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
If The Distance S Travelled By A Particle In Time T Is S A Sin T B Cos 2t 1) a 2) – a 3) 4b 4) – 4b Solution: (4) – 4b s = a sin t + b cos 2t ds / dt = a cost - 2b (sin 2t) d2s / dt2 = - a sint - 4b cos... View Article
If The Edge Of A Cube Increases At The Rate Of 60 Cm Per Second At What Rate The 1) 48600 cu cm per sec 2) 1458000 cu cm per sec 3) 4374000 cu cm per sec 4) None of the above Solution: (2) 1458000 cu cm per sec... View Article
A Ladder Is Resting With The Wall At An Angle Of 30 Degrees A Man Is Ascending 1) 3 ft/sec 2) (3 / 2) ft/sec 3) (2 / 4) ft/sec 4) (3 / √2) ft/sec Solution: (2) (3 / 2) ft/sec The rate of approaching the wall... View Article
If By Dropping A Stone In A Quiet Lake A Wave Moves In Circle At A Speed 1) 220 sq. cm/sec 2) 110 sq. cm/sec 3) 35 sq. cm/sec 4) 350 sq. cm/sec Solution: (1) 220 sq. cm/sec dr / dt = 3.5 cm/sec r = 10... View Article
A Rectangle Of Perimeter 24 Inches Is Rotated About One Of Its Sides So As To Form A Cylinder 1) 8, 4 2) 4, 4 3) 8, 8 4) None of these Solution: (1) 8, 4 V = πx2y given x + y = 12 V = πx2 (12 - x) V = 12πx2 - πx3 dV /... View Article
Water Is Flowing Into A Vertical Cylindrical Tank Of Radius 2ft At The Rate Of 8 Cubic Ft 1) π / 2 2) 2 / π 3) 2 4) None of these Solution: (2) 2 / π V = πr2h = 4πh dV / dt = 4π (dh / dt) (dh / dt) = (1 / 4π) (dV / dt)... View Article
If The Distance Travelled By A Point In Time T Is S 180t 16 T 2 Then The Rate 1) – 16 t unit 2) 48 unit 3) – 32 unit 4) None of these Solution: (3) – 32 unit s = 180t – 16 t2 ds / dt = 180 - 32t d2s / dt2... View Article
A Particle Is Moving In A Straight Line Its Displacement At Time T Is Given By 1) –2, –5 2) 2, 6 3) –2, 8 4) 2, 8 Solution: (1) –2, –5 Displacement s = - 4t2 + 2t Now velocity v = - 8t + 2 and its... View Article
Two Automobiles Start From A Point A At The Same Time One Travels Towards The West 1) 5√193 2) √193 3) 5 / √193 4) None of these Solution: (1) 5√193 At time t hours, the distance d is d2 = (60t)2 + (35t)2 When... View Article
Radius Of A Circle Is Increasing Uniformly At The Rate Of 3 Cm Sec 1) π cm2/s 2) 2π cm2/s 3) 10π cm2/s 4) None of these Solution: (4) None of these Let r be the radius of the circle. Rate of... View Article