PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

If A is a square matrix such that \[A \left( adj A \right) = \begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}\] , then write the value of |adj A|.

Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\]  interms of A.

If A and B are square matrices such that B = − A⁻¹ BA, then (A + B)² = ________ .

If \[A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix},\text{ then }A^5 =\] ____________ .

If A is a square matrix such that A² = I, then A⁻¹ is equal to _______ .

Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.

The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?

A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?

If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere ?

The pressure p and the volume v of a gas are connected by the relation pv^1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .

The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that k is small ?

1 Using differential, find the approximate value of the following:

\[\sqrt{25 . 02}\]