If \(\theta\) is the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) then \(|\hat{a}-\hat{b}|=\)

A bag contains 12 white and 18 red balls. Two balls are drawn in succession without replacement. The probability that the first is red and the second is white is:

The semi vertical angle of a right circular cone of maximum volume of a given slant height is

Consider the matrices \(A=\left[\begin{array}{ccc}9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 / 5 & 0 & 0 \\ 0 & 1 / 4 & 0 \\ 0 & 0 & 1 / 3\end{array}\right]\). The value of \(\left|(A B)^{-1}\right|\) is

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

If \(a>0\), then \(P(0<X \leq 2)\) is equal to

If a matrix has 24 elements, which of the following cannot be the possible order of the matrix?

Which of the following are correct about t-test statistics?
(A) The mean of t-test distribution is 0.
(B) It depends on the degrees of freedom.
(C) It depends on population standard deviation
(D) With more degrees of freedom, it closely resembles standard normal distribution.
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If the value of the refractive index of a denser medium with respect to the rarer medium is 1.414, then the critical angle is:

The sedative & painkiller drug useful for the patients who have undergone surgery is-

Identify the water pollinated plants from the following:
(A) Water hyacinth and Zostera
(B) Zostera and Hydrilla
(C) Water lily
(D) Vallisneria
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Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A} .\)
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart.
It is given by the expression \(\Lambda_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
Select the correct statement.

Two waves of amplitudes 3 m and 2 m , respectively superimpose at a point in the same phase. The resultant amplitude would be

Match List I with List II

LIST I	LIST II
A. Transforming Principle	I. Jacob and Monod
B. Replication of DNA	II. Frederick Griffith
C. Lac operon concept	III. Alec Jeffreys
D. DNA Fingerprinting	IV. Watson and Crick

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