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If F X X 3 E 3x X 0 Then The Maximum Value Of F X Is

1) e-3 2) 3e-3 3) 27e-9 4) ∞ Solution: (1) e-3 f (x) = x3 e-3x f’ (x) = 3x2 e-3x + x3 e-3x (-3) = 0 3x2 e-3x - 3x3 e-3x = 0... View Article

If P Is A Point On X 2 A 2 Y 2 B 2 1 With Foci S And S Dash Then The Maximum Of Delta Sps Dash Is

1) ab 2) abe2 3) abe 4) ab/e Solution: (3) abe (x2 / a2) + (y2 / b2) = 1 ΔSpS’ = (1 / 2) bh = (1 / 2) 2ae * b = abe... View Article

The Point On The Curve Y X 3 At Which Tangent Is Parallel To The Point 1 1 Is

1) (0, 0) 2) (1, - 1) 3) (-1, 1) 4) (-1, -1) Solution: (4) (-1, -1) y = x3 y’ = 3x2 At (1, 1), y’ = 3 (1)2 = 3 3x2 = 3 x =... View Article

The Point 0 5 Is Closer To The Curve X 2 2y At

1) (2√2, 0) 2) (0, 0) 3) (2, 2) 4) None of these Solution: (4) None of these Let any point on the curve be (h, k). h2 = 2k... View Article

Let F Be A Function Defined By F X Statement I X 0 Is A Point Of Minima Of F Statement Ii F 0 0

Let f be a function defined by f (x) = Statement I : x = 0 is a point of minima of f. Statement II : f’ (0) = 0 1) Statement I is correct,... View Article

For X Belongs To 0 To X Pi 2 Define F X Integral From 0 To X Root Of T Sint Dt Then F Is

1) local maximum π and 2π 2) local minimum at π and local maximum at 2π 3) local maximum at π and a local minimum at 2π 4) local maximum... View Article

The Least Value Of The Function F X Ax B X A 0 B 0 X 0 Is

1) √ab 2) 2 √a / b 3) 2 √b / a 4) 2√ab Solution: (4) 2√ab f (x) = ax + b / x f’ (x) = a - (b / x2) f’ (x) = 0 a = b / x2 or x =... View Article

The Maximum Value Of The Function F X X 8 2 X On Interval 1 6 Is

1) 1 2) 9/8 3) 13/12 4) 17/8 Solution: (4) 17 / 8 f (x) = (x / 8) + (2 / x) f’ (x) = d [(x / 8) + (2 / x)] / dx = (1 / 8) + 2 *... View Article

The Maximum Value Of Xe X Is

1) e 2) 1/e 3) -e 4) -1/e Solution: (2) 1 / e y = xe-x --- (1) dy / dx = xe-x (-1) + e-x = e-x [1 - x] --- (2) For maximum or... View Article

Let A B Belongs To R Be Such That The Function F Given By F X Log X Bx 2 Ax X 0 Has Extreme Values

Statement I : f has local maximum at x = -1 and x = 2. Statement II : a = 1 / 2 and b = -1 / 4 1) Statement I is incorrect, Statement II is... View Article

The Difference Between The Greatest And The Least Value Of The Function F X Sin2x X On Pi 2 Pi 2 Is

1) π 2) √3 - (π / 3) 3) -√3 + (π / 3) 4) None of these Solution: (2) √3 - (π / 3) y = f (x) = sin2x - x dy / dx = 2 cos 2x - 1 =... View Article

If At Each Point Of The Curve Y X 3 Ax 2 X 1 Tangent Is Inclined At An Acute Angle With The Positive Direction Of The X Axis Then

1) a ≤ √3 2) a > 0 3) - √3 < a < √3 4) None of these Solution: (3) - √3 < a < √3 Slope of the tangent = dy / dx =... View Article

The Equation Of The Tangent To The Curve Y E X At The Point Where The Curve Cuts The Line X 1 Is

1) e(x + y) = 1 2) y = ex = 1 3) x + y = e 4) None of these Solution: (4) None of these y = e-|x| y = e-x dy / dx = (-1)... View Article

If P X A 0 A 1 X 4 A 2x 4 A Nx 2n Be A Polynomial In A Real Variable X With 0 A 0 A 1 A 2 A N The Function P X Has

1) neither maximum nor minimum 2) only one maximum 3) only one minimum 4) None of the above Solution: (3) only one minimum P (x) =... View Article

The Intercepts On X Axis Made By Tangents To The Curve Y Integral Of 0 X T Dt X Belongs To R Which Are Parallel To The Line Y 2x Are

1) ± 1 2) ± 2 3) ± 3 4) ± 4 Solution: (1) ± 1 y = ∫0x |t| dt t > 0, y = ∫0x t dt = t2 / 2)0x = (x2 / 2) - 0 y = x2 / 2... View Article

The Function F X 2 Mod X Plus Mod X 2 X 2 X Has A Local Minimum Or A Local Maximum At

1) -2 2) -2/3 3) 2 4) 2/3 Solution: (1) -2 and (2) -2 / 3 f(x) = 2|x| + |x + 2|-||x - 2|x|| Case 1: x < -2 y = - 2x - x - 2 -... View Article

A Rectangular Sheet Of The Fixed Perimeter With Sides Having Their Lengths In The Ratio 8 15

1) 24 2) 32 3) 45 4) 60 Solution: (1) 24 and (3) 45 Let the side of the square be x. Volume = (15k - 2x) (8k - 2x) x = f (x) (dV... View Article

Let F 0 1 R The Set Of All Real Numbers Be A Function

Let f : [0,1] → R(the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies f... View Article

Let F 0 1 R The Set Of All Real Numbers Be A Function Suppose The Function F Is Twice Differentiable F 0 F 1 0 And Satisfies F X 2f X F X E X X Belongs To 0 1

1) 0 < f (x) < ∞ 2) -1 / 2 < f (x) < 1 / 2 3) -1 / 4 < f (x) < 1 4) - ∞ < f (x) < 0 Solution: (4) - ∞ < f... View Article

What Is The Difference Between Main Scale And Vernier Scale

The vernier calipers have two scales: the main scale and the vernier scale. The 10 divisions on the vernier scale are equal to 9 divisions on the... View Article

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