The Equation E X 8 2x 17 0 Has 1) one real root 2) two real roots 3) eight real roots 4) four real roots Solution: (1) one real root ex – 8 + 2x − 17 = 0 The... View Article
The Point On The Curve Y 2 X The Tangent At Which Makes An Angle Of 45 1) (1 / 2, 1 / 4) 2) (1 / 2, 1 / 2) 3) (2, 4) 4) (1 / 4, 1 / 2) Solution: (4) (1 / 4, 1 / 2) The slope of the tangent at that... View Article
The Points Of Contact Of The Tangent Drawn From 0 0 To The Curve 1) x2 - y2 = xy 2) x2 + y2 = x2y2 3) x2 - y2 = x2y2 4) None of these Solution: (3) x2 - y2 = x2y2 Let the tangent be drawn at the... View Article
The Angle At Which The Curve Y Ae Ax Intersects The Y Axis Is 1) tan-1 (a2) 2) sin-1 (1 / √1 + a4) 3) cot-1 (a2) 4) sin-1 (√1 + a4) Solution: (3) cot-1 (a2) y = aeax dy / dx = a2eax The... View Article
The Function Sin X Alpha Sin X Beta Has No Maximum Or Minimum If 1) β - ɑ = Kπ 2) β - ɑ ≠Kπ 3) β - ɑ = 2Kπ 4) None of these Solution: (2) β - ɑ ≠Kπ f (x) = [sin (x + ɑ)] / [sin (x + β)] f’ (x)... View Article
The Minimum Value Of Root E X 2 1 Is 1) 1 2) 0 3) 2 4) None of these Solution: (2) 0 f (x) = √ex^2 - 1 f’ (x) = [(2x) ex^2] / [ex^2 - 1] f’ (x) > 0, if x > 0... View Article
The Set Of All X For Which Log 1 X X Is 1) (0, ∞) 2) (-1, ∞) 3) (-∞, ∞) 4) (1, ∞) Solution: (2) (-1, ∞) Let f (x) = log (1 + x) - x f’ (x) = 1 / [1 + x] - 1 = - x / [1... View Article
Let F X X 1 A If X 1 2x 3 If X 1 If F X Has Local Minimum 1) a = 7 2) a = 8 3) a = 9 4) a ≤ 5 Solution: (4) a ≤ 5 Clearly f (x) = 1 - x + a if x ≤ 1 Since y = 1 - x + a is decreasing... View Article
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