A T.V. tower has a height of 200 m. By how much the height of the tower is increased to triple its coverage range?
1) 1600 m 2) 800 m 3) 1800 m 4) 600 m Answer: 1) 1600 m Solution: Here, h=200m,as d=√2hr and... View Article
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In order to cover a circular region of radius 128 km by a TV transmitter, what must be the height of the transmitting antenna?
1) 79 m 2) 1050 m 3) 1280 m 4) 1560 m Answer: 3) 1280 m Solution: Area of circular region... View Article
A rod AB of length 16 cm rests between the wall AD and a smooth peg, 1 cm from the wall, and makes an angle θ with the horizontal. The value of θ for which the height of G, the midpoint of the rod above the peg is minimum, is
(a) 150 (b) 300 (c) 600 (d) 750 Solution: We have AC = sec θ, AG = 8 CG =... View Article
The difference between greatest and least value of f(x) = 2 sin x + sin 2x, x ∈ [0, 3π/2] is
(a) 3√3/2 (b) 3√3/2 – 2 (c) (3√3/2) + 2 (d) none of these Solution: f(x) = 2 sin x... View Article
If OT is the perpendicular drawn from the origin to the tangent at any point t to the curve x = a cos3 t, y = a sin3 t, then OT is equal to
(a) a sin 2t (b) (a/2) sin 2t (c) 2a sin 2t (d) 2a Solution: Given x = a cos3... View Article
The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs Rs. 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to Rs. 300 per hour is
(a) 10 (b) 20 (c) 30 (d) 40 Solution: Let the speed of the train be v and distance to... View Article
The profit function, in rupees, of a firm selling x items (x≥ 0) per week is given by P(x) = – 3500 + (400 – x)x. How many items should the firm sell so that the firm has maximum profit?
(a) 400 (b) 300 (c) 200 (d) 100 Solution: Given P(x) = – 3500 + (400 – x)x = -3500... View Article
If f(x) = x ln x, then f(x) attains minimum value at which one of the following points?
(a) x = e–2 (b) x = e (c) x = e–1 (d) x = 2e–1 Solution: Given f(x) =... View Article
Area of the triangle formed by the normal to the curve x = esin y at (1, 0) with the coordinate axes is :
(a) 1/4 (b) 1/2 (c) 3/4 (d) 1 Solution: Given x = esin y Take log on both sides log... View Article
If the function y = (ax+b)/(x-1)(x-4) has turning point at P(2, -1), then
(a) a = b = 1 (b) a = b = 0 (c) a = 1, b = 0 (d)... View Article
A curve is represented by the equation x = sec2t and y = cot t, where t is a parameter. If the tangent at the point P on the curve where t = π/4 meets the curve again at the point Q, then |PQ| is equal to
(a) 5√3/2 (b) 5√5/2 (c) 2√5/3 (d) 3√5/2 Solution: Given x = sec2t y = cot t dx/dt = 2... View Article
A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 900. What is the maximum area which can be enclosed inside the quadrilateral?
(a) 68 cm2 (b) 70 cm2 (c) 71.25 cm2 (d) 72. 25 cm2 Solution: Let the length of the quadrilateral... View Article
How many tangents are parallel to x-axis for the curve y = x2 – 4x + 3?
(a) 1 (b) 2 (c) 3 (d) No tangent is parallel to x-axis Solution: Given y = x2 – 4x... View Article
The total number of parallel tangents of f1(x)= x2 – x + 1 and f2(x) = x3 – x2 -2x + 1 is
(a) 2 (b) 0 (c) 1 (d) infinite Solution: Given f1(x)= x2 – x + 1 ..(i) f2(x) = x3... View Article
f(x) = log(π+ x)/log (e+x) is
(a) increasing on [0, ∞) (b) decreasing on [0, ∞) (c) increasing on [0, π/e], decreasing on [π/e, ∞] (d)... View Article
Find the minimum value of the function 40/(3x4 + 8x3 -18x2 +60).
(a) 1/3 (b) 2/3 (c) 4/3 (d) 5/3 Solution: Let y = 40/(3x4 +8x3 -18x2 +60) For y to be... View Article
If the rate of change in volume of a spherical soap bubble is uniform, then the rate of change of the surface area varies as
(a) square of radius (b) square root of radius (c) inversely proportional to radius (d) cube of the radius Solution:... View Article
A stone thrown vertically upward satisfies the equation s = 64t – 16t2, where s is in meter and t is in second. What is the time required to reach the maximum height?
(a) 1s (b) 2s (c) 3s (d) 4s Solution: Given s = 64t – 16t2 Differentiate w.r.t.t ds/dt = 64... View Article
The equation of the normal to the curve y = |x2 – | x|| at x = -2.
(a) 3y = x + 8 (b) x = 3y + 4 (c) y = 2x +8 (d) y =... View Article
The approximate value of (0.007)13
(a) 23/120 (b) 27/120 (c) 19/120 (d) 17/120 Solution: Let y = f(x) = x1/3 f’(x) = ⅓ x-⅔ f(x... View Article
