Choose the correct or the most suitable answer from the given four alternatives : Mathematics - Applications of Differential Calculus

Choose the correct or the most suitable answer from the given four alternatives :

1. The volume of a sphere is increasing in volume at the rate of 3*Ï€* cm3 / sec .

The rate of change of its radius when radius is 1/2 cm

(1) 3 cm/s

(2) 2 cm/s

(3) 1 cm/s

(4) 1/2 cm/s

2. A balloon rises straight up at 10 m/s. An observer is 40* m *away from the spot where the balloon left the ground. The rate of change of the balloonâ€™s angle of elevation in radian per second when the balloon is 30 metres above the ground.

(1) 3/25 radians/sec

(2) 4/25 radians/sec

(3) 1/5 radians/sec

(4) 1/3 radians/sec

3. The position of a particle moving along a horizontal line of any time *t* is given by s (*t*) = 3*t*2 âˆ’ 2*t* âˆ’ 8 . The time at which the particle is at rest is

(1) t = 0

(2) t = 1/3

(3) t = 1

(4) t = 3

4. A stone is thrown up vertically. The height it reaches at time t seconds is given by* x *= 80*t* âˆ’16*t*2 . The stone reaches the maximum height in time *t* seconds is given by

(1) 2

(2) 2.5

(3) 3

(4) 3.5

5. The point on the curve 6*y *= x3 + 2 at which y-coordinate changes 8 times as fast as *x-*coordinate is

(1) (4,11)

(2) (4, âˆ’11)

(3) (âˆ’4,11)

(4) (âˆ’4, âˆ’11)

6. The abscissa of the point on the curve *f (x)* = âˆš(8âˆ’2x) at which the slope of the tangent is âˆ’0.25 ?

(1) âˆ’8

(2) âˆ’4

(3) âˆ’2

(4) 0

7. The slope of the line normal to the curve *f (x)* = 2 cos 4x at* x *= Ï€/12 is

(1) âˆ’4âˆš3

(2) âˆ’4

(3) âˆš3 / 12

(4) 4âˆš3

8. The tangent to the curve* y*2 âˆ’ x*y +* 9 = 0 is vertical when

(1) *y* = 0

(2)* y *= Â± âˆš3

(3)* y *= 1/2

(4)* y *= Â±3

9. Angle between* y*2 =* x *and* x*2 =* y *at the origin is

(1) tanâˆ’1 (3/4)

(2) tan-1 (4/3)

(3) Ï€/2

(4) Ï€/4

10. The value of the limit or limx â†’0 ( cot* x *â€“ 1/*x* )is

(1) 0

(2) 1

(3) 2

(4) âˆž

11. The function sin4* x *+ cos4* x *is increasing in the interval

Answer: (3)

12. The number given by the Rolleâ€™s theorem for the function* x*3 âˆ’ 3x2 ,* x *âˆˆ[0, 3] is

(1) 1

(2) âˆš2

(3) 3/2

(4) 2

13. The number given by the Mean value theorem for the function 1/*x* ,* x *âˆˆ[1, 9] is

(1) 2

(2) 2.5

(3) 3

(4) 3.5

14. The minimum value of the function | 3 âˆ’* x *| + 9 is

(1) 0

(2) 3

(3) 6

(4) 9

15. The maximum slope of the tangent to the curve* y *= ex sin* x *,* x *âˆˆ[0, 2Ï€ ] is at

(1) x = Ï€/4

(2)* x *= Ï€/2

(3)* x *= Ï€

(4)* x *= 3Ï€/2

16. The maximum value of the function* x*2 eâˆ’2*x** *,* x *> 0 is

(1) 1/e

(2) 1/2e

(3) 1/e2

(4) 4/e4

17. One of the closest points on the curve* x*2 âˆ’ y2 = 4 to the point (6, 0) is

(1) (2, 0)

(2) (âˆš5,1)

(3) (3, âˆš5 )

(4) (âˆš13, âˆ’âˆš3)

18. The maximum value of the product of two positive numbers, when their sum of the squares is 200, is

(1) 100

(2) 25âˆš7

(3) 28

(4) 24âˆš14

19. The curve* y *= a*x*4 + b*x*2 with *ab* > 0

(1) has no horizontal tangent

(2) is concave up

(3) is concave down

(4) has no points of inflection

20. The point of inflection of the curve* y *= (*x* âˆ’1)3 is

(1) (0, 0)

(2) (0,1)

(3) (1, 0)

(4) (1,1)

Tags : Applications of Differential Calculus | Mathematics , 12th Maths : UNIT 7 : Applications of Differential Calculus

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12th Maths : UNIT 7 : Applications of Differential Calculus : Exercise 7.10: Choose the correct or the most suitable answer | Applications of Differential Calculus | Mathematics

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