Differentials, Errors and Approximations - Maharashtra Board STD 12 Science Maths Questions

Q 1MCQ1 Mark

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

A
$k\%$
✓
$2k\%$
C
$\frac{\text{K}}{2}\%$
D
$3k\%$

Answer: B.

Q 2MCQ1 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:

A
$\lambda\%$
B
$2\lambda\%$
✓
$3\lambda\%$
D
$\text{None of these}$

Answer: C.

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Q 3MCQ1 Mark

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

✓
$\frac{1}{14}$
B
$0.01$
C
$\frac{1}{7}$
D
$\text{None of these}$

Answer: A.

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Q 4MCQ1 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:

A
Even and increasing.
✓
Odd and increasing.
C
Even and decreasing.
D
Odd and decreasing.

Answer: B.

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Q 5MCQ1 Mark

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

A
$k\%$
✓
$3k\%$
C
$2k\%$
D
$\frac{\text{k}}{3}\%$

Answer: B.

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Q 6Solve the Following Question.(2 Marks)2 Marks

For the function $y = x ^2$, if $x =10$ and $\Delta x =0.1$. Find $\Delta y$.

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Q 7Solve the Following Question.(2 Marks)2 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 8Solve the Following Question.(3 Marks)3 Marks

If $y =\log _{ e } x$, then find $\Delta y$ when $x =3$ and $\Delta x =0.03$

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Q 9Solve the Following Question.(3 Marks)3 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 10Solve the Following Question.(3 Marks)3 Marks

If the percentage error in the radius of a sphere is $\alpha,$ find the percentage error in its volume.

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Q 11Solve the Following Question.(3 Marks)3 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 12Solve the Following Question.(3 Marks)3 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 13Solve the Following Question.(5 Marks)5 Marks

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.

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Q 14Solve the Following Question.(5 Marks)5 Marks

Using differentials, find the approximate values of the following:
$\sin\Big(\frac{22}{14}\Big)$

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Q 15Solve the Following Question.(5 Marks)5 Marks

Using differentials, find the approximate values of the following:
$\cos\Big(\frac{11\pi}{36}\Big)$

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Q 16Solve the Following Question.(5 Marks)5 Marks

Using differentials, find the approximate values of the following:
$(66)^{\frac{1}{3}}$

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Q 17Solve the Following Question.(5 Marks)5 Marks

Using differentials, find the approximate values of the following:
$\Big(\frac{17}{81}\Big)^{\frac{1}{4}}$

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

Differentials, Errors and Approximations question types

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