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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
A particle moves along the curve 6y = x3 + 2.
Assertion (A): The curve meets the Y axis at three points.
Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Directions : In the following questions, A statement of Assertion (A)...
On Y axis, x = 0. The curve meets the Y axis at only one point, i.e., (0,⅓)
Hence A is false.
Put x = 2 and –2 in the given equation to get y
∴ The points are (2, 5/3), (-2,-1)
R is true.
Most Upvoted Answer
Directions : In the following questions, A statement of Assertion (A)...
Statement A: The curve meets the Y axis at three points.
Statement R: At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.
Explanation:
To understand the given statement, let's analyze the curve 6y = x^3.
The equation of the curve is given by 6y = x^3. This can also be written as y = (1/6)x^3.
Key Points:
1. The curve is a cubic function.
2. The coefficient of x^3 is positive, indicating that the curve opens upwards.
To find the points where the curve meets the Y-axis, we set x = 0 in the equation y = (1/6)x^3.
When x = 0, y = (1/6)(0)^3 = 0.
So, the curve passes through the origin (0,0).
Since the curve is a cubic function and opens upwards, it will intersect the Y-axis at three points - once at the origin (0,0) and two more points above and below the origin.
Hence, Statement A is true.
Now, let's analyze Statement R.
Statement R states that at the points (2,5/3) and (-2,-1), the ordinate changes two times as fast as the abscissa.
To verify this, we can calculate the slope of the curve at these points.
The slope of the curve at any point (x,y) is given by dy/dx, which represents the rate at which the ordinate (y) changes with respect to the abscissa (x).
Differentiating the equation y = (1/6)x^3 with respect to x, we get:
dy/dx = (1/6) * 3x^2 = (1/2)x^2
At the point (2,5/3), the slope dy/dx = (1/2)(2)^2 = (1/2)(4) = 2.
At the point (-2,-1), the slope dy/dx = (1/2)(-2)^2 = (1/2)(4) = 2.
So, at both points, the slope is 2, which means that the rate of change of the ordinate (y) with respect to the abscissa (x) is 2.
Hence, Statement R is also true.
However, Statement R does not provide a correct explanation for Statement A. The fact that the ordinate changes two times as fast as the abscissa at the given points does not directly explain why the curve meets the Y-axis at three points.
Therefore, the correct answer is option D: A is false and R is true.
Statement R: At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.
Explanation:
To understand the given statement, let's analyze the curve 6y = x^3.
The equation of the curve is given by 6y = x^3. This can also be written as y = (1/6)x^3.
Key Points:
1. The curve is a cubic function.
2. The coefficient of x^3 is positive, indicating that the curve opens upwards.
To find the points where the curve meets the Y-axis, we set x = 0 in the equation y = (1/6)x^3.
When x = 0, y = (1/6)(0)^3 = 0.
So, the curve passes through the origin (0,0).
Since the curve is a cubic function and opens upwards, it will intersect the Y-axis at three points - once at the origin (0,0) and two more points above and below the origin.
Hence, Statement A is true.
Now, let's analyze Statement R.
Statement R states that at the points (2,5/3) and (-2,-1), the ordinate changes two times as fast as the abscissa.
To verify this, we can calculate the slope of the curve at these points.
The slope of the curve at any point (x,y) is given by dy/dx, which represents the rate at which the ordinate (y) changes with respect to the abscissa (x).
Differentiating the equation y = (1/6)x^3 with respect to x, we get:
dy/dx = (1/6) * 3x^2 = (1/2)x^2
At the point (2,5/3), the slope dy/dx = (1/2)(2)^2 = (1/2)(4) = 2.
At the point (-2,-1), the slope dy/dx = (1/2)(-2)^2 = (1/2)(4) = 2.
So, at both points, the slope is 2, which means that the rate of change of the ordinate (y) with respect to the abscissa (x) is 2.
Hence, Statement R is also true.
However, Statement R does not provide a correct explanation for Statement A. The fact that the ordinate changes two times as fast as the abscissa at the given points does not directly explain why the curve meets the Y-axis at three points.
Therefore, the correct answer is option D: A is false and R is true.
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.A particle moves along the curve 6y = x3 + 2.Assertion (A): The curve meets the Y axis at three points.Reason (R): At the points (2,5/3) and (–2, –1) the ordinate changes two times as fast as the abscissa.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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