\). The probability of winning a match against teams \(T_1, T_2\) and \(T_3\) are \(0.2,0.3\) and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he
(A) wins all the 3 matches is 0.054
(B) wins no match is 0.054
(C) wins exactly two matches is 0.348
(D) wins exactly one match is 0.542
Choose the correct answer from the options given below :

For the function, \(f(x)=\frac{-3}{4} x^4-8 x^3-\frac{45}{2} x^2-350\), which of the following statements are correct?
(A) \(x=-3\) and \(x=-5\) are the only critical points of the given function.
\((B) x=-3\) is a point of local minimum.
(C) The local minimum value at \(x =-3\) is 231.
\((D) x=-5\) is a point of local maximum.
Choose the correct answer from the options given below:

Area of the region enclosed by the curves \(y=\sqrt{x}\) and \(y=x^2\) is :

In a time series, the variations which occur due to general tendency of the data to increase or decrease over a long term are known as :

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
Faraday's laws of electrolysis are related to:

An object is placed at 5 cm in front of a concave mirror with a radius of curvature of 20 cm. The distance of the image from mirror and its nature are

Single step large mutation leading to speciation is also called:

A die is rolled in such a way that an even number is twice likely to occur as an odd number.
If the die is rolled twice, then the mean of the number of perfect squares in two tosses is :

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
To make an octahesral complex of \(Mg ^{2+}\) ion, how many molecules of \(EDTA\) are used?

Read the passage given below and answer the question.
The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence (Cu, Zn). Thus early in the series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti (III) or Ti (II). At the other end, the only oxidation state of zinc is +2 (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum of the s- and d-electrons upto manganese (\(TiO_2, VVO^+, CrVIO_4^{2-}, MnVIIO_4\)) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe^{II,III}, Co^{II,III}, Ni^{II}, Cu^{I,II}, Zn^{II}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g. \(V^{II}, V^{III}, V^{IV}, V^{V}\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit of two.
An interesting feature in the variability of oxidation states of the d-block elements is noticed among the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of d-block. For example, in group 6, Mo(VI) and W(VI) are found to be more stable than Cr(VI). The Cr(VI) in the form of dichromate in acidic medium is a strong oxidising agent, whereas \(MoO_3\) and \(WO_3\) are not.
Low oxidation states are found when a complex compound has ligands capable of \(\pi\)-acceptor character in addition to the \(\sigma\)-bonding. For example, in \(Ni(CO)_4\) and \(Fe(CO)_5\), the oxidation state of nickel and iron is zero.
The elements giving minimum number of oxidation states are in extreme left and right in 3d series.
This is because :