Practice Test

Q1) The area bounded by the curve y = x|x|, X- axis and the coordinates x = -1 and x = 1 is given by Show Answer

Q2) Using integration, the area of the region bounded by the line
2y = 5 x + 7, X - axis and the lines x = 2 and x = 8 is Show Answer

Q3) The area bounded by the curve
|x| + y = 1 and axis of x is Show Answer

Q4) The area of the region bounded by the curve xy -3x -2y -10 = 0, X-axis and the lines x = 3, x = 4, is Show Answer

Q5) The area bounded by x = 1, x = 2, xy = 1 and X-axis is Show Answer

Q6) Using integration the area of region bounded by the triangle whose vertices are (-1,0), (1,3) and (3,2) is Show Answer

Q7) The larger of the area bounded by y = cos x, y = x + 1 and y = 0 is Show Answer

Q8) A curve y = f(x) passes through the origin and lies entirely in the first quadrant. Through any point P(x, y) on the curve, lines are drawn parallel to the coordinate axes. If the curve divides the area formed by these lines and coordinates area in m : n, then the value of f(x) is equal to Show Answer

Q9) The area bounded by the curve
y = log x, y = log |x|, y = | log x | and y = | log |x|| is Show Answer

Q10) The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one such region is Show Answer

Q11) Let y be the function which passes through (1, 2) having slope
(2x + 1). The area bounded between the curve and X- axis is Show Answer

Q12) Area bounded by the curve
y = (x - 1) (x - 2) (x - 3) and x-axis lying between the ordinates x = 0 and x = 3 is equal to Show Answer

Q13) 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 ) Show Answer

Q14) 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 Show Answer

Q15) Area bounded by lines y = 2 + x, y = 2 - x and x = 2 is Show Answer

Q16) The sine and cosine curves intersects infinitely many times giving bounded regions of equal areas. The area of one of such region is Show Answer

Q17) Ratio of the area cut off a parabola by any double ordinate is that corresponding rectangle contained by
that double ordinate and its distance from the vertex is Show Answer