Page 1 CBSE TEST PAPER-05 CLASS - XII MATHEMATICS (Calculus : Application of Integrals) Topic: - Application of Integrals Note : Each Question carries 6 marks. 1. Find the area of the smaller region bounded by the ellipse 2 2 2 2 1 x y a b + = and the line 1. x y a b + = 2. Find the area of the region enclosed by the parabola x 2 = y, the line y = x +2 and the x – axis. 3. Using method of integration, find the area bounded by the curve |x| + |y| = 1. 4. Find area bounded by curves ( ) { } 2 , : and | | . x y y x y x = = 5. Using method of integration find the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3). 6. Using method of integration, find the area of the region bounded by lines: 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0. 7. Find the area of two regions ( ) { } 2 2 , : 4 ,4 2 4 9 . x y y x x y = + = 8. Find the area of the circle x 2 = y 2 = 15 exterior to the parabola y 2 = 6x 9. Find the area bounded by the y – axis, y = cosx and y = sinx, 0 2 x p = = 10. Using integration, find the area of the region in the first quadrant enclosed by the x – axis, the line y = x and the circle x 2 + y 2 = 32.Read More

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