Which frequency range is used for optical communication?
1) 100000 GHz to 400000 GHz 2) 200 kHz to 3 MHz 3) 30000 GHz to 6000 GHz 4) None... View Article
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If an equation of a tangent to the curve, y = cos(x + y), -1 ≤ x ≤ 1+ π, is x + 2y = k then k is equal to :
(a) 1 (b) 2 (c) π/2 (d) π/4 Solution: Let y = cos (x + y) ..(i) Differentiate w.r.t.x dy/dx... View Article
A lamp is 50 ft. above the ground. A ball is dropped from the same height from a point 30 ft. away from the light pole. If ball falls a distance s = 16t2 ft. in t seconds, then the speed of the shadow of the ball moving along the ground 1/2 s later is
(a) – 1500 ft/s (b) 1500 ft/s (c) – 1600 ft/s (d) 1600 ft/s Solution: At time t, ball drops... View Article
The velocity v of a particle at any instant t moving in a straight line is given by v = s + 1 where s metre is the distance travelled in t seconds. What is the time taken by the particle to cover a distance of 9m?
(a) 1 s (b) (log 10) s (c) 2 (log 10) s (d) 10 s Solution: Given v = s+1... View Article
What is the slope of the tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at t = 2?
(a) 7/6 (b) 6/7 (c) 1 (d) 5/6 Solution: Given x = t2 + 3t – 8 dx/dt = 2t... View Article
What is the slope of the tangent to the curve y = sin-1 (sin2x) at x = 0?
(a) 0 (b) 1 (c) 2 (d) None of these Solution: Given y = sin-1 (sin2x) Differentiate w.r.t.x dy/dx =... View Article
The equation of one of the tangents to the curve y = cos (x +y), -2π ≤ x ≤ 2π that is parallel to the line x + 2y = 0, is
(a) x + 2y = 1 (b) x + 2y = π/2 (c) x + 2y = π/4 (d) None... View Article
Let f and g be functions from the interval [0, ∞) to the interval [0, ∞), f being an increasing and g being a decreasing function. If f{g(0)} = 0 then
(a) f{g(x)} ≥ f{g(0)} (b) g{f (x)} ≤ g{f (0)} (c) f {g(2)} = 7 (d) None of these Solution:... View Article
The largest area of a trapezium inscribed in a semicircle of radius R, if the lower base is on the diameter, is
(a) 3√3R2/4 (b) (√3/2)R2 (c) (3√3/8)R2 (d) R2 Solution: ABCD is the trapezium. Centre of semicircle is O. ∠ADB =... View Article
If at any instant t, for a sphere, r denotes the radius, S denotes the surface area and V denotes the volume, then what is dV/dt equal to?
(a) ½ S (dr/dt) (b) ½ r (dS/dt) (c) r dS/dt (d) ½ r2 dS/dt Solution: Surface area of sphere... View Article
The function f(x) = 2 log (x – 2) – x2 + 4x + 1 increases on the interval
(a) (1, 2) (b) (2, 3) (c) (5/2, 3) (d) (2, 4) Solution: Given f(x) = 2 log (x –... View Article
The straight line x/a + y/b = 2 touches the curve (x/a)n + (y/b)n = 2 at the point (a, b) for
(a) n = 1, 2 (b) n = 3, 4, -5 (c) n = 1, 2, 3 (d) any value... View Article
The number of solutions of the equation 3 tan x + x3 = 2 in (0, π/4) is
(a) 0 (b) 1 (c) 2 (d) 3 Solution: Let f(x) = 3 tan x + x3 – 2 Differentiate... View Article
What is the minimum value of px + qy (p > 0, q > 0) when xy = r2 ?
(a) 2r√(pq) (b) 2pq√r (c) – 2r√(pq) (d) 2 rpq Solution:Given xy = r2 => y = r2/x Let S... View Article
The curve y = xex has minimum value equal to
(a) -1/e (b) 1/e (c) -e (d) e Solution: Given y = xex Differentiate w.r.t.x => dy/dx = ex +... View Article
The number of tangents to the curve x3/2 + y3/2 = 2a3/2, a > 0, which are equally inclined to the axes, is
(a) 2 (b) 1 (c) 0 (d) 4 Solution: Given curve x3/2 + y3/2 = 2a3/2 ..(i) Differentiate w.r.t.x =>... View Article
The motion of a particle is described as s = 2 – 3t + 4t3. What is the acceleration of the particle at the point where its velocity is zero?
(a) 0 (b) 4 unit (c) 8 unit (d) 12 unit Solution: Given s = 2 – 3t + 4t3... View Article
The function f (x) = x2/ex monotonically increasing if
(a) x < 0 only (b) x > 2 only (c) 0 < x < 2 (d) x ∈ (-∞,... View Article
The cost of running a bus from A to B is Rs. (av + b/v) where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be Rs. 75 while at 40 km/h, it is Rs. 65. Then the most economical speed (in km/ h) of the bus is :
(a) 45 (b) 50 (c) 60 (d) 40 Solution: Given that cost, C = av+b/v When the bus travels at... View Article
If the curve y = ax2 – 6x + b passes through (0, 2) and has its tangent parallel to the x-axis at x = 3/2 then
(a) a = b = 0 (b) a = b = 1 (c) a = b = 2 (d) a... View Article
