The effective rate, which is equivalent to a nominal rate of \(12 \%\) compounded semi-annually, is

The curve \(y = f ( x )\) is normal probability curve, then which of the following statements are correct?
(A) mean, median and mode of the distribution coincide.
(B) the area bounded by the curve \(y = f ( x )\) and \(x\)-axis is one unit.
(C) The curve is symmetrical about the line \(x =\mu\), where \(\mu\) is the mean.
(D) y -axis is an asymptote to the curve.
Choose the correct answer from the options given below :

If two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|=2,|\vec{b}|=3\) and \(\vec{a} \cdot \vec{b}=4\), then \(|\vec{a}-2 \vec{b}|\) is :

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is:

If \(n\) is the sample size of the population, then degree of freedom in t-distribution is

Year(x)	2011	2012	2013	2014	2015	2016	2017
Sales (in lakh Rs. ) (y)	65	68	70	72	75	67	73

If \(y=70+0.964(x-2014)\) be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is :

Let \(R\) be a relation on the set of integers given by \((x, y) \in R \Longleftrightarrow|x-y| \leq 1\). Then \(R\) is
(A) Reflexive relation
(B) Symmetric relation
(C) Transitive relation
(D) \(R\) is not a function
(E) Empty relation
Choose the correct answer from the options given below:

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is:

The integral \(I=\int e^x\left(\frac{x-1}{3 x^2}\right) d x\) is equal to:

Arrange the steps followed during nucleophilic addition on a carbonyl group.
A. \(s p^2\) hybridised carbon of \(>C=O\) group changes to \(s p^3\) hybridised carbon
B. Nucleophile attacks the electrophilic carbon
C. Tetrahedral alkoxide ion is formed
D. Intermediate captures \(H ^{+}\)to give neutral product.
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Sodium dichromate \(Na _2 Cr _2 O _7\) and Potassium dichromate \(K _2 Cr _2 O _7\) are strong oxidizing agents; in acidic solution, its oxidising action can be represented as follows :
\(Cr _2 O _7^{2-}+14 H ^{+}+6 e^{-} \rightarrow 2 Cr ^{3+}+7 H _2 O \left( E ^{\circ}=1.33 V\right)\)
The chromates and dichromates are interconvertible in aqueous solution depending upon pH of the solution.
The chromate ion is tetrahedral whereas the dichromate ion consists of two tetrahedra sharing one corner with \(Cr - O - Cr\) bond angle of \(126^{\circ}\)
Potassium permanganate is prepared by fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidising agent like \(KNO _3\).
This produces the dark green \(K _2 MnO _4\) which disproportionates in a neutral or acidic solution to give permanganate. It is a strong oxidizing agent. Hydrogen ion concentration of the solution plays
an important part in the reduction of permanganate to manganate, manganese dioxide and manganese(II) salt.
Potassium permanganate forms dark purple (almost black) crystals which are isostructural with those of \(KClO _4\).
The salt is not very soluble in water \((6.4 g / 100 g\) of water at 293 K ), but when heated it decomposes at 513 K .
Choose the correct statement from the options given below :

Monochromatic light of wavelength 600 nm is incident from air on to water surface. The frequency of refracted light is

A galvanic cell can be converted to an electrolytic cell when