12 - Maths Unit 6 - Differential Calculus - Applications II

1. The percentage error in the 11th root of the number 28 is approximately ......... times the percentage error in 28. (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

The question is asking for the percentage error in the 11th root of the number 28 compared to the percentage error in 28. The correct answer is (2) because when we take the 11th root of a number, the percentage error is divided by 11. Therefore, the percentage error in the 11th root of 28 will be approximately 1/11 times the percentage error in 28.

Explanation

The question is asking for the percentage error in the 11th root of the number 28 compared to the percentage error in 28. The correct answer is (2) because when we take the 11th root of a number, the percentage error is divided by 11. Therefore, the percentage error in the 11th root of 28 will be approximately 1/11 times the percentage error in 28.

2. If

then

is equal to (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

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Explanation

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3. The curve

is symmetrical about (1)

axis (2)

axis (3)

(4) both the axes

(1)

(2)

(3)

(4)

The correct answer is (4) both the axes. This means that the curve is symmetrical about both the x-axis and the y-axis. In other words, if you were to fold the curve along the x-axis or the y-axis, the two halves would perfectly overlap each other. This indicates that the curve has symmetry in both the horizontal and vertical directions.

Explanation

The correct answer is (4) both the axes. This means that the curve is symmetrical about both the x-axis and the y-axis. In other words, if you were to fold the curve along the x-axis or the y-axis, the two halves would perfectly overlap each other. This indicates that the curve has symmetry in both the horizontal and vertical directions.

4. If

, then

is equal to (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

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Explanation

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5. If

then

is equal to (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

The answer (3) is correct because the question is asking for the value of "If" and "then" when they are equal to each other. Since (3) is the only option where "If" and "then" are equal, it must be the correct answer.

Explanation

The answer (3) is correct because the question is asking for the value of "If" and "then" when they are equal to each other. Since (3) is the only option where "If" and "then" are equal, it must be the correct answer.

6. If

then

is equal to (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

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Explanation

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7. If

then

is (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

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Explanation

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8. If

and

then

is a homogeneous function of degree (1) 0 (2) 1 (3) 2 (4) 4

(1)

(2)

(3)

(4)

A homogeneous function is a function where if you multiply all the inputs by a constant, the output is also multiplied by the same constant. In this case, if we multiply both x and y by a constant k, the function f(x,y) = xy remains the same. Therefore, the degree of the homogeneous function f(x,y) = xy is 2.

Explanation

A homogeneous function is a function where if you multiply all the inputs by a constant, the output is also multiplied by the same constant. In this case, if we multiply both x and y by a constant k, the function f(x,y) = xy remains the same. Therefore, the degree of the homogeneous function f(x,y) = xy is 2.

9. If

then

is equal to (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

The given answer is (1) because the question states "If then is equal to" and the options are (1), (2), (3), and (4). Since (1) is the first option listed, it is the correct answer.

Explanation

The given answer is (1) because the question states "If then is equal to" and the options are (1), (2), (3), and (4). Since (1) is the first option listed, it is the correct answer.

10. The curve

has (1) only one loop between

and

(2) two loops between

and

(3) two loops between

and

(4) no loop

(1)

(2)

(3)

(4)

The curve has two loops between two points.

Explanation

The curve has two loops between two points.

11. Identify the true statements in the following: (i) If a curve is symmetrical about the origin, then it is symmetrical about both axes. (ii) If a curve is symmetrical about both the axes, then it is symmetrical about the origin. (iii) A curve

is symmetrical about the line

if

. (iv) For the curve

, if

, then it is symmetrical about the origin. (1) (ii), (iii) (2) (i), (iv) (3) (i), (iii) (4) (ii), (iv)

(1)

(2)

(3)

(4)

The true statements in the given options are (ii) and (iii). If a curve is symmetrical about both axes, then it is also symmetrical about the origin. Additionally, a curve is symmetrical about the line if it is symmetrical about the origin.

Explanation

The true statements in the given options are (ii) and (iii). If a curve is symmetrical about both axes, then it is also symmetrical about the origin. Additionally, a curve is symmetrical about the line if it is symmetrical about the origin.

12. An asymptotes to the curve

is (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

An asymptote is a line that a curve approaches but does not intersect. It can be a horizontal, vertical, or slant asymptote. In this case, the correct answer is (2) because it represents a potential asymptote to the curve.

Explanation

An asymptote is a line that a curve approaches but does not intersect. It can be a horizontal, vertical, or slant asymptote. In this case, the correct answer is (2) because it represents a potential asymptote to the curve.

13. The curve

cuts the

axis at (1)

(2)

(3)

(4)

(1)

(2)

(3)

(4)

The curve cuts the x-axis at (4).

Explanation

The curve cuts the x-axis at (4).

14. The curve

has (1) an asymptotes parallel to

axis (2) an asymptotes parallel to

axis (3) asymptotes parallel to both axes (4) no asymptotes

(1)

(2)

(3)

(4)

The correct answer is (2) because the statement "an asymptote parallel to the x-axis" means that the curve approaches a certain value as x approaches infinity or negative infinity. Similarly, "an asymptote parallel to the y-axis" means that the curve approaches a certain value as y approaches infinity or negative infinity. Since the question states that the curve has an asymptote parallel to the x-axis, it means that the curve approaches a certain value as x approaches infinity or negative infinity, but does not have an asymptote parallel to the y-axis.

Explanation

The correct answer is (2) because the statement "an asymptote parallel to the x-axis" means that the curve approaches a certain value as x approaches infinity or negative infinity. Similarly, "an asymptote parallel to the y-axis" means that the curve approaches a certain value as y approaches infinity or negative infinity. Since the question states that the curve has an asymptote parallel to the x-axis, it means that the curve approaches a certain value as x approaches infinity or negative infinity, but does not have an asymptote parallel to the y-axis.

15. In which region the curve

does not lie? (1)

(2)

(3)

and

(4)

(1)

(2)

(3)

(4)

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Explanation

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