Q2.The area bounded by the curve |x|+y=1 and the x –axis is
Answer : Option BExplaination / Solution: The given curve consists of two straight lines x + y = 1 ( x ≥ 0 )and -x + y = 1 ( x < 0 ) Required area : = 2∫01ydx = 2∫01(1−|x|)dx=2∫01(1−x)dx=2[x−x22]10 = 1sq.unit
Q3.The area enclosed by the curve x225+y216=1is equal to
Answer : Option AExplaination / Solution:
The area of the standard ellipse is given by ;πab. Here , a = 5 and b = 4 Therefore , the area of curve is π(5)(4)=20π.
Q9.The area bounded by the parabola y = x2 + 1 and the straight line x + y = 3 is given by
Answer : Option BExplaination / Solution: The two curves parabola and the line meet where, 3 - x =x2+1⇒x2+x−2 = 0 ⇒x=−2,1. Required area ; ∫−21{3−x−(x2+1)}dx = [2x−x22−x33]1−2= 92
Q10.The area bounded by the curves y2 = x andy = x2 is
Answer : Option AExplaination / Solution: The two curves meet in ( 0 , 0 ) and ( 1, 1 ).The required area lies above the curve y = x2 and below x = y2 and is equal to ;
x32−x33]10=23−13=13
Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0