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
The Equation Of The Tangent To The Curve X 2 2xy Y 2 2x Y 6 0 At 2 2 Is 1) 2x + y - 6 = 0 2) 2y + x - 6 = 0 3) x + 3y - 8 = 0 4) 3x + y - 8 = 0 5) x + y - 4 = 0 Solution: (1) 2x + y - 6 = 0 y = x2 -... View Article
The Equation Of The Tangent To The Curve Y 4e X 4 At The Point Where The Curves Crosses Y Axis Is Equal To 1) 3x + 4y = 16 2) 4x + y = 4 3) x + y = 4 4) 4x - 3y = -12 5) x - y = -4 Solution: (3) x + y = 4 Since the curve crosses the... View Article
If The Curves X 2 A 2 Y 2 16 1 And Y 3 8x Interest At Right Angle Then The Value Of A 2 Is 1) 16 2) 12 3) 8 4) 4 5) 2 Solution: (4) 4 (x2 / a2) + (y2 / b2) = 1 (2x / a2) + (2yy’ / 12) = 0 y’ = -12x / a2y = m1 y3 =... View Article
The Equation Of The Tangent To The Curve Y 4 X E X At 1 4 E Is 1) y = - 1 2) - (4/e) 3) x = - 1 4) x = -4/e Solution: (2) - (4 / e) m = dy / dx m = d (4xex) / dx = 4 [xex + ex] m(-1, -4 / e)=... View Article
The Shortest Distance Between The Line Y X 1 And The X Y 2 2 Is 1) 3√2 / 8 2) 2√3 / 8 3) 3√2 / 5 4) √3 / 4 Solution: (1) 3v2 / 8 y2 = x y2 = 4ax a = 1 / 4 Points will be (t2 / 4, t / 2) yy1... View Article
Let P X X 4 A X 3 B X 2 C X D Such That X 0 Is The Only Real Root Of P Dash X Equal To 0 1) P(-1) is the minimum and P(1) is the maximum of P 2) P(-1) is not minimum but P(1) is the maximum of P 3) P(-1) is minimum and P(1) is... View Article
The Minimum Value Of F X E X 4 X 3 X 2 Is 1) e 2) -e 3) 1 4) -1 Solution: (3) 1 f (x) = e(x^4 - x^3 + x^2) f’ (x) = e(x^4 - x^3 + x^2) (4x3 - 3x2 + 2x) f’ (x) = 0... View Article
If The Line Ax By C 0 Is A Tangent To The Curve Xy 4 Then 1) a < 0, b > 0 2) a = 0, b > 0 3) a < 0, b < 0 4) a = 0, b < 0 Solution: (3) a < 0, b < 0 xy = 4 y = 4 /... View Article
Let F R R Be Defined By F X If F Has A Local Minimum At X Equals 1 Then A Possible Value Of K Is 1) 1 2) 0 3) -(1/2) 4) -1 Solution: (4) -1 f (x) = lim x=-1- f (x) = lim x=-1+ f (x) LHL = RHL lim x=-1- (k - 2x) = lim... View Article
For Any Integer N Greater Than 1 The Sum Sigma N Eq 1 To N K K Plus 2 Is Equal To For any integer n = 1, the sum Sk=1n k(k+2) is equal to (1) n(n+1)(n+2)/2 (2) n(n+1)(2n+1)/6 (3) n(n+1)(2n+7)/6 (4) n(n+1)(2n+9)/6... View Article
