Mathematics - Areas
Exam Duration: 45 Mins Total Questions : 30
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)
\(<\int _{ 0 }^{ \pi /4 }{ \frac { tanx }{ x } dx } \)
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
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
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
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
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
The area of the figure bounded by f(x) = sin x, g(x) = cos x in the first quadrant is
- (a)
2(\(\sqrt2\)-1) sq unit
- (b)
2(\(\sqrt3\)-1) sq unit
- (c)
2(\(\sqrt3\)-1) sq unit
- (d)
none of these
The area bounded by the curve y = x4 - 2x3 + x2 + 3, the axis of abscissas and two ordinates corresponding to the points of minimum of the function y(x) is
- (a)
10/3 sq unit
- (b)
27/10 sq unit
- (c)
21/10 sq unit
- (d)
none of these
The area bounded by the curve y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) cos (3b + 4) sq unit. Then f(x) is given by
- (a)
(x - 1) sin (3x + 4)
- (b)
3 (x - 1) sin (3x + 4) + cos (3x + 4)
- (c)
cos (3x + 4) - 3(x - 1) sin (3x + 4)
- (d)
none of the above
polynomial P is positive for x > 0 and the area of the region bounded by P(x), the x-axis and the vertical lines x=0 and x = \(\lambda\) sq unit. en polynomial p(x) is
- (a)
X2 + 2x
- (b)
X2 + 2x + 1
- (c)
X2 + X + 1
- (d)
x3 + 2X2 + 2
For which of the following values of m, is the area of the region bounded by the curve y = x - x2 and the line y = mx equals 9/2 sq unit?
- (a)
-4
- (b)
-2
- (c)
2
- (d)
4