MCQ : Area Bounded Region

Q:1. The area bounded by y = |x| -1 and y = -|x| + 1 is

(A) 1

(B) 2

(C) 2√2

(D) 4

Q:2. The curve y = x2 –7x +10 intersects the x–axis at the points A and B then the area bounded by the curve and the line AB is

(A) 4 (1/2)sq. units

(B) 4 sq. units

(C) 6 sq. units

(D) 2 sq. units

Q:3. P is any point inside or on the boundary of ΔABC having perimeter p and area Δ . R is any point in the plane of ΔABC such that PR ≤ 5. The area of the region in which the point R lies is

(A) 25π + 5p + Δ

(B) 5π + 25p + Δ

(C) 5π + 5p + Δ

(D) 5(π + p) + 25Δ

Q:4. The area bounded by the curves y = sin (x – [x]), y = sin 1, x = 0, x = 2 and the x–axis is

(A) sin 1

(B) 1 – sin 1

(C) 1 + sin 1

(D) none of these

Q:5. The area bounded by y = f(x), x-axis and the line y = 1, where $\large f(x) = 1 + \frac{1}{x}\int_{1}^{x} f(t) dt $ is

(A) 2(e + 1)

(B) 2(1 – 1/e)

(C) 2(e – 1)

(D) none of these

Q:6. The area cut off from the parabola 4 y = 3 x2 by the straight line 2y = 3x + 12 is

(A) 25 sq. units

(B) 27 sq. units

(C) 36 sq. units

(D) 16 sq. units

Q:7.The area bounded by the curve y = x2 + 2x + 1, the tangent at (1, 4) and the y–axis is

(A) 1

(B) 1/2

(C) 1/3

(D) 1/4

Q:8. If f (x) = x – 1 and g (x) = |f (|x|) – 2|, then the area bounded by y = g (x) and the curve
x2 – 4y + 8 = 0 is equal to

(A) $\frac{4}{3} (4\sqrt{2}-5) $

(B) $\frac{4}{3} (4\sqrt{2}-3) $

(C) $\frac{8}{3} (4\sqrt{2}-3) $

(D) $\frac{8}{3} (4\sqrt{2}-5) $

Q:9. The area of the region bounded by the curve y = 2x – x2 and the line y = x is

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1/6

Q:10. The area of the smaller region bounded by the circle x2 + y2 = 1 and the lines |y| = x +1 is

(A) π/4 – 1/2

(B) π/2 – 1

(C) π/2

(D) π/2 + 1

Answer:
1. (B) 2. (A)  3. (A) 4. (A)  5. (B)
6. (B) 7. (C) 8. (A)  9. (D) 10. (B)

Q:11. Area bounded by the curves $\large y = sin\frac{\pi x}{2}$ and y = x3 is equal to

(A) $\large \frac{4-\pi}{\pi} sq. units $

(B) $\large \frac{4-\pi}{2 \pi} sq. units $

(C) $\large \frac{8-\pi}{\pi} sq. units $

(D) $\large \frac{8-\pi}{2 \pi} sq. units $

Q:12. The area defined by |2x + y| + |x – 2y|  ≤  4 in the x–y coordinate plane is

(A) 32

(B)32/5

(C) 16

(D) none of these

Q:13. Area of the parabolic segment cut by the straight line y = 2x + 3 of the parabola y = x2is

(A) 31/3 sq. units

(B) 32/3 sq. units

(C) 20/3 sq. units

(D) 25/3 sq. units

Q:14. The area bounded by y = min { x – [x] , –x – [–x] } and the x–axis is

(A) 1/2

(B) 1

(C) 2

(D) none of these

Q:15. The area common to the circle x2 + y2 = 64 and the parabola y2 = 12x is equal to

(A) $\large \frac{16}{3}(4\pi + \sqrt{3}) $

(B) $\large \frac{16}{3}(8\pi – \sqrt{3}) $

(C) $\large \frac{16}{3}(4\pi – \sqrt{3}) $

(D) none of these

Q:16. The area bounded by y = 2 – |2-x| , y = 3/|x| is

(A) $\large \frac{5 – 4ln2}{3} $

(B) $\large \frac{2 – ln3}{2} $

(C) $\large \frac{4 – 3 ln3 }{2} $

(D) None of these

Q:17. The area of the region bounded by the curves y = x2 and $\large y = \frac{2}{(1 + x^2)} $ is

(A) π

(B) π – 1/2

(C) π – 2/3

(D) none of these

Q:18. The area enclosed in the region $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} \le 1 $ and $\large \frac{x}{a} + \frac{y}{b} \ge 1 $ is

(A) $\large \frac{\pi a b}{4}- \frac{1}{2}a b $

(B) $\large \frac{\pi a b}{4} $

(C) πab

(D) none of these

Q:19. Area enclosed by $\large (y-sin^{-1})^2 = x – x^2 $ is equal to,

(A) π/2 sq. units

(B) π/4 sq. units

(C) π/8 sq. units

(D) None of these

Q:20. The area enclosed by y = ln x, its normal at (1, 0) and y–axis is

(A) 1/2

(B) 3/2

(C) Not defined

(D) none of these

Answer:
11. (D) 12. (B) 13. (B) 14. (A) 15. (A)
16. (C) 17. (C) 18. (A) 19. (B) 20. (B)