Class XII Maths Applications of Derivatives 5

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Question 1

The normal to the curve x = a(cosθ + θ sinθ), y = a( sinθ - θ cosθ) at any point ‘θ’ is such that

• Ait passes through the origin
• Bit makes angle - θ with the x-axis
• Cit passes through
• Dit is at a constant distance from the origin

Question 2

The normal to the curve x² + 2xy – 3y² = 0, at (1, 1)

• Adoes not meet the curve again
• Bmeets the curve again in the second quadrant
• Cmeets the curve again in the third quadrant.
• Dmeets the curve again in the fourth quadrant.

Question 3

A function y = f(x) has a second order derivative f″(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is

• A
• B
• C
• D

Question 4

Tangent to a curve intersects the y-axis at a point P. A line perpendicular to this tangent through P passes through another point (1, 0). The differential equation of the curve is

• Ay= 0
• B = 1
• Cy
• D = 5

Question 5

If m be the slope of a tangent to the curve e^2y = 1 + 4x², then -

• Am < 1
• B|m| ≤ 1
• C|m| > 1
• DNone of these

Question 6

The number of values of c such that the straight line 3x + 4y = c touches the curve is

• A0
• B1
• C2
• D4

Question 7

All the points on the curve y = at which the tangents is || to x axis lie on

• Astraight line
• Bcircle
• Cparabola
• Dellipse

Question 8

The point of intersection of the tangents drawn to the curve x²y = 1–y at the points where it is meet by the curve xy = 1– y, is given by

• A(0, –1)
• B(1, 1)
• C(0, 1)
• DNone of these

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