If Ax 2 Bx 4 Attains Its Minimum Value 1 At X 1 Then The Values Of A And B Are Respectively 1) 5, -10 2) 5, -5 3) 10, -5 4) 10, 10 Solution: (1) 5, -10 f (x) = ax2 + bx + 4 f' (x) = 2ax + b Put f' (x) = 0 x = -b / 2a... View Article
The Stone Is Thrown Vertically Upwards And The Height X Feet Reached By The Stone In T Sec Is Given 1) 2 s 2) 2.5 s 3) 3 s 4) 1.5 s Solution: (2) 2.5 s x = 80t - 16t2 dx / dt = 80 - 32t dx / dt = 0 80 = 32t t = 80 / 32 = 5 /... View Article
The Maximum Value Of Logx X In 2 Infinity Is 1) 1 2) 2/e 3) e 4) 1/e Solution: (4) 1 / e y = logx / x dy / dx = [1 - logx] / x2 Put dy / dx = 0 [1 - logx] / x2 = 0 log x... View Article
Divide 12 Into Two Parts Such That The Product Of The Square Of One Part And The Fourth Power Of The Second Part Is Maximum Are 1) 6, 6 2) 5, 7 3) 4, 8 4) 3, 9 Solution: (3) 4, 8 Let the parts be x and 12 - x. f (x) = x4 (12 - x)2, where 0 < x < 12 =... View Article
The Slope Of The Tangent To The Curves 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) -7 Solution: (2) 6 / 7 m = dy / dx = (dy / dt) / (dx / dt) = [4t - 2] / [2t + 3] x = t2 + 3t - 8 t2 - 3t... View Article
The Point Of The Curve Y 2 2 X 3 At Which The Normal Is Parallel To The Line Y 2x 1 0 Is 1) (5, 2) 2) (-(1/2), -2) 3) (5, -2) 4) (3/2, 2) Solution: (3) (5, -2) y2 = 2(x - 3) 2y (dy / dx) = 2 m1 = dy / dx = 1 / y m1m2... View Article
The Abscissa Of The Points Where The Tangent To Curve Y X 3 3x 2 9x 5 Is Parallel To X Axis Are 1) x = 0 and 0 2) x = 1 and -1 3) x = 1 and -3 4) x = -1 and 3 Solution: (4) x = -1 and 3 y = x3 - 3x2 - 9x + 5 dy / dx = 3x2 -... View Article
If The Cubic Equation X 3 Px Q Has Three Distinct Real Roots Where P 0 And Q 0 1) The cubic has maxima at both √p / 3 and - √p / 3 2) The cubic has minima at both √p / 3 and - √p / 3 3) The cubic has minima at both -... View Article
For The Function F X Xe X The Point 1) x = 0 is a maximum 2) x = 0 is a minimum 3) x = -1 is a maximum 4) x = -1 is a minimum Solution: (4) x = -1 is a minimum f (x)... View Article
If F X X 2 4x 1 Then 1) f (x) = f (-x), ? x 2) f (x) ? 1, ? x = 0 3) f '' (x) > 0, ? x 4) f (x) = 1, for x = - 4 Solution: (4) f (x) = 1, for x = - 4... View Article
The Normal At Point 1 1 Of The Curve Y 2 X 3 Is Parallel To The Line 1) 3x - y - 2 = 0 2) 2x + 3y - 7 = 0 3) 2x - 3y + 1 = 0 4) 2y - 3x + 1 = 0 Solution: (2) 2x + 3y - 7 = 0 y2 = x3 2yy’ = 3x2... View Article
The maximum value of function f (x) = sinx (1 + cosx) x ϵ R is 1) 33/2 / 4 2) 35/3 / 4 3) 3 / 2 4) 37/5 / 4 Solution: (1) 33/2 / 4 f (x) = sinx (1 + cosx) f’ (x) = cosx + (cos2x / 2) * 2 =... View Article
The Function F X X 3 Ax 2 Bx C A 2 3b Has 1) one maximum value 2) one minimum value 3) no extreme value 4) one maximum and one minimum value Solution: (3) no extreme value... View Article
If Y Sin X A Sin X B A Not Equal To B Then Y Is 1) minimum at x = 0 2) maxima at x = 0 3) neither minima nor maxima at x = 0 4) None of the above Solution: (3) neither minima nor... View Article
If Sum Of Two Numbers Is 6 Then The Minimum Value Of The Sum Of Their Reciprocals Is 1) 6/5 2) 3/4 3) 2/3 4) 1/2 Solution: (3) 2 / 3 Let the 2 numbers be a and b. a + b = 6 b = 6 - a s = (1 / a) + (1 / b) = (1 /... View Article
The Smallest Circle With Centre On Y Axis And Passing Through The Point 7 3 Has Radius 1) √58 2) 7 3) 3 4) 4 Solution: (2) 7 Centre = (h, k) D = √(7 - 0)2 + (3 - k)2 = √49 + (3 - k)2 D2 = 49 + (3 - k)2 2D .... View Article
The Length Of The Normal To The Curve X A Theta Sin Theta Y A 1 Cos At Theta Pi 2 Is 1) 2a 2) a/2 3) a/√2 4) √2a Solution: (4) √2a Length of normal = y √1 + (dy / dx)2 dy / dx = (dy / dθ) / (dx / dθ) = a sin θ /... View Article
The Angle Between Y 2 X And X 2 Y At The Origin Is 1) 2 tan-1 (3/4) 2) tan-1 (4/3) 3) π/2 4) π/4 Solution: (3) π / 2 y2 = x and x2 = y 2y (dy / dx) = 1 and 2x = dy / dx (dy / dx)... View Article
If A And B Are Positive Numbers Such That A B Then The Minimum Value Of A Sec Theta B Tan Theta Where 0 Pi 2 Is 1) 1 / √a2 - b2 2) 1 / √a2 + b2 3) √a2 + b2 4) √a2 - b2 5) a2 - b2 Solution: (4) √a2 - b2 y = a sec θ - b tan θ dy / dθ = a... View Article
The Angle Between The Curves Y A X And Y B X Is Equal To 1) tan-1 [|(a - b) / (1 + ab)|] 2) tan-1 [|(a - b) / (1 - ab)|] 3) tan-1 [|(log b + log a) / (1 + log a log b)|] 4) tan-1 [|(log b + log... View Article
