The area of the region bounded by the parabola (y – 2)2 = x �

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

11.

The area (in square units) bounded by the curves y = straight y space equals space square root of straight x comma 2y-x+3 =0, X -axis and lying in the first quadrant is 

  • 9

  • 36

  • 18

  • 18

154 Views

12.

The intercepts on X- axis made by tangents to the curve, straight y space equals space integral subscript 0 superscript straight x vertical line straight t vertical line space dt comma space straight x space straight epsilon space straight R which are parallel to the line y =2x, are equal to

  • ±1

  • ±2

  • ±3

  • ±3

160 Views

13.

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equationd V(t)/dt = - k(T - t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

  • straight T squared minus 1 over straight k
  • straight I space minus KT squared over 2
  • straight I space minus space kT squared over 2
  • straight I space minus space kT squared over 2
290 Views

14.

For x ∈, (0, 5π/2) define f(x). Then f (x) = integral subscript 0 superscript straight x space square root of straight t space sin space straight t space dt has

  • local maximum at Ï€ and 2Ï€.

  • local minimum at Ï€ and 2Ï€

  • local minimum at Ï€ and the local maximum at 2Ï€.

  • local minimum at Ï€ and the local maximum at 2Ï€.

95 Views

Advertisement
15.

The area of the region enclosed by the curves y = x, x = e, y =1/x and the positive x-axis is

  • 1/2 square units

  • 1 square units

  • 3/2 square units

  • 3/2 square units

139 Views

16.

The area bounded by the curve y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is 

  • left parenthesis 4 minus square root of 2 minus 2 right parenthesis space sq space units
  • left parenthesis 4 minus square root of 2 plus 2 right parenthesis space sq space units
  • left parenthesis 4 minus square root of 2 minus 1 right parenthesis space sq space units
  • left parenthesis 4 minus square root of 2 minus 1 right parenthesis space sq space units
444 Views

17.

Solution of the differential equation
cos x dy = y (sin x - y) dx, 0 < x < π/2, is 

  • sec x = (tan x + C ) y 

  •  y sec x = tan x + C

  •  y tan x = sec x + C 

  •  y tan x = sec x + C 

243 Views

18.

The area (in sq. units) of the region
{(x, y} : x  ≥ 0, x + y ≤ 3, x2 ≥ 4y and y ≤ 1 +√x}

  • 5/2

  • 59/12

  • 3/2

  • 3/2

559 Views

Advertisement
Advertisement

19.

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is 

  • 3

  • 6

  • 9

  • 9


C.

9

Equation of tangent at (2, 3) 



≡ x – 2y + 4 = 0
Required Area

space equals space integral subscript 0 superscript 3 space left square bracket space left parenthesis straight y minus 2 right parenthesis squared space plus space 1 minus 2 straight y plus 4 right square bracket space dy
space equals space integral subscript 0 superscript 3 space left square bracket space left parenthesis straight y minus 2 right parenthesis squared space minus space 2 straight y space plus 5 right square bracket space dy
space equals 9 space sq. space units

212 Views

Advertisement
20.

The area of the plane region bounded by the curves x + 2y2= 0 and x + 3y2= 1 is equal to 

  • 5/3

  • 1/3

  • 2/3

  • 2/3

163 Views

Advertisement