Irregular variations in a time series are not caused by:

If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along the co-ordinate axes OX, OY and OZ respectively, then
(A) \(\hat{i} \times \hat{j}=\hat{k}\)
(B) \(\hat{k} \times \hat{i}=-\hat{j}\)
(C) \(\hat{j} \cdot \hat{j}=1\)
(D) \(\hat{j} \cdot \hat{k}=0\)
Choose the \{correct} answer from the options given below:

The mean of the number of heads in the two tosses of a coin is

If the mean of Binomial distribution is 5 and Variance is 3 then the value of \(p\) (probability of success) is :

Let * be a binary operation defined on \(Q ^{+}\)(the set of positive rational numbers) by the rule \(a * b=\frac{a b}{7}\) for all \(a, b \in Q ^{+}\). Then inverse of \(2 * 7\) is:

The points on the curve \(9 y^2=x^3\) where normal to the curve makes equal intercepts with the axes is/are:

General solution of the differential equation \(\frac{d y}{d x}=e^{\frac{5^2}{5}}+x y\) is :

The one which is a covalent green oil is:

Which of the following statements are correct?
A. Two major types of resistors are wire bound resistors and carbon resistors.
B. Mobility is the drift velocity per unit electric field.
C. The internal resistance of dry cells is much lower than the common electrolytic cells.
D. In electrolytic liquids, electrons carry the electric current.
E. Potentiometer is unaffected by the internal resistance of the source.
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"Answer the question on basis of passage given below :
Carboxylic acids are weaker than mineral acids, but they are stronger acids than alcohols and many simple phenols (\(\text{pKa}\) is ~ 16 for ethanol and 10 for phenol). The higher acidity of carboxylic acids as compared to phenols can be understood similarly. The conjugate base of carboxylic acid, a carboxylate ion, is stabilised by two equivalent resonance structures in which the negative charge is at the more electronegative oxygen atom. The conjugate base of phenol, a phenoxide ion, has non-equivalent resonance structures in which the negative charge is at the less electronegative carbon atom. Further, the negative charge is delocalised over two electronegative oxygen atoms in carboxylate ion whereas it is less effectively delocalised over one oxygen atom and less electronegative carbon atoms in phenoxide ion. Thus, the carboxylate ion is more estabilised than phenoxide ion, so carboxylic acids are more acidic than phenols.
Effect of substituents on the acidity of carboxylic acids: substituents may affect the stabliity of the conjugate base and thus, also affect the acidity of the carboxylic acids. Electron withdrawing group increase the acidity of carboxylic acids by stabilising the conjugate base through delocalisation of the negative charge by inductive and/or resonance effects. Conversely, electron donating groups decrease the acidity by destabilising the conjugate base.
Which of the following compounds would have the smallest value of \(\text{pKa}\)?"

Match List-I and List-II

List-I	List-II
A. Alchohol + water	I. Ideal solution
B. Benzene + Toluene	II. Positive deviation
C. Water + Nitric acid	III. Negative deviation

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The unit of rate constant of a reaction with the rate law, Rate \(=k[A]^{3 / 2}[B]^{-1}\) is

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon which can be expressed by means of an empirical relationship know as Freundlich Adsorption isotherm. The relationship given by \(\frac{x}{m} = Kp^{\frac{1}{n}}\ (n > 1)\)
x = Mass of the gas adsorbed
m = Mass of adsorbent
p = Pressure at which adsorption takes place
K and n are constant
Which electrolyte/electrolytes can coagulate a ferric hydroxide sol most effectively?
A. \(K _3\left[ Fe ( CN )_6\right]\)
B. \(Na _3 PO _4\)
C. \(Na _2 SO _4\)
D. \(KNO _2\)
E. KI
Choose the correct answer from the options given below: