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Observe The Statements Given Below Assertion A F X Xe X Has The Maximum At X 1

1) Both A and R are correct and R is the correct reason for A 2) Both A and r correct but R is not the correct reason for A 3) A is... View Article

The Condition F X X 3 Px 2 Qx R X Belongs To R To Have No Extreme Value Is

1) p2 < 3q 2) 2p2 < q 3) p2 < 1/4q 4) p2 > 3q Solution: (1) p2 < 3q f (x) = x3 + px2 + qx + r f’ (x) ≠ 0 f’ (x) =... View Article

The Length Of Tangent Subtangent Normal And Subnormal For The Curve

1) B, D, A, C 2) B, A, C, D 3) A, B, C, D 4) B, A, D, C Solution: (4) B, A, D, C y = x2 + x - 1 (dy / dx) = 2x + 1 (dy / dx)(1, 1) = 3 A... View Article

The Line X A Y B 2 Touches The Curve X N A N Plus Y N B N 2 At

1) (b, a) 2) (-b, -a) 3) (a, b) 4) None of these Solution: (3) (a, b) (xn / an) + (yn / bn) = 2 [nxn-1 / an] + [nyn-1 / bn] y’ =... View Article

The Maximum Value Of F X X 4 X X 2 On 1 1 Is

1) - (1/3) 2) - (1/4) 3) 1/4 4) 1/6 Solution: (4) 1 / 6 f (x) = x / [4 + x + x2] f’ (x) = 0 f’’ (x1) > 0, [x = x1 minimum]... View Article

The Maximum Slope Of The Curve Y X 3 3x 2 2x 27 Is

1) 5 2) -5 3) 1/5 4) None of these Solution: (1) 5 y = - x3 + 3x2 + 2x - 27 y’ = - 3x2 + 6x + 2 y’’ = - 6x + 6 = 0 y’’’ = -6... View Article

If The Curves X 2 9a 9 Y And X 2 A Y 1 Intersect Orthogonally Then The Value Of A Is

1) 3 2) 4 3) 5 4) 7 5) 9 Solution: (2) 4 x2 = 9a(9 - y) --- (1) x2 = a(y + 1) ---- (2) From equation (1) and (2), 9a(9 - y)... View Article

The Length Of The Subtangent To The Curve X 2 Y 2 A 4 At A A Is

1) a/2 2) 2a 3) a 4) a/3 Solution: (2) 2a x2y2 = a4 y2 = a4 / x2 2y (dy / dx) = - 2a4 / x3 (dy / dx)(-a, a) = - 2a4 / [2... View Article

A Missile Is Fired From The Ground Level Rises X Metres Vertically Upwards In T Sec

1) 200 m 2) 125 m 3) 190 m 4) 300 m Solution: (1) 200 m x = 100t - (25 / 2) t2 Maximum height will be reached when dx / dt = 0.... View Article

The Point On The Curve Y 2 X The Tangent At Which Makes An Angle 45 With X Axis Is

1) (1 / 4, 1 / 2) 2) (1 / 2, 1 / 4) 3) (1 / 2, - 1 / 2) 4) (1 / 2, 1 / 2) Solution: (1) (1 / 4, 1 / 2) Slope of the tangent = m =... View Article

If The Function F X 2x 3 9ax 2 12a 2x 1 Attains Its Maximum And Minimum At P And Q

1) 0 2) 1 3) 2 4) None of these Solution: (3) 2 f (x) = 2x3 - 9ax2 + 12a2x + 1 f’ (x) = 6x2 - 18ax + 12a2 = 0 f’’ (x) = 12x -... View Article

The Maximum Area Of The Rectangle That Can Be Inscribed In A Circle Of Radius R Is

1) πr2 2) r2 3) πr2 / 4 4) 2r2 Solution: (4) 2r2 (2r)2 = l2 + b2 4r2 = l2 + b2 b2 = 4r2 - l2 b = √4r2 - l2 Area = l *... View Article

The Angle Between The Tangents At Those Points On The Curve X T 2 1 And Y T 2 T 6

1) ± tan-1 (4 / 29) 2) ± tan-1 (5 / 49) 3) ± tan-1 (10 / 49) 4) ± tan-1 (8 / 29) Solution: (3) ± tan-1 (10 / 49) x = t2 + 1 dx /... View Article

If The Function F X X 2 E 2x X 0 Then The Maximum Value Of F X Is

1) 1/e 2) 1/2e 3) 1/e2 4) 4/e4 Solution: (3) 1 / e2 f (x) = x2 e-2x f’ (x) = e-2x (2x) - (2x2) e-2x f’ (x) = 2e-2xx (1 - x)... View Article

The Minimum Value Of 2x 3y When Xy 6 Is

1) 9 2) 12 3) 8 4) 6 Solution: (2) 12 f (x) = 2x + 3y f (x) = 2x + (18 / x) f’ (x) = 2 - (18 / x2) Put f’ (x) = 0 for maximum... View Article

The Normal To A Curve At P X Y Meets The X Axis At G

1) ellipse 2) parabola 3) circle 4) hyperbola Solution: (1) ellipse and (3) circle The equation of the normal is Y - y = (dy / dx)... View Article

The Equation Of Normal To The Curve X 2y X 2 3x 6 At The Point With Abscissa X 3 Is

1) 3x + 27y = 79 2) 27x - 3y = 79 3) 27x + 3y = 79 4) 3x - 27y = 79 Solution: (2) 27x - 3y = 79 x2y = x2 - 3x + 6 .... (i) At x =... View Article

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

1) (2, 2) 2) (3, 3) 3) (4, 4) 4) (0, 0) Solution: (4) (0, 0) y = x3 dy / dx = 3x2 Since the tangent to the curve is parallel... View Article

The Function F X X 1 X Has

1) a local maxima at x = 1 and a local minima at x = - 1 2) a local minima at x = 1 and a local maxima at x = - 1 3) absolute maxima at x =... View Article

The Abscissa Of The Point On The Curve Y A E X A E X A Where The Tangent Is Parallel To The X Axis Is

1) 0 2) a 3) 2a 4) -2a Solution: (1) 0 y = a (ex/a + e-x/a) (dy / dx) = 0 a [ex/a (1 / a) + e-(x/a) (- 1 / a)] = 0 ex/a - e-x/a... View Article

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