RD Sharma solutions for Mathematics [English] Class 12 chapter 14 - Differentials, Errors and Approximations [Latest edition]

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 \[\sin\left( \frac{22}{14} \right)\] ?

Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?

Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\sqrt{26}\] ?

Using differential, find the approximate value of the  \[\sqrt{37}\] ?

Using differential, find the approximate value of the  \[\sqrt{0 . 48}\] ?

Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?

Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?

Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?

Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?

Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?

Using differential, find the approximate value of the  \[\sqrt{0 . 082}\] ?

If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?

If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?

Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?

For the function y = x², if x = 10 and ∆x = 0.1. Find ∆y.

If y = log_e x, then find ∆y when x = 3 and ∆x = 0.03 ?

A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?

If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is

If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is

The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is

While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is

If log_e 4 = 1.3868, then log_e 4.01 =

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is

If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is

The pressure P and volume V of a gas are connected by the relation PV^1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is

If y = xⁿ  then the ratio of relative errors in y and x is

The approximate value of (33)^1/5 is

The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is