OA and OB are two roads enclosmng an angle of 120°. X and Y s

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

231.

The perimeter of a sector is P. The area of the sectoris maximum when its radius is

  • 1P

  • P2

  • P4

  • P


232.

The function f(x) = x3 - 3x is

  • increasing on - , - 1  [1, ) and decreasing on (- 1, 1)

  • decreasing on - , - 1  [1, ) and increasing on (- 1, 1)

  • increasing on (0, ) and decreasing on (- , 0)

  • decreasing on (0, ) and increasing on (- , 0)


233.

A population p(t) of 1000 bacteria introduced into nutrient medium grows according to the relation p(t) = 1000 + 1000t100 +t2. The maximum 100+t size of this bacterial population is

  • 1100

  • 1250

  • 1050

  • 5250


234.

If ST and SN are the lengths of the subtangent and the subnormal at the point θ = π2 on the curve x = aθ + sinθ, y = a1 - cosθa  1, then

  • ST = SN

  • ST = 2SN

  • ST2 = aSN3

  • ST3 = aSN


Advertisement
235.

A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increases of the surface area ofthe balloon when its diameter is 14cm, is

  • 7 sq cm/min

  • 10 sq cm/min

  • 17.5 sq cm/min

  • 28 sq cm/min


236.

If the curve y = 2x3 + ax2 + bx + c passes through the origin and the tangents drawn to it at x = - 1 and x = 2 are parallel to the x-axis, then the values of a, b and c are respectively :

  • 12, - 3 and 0

  • - 3, - 12 and 0

  • - 3, 12 and 0

  • 3, - 12 and 0


237.

A circular sector of perimeter 60 m with maximum area is to be constructed. The radius of the circular arc in metre must be :

  • 20

  • 5

  • 15

  • 10


238.

The tangent and the normal drawn to the curve y = x2 - x + 4at P(1, 4) cut the x-axis at A and B respectively. If the length of the subtangent drawn to the curve at P is equal to the length of the subnormal, then the area of the triangle PAB in sq unit is :

  • 4

  • 32

  • 8

  • 16


Advertisement
239.

The range in which y = - x2 + 6x - 3 is increasing is

  • x < 3

  • x > 3

  • 7 < x < 8

  • 5 < x < 6


Advertisement

240.

OA and OB are two roads enclosmng an angle of 120°. X and Y start from 'O' at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h.The rate at which the shortest distance between X and Y is increasing after 1 h is

  • 37 km /h

  • 37 km/h

  • 13 km/h

  • 13 km/h


A.

37 km /h

Given, speed of x is 4 km/h and y is 3 km/h .

After time t the distance covered by x is 4t and y is 3t.

Let shortest distance between x and y = A.

Then by cosine law

     A2 = 4t2 + 3t2 - 4t3t2cos120° A2 = 16t2 + 9t2 - 24t2- 12 A2 = 25t2 + 12t2 A2 = 37t2  A = 37tIf     t = 1 h, then A = 37 kmNow, differentiatmg Eq. (i) w.r.t. t, we get      2AA' = 372tAfter t = 1 h, we get237 A' = 237      A' = 37

Thus, rate at which shortest distance A changes with tlme is 37 km/h.


Advertisement
Advertisement