JEE Main Mathematics - Areas
Exam Duration: 60 Mins Total Questions : 30
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
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)
\(\frac { x }{ \sqrt { (1+{ x }^{ 2 }) } } \)
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 bounded by y = x e1xl and lines Iex|= y = 0 is
- (a)
4 sq unit
- (b)
6 sq unit
- (c)
1 sq unit
- (d)
2 sq unit
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
If the area bounded by the x-axis, the curve y = f(x) and the lines x = c and x = d is independent of d, \(\forall \)d > c (c is a constant), then f is
- (a)
the identity function
- (b)
the zero function
- (c)
a non-zero constant function
- (d)
none of the above
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