At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000 ?

Which of the following is correct about the Sinking Fund?

If \(y=\frac{\log x}{x^2}\), then find \(\frac{d^2 y}{d x^2}\).

The remainder, when \(5^{60}\) is divided by 7 , is :

Choose the correct statement about CAGR (compound annual growth rate)?

Match List - I with List - II.

LIST-I	LIST-I
(A) \(\csc ^{-1} x\)	(I) \((0, \pi)\)
(B) \(\sec ^{-1} x\)	(II) \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)
(C) \(\tan ^{-1} x\)	(III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
(D) \(\cot ^{-1} x\)	(IV) \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)

Choose the correct answer from the options given below:

Let \(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=-4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=34\), then \(|\vec{d}|\) is equal to

The equation of tangent to the curve given by \(x=a \sin ^3 t, y=b \cos ^3 t\) at a point where \(t=\frac{\pi}{2}\) 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 ___________

Which one of the following diseases can be treated by human protein (a -1- antitrypsin) produced by transgenic animals?

Detritus food chain begins with :

The corner points of feasible region determined by the following systems of linear inequalities :
\(2 x+y \leq 10, x+3 y \leq 15, x \geq 0, y 0\) are \((0,0),(5,0),(3,4)\) and \((0,5)\)
Let \(z=p x+q y\), when \(p, q>0\) then the relation between \(p\) and \(q\), so that maximum of \(z\) occurs at both points \((3,4)\) and \((0,5)\) is:

The correct sequence of reactions to convert benzene to 3-bromobenzamine is :