The variable line x/a+y/b=1 is such that a+b=10, the locus of the midpoint of the portion of the line intercepted between the axes is:
A. x+y=10
B. 10x+5y=1
C. x+y=5
D. 5x+10y=1
The value of c for which the area bounded by the curve y=8x2-x5,the lines x=1,x=c and x-axis is 16/3 is
A. 1
B. 0
C. -1
D. -2
The area of the region bounded by the curves y=x2+2,y=x,x=0 and x=3 is
A. 4/3 sq.unit
B. 2/3 sq.unit
C. 21/2 sq.unit
D. 27 sq.unit
The area of the plane region bounded by the curve x + 2y2 = 0 and 3y2 = 1 is equal to
A. 2/3
B. 4/3
C. 5/3
D. 1/3
The area bounded by the curve y2=4x and the lines x=1,x=9 is
A. 436/15
B. 208/3
C. 236/5
D. 340/13
If a is the area bounded by the curve y=4x-x2-3 with x-axis,b is the area bounded by y=11x-24-x2 with x-axis and c is the area bounded by y=(x-4)(x-1) with x-axis then the descending order of a,b,c is
A. a,b,c
B. b,c,a
C. a,c,b
D. c,a,b
If y = sin (logex) then x2 (d2y/dx2) + x (dy/dx) =
A. sin (logex)
B. cos (logex)
C. y2
D. - y
The area of the region bounded by the curve y=x3,x-axis and the ordinates x=1,x=4 is
A. 255/4
B. 155/4
C. 55/4
D. 355/4
If area bounded by the curves y2=4ax and y=mx is a2/3,then the value of m is
A. 2
B. -2
C. 1/2
D. none
The area of the region bounded by the curve y=(x2+2)2+2x between the ordinates x=0,x=2 is
A. 436/15
B. 208/3
C. 236/5
D. 340/13
If a is the area bounded by x=4-y2 with y-axis,b is the area bounded by x=6+5y-y2 with y axis and c is the area bounded by 2x=y2-1 with y-axis then the ascending order of a,b,c is
A. a,b,c
B. b,c,a
C. a,c,b
D. c,a,b
The area bounded by the curve xy=4,x-axis and the ordinates x=2,x=5 is
A. 2 log 5/2
B. 4 log 5/2
C. 5 log 5/2
D. 3 log 5/2
The area under the curve y=x2-3x+2 with boundaries as x-axis and the ordinates at x=0,x=3 is
A. 3/8
B. 2/3
C. 3/5
D. 9/2
The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is
A. 10/3
B. 5/3
C. 20/3
D. none
The area of the region bounded by the curve y2=4x,y-axis and the lines y=1,y=3 is
A. 28/3
B. 32/3
C. 13/6
D. 23/3