\(\int_1^2 \frac{1}{x(x+1)} d x, x>0\) equals

The function \(f(x)=|x-1|, x \in R\) is:

The region represented by the constraints \(x \geq 0, y \geq 0\) of an LPP is

Probability that A speaks truth is \(\frac{4}{5}\). A coin is tossed. A reports that a head appears. The probability that actually there was head is:

Solution of \(\frac{d y}{d x}=\left(1+x^2\right)\left(1+y^2\right)\) is :

If the direction ratios of two lines are \(a, b, c\) and \((b-c),(c-a),(a-b)\) respectively, then the angle between these lines is :

Three bad eggs are mixed with 7 good ones
If two eggs are drawn one by one without replacement
then the probability distribution of the number X of bad eggs drawn is

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.
SI units of conductance and conductivity, respectively, are ___________

An infinite line charge produces an electric field of \( 9 \times 10^6 \text{ N/C} \) at a distance of \( 20 \text{ cm} \). The linear charge density will be :

GM plant/crop are:
(A) Rich in vitamins
(B) Pest resistant
(C) Prone to post harvest loss
(D) More tolerant to drought
Choose the correct answer from the options given below:

Maximize \(z=2 x-y\)
Subject to constraints
\(x+y \leq 4, \quad x+3 y \leq 6, \quad x \geq 0, \quad y \geq 0 .\)
The corner points of the feasible region are:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders
Which of the following is an example of a sex linked disease?

Which of the following statements are correct?
A. The algebraic sum of potential drops around any closed loop is zero.
B. Metals have high resistivity.
C. The potentiometer is a device in which a condition of no current flow applies.
D. Kirchhoff's junction rule is based on conservation of charge.
E. Bending the wire changes the validity of Kirchhoff's junction rule.
Choose the correct answer from the options given below: