Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

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:

\[\sqrt{25 . 02}\]

Using differential, find the approximate value of the following:  \[\left( 0 . 009 \right)^\frac{1}{3}\]

Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]

Using differential, find the approximate value of the \[\sqrt{401}\] ?

Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?

Using differential, find the approximate value of the log_e 4.04, it being given that log₁₀4 = 0.6021 and log₁₀e = 0.4343 ?

Using differential, find the approximate value of the log_e 10.02, it being given that log_e10 = 2.3026 ?

Using differential, find the approximate value of the  log₁₀ 10.1, it being given that log₁₀e = 0.4343 ?

Using differentials, find the approximate values of the cos 61°, it being given that sin60° = 0.86603 and 1° = 0.01745 radian ?

Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?

Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?