A Particle Moves Along A Straight Line According To The Law S 16 2t 3t 3 Where S Metres Is The Distance Of The Particle From A Fixed Point At The End Of T Sec 1) 36 m/s2 2) 34 m/s2 3) 36 m 4) None of these Solution: (1) 36 m / s2 s = 16 – 2t + 3t3 a = d2s / dt2 ds / dt = -2 + 9t2... View Article
If The Distance S Covered By A Particle In Time T Is Proportional To The Cube Root Of Its Velocity Then The Acceleration Is 1) a constant 2) proportional to s3 3) proportional to 1/s3 4) proportional to s5 5) proportional to 1/s5 Solution: (4)... View Article
Ob And Oc Are Two Roads Enclosing An Angle Of 120 Degrees X And Y Start From O At The Same Time 1) √37 km/h 2) 37 km/h 3) 13 km/h 4) √13 km/h Solution: (1) √37 km / h The speed of x = 4 km / h and y = 3 km / h Let the shortest... View Article
A Point On The Parabola Y 2 18x At Which The Ordinate Increases At Twice The Rate Of The Abscissa Is 1) (2, 4) 2) (2, -4) 3) (-9/8, 9/2) 4) (9/8, 9/2) Solution: (4) (9 / 8, 9 / 2) y2 = 18x dy / dt = 2 (dx / dt) 2y (dy / dt) = 18... View Article
The Radius Of A Cylinder Is Increasing At The Rate Of 3 M S And Its Altitude Is Decreasing At The Rate Of 4 M S The Rate Of Change Of Volume When Radius Is 4 M And Altitude Is 6 M Is 1) 80 π cu m/s 2) 144 π cu m/s 3) 80 cu m/s 4) 64 cu m/s Solution: (1) 80πm3 / s dr / dt = 3 m / s dh / dt = -4 m / s V = πr2h... View Article
If A Particle Moves Along A Straight Line With The Law Of Motion Given By S 2 At 2 2bt C Then The Acceleration Varies Are 1) 1/s3 2) 1/s 3) 1/s4 4) 1/s2 Solution: (1) 1 / s3 s2 = at2 + 2bt + c s = √at2 + 2bt + c A = ks-3 A = d2s / dt2 ds / dt =... View Article
A Man Of 2 M Height Walks At A Uniform Speed Of 6 Km H Away From A Lamp Post Of 6 M Height The Rate At Which The Length Of His Shadow Increase Is 1) 2 km/h 2) 1 km/h 3) 3 km/h 4) 6 km/h Solution: (3) 3 km / h Let the length of the shadow be ‘y’ m and the distance from the... View Article
A Spherical Iron Ball Of Radius 10 Cm Coated With A Layer Of Ice Of Uniform Thickness Melts At A Rate Of 100 Pi Cubic Cm Min The Rate At Which The Thickness Layer Decreases When The Thickness Of Ice Is 5 Cm Is 1) 1 cm/min 2) 2 cm/min 3) 1/376 cm/min 4) 5 cm/min 5) 3 cm/min Solution: (1) 1 cm / min dV / dt = 100 cm3 / min V = (4 / 3)... View Article
If Gas Is Being Pumped Into A Spherical Balloon At The Rate Of 30 Cubic Feet Min Then The Rate At Which The Radius Increases When It Reaches The Value 15 Ft Is 1) 1/15π ft/min 2) 1/30π ft/min 3) 1/20 ft/min 4) 1/25 ft/min Solution: (2) (1 / 30π) ft / min dV / dt = 30 ft3 / min V = (4 / 3)... View Article
A Spherical Balloon Is Expanding If The Radius Is Increasing At The Rate Of 2 Cm Min Then The Rate At Which The Volume Increases In Cm 3 Min When The Radius Is 5 Cm Is 1) 10 π 2) 100 π 3) 200 π 4) 50 π Solution: (3) 200π dr / dt = 2cm / min V = (4 / 3) πr3 dV / dt = (4 / 3) π (3r2 [dr / dt])... View Article
If There Is 2 Percent Error In Measuring The Radius Of Sphere Then Will Be The Percentage Error In The Surface Area 1) 3% 2) 1% 3) 4% 4) 2% Solution: (3) 4% SA = 4πr2 (Δr / r) = 2 / 100 Δr = 2r / 100 dA / dr = 8πr dA = 8πr (dr) ΔA = 8πr... View Article
The Distance Covered By A Particle In T Sec Is Given By X 3 8t 4t 2 After 1s Its Velocity Will Be 1) 0 unit 2) 3 units 3) 4 units 4) 7 units Solution: (1) 0 unit x = 3 + 8t - 4t2 v = dx / dt = 0 + 8 - 4 * 2t = 8 - 8t At t =... View Article
A Particle Is Moving In A Straight Line At Time T The Distance Between The Particle From Its Starting Point Is Given By X T 6t 2 T 3 Its Acceleration Will Be Zero At 1) t = 1 unit time 2) t = 2 units time 3) t = 3 units time 4) t = 4 units time Solution: (2) t = 2 units time x = t - 6t2 + t3... View Article
If The Diagonal Of A Square Is Changing At The Rate Of 0 5 Cm S Then The Rate Of Change Of Area When The Area Is 400 Cm 2 Is 1) 20√2 cm2 / s 2) 10 √2 cm2 / s 3) [1 / 10 √2] cm2 / s 4) [10 / √2] cm2 / s 5) 5√2 cm2 / s Solution: (2) [10 √2] cm2 / s b =... View Article
A Stone Is Thrown Vertically Upwards From The Top Of A Tower 64 M High According To The Law S 48t 16t 2 The Greatest Height Attained By The Stone Ground Is 1) 36 m 2) 32 m 3) 100 m 4) 64 m Solution: (1) 36m s = 48t - 16t2 ds / dt = 48 - 32t t = 48 / 32 = (3 / 2) s s = 48 * (3 / 2)... View Article
The Equation Of Motion Of A Particle Moving Along A Straight Line Is S 2t 3 9t 2 12 T Where The Units Of S And T Are Cm And S The Acceleration Of The Particle Will Be Zero After 1) 3/2 s 2) 2/3 s 3) 1/2 s 4) 1 s Solution: (1) 3 / 2 seconds s = 2t3 - 9t2 + 12t a = ds2 / dt2 ds / dt = 6t2 - 18t + 12 ds2... View Article
If The Error Committed In Measuring The Radius Of The Circle Is 0 01 Percent Then The Corresponding Error In Calculating The Area Is 1) 0.05% 2) 0.02% 3) 0.25% 4) 0.1% 5) 0.2% Solution: (2) 0.02% (Δr / r) * 100 = 0.01% A = πr2 Taking log on both sides log... View Article
An Edge Of A Variable Cube Is Increasing At The Rate Of 10 Cm S How Fast The Volume Of The Cube Will Increase When The Edge Is 5 Cm Long 1) 750 cm3 / s 2) 75 cm3 / s 3) 150 cm3 / s 4) 25 cm3 / s Solution: (1) 750 cm3 / s Let the edge of the cube be “x” cm. dx / dt =... View Article
The Distance Travelled By A Bus In T Sec After The Brakes Are Applied Is 1 2t 2t 2 Metres The Distance Travelled By The Bus Before It Stops Is Equal To 1) 0.5 m 2) 1 m 3) 1.5 m 4) 2.5 m Solution: (3) 1.5m S = 1 + 2t - 2t2 V = dS / dt = 0 = 2 - 4t t = 1 / 2 S = 1 + 2 (1 / 2) -... View Article
The Distance In Metres Travelled By A Vehicle In Time T In Seconds Is Given By The Equation S 3t 3 2t 2 T 1 The Difference In The Acceleration Between T 2 And T 4 Is 1) 36 m/s2 2) 38 m/s2 3) 45 m/s2 4) 46 m/s2 Solution: (1) 36 m / s2 s = 3t3 + 2t2 + t + 1 ds / dt = 9t2 + 4t + 1 d2s / dt2 = 18t... View Article