HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Absolute error

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Relative error

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Percentage error

A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:

Change in the volume

A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:

Change in the surface area

The time T, taken for a complete oscillation of a single pendulum with length l, is given by the equation T = `2pi sqrt(l/g)` where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l

Show that the percentage error in the n^th root of a number is approximately `1/"n"` times the percentage error in the number

Find the differential dy for the following functions:

y = `(1 - 2x)^3/(3 - 4x)`

Find the differential dy for the following functions:

y = `(3 + sin(2x))^(2/3)`

Find the differential dy for the following functions:

y = `"e"^(x^2 - 5x + 7) cos(x^2 - 1)`

Find df for f(x) = x² + 3x and evaluate it for x = 2 and dx = 0.1

Find df for f(x) = x² + 3x and evaluate it for x = 3 and dx = 0.02

Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x³ – 2x², x = 2, Δx = dx = 0.5

Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x² + 2x + 3, x = – 0.5, Δx = dx = 0.1

Assuming log₁₀ e = 0.4343, find an approximate value of Iog₁₀ 1003

The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. Approximately how much did the tree diameter grow?

The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?

An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5 mm and the radius to the outside of the shell is 5.3 mm, find the volume of the shell approximately

Assume that the cross-section of the artery of human is circular. A drug is given to a patient to dilate his arteries. If the radius of an artery is increased from 2 mm to 2.1 mm, how much is cross-sectional area increased approximately?

In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t² – t³, 0 ≤ t ≤ 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to `4 1/6` years