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How do you plot a hysteresis curve

When a substance is placed in a magnetic field it gets magnetised. The molecular magnets or magnetic dipoles orient themselves in the direction... View Article

Two pillars of equal height stand on either side of a road-way which is 60 m wide. At a point in the road-way between the pillars, the elevation of the top of pillars is 60° and 30°. The height of the pillars is

1) 15√3 m 2) 15/√3 m 3) 15 m 4) 20 m Solution: (1) 15√3 m AB and CD are the two pillars. BD = 60m ∠APB = 60o and ∠CPD = 30o In triangle... View Article

The angle of elevation of the top of the tower observed from each of the three points A B and C on the ground forming a triangle is the same i.e. ∠α. If R is the circumradius of the ∆A BC, then the height of the tower is

1) R sin α 2) R cos α 3) R cot α 4) R tan α Solution: (4) R tan α The triangle formed on the ground be ABC. From the figure, PQ is the tower... View Article

A person standing on the bank of the river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60 degrees. When he was 40m away from the bank he found the angle of elevation to be 30 degrees. Find the width of the river.

1) 20 m 2) 10 m 3) 5 m 4) 1 m Solution: (1) 20 m Let x be the width of the river and h be the height of the tree. tan 60o = h / x √3 = h / x... View Article

The angle of elevation of an object from a point on the level ground is α. Moving d metres on the ground towards the object, the angle of elevation is found to be β. Then, the height (in metres) of the object is

1) d tan α 2) d cot β 3) d / (cot α + cot β) 4) d / (cot α - cot β) Solution: (3) d / (cot α + cot β) Assume the height of the object to... View Article

The angle of elevation of the Sun, if the length of the shadow of a tower is √3 times the height of the pole, is

1) 150o 2) 30o 3) 60o 4) 45o Solution: (2) 30o From the figure, let AB be the pole and BC - the shadow. θ is the angle of elevation. AB... View Article

A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window is 64 m, then the distance between the two houses is

1) 48 m 2) 36 m 3) 54 m 4) 72 m Solution: (1) 48 m Assume d to be a distance between the 2 houses. From the figure, in triangle BCD, 64... View Article

From a point on the ground, the angle of elevation of the top of a tower is observed to be 60 degrees. From a point, 40m vertically above the first point of observation, the angle of elevation of the top of the tower is 30 degrees. The horizontal distance from the point of observation is

1) - 20√3 m 2) √3/20 m 3) - √3/20 m 4) 20√3 m Solution: (4) 20 √3 m ∠QAP = 60o ∠QBR = 30o AB = PR = 40m AP = BR In triangle QAP, tan... View Article

The horizontal distance between two towers is 60 m and the angle of depression of the top of the first tower as seen from the top of the second is 30°. If the height of the second tower is 90 m, then the height of the first tower is

1) 90 m 2) (150 - 60√3)m 3) (150 - 20√3)m 4) None of these Solution: (4) None of these From the figure, DE and AB are the first and... View Article

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower and the angle of elevation of the top of the first tower from A or B is 30°. The height of the tower is

1) 2a / √3 2) 2a √3 3) a / √3 4) √3 Solution: (3) a / √3 Let OP be the tower. OAB forms an equilateral triangle. OA = OB = AB = a In... View Article

A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is 60. If the distance between the two houses is 6 m, then the height of the first house is

1) 8√3 m 2) 6√3 m 3) 4√3 m 4) None of these Solution: (1) 8 √3 m From the figure, ∠DBC = 60o, ∠ADB = 90o, ∠EDB = ∠DBC = 60o ∠ADB = ∠ADE... View Article

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 30°. After walking 120 m towards it on level ground, the elevation is found to be 60°. Then, the height (in metres) of the object is

1) 120 2) 60√3 3) 120√3 4) 60 Solution: (2) 60 √3 tan 60o = h / d tan 30o = h / [d + 120] 3 = [d + 120] / d d = 60 h = 60 √3... View Article

From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be 30° and 60°, respectively. The height (in km) at which the aeroplane is flying, is

1) 4/√3 2) √3/2 3) 2/√3 4) 2 Solution: (2) √3 / 2 In triangle BCD, √3 = h / x x = h / √3 tan 30o = h / [x + 1] 1 / √3 = h / [x + 1] (h... View Article

A flagpole stands on a building of height 450 ft and an observer on level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is 30° and the height of the flagpole is 50 ft. If 0 is the angle of elevation of the top of the flagpole, then tanθ is

1) 4/3√3 2) √3/2 3) 9/2 4) √3/5 5) (4√3+1)/6 Solution: (1) 4 / [3√3] In triangle DCE, tan 30o = 150 / CD CD = √3 * 150 In triangle... View Article

The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are α, 2α and 3α, respectively. If AB = α, then the height of the tower is

1) a tan α 2) a sin α 3) a sin 2α 4) a sin 3α Solution: (3) a sin 2α In triangle BCE, using sine rule, BE / [sin (180 - 3α)] = CE / [sin... View Article

The shadow of the tower standing on level ground is x meters long when the sun’s altitude is 30°, while it is y meters long when the altitude is 60°. If the height of the tower is 45.√3/2 m then x – y is equal to

1) 45 m 2) 45 √3 m 3) 45/√3 m 4) 45 [√3 / 2] m Solution: (1) 45 m x = (45) * (3 / 2) y = 45 * (1 / 2) x - y = 45... View Article

A round balloon of radius r subtends an angle ɑ at the eye of the observer, while the angle of elevation of its centre is β. The height of the centre of the balloon is

1) r cosec ɑ sin (β / 2) 2) r sin ɑ cosec (β / 2) 3) r sin (ɑ / 2) cosec (β) 4) r cosec (ɑ / 2) sin (β) Solution: (4) r cosec (ɑ / 2) sin (β)... View Article

The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are 30° and 60°. If the height of the cliff is 500 m, then the diameter of the base of the cliff is

1) 2000/√3 m 2) 1000/√3 m 3) 2000/√2 m 4) 1000√3 m Solution: (1) 2000 / √3 m In triangle AEC, tan 60o = 500 / d1 d1 = 500 / √3 m In... View Article

From the top of a hill h meters high, the angles of depressions of the top and the bottom of a pillar are α and β, respectively. The height (in metres) of the pillar is

1) h [tan β - tan α] / [tan β] 2) h [tan α - tan β] / [tan α] 3) h [tan α + tan β] / [tan β] 4) h [tan α + tan β] / [tan α] Solution: (1) h... View Article

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of point A from a certain point on the ground is 60°. It moves away from the pole along the line BC to a point D such that CD = 7 m. From D, the angle of elevation of the point A is 45°. Then, the height of the pole is

1) (7 √3 / 2) [1 / (√3 + 1)] m 2) (7 √3 / 2) [1 / (√3 - 1)] m 3) (7 √3 / 2) [(√3 + 1)] m 4) (7 √3 / 2) [(√3 - 1)] m Solution: (3) (7 √3 / 2)... View Article

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