Mathematics - Areas

Question - 1

The area bounded by y =  \(\frac { sinx }{ x } \)x-axis and the ordinates x=0, x = \(\frac { \pi }{ 4 } \) is

  • A = \(\frac { \pi }{ 4 } \)
  • B < \(\frac { \pi }{ 4 } \)
  • C > \(\frac { \pi }{ 4 } \)
  • D \(<\int _{ 0 }^{ \pi /4 }{ \frac { tanx }{ x } dx } \)

Question - 2

If An is the area bounded by y = (1- x2)n and coordinate axes, n\(\in\)N, then

  • A An = An-1
  • B An < An-1
  • C An > An-1
  • D An = 2An-1

Question - 3

Area bounded by the curve y = \(\sqrt { (sin[x]+[sinx]) } \) Where [.]denotes the greatest integer function, lines x = 1 and x = \(\frac { \pi }{ 2 } \): and the x-axis is

  • A \(\left( \frac { \pi }{ 2 } -1 \right) \) sq unit
  • B \(\sqrt { sin1 } \left( \frac { \pi }{ 2 } -1 \right) \) sq unit
  • C \(\sqrt { cos1 } \left( \frac { \pi }{ 2 } -1 \right) \)  sq unit
  • D \(\sqrt { \frac { \pi }{ 2 } } \left( \frac { \pi }{ 2 } -1 \right) \) sq unit

Question - 4

The area between the curve y = 2X4 - X2, the x-axis and the ordinates of two minima of the curve is

  • A 7/120 sq unit
  • B 9/120 sq unit
  • C 11/120 sq unit
  • D 13/120 sq unit

Question - 5

The area bounded by the x-axis, the curve y = f(x) and the lines x = 1and x = b is equal to \((\sqrt { ({ b }^{ 2 }+1) } -\sqrt { 2 } )\) b>1, then f(x) is

  • A \(\sqrt { (x-1) } \)
  • B \(\sqrt { (x+1) } \)
  • C \(\sqrt { ({ x }^{ 2 }+1) } \)
  • D \(\frac { x }{ \sqrt { (1+{ x }^{ 2 }) } } \)

Question - 6

Let f(x) = min {x + \(\sqrt{(1-x)}\))(1- x)}, then area bounded by f(x) and x-axis is

  • A 1/6 sq unit
  • B 5/6 sq unit
  • C 7/6 sq unit
  • D 11/6 sq unit

Question - 7

The area bounded by the graph y = |[x - 3]|, the x-axis and the lines x = -2 and x = 3 is ([.] denotes the greatest integer function)

  • A 7 sq unit
  • B 15 sq unit
  • C 21 sq unit
  • D 28 sq unit

Question - 8

The value of c for which the area of the figure bounded by the curve y = 8x2- x5, the straight lines x = 1 and x = c an d the x-axis is equal to16/3 is

  • A 2
  • B \(\sqrt{8-{\sqrt17}}\)
  • C 3
  • D -1

Question - 9

The slope of the tangent to a curve y = f(x) at (x, f(x)) is 2x + 1. If the curve passes through the point (1, 2), then the area of the region bounded by the curve, the x-axis and the line x = 1 is

  • A 5/6 sq unit
  • B 6/5  sq unit
  • C 1/6  sq unit
  • D 6  sq unit

Question - 10

The area of the region bounded by the curve a4y2 = (2a - x) X5 is to that of the circle whose radius is a, is given by the ratio

  • A 4 : 5
  • B 5 : 8
  • C 2 : 3
  • D 3 : 2
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