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A Curve Passes Through The Point 2 0 And The Slope Of The Tangent

1) (0, 2 / 3) 2) (0, 1) 3) (0, 4 / 3) 4) (4 / 3, 0) Solution: (3) (0, 4 / 3) Slope of the tangent dy / dx = x2 - 2x = d [(x3 / 3)... View Article

The Number Of Solutions Of The Equation A F X G X 0

1) 1 2) 2 3) 0 4) ∞ Solution: (3) 0 af(x) + g(x) = 0 x ∈ R There exist 0 solution.... View Article

Let F X X 2 1 N X 2 X 1 Then F X Has Local Extremum

1) 2 2) 3 3) 5 4) 7 Solution: (1) 2 f (x) = (x2 - 1)n g (x) where g (x) = x2 + x + 1 f’ (x) = n (x2 - 1)n-1 2x g (x) + (x2 - 1)n... View Article

The Maximum And Minimum Value Of Ab Sinx B 1 A 2 Cosx C

1) [b - c, b + c] 2) (b - c, b + c) 3) [c - b, b + c] 4) None of these Solution: (3) [c - b, b + c] f (x) = ab sinx + b √1 - a2... View Article

The Equation Of The Tangent To The Curve Y 2x 1 E 2 1 X

1) y = 1 2) x = 1 3) x + y = 1 4) x - y = - 1 Solution: (1) y = 1 y = (2x - 1) e2(1-x) (dy / dx) = 2e2(1-x) - 2 (2x - 1)e2(1-x)... View Article

The Length Of The Chord Along The Normal At Ct C T

1) (6 / t3) (1 + t4)3/2 2) - (6 / t3) (1 + t4)3/2 3) - (6 / t3) (1 - t4)3/2 4) None of these Solution: (1) (6 / t3) (1 + t4)3/2 xy... View Article

The Interval Increases Of The Function Y X E X Tan Pi 7 Is

1) (–∞, 0) 2) (0, ∞) 3) (–∞, ∞) 4) (1, ∞) Solution: (1) (–∞, 0) y = x - ex + tan (π / 7) f (x) = y = x - ex + tan (π / 7) For f... View Article

The Point Of Intersection Of The Tangents Drawn To The Curve

1) (2, –1) 2) (1, 2) 3) (0, 1) 4) None of these Solution: (3) (0, 1) xy = 1 - y y = 1 / [1 + x] The other curve is x2y = 1 - y... View Article

The Angle Formed By The Abscissa And The Tangent To The Parabola

1) tan-1 4 2) tan-1 6 3) tan-1 9 4) None of these Solution: (3) tan-1 9 y = x2 + 4x - 17 y’ = 2x + 4 At (5 / 2, 3 / 4), dy / dx... View Article

The Function F X 1 X Sinx Cosx 0 X Pi 2

1) is continuous on (0, π / 2) 2) is strictly increasing on (0, π / 2) 3) is strictly decreasing on (0, π / 2) 4) None of these... View Article

The Distance Between The Origin And The Normal To The Curve

1) √3 2) 1 / √3 3) 2 / √5 4) None of these Solution: (3) 2 / √5 y = e2x + x2 y’ = 2e2x + 2x y = mx + c y = - (1 / 2) + c At... View Article

If The Point On Y X Tan Alpha Ax 2 2u 2cos 2 Alpha 0

1) π / 6 2) π / 4 3) π / 3 4) π / 2 Solution: (3) π / 3 dy / dx = tan ɑ - [gx / u2 cos2 ɑ] Since the tangent is parallel to y =... View Article

The Area Of The Triangle Formed By The Positive X Axis And The Normal

1) √3 2) 2√3 3) 4√3 4) none of these Solution: (2) 2√3 The equation of the normal = y = √3x The equation of the tangent is y - √3... View Article

If The Tangent At P 1 1 On Y 2 X 2 X 2 Meets The Curve

1) (-4, 4) 2) (1, -2) 3) (9 / 4, 3 / 8) 4) None of these Solution: (3) (9 / 4, 3 / 8) The given curve is y2 = x (2 - x)2 ⇒ 2y... View Article

The Equation Of The Tangent To The Curve Y E X At The Point

1) x + y = e 2) y + ex = 1 3) x + y = 1 / e 4) x + ey = 2 Solution: (4) x + ey = 2 Put x = 1 in y = e|-x| y = 1 / e dy / dx =... View Article

The Curve Given By X Y E Xy Has A Tangent Parallel To The Y Axis At The Point

1) (0,1) 2) (1, 1) 3) (0, 0) 4) (1, 0) Solution: (4) (1, 0) x + y = exy 1 + (dy / dx) = exy [y + x (dy / dx)] dy / dx = [yexy... View Article

If M Is The Slope Of A Tangent To The Curve E Y 1 X 2 Then

1) | m | < 1 2) | m | ≤ 1 3) | m | > 1 4) m < 1 Solution: (2) | m | ≤ 1 ey = 1 + x2 (dy / dx) = 2x / [1 + x2] |m| =... View Article

07 Jan 2021: PIB Summary & Analysis

January 7th, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. Pravasi Bharatiya Divas 2021 2. Central Sector Scheme for Industrial... View Article

08 Jan 2021: UPSC Exam Comprehensive News Analysis

8 Jan 2021 CNA:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related INTERNATIONAL RELATIONS 1. USTR slams India’s digital tax,... View Article

What Is The Primary Product Of Nitrogen Fixation

Through nitrogen fixation, nitrogen present in the atmosphere is converted either by industrial or natural means to a form of nitrogen such as... View Article

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