Archives

The area ( in sq units ) of the region bounded by the curves 2x = y² – 1 and x = 0 is

1) 1/3 sq units 2) 2/3 sq units 3) 1 sq units 4) 2 sq units Solution: (2) 2/3 sq units... View Article

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to

1) 4/3 sq units 2) 5/3 sq units 3) 1/3 sq units 4) 2/3 sq units Solution: (1) 4/3 sq units... View Article

The area of the region between the curves y = √(1 + sin x) / (cos x) and y = √(1 – sin x) / cos x bounded by the lines x = 0 and x = π / 4 is

1) ∫0√2-1 {t / [(1 + t2) (√1 - t2)]} dt 2) ∫0√2-1 {4t / [(1 + t2) (√1 - t2)]} dt 3) ∫0√2+1 {4t / [(1 + t2) (√1 - t2)]} dt 4) ∫0√2+1 {t /... View Article

The area bounded by the curve y = x|x|, x-axis and the ordinates x = 1, x = -1 is given by

1) 0 2) 1/3 3) 2/3 4) None of these Solution: (3) ⅔... View Article

The area of the region bounded by the curves y = e^x, y = log_e x and lines x = 1, x = 2 is

1) (e - 1)2 2) e2 - e + 1 3) e2 - e + 1 - 2 loge 2 4) e2 + e - 2 loge 2 Solution: (3) e2 - e + 1 - 2 loge 2... View Article

The line x = π/4 divides the area of the region bounded by y = sin x, y = cos x and x-axis (0 ≤ x ≤ π/2) into two regions of areas A₁ and A₂. Then, A₁ : A₂ equals to

1) 4 : 1 2) 3 : 1 3) 2 : 1 4) 1 : 1 Solution: (4) 1 : 1... View Article

If f (x) is continuous function such that the area bounded by the curve y = f (x), the x-axis and the lines x = a and x = 0 is (a² / 2) + (a / 2) sin a + (π / 2) cos a. Then the value of f (π / 2) is

1) 1/2 2) a/2 3) a2/2 4) π/2 Solution: (1) ½... View Article

The area of the region bounded by curves y = x log x and y = 2x – 2x² is

1) 1/2 sq units 2) 3/12 sq units 3) 7/12 sq units 4) None of these Solution: (3) 7/12 sq units... View Article

The area bounded by = |sin x|, x-axis and the lines |x| = π is 1) 2 sq units 2) 3 sq units 3) 4 sq units 4) None of these

Solution: (3) 4 sq units |x| = π x = - π, π Area = 2 ∫0π sin x dx = 2 [- cos x]0π = - 2 [cos x]0π = - 2 (- 1 - 1) = 4... View Article

The given figure shows a ∆AOB and the parabola y = x². The ratio of the area of the ∆AOB to the area of the region AOB of the parabola y = x² is equal to

1) 3/5 2) 3/4 3) 7/8 4) 5/6 5) 2/3 Solution: (2) ¾... View Article

The area bounded between the parabola y² = 4x and the line y = 2x – 4 is equal to

1) 17/3 sq units 2) 19/3 sq units 3) 9 sq units 4) 15 sq units Solution: (3) 9 sq units... View Article

The area bounded by the curves y = √5 – x² and y = |x – 1| is

1) [(5π / 4) - 2] square units 2) [(5π - 2) / 4] square units 3) [(5π - 2) / 2] square units 4) [(π / 2) - 5] square units Solution:... View Article

The area of the region bounded by the parabola (y – 2)² = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is

1) 6 sq units 2) 9 sq units 3) 12 sq units 4) 3 sq units Solution: (2) 9 sq units... View Article

M	T	W	T	F	S	S
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Archives

The area ( in sq units ) of the region bounded by the curves 2x = y² – 1 and x = 0 is

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to

The area of the region between the curves y = √(1 + sin x) / (cos x) and y = √(1 – sin x) / cos x bounded by the lines x = 0 and x = π / 4 is

The area bounded by the curve y = x|x|, x-axis and the ordinates x = 1, x = -1 is given by

The area of the region bounded by the curves y = e^x, y = log_e x and lines x = 1, x = 2 is

The line x = π/4 divides the area of the region bounded by y = sin x, y = cos x and x-axis (0 ≤ x ≤ π/2) into two regions of areas A₁ and A₂. Then, A₁ : A₂ equals to

If f (x) is continuous function such that the area bounded by the curve y = f (x), the x-axis and the lines x = a and x = 0 is (a² / 2) + (a / 2) sin a + (π / 2) cos a. Then the value of f (π / 2) is

The area of the region bounded by curves y = x log x and y = 2x – 2x² is

The area bounded by = |sin x|, x-axis and the lines |x| = π is 1) 2 sq units 2) 3 sq units 3) 4 sq units 4) None of these

The given figure shows a ∆AOB and the parabola y = x². The ratio of the area of the ∆AOB to the area of the region AOB of the parabola y = x² is equal to

The area bounded between the parabola y² = 4x and the line y = 2x – 4 is equal to

The area bounded by the curves y = √5 – x² and y = |x – 1| is

The area of the region bounded by the parabola (y – 2)² = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is

The area of the region bounded by the curves y² = x and y = |x| is

The area (in sq units) of the plane region bounded by the curve x = y² – 2 and the line y = -x is

The area enclosed by y = 3x – 5, y = 0, x = 3 and x = 5 is

Match List-I with List-II.

Which among the following pairs of Vitamins is stored in our body relatively for longer duration?

In chromatography technique, the purification of a compound is independent of:

Which of the following is Lindlar catalyst?

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