The Slope Of Tangent To The Curve X T 2 3t 8 Y 2t 2 2t 5 At The Point 2 1 Is 1) 22 / 7 2) 6 / 7 3) –6 4) None of these Solution: (2) 6 / 7 x = t2 + 3t – 8, y = 2t2 – 2t – 5 dx / dt = 2t + 3 dy / dt = 4t -... View Article
The Area Of The Triangle Formed By The Coordinate Axes And A Tangent To The Curve 1) a2x1 / y1 2) a2y1 / x1 3) 2a2 4) 4a2 Solution: (3) 2a2 Since y = a2 / x dy / dx = - a2 / x2 At (x1, y1), dy / dx = - a2 /... View Article
The Point On The Curve Y 12x X 3 At Which The Gradient Is Zero Are 1) (0, 2), (2, 16) 2) (0, -2), (2, -16) 3) (2, -16), (-2, 16) 4) (2, 16), (-2, -16) Solution: (4) (2, 16), (-2, -16) y = 12x - x3... View Article
The Population P T At Time Of A Certain Mouse Species Satisfies The Differential Equation 1) 2 ln 18 2) ln 19 3) (1 / 2) ln 18 4) ln 18 Solution: (1) 2 ln 18 [dp (t)] / dt = 0.5 p(t) - 450 ∫850p [2dp / [p - 900]] = ∫0t... View Article
A Spherical Balloon Is Filled With 450 Pi Cubic Meters Of Helium Gas 1) 9 / 7 2) 7 / 9 3) 2 / 9 4) 9 / 2 Solution: dv / dt = - 72 π m3 / min, v0 = 4500π v = (4 / 3) πr3 dv / dt = (4 / 3) π (3r2)... View Article
The Displacement X Of A Particle At Time T Is Given By X At 2 Bt C 1) 4 AC + B2 2) 4 AC - B2 3) 2 AC - B2 4) 2 AC + B2 Solution: (2) 4 AC - B2 x = At2 + Bt + C v = 2At + B v2 = 4A2t2 + 4ABt + B2... View Article
If The Displacement Velocity And Acceleration Of A Particle At Time T 1) f = v3 (d2t / dx2) 2) f = - v3 (d2t / dx2) 3) f = v2 (d2t / dx2) 4) f = - v2 (d2t / dx2) Solution: (2) f = - v3 (d2t / dx2) d2t... View Article
A Ladder 10 M Long Against A Vertical Wall With The Lower And On The Horizontal Ground 1) 4√3 m 2) 5√3 m 3) 5√2 m 4) 8m 5) 6m Solution: (5) 6m x2 + y2 = 102 x2 + y2 = 100 dx / dt = 3 cm/sec dy / dt = 4... View Article
The Radius Of A Cylinder Is Increasing At The Rate Of 3 M Sec And Its Altitude 1) 80 π cu. m/sec 2) 144 π cu. m/sec 3) 80 cu. m/sec 4) 64 cu. m/sec 5) -80 π cu. m/sec Solution: (3) 80 cu. m/sec dr / dt = 3... View Article
If A Particle Moves Such That The Displacement Is Proportional To The 1) Proportion to s2 2) Proportional to 1 / s2 3) Proportional to s 4) Proportional to 1/s 5) constant Solution: (5) constant If... View Article
A Population P T Of 1000 Bacteria Introduced Into The Nutrient Medium Grows 1) 1100 2) 1250 3) 1050 4) 5250 Solution: (3) 1050 p (t) = 1000 + (1000t / 100 + t2) dp / dt = 0 for maximisation [0 + (100 +... View Article
The Diagonal Of A Square Is Changing At A Rate Of 0 5 Cm Sec Then The Rate Of Change 1) 20 √2 cm2/sec 2) 10√2 cm2/sec 3) 1 / [10√2] cm2/sec 4) [10 √2] cm2/sec 5) 5√2 cm2/sec Solution: (2) 10√2 cm2/sec dD / dt =... View Article
If Cot Theta Plus Cot Pi 4 Plus Theta 2 Then 1) 2nπ ± π/6 2) 2nπ ± π/3 3) nπ ± π/3 4) nπ ± π/6 Answer: (4) nπ ± π/6 Solution: Given, cot θ + cot(π/4 + θ) = 2 cot θ + [(cot... View Article
Cos 2x Plus K Sin X 2k Minus 7 Has A Solution For 1) k > 3 2) k < 2 3) k > 3 4) 2 ≤ k ≤ 6 Answer: (4) 2 ≤ k ≤ 6 Solution: Given, cos 2x + k sin x = 2k - 7 Using the... View Article
If Tan Square Theta Minus 1 Plus Root3 Tan Theta Plus Root3 1) nπ + π/4, nπ + π/3 2) nπ - π/4, nπ + π/3 3) nπ + π/4, nπ - π/3 4) nπ - π/4, nπ - π/3 Answer: (1) nπ + π/4, nπ + π/3 Solution:... View Article
If Cot Theta Plus Tan Theta 2 Cosec Theta Then 1) nπ ± π/3 2) nπ ± π/6 3) 2nπ ± π/3 4) 2nπ ± π/6 Answer: (3) 2nπ ± π/3 Solution: Given, cot θ + tan θ = 2 cosec θ (cos θ/sin θ)... View Article
If Cos Theta Plus Sec Theta 5 2 Then The General Value Of Theta 1) nπ ± π/3 2) 2nπ ± π/6 3) nπ ± π/6 4) 2nπ ± π/3 Answer: (4) 2nπ ± π/3 Solution: Given, cos θ + sec θ = 5/2 cos θ + (1/cos θ) =... View Article
If 1 Minus Tan Square Theta Sec Square Theta 1 2 Then 1) nπ ± π/6 2) nπ + π/6 3) 2nπ ± π/6 4) None of these Answer: (1) nπ ± π/6 Solution: Given, (1 - tan2θ)/sec2θ = 1/2 Using the... View Article
If Cos 7theta Cos Theta Minus Sin 4theta Then 1) nπ/4, nπ/4 + π/18 2) nπ/3, nπ/3 + (-1)n π/18 3) nπ/4, nπ/3 + (-1)n π/18 4) nπ/6, nπ/3 + (-1)n π/18 Answer: (4) nπ/4, nπ/3 + (-1)n... View Article
If A1 A2 A3 An Are In Ap With Common Difference 5 And If Aiaj 1 Then Tan 1 5 1 A1a2 Tan 1 5 1 A2a3 Tan 1 5 Is Equal To (1) tan-1 5/(1+anan-1) (2) tan-1 5a1/(1+ana1) (3) tan-1 (5n-5)/(1+ana1) (4) none of these Solution: Given a1, a2, a3 ...an... View Article