#### 12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. The volume of a sphere is increasing in volume at the rate of 3 πcm3 sec. The rate of change of its radius when radius is $\cfrac { 1 }{ 2 }$ cm

(a)

3 cm/s

(b)

2 cm/s

(c)

1 cm/s

(d)

$\cfrac { 1 }{ 2 } cm/s$

2. The slope of the line normal to the curve f(x) = 2cos 4x at $x=\cfrac { \pi }{ 12 }$

(a)

$-4\sqrt { 3 }$

(b)

-4

(c)

$\cfrac { \sqrt { 3 } }{ 12 }$

(d)

$4\sqrt { 3 }$

3. The number given by the Rolle's theorem for the functlon x3-3x2, x∈[0,3] is

(a)

1

(b)

$\\ \\ \\ \sqrt { 2 }$

(c)

$\cfrac { 3 }{ 2 }$

(d)

2

4. One of the closest points on the curve x2 - y2.= 4 to the point (6, 0) is

(a)

(2,0)

(b)

$\left( \sqrt { 5 } ,1 \right)$

(c)

$\left( 3,\sqrt { 5 } \right)$

(d)

$\left( \sqrt { 13 } ,-\sqrt { 3 } \right)$

5. If a particle moves in a straight line according to s = t3-6t2-15t, the time interval during which the velocity is negative and acceleration is positive is

(a)

2 < t < 5

(b)

2 ≤ t ≤ 5

(c)

t ≥ 2

(d)

t ≤ 2

6. The least value of a when f f(x) =x2+ax+1 is increasing on (1, 2) is

(a)

-2

(b)

2

(c)

1

(d)

-1

7. The angle made by any tangent to the curve y = x5 + 8x + 1 with the X-axis is a

(a)

obtuse

(b)

right angle

(c)

acute angle

(d)

no angle

8. If the slope of the curve 2y2=ax2+b at (1,-1) is - 1, then the values of a, b is

(a)

2, 0

(b)

0, 2

(c)

0, 0

(d)

2, 2

9. The function -3x+12 is ________ function on R.

(a)

decreasing

(b)

strictly decreasing

(c)

increasing

(d)

strictly increasing

10. $\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx }$ is _________

(a)

1

(b)

-1

(c)

0

(d)