### 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