Application of Derivatives - Online Test
Q1. The curves cut orthogonally when
Answer : Option C
Explaination / Solution:
Q2. The slope of the tangent to the curve x = a sin t, y = a at the point ‘t’ is
Answer : Option D
Explaination / Solution:
Q3. Tangents to the curve at the points (1, 1) and ( – 1, – 1) are
Answer : Option D
Explaination / Solution:
Q4. The line touches the curve at the point
Answer : Option C
Explaination / Solution:
Q5.
Tangents to the curve at the points (1, 1) and ( – 1, 1)
Answer : Option D
Explaination / Solution:
therefore , slope of tangent at (1,1) = - 1 and the slope of tangent at ( - 1 ,1 )= 1 .
Now product of the slopes=1.-1= -1
Hence , the two tangents are at right angles.
Q6. Equation of the tangent to the curve at the point (a, b) is
Answer : Option D
Explaination / Solution:
Q7. An edge of a variable cube is increasing at the rate of 3cm/sec.Find the rate at which the volume of the cube is increasing when the edge is 10cm long
Answer : Option D
Explaination / Solution:
Q8. The slope of the tangent to the curvex = a ( cos θ + θ sin θ),y = a (sin θ – θ cos θ) at any point ‘θ’ is
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. The curve y = has at (0, 0)
Answer : Option B
Explaination / Solution:
Q10. The point on the curve where tangent makes an angle of with the X – axis is
Answer : Option A
Explaination / Solution:
