If Sin Inverse 1 X Plus 2 Sin Inverse X Pi 2 Then X 1) (0, -1/2) 2) (1/2, 0) 3) {0} 4) (-1, 0) Answer: (2) (1/2, 0) Solution: Given, sin-1(1 - x) + 2 sin-1(x) = π/2 sin-1(1 - x) =... View Article
If Cos Of 2 Sin Inverse X 1 9 Then X Equal To 1) only 2/3 2) only -2/3 3) 2/3, -2/3 4) Neither 2/3 nor -2/3 Answer: (3) 2/3, -2/3 Solution: Given, cos[2 sin-1(x)] = 1/9 Let... View Article
If A Equal To Tan Inverse X Then Sin 2a 1) 2x/√(1 - x2) 2) 2a/(1 - x2) 3) 2x/(1 + x2) 4) None of these Answer: (3) 2x/(1 + x2) Solution: Given, A = tan-1(x) tan A = x... View Article
Tan 1 2 Sin Inverse 2a 1 Plus A Square Plus 1 2 1) 2a/(1 + a2) 2) (1 - a2)/(1 + a2) 3) 2a/(1 - a2) 4) None of these Answer: (3) 2a/(1 - a2) Solution: tan[(1/2) sin-1{2a/(1 + a2)}... View Article
Cot Inverse Cos Alpha Power 1 2 Minus Tan Inverse Cos Alpha 1) tan2(α/2) 2) cot2(α/2) 3) tan α 4) cot α/2 Answer: (1) tan2(α/2) Solution: Given, cot-1[(cos α)1/2] - tan-1[(cos α)1/2] = x... View Article
If Cos Inverse Root P Plus Cos Inverse Root 1 Minus P 1) 1 2) 1/√2 3) 1/3 4) 1/2 Answer: (4) 1/2 Solution: Given, cos-1√p + cos-1√(1 - p) + cos-1√(1 - q) = 3π/4 cos-1√p + cos-1√[1 -... View Article
The Equation Of Particle Is X T 3 9t 2 3t 1 And V 24 Then A 1) 3 2) 2 3) 1 4) 0 Solution: (4) 0 Velocity of the ball (v) = ds/ dt = u - 9.8t Terminal velocity v = 0 and t = 3 seconds u = 9.8 (3) =... View Article
A Particle Is Moving On A Straight Line Where Its Position S In Metre Is A Function 1) –1 m / s2 2) (5 / 4) m / s2 3) (1 / 2) m / s2 4) (- 5 / 4) m / s2 Solution: (2) (5 / 4) m / s2 s = at2 + bt + 6 v = 2at + b... View Article
If Y X 3 5 And X Changes From 3 To 2 99 Then The Approximate Change In Y Is 1) 2.7 2) –0.27 3) 27 4) None of these Solution: (2) –0.27 y = x3 + 5 dy = 3x2 dx = 3 (3)2 - 0.01 = - 0.27... View Article
A Triangular Park Is Enclosed On Two Sides On Two Sides By A Fence 1) (3 / 2) x2 2) √x3 / 8 3) (1 / 2) x2 4) πx2 Solution: (3) (1 / 2) x2 Area of triangle = (1 / 2) base * height = (1 / 2) (2x2... View Article
A 10 Cm Long Rod Ab Moves With Its Ends On Two Mutually 1) (8 / 3) cm / sec 2) (4 / 3) cm / sec 3) (2 / 9) cm / sec 4) None of these Solution: (1) (8 / 3) cm / sec x2 + y2 = 100... View Article
A Particle Is Moving In A Straight Line According To The Formula S T 2 8t 12 1) 14 m/sec 2) 13 m/sec 3) 15 m/sec 4) None of these Solution: (2) 13 m/sec Average velocity in third second = Distance travelled... View Article
The Equation Of Motion Of A Particle Moving Along A Straight Line Is 1) 3 / 2 sec 2) 2 / 3 sec 3) 1 / 2 sec 4) Never Solution: (1) 3 / 2 sec s = 2t3 – 9t2 + 12t a = d2s / dt2 ds / dt = 6t2 - 18t... View Article
If T V 2 2 Then Df Dt Is Equal To Where F Is Acceleration 1) f2 2) f3 3) - f3 4) - f2 Solution: (3) - f3 t = v2 / 2 v2 = 2t 2v (dv / dt) = 2 dv / dt = 1 / v = f df / dt = (- 1 / v2)... View Article
If 2t V 2 Then Dv Dt 1) 0 2) 1 / 4 3) 1 / 2 4) 1 / v Solution: (4) 1 / v 2t = v2 2v (dv /dt) = 2 dv / dt = 1 / v... View Article
A Stone Is Thrown Vertically Upwards From The Top Of A Tower 64 Metres High According 1) 100 metre 2) 64 metre 3) 36 metre 4) 32 metre Solution: (1) 100 metre v = 0, ds / dt = 0 48 - 32t = 0 t = 36m (height... View Article
The Equations Of Motion Of Two Stones Thrown Vertically Simultaneously 1) h / 3 2) 2h 3) h 4) 0 Solution: (4) 0 Time taken by 1st stone to attain maximum height = t = u / g = 19.6 / 9.8 = 2sec Time... View Article
The Length Of The Side Of A Square Sheet Of Metal Is Increasing At The Rate Of 4 Cm Sec 1) 16 cm2/sec 2) 8 cm2/sec 3) 64 cm2/sec 4) None of these Solution: (3) 64 cm2/sec A = a2 dA / dt = 2a (dA / dt) = 2 * 8 * 4 =... View Article
A Body Moves According To The Formula V 1 T 2 Where V Is The Velocity 1) 24 cm/sec2 2) 12 cm/sec2 3) 6 cm/sec2 4) None of these Solution: (3) 6 cm/sec2 Acceleration f = dv / dt = 2t, then acceleration... View Article
The Equation Of Motion Of A Stone Thrown Vertically Upwards From The Surface Of A Planet 1) (10 / 3) sec 2) (5 / 3) sec 3) (20 / 3) sec 4) (5 / 6) sec Solution: (1) (10 / 3) sec ds / dt = 10 - 6t = v But v = 0 (at... View Article