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JEE • MATHEMATICS • ERRORS & APPROXIMATION

Errors & approximation practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Medium

1 of 16

Application +4 | -1

\log _{10} 2=0.3010

and

\log _{10} 3=0.4771

then number of ciphers after decimal before a significant figure comes in

\left(\frac{5}{3}\right)^{-100}

View answer and explanation

Correct option: B

Option C (23) is incorrect, but Option B (22) is correct because the characteristic of the logarithm is -23, implying 22 ciphers after the decimal point.

2 Hard

2 of 16

Application +4 | -1

The percentage error in calculating the volume of a cubical box if an error of

1 \%

is made in measuring the length of edges of the cube, is

View answer and explanation

Correct option: C

3 \%

Option C (3%) is correct because the percentage error in volume is approximately three times the percentage error in the edge length.

3 Easy

3 of 16

Application +4 | -1

In a

\triangle A B

Cif sides a and b remain constant such that

\alpha

is the error in

C

, then relative error in its area, is

View answer and explanation

Correct option: A

\alpha \cot C

Option A (

\alpha \cot C

) is correct because it represents the relative error in the area of the triangle.

4 Medium

4 of 16

Application +4 | -1

The approximate value of

\sqrt[3]{{28}}

View answer and explanation

Correct option: B

3.037

Option B (3.037) is correct because it is the approximate cube root of 28 calculated using logarithms.

5 Easy

5 of 16

Application +4 | -1

If the percentage error in measuring the surface area of a sphere is

\alpha \%

, then the error in its volume, is

View answer and explanation

Correct option: A

\frac{3}{2} \alpha \%

Option A (

\frac{{3}}{{2}} \alpha %

) is correct because the error in volume is 3/2 times the error in surface area.

6 Medium

6 of 16

Application +4 | -1

If the ratio of base radius and height of a cone is

1:2

and percentage error in radius is

\lambda \%

, then the error in its volume is

View answer and explanation

Correct option: C

3\lambda \,\%

Option C (

3\lambda \,\%

) is correct because the error in volume is three times the error in the radius when the height is twice the radius.

7 Easy

7 of 16

Application +4 | -1

The melting point of ice is

0^\circ C

at 1 atm at what pressure it will be

- 1^\circ C

View answer and explanation

Correct option: B

133 atm

Option B (133 atm) is correct because it uses the Clausius-Clapeyron equation to relate pressure and temperature change during phase transition.

8 Easy

8 of 16

Application +4 | -1

The approximate value of

\cos 31^{\circ}

View answer and explanation

Correct option: B

0.851

Option B (0.851) is correct because it is the approximate value of

\cos 31^{\circ}

calculated using the derivative of the cosine function near

\cos 30^{\circ}

9 Hard

9 of 16

Application +4 | -1

The area of a triangle is computed using the formula

S=\frac{1}{2} b c \sin A

. If the relative errors made in measuring

b, c

and calculating

S

are respectively

0.02,0.01

and

0.13

the approximate error in

A

when

A=\pi / 6

, is

View answer and explanation

Correct option: A

0.05

radians

Option A (0.05 radians) is correct because it represents the approximate error in angle A, calculated using the given relative errors.

10 Easy

10 of 16

Remembering +4 | -1

An approximate value of

\cos 40^{\circ}

View answer and explanation

Correct option: A

0.7688

Option A (0.7688) is the closest approximate value of cos 40° using differentials.

11 Medium

11 of 16

Application +4 | -1

y=x^4-10

and if

x

changes from 2 to

1.99

, than the approximate change in

y

View answer and explanation

Correct option: B

-0.32

Option B (-0.32) is correct because it represents the approximate change in y calculated using differentials.

12 Easy

12 of 16

Application +4 | -1

The focal length of a mirror is given by

\frac{1}{v}-\frac{1}{u}=\frac{2}{f}

. If equal errors are made in measuring

u

and

v

, then the relative error in

f

, is

View answer and explanation

Correct option: B

\alpha\left(\frac{1}{u}+\frac{1}{v}\right)

Option B (

\alpha\left(\frac{{1}}{{u}} + \frac{{1}}{{v}}\right)

) is correct because it represents the relative error in f calculated using differentials.

13 Easy

13 of 16

Application +4 | -1

The circumference of a circle is measured as

56 \mathrm{~cm}

with an error

0.02 \mathrm{~cm}

. The percentage error in its area, is

View answer and explanation

Correct option: C

\frac{1}{14}

Option C (

\frac{{1}}{{14}}

) is correct because it represents the percentage error in the area of the circle, calculated using differentials.

14 Easy

14 of 16

Application +4 | -1

y = {x^n},

then the ratio of relative errors in

y

and

x

View answer and explanation

Correct option: D

n:1

Option D (

n:1

) is correct because the relative error in

y

n

times the relative error in

x

, as derived from logarithmic differentiation.

15 Medium

15 of 16

Application +4 | -1

{\log _e}4 = 1.3868,

, then

{\log _e}4.01 =

View answer and explanation

Correct option: C

1.3893

Option C (1.3893) is correct because it is the approximate value of

{\log _e}4.01

calculated using differentials.

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16 Easy

16 of 16

Application +4 | -1

A circular metal plate expands under heating so that its radius increases by

2 \%

. The approximate increase in the area of the plate if the radius of the plate before heating is

10 \mathrm{~cm}

, is

View answer and explanation

Correct option: D

4 \pi

Option D (

4 \pi

) is correct because it represents the approximate increase in the area of the plate calculated using differentials.

Revision notes and key takeaways

Review ERRORS & APPROXIMATION in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 16 single-correct-answer MCQs on ERRORS & APPROXIMATION.
✓ Try each question before opening its answer. Read the explanation where one is available.
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