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Differentials, Errors and Approximations Maths - Differentials, Errors and Approximations

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 61 questions in this chapter.

Question types

Differentials, Errors and Approximations question types

61 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

61
Questions
4
Question groups
5
Question types
Sample Questions

Differentials, Errors and Approximations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is:
  1. k%
  2. 2k%
  3. $\frac{\text{K}}{2}\%$
  4. 3k%
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Q 2M.C.Q (1 Marks)1 Mark
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:
  1. $\lambda\%$
  2. $2\lambda\%$
  3. $3\lambda\%$
  4. $\text{None of these}$
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Q 3M.C.Q (1 Marks)1 Mark
The circumference of a circle is measured as 28cm with an error of 0.01cm. The percentage error in the area is:
  1. $\frac{1}{14}$
  2. $0.01$
  3. $\frac{1}{7}$
  4. $\text{None of these}$
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Q 4M.C.Q (1 Marks)1 Mark
The function $\text{f}(\text{x})=\log_\text{e}\Big(\text{x}^3+\sqrt{\text{x}^6+1}\Big)$ is of the following type:
  1. Even and increasing.
  2. Odd and increasing.
  3. Even and decreasing.
  4. Odd and decreasing.
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Q 62 Marks2 Marks
If the relative error in measuring the radius of a circular plane is $\alpha,$ find the relative error in measuring its area.
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Q 93 Marks3 Marks
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1%.
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Q 113 Marks3 Marks
If $\text{y}=\sin\text{x}$ and x changes from $\frac{\pi}{2}$ to $\frac{22}{14}$, what is the approximate change in y?
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Q 123 Marks3 Marks
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.
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Q 134 Marks4 Marks
Using differentials, find the approximate values of the following:
$\Big(\frac{17}{81}\Big)^{\frac{1}{4}}$
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Q 174 Marks4 Marks
If the radius of a sphere is measured as 9cm with an error of 0.03m, find the approximate error in calculating its surface area.
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