Area lying between the curves \(y^2=9 x\) and \(y=3 x\) is:

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

Order and degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^3\right]^{\frac{5}{4}}=\frac{d^2 y}{d x^2}\) are:

The non-negative remainder when 7³⁶ is divided by 5 is:

If a moneylender charges interest at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is :

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where k > 0 is 30 sq. units, then the value of k is

If the system of equation
\(x-y+z=4\)
\(x-2 y-2 z=9\)
\(2 x+y+\lambda z=1\)
has a unique solution, then

Ethanol is treated with concentrated sulphuric acid. The product formed is :

The rate of a gaseous reaction becomes half when the volume of the vessel is doubled. The order of the reaction is

If the flux of the electric field through a closed surface is zero.
(A) The electric field must be zero everywhere on the surface.
(B) The electric field may be zero everywhere on the surface.
(C) The charge inside the surface must be zero.
(D) The charge in the vicinity of its surface must be zero.
(E) The charge inside the surface may be zero.
Choose the correct answer from the options given below :

Given \(\sum p_0 q_0=800, \sum p_0 q_1=1500, \sum p_1 q_1=1300\) and \(\sum p_1 q_0=900\), where subscripts 0 and 1 are used for base year and current year respectively. The Paasche's

Two similar coils of radius r are placed concentrically with their planes at right angles to each other. The currents flowing in them are I and 3I, respectively. The resultant magnetic induction at the centre 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.\(A_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches sero, 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 ionisation constant of a weak acid.
The limiting molar conductivity values for \(HCl , NaCl\) and \(CH _3 COONa\) are \(425.9,126.4\) and \(91.0 S cm ^2 mol^{-1}\), respectively.
Calculate the limiting molar conductivity value for acetic acid.