Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5.Assertion (A): The value of a is ±2Reason (R): The value of b is ±7a)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 'C'. 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.

The equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5.

Assertion (A): The value of a is ±2

Reason (R): The value of b is ±7

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 'C'. Can you explain this answer?

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Most Upvoted Answer

Directions : In the following questions, A statement of Assertion (A)...

y² = ax³ + b

Differentiate with respect to x,

Since (2, 3) lies on the curve

y² = ax³ + b

Or 9 = 8a + b …. (i)

Also from equation of tangent

y = 4x – 5

slope of the tangent = 4

either, a = 2 or a = - 2

For a = 2,

9 = 8(2) + b

or b = - 7

∴ a = 2 and b = - 7 and

for a = - 2,

9 = 8(- 2 )+b or b = 25

or a = - 2 and b = 25

Hence A is true and R is false.

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Directions : In the following questions, A statement of Assertion (A)...

Assertion (A): The value of a is ±2
Reason (R): The value of b is ±7

The given equation is y^2 = ax^3 + b.

To find the equation of the tangent at (2, 3), we need to find the slope of the tangent at that point.

Differentiating the given equation with respect to x, we get:
2y(dy/dx) = 3ax^2

Substituting the coordinates of the point (2, 3), we get:
2(3)(dy/dx) = 3a(2)^2
6(dy/dx) = 12a
(dy/dx) = 2a

Since the slope of the tangent is 4 (from the given equation y = 4x - 5), we can set up the following equation:
2a = 4
a = 2

Therefore, the value of a is 2.

Assertion (A) is true.

Now, let's check the reason (R).

Since we have already determined that a = 2, we can substitute this value into the given equation to find the value of b.

Using the point (2, 3), we get:
(3)^2 = 2(2)^3 + b
9 = 2(8) + b
9 = 16 + b
b = 9 - 16
b = -7

Therefore, the value of b is -7.

Reason (R) is true.

Since both the assertion and reason are true, and the reason is a correct explanation for the assertion, the correct choice is:
Both A and R are true and R is the correct explanation of A (option C).

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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.The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5.Assertion (A): The value of a is ±2Reason (R): The value of b is ±7a)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 'C'. Can you explain this answer?

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