12 - Maths Unit 6 - Differential Calculus - Applications II

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12 - Maths Unit 6 - Differential Calculus - Applications II - Quiz

Prepard by, R VISVANATHAN, PG ASST IN MATHS, GHSS, PERIYATHACHUR, TINDIVANAM TK-605651
  ; &nbs p; & www. Padasalai. Net


Questions and Answers
  • 1. 

    If  then  is equal to (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 2. 

    If then  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 3. 

    If  then  is equal to (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    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.

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  • 4. 

    The curve  has (1)  only one loop between  and   (2)  two loops between  and  (3)  two loops between  and    (4)  no loop

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    Explanation
    The curve has two loops between two points.

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  • 5. 

    The percentage error in the 11th root of the number 28 is approximately ......... times the percentage error in 28. (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    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.

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  • 6. 

    If , then is equal to  (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
  • 7. 

    If  then  is equal to (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
  • 8. 

    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)

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    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.

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  • 9. 

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

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
    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.

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  • 10. 

    The curve has  (1)  an asymptotes parallel to axis  (2)  an asymptotes parallel to axis (3)  asymptotes parallel to both axes     (4)  no asymptotes

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    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.

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  • 11. 

    In which region the curve  does not lie? (1)    (2)    (3)   and   (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    C. (3)
  • 12. 

    An asymptotes to the curve  is (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    B. (2)
    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.

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  • 13. 

    The curve  is symmetrical about (1)   axis  (2)  axis   (3)    (4)  both the axes

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    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.

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  • 14. 

    If then is equal to (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    A. (1)
    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.

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  • 15. 

    The curve  cuts the axis at (1)    (2)    (3)    (4)  

    • A.

      (1)

    • B.

      (2)

    • C.

      (3)

    • D.

      (4)

    Correct Answer
    D. (4)
    Explanation
    The curve cuts the x-axis at (4).

    Rate this question:

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