If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identity matrix of same order as \(A\), then the matrix \((2 I+A)^3-19 A-3 I\) is equal to

For fixed radii of curvature of a lens, power is proportional to :

For the function \(f(x)=2 x^3-3 x^2-12 x+5\), the difference of maximum and minimum value of \(f(x)\) is

If A and B are square matrices of order 3 such that \(|A|=-1,|B|=3\) then \(|3 A B|\) is:

The point on the curve \(y^2=x\), where the tangent makes an angle of \(\frac{\pi}{4}\) with x-axis is:

In a game, A can give 36 points to B, A can give 42 point to C, B can give 10 points to C. How many points make the game?

If the lines \(\frac{x+3}{k-5}=\frac{y-1}{1}=\frac{5-z}{-2 k-1}\) and \(\frac{x+2}{-1}=\frac{2-y}{-k}=\frac{z}{5}\) are perpendicular, then the value of \(k\) is

If \(\left|\begin{array}{ccc}x-2 & 1 & 2 \\ 1 & 2 x & 1 \\ -1 & 1 & 1\end{array}\right|=3\) then the values of x are:

Karyotype of an individual is 47, XXY. The individual is suffering from :

Sexual stages of Plasmodium which develop in human RBCs are known as:-

On passing ammonia gas through a solution of copper sulphate, a deep blue solution is obtained.
The deep blue colour of the solution is due to the formation of :

Four resistors of \( 8 \ \Omega \) each are connected in parallel, five such combinations are then connected in series. What is the total resistance?

"Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l}\)=k (both \(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length (\(l\)). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte),
\(\Lambda_m = \kappa V\)
If the length \(l\) in the column of an electrolytic cell is halved and its area of cross-section is tripled, then conductance (\(G\)) would become:"