13 Jan 2021: The Hindu Analysis UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 13th January 2021. Important news and views to... View Article
A Spherical Iron Ball 10cm In Radius Is Coated With A Layer Of Ice Of Uniform Thickness 1) (1 / 54Ï€) cm/min 2) (5 / 6Ï€) cm/min 3) (1 / 36Ï€) cm/min 4) (1 / 18Ï€) cm/min Solution: (4) (1 / 18Ï€) cm/min dV / dt = 50 cm3/min... View Article
A Point On The Parabola Y 2 18x At Which The Ordinate Increases At Twice The Rate 1) (9 / 8, 9 / 2) 2) (2, - 4) 3) (- 9 / 8, 9 / 2) 4) (2, 4) Solution: (1) (9 / 8, 9 / 2) y2 = 18x dy / dt = 2 (dx / dt) 2y (dy /... View Article
A Particle Moves In A Straight Line So That S Root T Then Its Acceleration Is Proportional To 1) velocity 2) (velocity)3/2 3) (velocity)3 4) (velocity)2 Solution: (3) (velocity)3 s = √t = t1/2 v = ds / dt = (1 / 2) t-½... View Article
If The Distance S Metre Traversed By A Particle In T Seconds Is Given By 1) 3 2) –2 3) –3 4) 2 Solution: (3) –3 s = t3 – 3t2 ds / dt = v = 3t2 - 6t d2s / dt2 = a = 6t - 6 a = 0 6t - 6 = 0 t = 1 v... View Article
Gas Is Being Pumped Into A Spherical Balloon At The Rate Of 30 Ft 3 Min 1) (1 / 30Ï€) ft/min 2) (1 / 15Ï€) ft/min 3) (1 / 20) ft/min 4) (1 / 25) ft/min Solution: (1) (1 / 30Ï€) ft/min dV / dt = 30 ft3/min... View Article
The Position Of A Point In Time T Is Given By X A Bt Ct 2 Y At Bt 2 1) b – c 2) b + c 3) 2b – 2c 4) 2√b2 + c2 Solution: (4) 2√b2 + c2 x = a + bt – ct2 y = at + bt2 Acceleration in x-direction... View Article
Moving Along The X Axis Are Two Points With X 10 6t X 3 T 2 1) 16 cm/sec 2) 20 cm/sec 3) 8 cm/sec 4) 12 cm/sec Solution: (3) 8 cm/sec 10 + 6t = 3 + t2 t2 - 6t - 7 = 0 (t - 7) (t + 1) = 0... View Article
The Rate Of The Change Of The Surface Area Of A Sphere Of Radius R When The 1) 1 / r 2) 1 / r2 3) r 4) r2 Solution: (3) r S = 4Ï€r2 [surface area of the sphere] dr / dt = 2 ds / dt = 4Ï€ (2r) (dr / dt) =... View Article
The Sides Of An Equilateral Triangle Are Increasing At The Rate Of 2 Cm Sec 1) √3 sq.unit/sec 2) 10 sq. unit/sec 3) 10√3 sq.unit/sec 4) 10 / √3 sq.unit/sec Solution: (3) 10√3 sq.unit/sec Area of an... View Article
A Particle Is Moving Along The Curve X At 2 Bt C If Ac B 2 Then The Particle 1) Rotation 2) Velocity 3) Acceleration 4) retardation Solution: (3) Acceleration x = at2 + bt + c v = dx / dt = 2at + b a = dv... View Article
The Speed V Of A Particle Moving Along A Straight Line Is Given By 1) bx 2) x / a 3) x / b 4) x / ab Solution: (3) x / b a = dv / dt a + bv2 = x2 0 + b [2v dv / dt] = 2x (dx / dt) bv (dv / dt)... View Article
The Rate Of Change Of Root Of X 2 16 With Respect To X X 1 At X 3 Is 1) 2 2) 11 / 5 3) 12 / 5 4) –3 Solution: (3) 12 / 5 Let y = √(x2 + 16) and z = [x/(x – 1)] (dy / dx) = x (x2 + 16) – (1 / 2) and... View Article
The Distance S Metre Covered By A Body In T Seconds Is Given By 1) 1 sec 2) 3 / 4 seconds 3) 4 / 3 seconds 4) 4 sec Solution: (3) 4 / 3 seconds s = 3t2 – 8t + 5 ds / dt = 6t - 8 ds / dt = 0... View Article
A Particle Moves Along A Straight Line So That Is Distance S In Time T Sec Is 1) 2 sec 2) 3 sec 3) 4 sec 4) 6 sec Solution: (1) 2 sec s = t + 6t2 – t3 ds / dt = 1 + 12t - 3t2 d2s / dt2 = 12 - 6t ds2 /... View Article
A Stone Thrown Vertically Upwards Rises S Metre In T Seconds Where S 80t 16t 2 1) 8 m/sec 2) 16 m/sec 3) 32 m/sec 4) 64 m/sec Solution: (2) 16 m/sec s = 80t – 16t2 v = ds / dt = 80 - 32t At t = 2 seconds,... View Article
If The Rate Of Increase Of The Area Of A Circle Is Not Constant But The Rate Of 1) As the square of the perimeter 2) Inversely as the perimeter 3) As the radius 4) Inversely as the radius Solution: (3) As the... View Article
If The Path Of A Moving Point Is The Curve X At Y B Sin At Then Its 1) Is constant 2) Varies as the distance from the axis of y 3) Varies as the distance from the axis of y 4) Varies as the distance of... View Article
If The Volume Of A Spherical Balloon Is Increasing At The Rate 900 Cm 3 Sec 1) 22 / 7 2) 22 3) 7 / 22 4) None of these Solution: (3) 7 / 22 dv / dt = 900 cm3/sec Volume of sphere = (4 / 3) πr3 dv / dt =... View Article
A Particle Moves So That S 6 48t T 3 The Direction Of Motion Reverses 1) 63 2) 104 3) 134 4) 288 Solution: (3) 134 S = 6 + 48t – t3 v = dS / dt = 0 + 48 − 3t2 When direction of motion reverses,... View Article