Applications of Derivatives Test

Result

Applications of Derivatives Test - 50

Score
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Weekly Quiz Competition

Question 1
4 / -1

For the curve xy = c² the subnormal at any point varies as

A
x²

B
x³

C
y²

D
y³

Solution
Question 2
4 / -1

The angle between the curves y = sin x and y = cos x is

A

B

C

D

Solution
Question 3
4 / -1

If a tangent to the curve y = 6x – x² is parallel to the line 4x – 2y –1 = 0, then the point of tangency on the curve is

A
(2, 8)

B
(8, 2)

C
(6, 1)

D
(4, 2)

Solution
Question 4
4 / -1

The normal to the curve x = a(1 + cos θ), y = a sin θ at ‘θ’ always passes through the fixed point

A
(a, a)

B
(0, a)

C
(0, 0)

D
(a, 0)

Solution
Question 5
4 / -1

If ST and SN are the lengths of the subtangent and the subnormal at the point θ = π/2 on the curve x a (θ + sin θ), y = a(1 – cos θ), a ≠ 1, then

A
ST = SN

B
ST = 2SN

C
ST² = aSN³

D
ST³ = aSN

Solution
Question 6
4 / -1

The abscissa of the point on the curve y = a(e^x/a + e^–x/a) where the tangent is parallel to the x - axis is

A
0

B
a

C
2a

D
–2a

Solution
Question 7
4 / -1

If the line ax + by + c = 0 is normal to the curve xy = 1 then

A
a > 0, b < 0

B
a > 0, b > 0

C
a < 0, b < 0

D
Data is unsufficient

Solution
Question 8
4 / -1

The equation of the tangent to the curve y = (1 + x)^y + sin^–1 (sin² x) at x = 0 is

A
x + y = 1

B
x + y + 1 = 0

C
2x – y + 1 = 0

D
x + 2y + 2 = 0

Solution
Question 9
4 / -1

A

B

C

D

Solution
Question 10
4 / -1

The equation of the curve with passes through the point (0, 1) and the slope 3x² + 2x + 5 at any point (x, y) is

A
y = 3x³ + 2x² + 5x + 1

B
y = 2x³ + 3x² + 5x + 1

C
y = x³ + x² + 5x + 1

D
y = x³ + x² + 5x –1

Solution