If Slope Of Tangent To Curve Y X 3 At A Point Is Equal To Ordinate Of A Point Then Point Is 1) (27, 3) 2) (3, 27) 3) (1, 2) 4) (–1, 3) Solution: (2) (3, 27) y = x3 dy / dx = 3x2 Now, 3x2 = y 3x2 = x3 x = 0, 3... View Article
If The Curves X 2 A 2 Y 2 12 1 And Y 3 8x Intersect At Right Angles 1) 16 2) 12 3) 8 4) 4 5) 2 Solution: (4) 4 (x2 / a2) + (y2 / 12) = 1 (2x / a2) + (2y / 12) (dy / dx) = 0 (dy / dx) = - 12x /... View Article
The Tangent Of The Curve Y Sin Root Cosx At X Pi 2 Has Gradient 1) 0 2) ∞ 3) -∞ 4) - 1 / 2 Solution: (1) 0... View Article
The Length Of The Subtangent At T On The Curve X A T Sin T Y A 1 Cos T Is 1) 2asin (t / 2) 2) 2asin3 (t / 2) sec (t / 2) 3) a sint 4) 2asin (t / 2) tan (t / 2) Solution: (3) a sint x = a (t + sin t), y =... View Article
The Point On The Curve Y 2 X The Tangent At Which Makes An Angle 45 Degrees 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
The Equation Of The Curve With Passes Through The Point 0 1 And The Slope 1) y = 3x3 + 2x2 + 5x + 1 2) y = 2x3 + 3x2 + 5x + 1 3) y = x3 + x2 + 5x + 1 4) y = x3 + x2 + 5x – 1 Solution: (3) y = x3 + x2 + 5x +... View Article
If The Normal To The Curve Y F X At 3 4 Makes And Angle 3 Pi 4 With The Positive 1) -1 2) 3 / 4 3) 1 4) - 3 / 4 Solution: (3) 1 y = f (x) y’ = f ‘(x) Slope of tangent = f’ (x) Slope of normal = -1 / f’ (x)... View Article
The Equation Of Tangent To The Curve X 2 3 Y 2 2 1 Which Is Parallel To Y X Is 1) y = x ± 1 2) y = x - (1 / 2) 3) y = x + (1 / 2) 4) y = 1 - x Solution: (1) y = x ± 1 x2 / 3 - (y2 / 2) = 1 (2x / 3) - y (dy /... View Article
The Equation Of The Tangent To The Curve Y 1 X Y Sin 1 Sin 2 X 1) x + y = 1 2) x + y + 1 = 0 3) 2x – y + 1 = 0 4) x + 2y + 2 = 0 Solution: (1) x + y = 1 y = (1 + x)y + sin–1 (sin2 x) (dy / dx)... View Article
The Normal To The Curve At P X Y Meets The X Axis At G 1) Ellipse 2) Parabola 3) Circle 4) Hyperbola Solution: (4) Hyperbola Equation of normal is Y - y = - (dx / dy) (X - x) Intercept... View Article
The Tangent And The Normal Drawn To The Curve Y X 2 X 4 At P 1 4 1) 4 2) 32 3) 8 4) 16 Solution: (4) 16 y = x2 – x + 4 Slope of the tangent P (1, 4) is dy / dx = 2x – 1 (dy / dx)1,4 = 2 – 1 =... View Article
If The Line Ax By C 0 Is Normal To The Curve Xy 1 Then 1) a > 0, b < 0 2) a > 0, b > 0 3) a < 0, b < 0 4) Data is insufficient Solution: (1) a > 0, b < 0 xy = 1... View Article
The Abscissa Of The Point On The Curve Y A E X A E X A Where The Tangent 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
The Equation Of The Tangent To The Curve X 2 Cos 3 Theta And Y 3 Sin 3 Theta 1) 2x + 3y = 3√2 2) 2x - 3y = 3√2 3) 3x + 2y = 3√2 4) 3x - 2y = 3√2 Solution: (3) 3x + 2y = 3√2 x|θ = π/4 = 2 / 2√2 = 1 / √2 y|θ... View Article
If St And Sn Are The Lengths Of The Subtangent And The Subnormal 1) ST = SN 2) ST = 2SN 3) ST2 = aSN3 4) ST3 = aSN Solution: (1) ST = SN x = a (θ + sin θ) dx / dθ = a (1 + cos θ) y = a (1 – cos... View Article
The Normal To The Curve X A 1 Cos Theta Y A Sin Theta At Always Passes 1) (a, a) 2) (0, a) 3) (0, 0) 4) (a, 0) Solution: (4) (a, 0) The equation of normal at θ is (y - y1) = -1 / (dy / dx) (x - x1) y... View Article
If A Tangent To The Curve Y 6x X 2 Is Parallel To The Line 4x 2y 1 0 1) (2, 8) 2) (8, 2) 3) (6, 1) 4) (4, 2) Solution: (1) (2, 8) y = 6x - x2 dy / dx = 6 - 2x The tangent is parallel to the line... View Article
If The Normal To The Curve Y 2 5x 1 At The Point 1 2 Is Of The Form 1) 4, –14 2) 4, 14 3) –4, 14 4) –4, –14 Solution: (1) 4, –14 y2 = 5x - 1 At (1, -2), dy / dx = [5 / 2y](1, - 2) = -5 / 4 The... View Article
The Angle Between The Curves Y Sin X And Y Cos X Is 1) tan-1 (2√2) 2) tan-1 (3√2) 3) tan-1 (3√3) 4) tan-1 (5√2) Solution: (1) tan-1 (2√2) The point of intersection is (π / 4, 1 / √2)... View Article
For The Curve Xy C 2 The Subnormal At Any Point Varies As 1) x2 2) x3 3) y2 4) y3 Solution: (4) y3 xy = c2 Subnormal is y (dy / dx). y = c2 / x dy / dx = - c2 / x2 Subnormal is [y... View Article