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The Number Of Solutions Of The Equation 1 Sin X Sin 2 X 2 0 Is

1) 0 2) 1 3) 2 4) 3 Answer: (1) 0 Solution: Given, 1 + sin x sin2 x/2 = 0 Using the formula cos 2A = 1 - 2 sin2A, 1 + sin x [(1... View Article

The Number Of Solutions Of The Pair Of Equations 2 Sin 2 Theta Cos 2theta 0 And 2 Cos 2 Theta

1) 0 2) 1 3) 2 4) 4 Answer: (3) 2 Solution: Given, 2 sin2θ - cos 2θ = 0 2 sin2θ - (1 - 2 sin2θ) = 0 2 sin2θ - 1 + 2 sin2θ = 0 4... View Article

The Number Of Solutions Of Sin X Sin 2x Between Minus Pi 2 And Pi 2 Is

1) 3 2) 2 3) 1 4) 0 Answer: (1) 3 Solution: Given, sin x = sin 2x sin 2x - sin x = 0 2 sin x cos x - sin x = 0 sin x(2 cos x -... View Article

If Cos X Not Equal To 1 2 Then Solutions Of Cos X Cos 2x Cos 3x 0 Are

1) 2nπ ± π/4, n ∈ Z 2) 2nπ ± π/3, n ∈ Z 3) 2nπ ± π/6, n ∈ Z 4) 2nπ ± π/2, n ∈ Z Answer: (1) 2nπ ± π/4, n ∈ Z Solution: Given, cos... View Article

X Belongs To R Such That Cos 2x 2 Cos 2 X 2 Is Equal To

1) {2nπ + π/3, n ∈ Z} 2) {nπ ± π/6, n ∈ Z} 3) {nπ + π/3, n ∈ Z} 4) {2nπ - π/3, n ∈ Z} Answer: (2) {nπ ± π/6, n ∈ Z} Solution:... View Article

The Number Of Values Of X In 0 2pi Satisfying The Equation 3 Cos 2x 10 Cos X 7 0 Is

1) 1 2) 2 3) 3 4) 4 Answer: (4) 4 Solution: Given, 3 cos 2x - 10 cos x + 7 = 0 3(2 cos2x - 1) - 10 cos x + 7 = 0 3 cos2x - 5 cos... View Article

The Solution Of The Equation 4 Sin 2 X Cos 2 X 1 Is

1) x = 2nπ 2) x = nπ + 1 3) x = (n + 2) π 4) None of these Answer: (4) None of these Solution: Given, 4 sin2x + cos2x = 1 3 sin2x... View Article

If 2 Sin 2 Theta Root3 Cos Theta 1 0 Then The Value Of Theta Is

1) π/6 2) 2π/3 3) 5π/6 4) π Answer: (3) 5π/6 Solution: Given, 2sin2θ + √3 cos θ + 1 = 0 2(1 - cos2θ) + √3 cos θ + 1 = 0 2 - 2... View Article

The Most General Value Of Theta Satisfying The Equations Sin Theta Sin Alpha And Cos Theta Cos Alpha

1) 2nπ + α 2) 2nπ - α 3) nπ + α 4) 2nπ - α Answer: (3) nπ + α Solution: Given, sin θ = sin α....(1) cos θ = cos α....(2)... View Article

The Equation Root3 Sin X Cos X 4 Has

1) infinitely many solutions 2) no solution 3) two solution 4) only one solution Answer: (2) Solution: Given, √3 sin x + cos x = 4... View Article

The Distance Between The Origin And The Normal To The Curve Y E 2x X 2 At X 0 Is

1) 2 2) 2/√3 3) 2/√5 4) 1/2 5) 1/√5 Solution: (5) 1 / √5 y = e2x + x2 At x = 0, y = 1 dy / dx = 2e2x + 2x Slope of tangent at (0,1)... View Article

The Angle Between The Curves Y X 2 And Y 2 X 0 At The Point 1 1 Is

1) π/2 2) tan-1 4/3 3) π/3 4) π4 5) tan-1 3/4 Solution: (5) tan-1 (3 / 4) y = x2 and y2 - x = 0 dy / dx = 0 (dy / dx) x = (1,... View Article

The Point On The Curve X 2 Y 2 A 2 Y 0 At Which The Tangent Is Parallel To The X Axis Is

1) (a, 0) 2) (-a, 0) 3) (a / 2, √3 / 2 a) 4) (0, a) 5) (0, a2) Solution: (4) (0, a) x2 + y2 = a2 2x + 2y (dy / dx) = 0 Now... View Article

The Coordinates Of The Point On The Curve Y X 2 3x 2 Where The Tangent Is Perpendicular To The Straight Line Y X Are

1) (0, 2) 2) (1, 0) 3) (-1, 6) 4) (2, -2) Solution: (2) (1, 0) Given y = x Slope = m = 1 m mt = -1 1 * mt = -1 mt = -1 y = x2... View Article

If The Normal To The Curve Y F X At The Point 3 4 Make An Angle 3 Pi 4 With The Positive X Axis Then F Dash 3 Is

1) 1 2) -1 3) - (3/4) 4) 3/4 Solution: (1) 1 y = f (x) y’ = f ‘(x) Slope of tangent = f’ (x) Slope of normal = -1 / f’ (x) At... View Article

The Point In The Interval 0 2 Pi Where F X Ex Sin X Has Maximum Slope Is

1) π/4 2) π/2 3) π 4) 3π/2 Solution: (2) π / 2 f (x) = ex sin x f’ (x) = ex cosx + sinx ex f’’ (x) = - ex sinx + cosx ex + ex... View Article

The Equation Of The Tangent Of The Curve Y X 4 X 2 That Is Parallel To The X Axis Is

1) y = 0 2) y = 1 3) y = 2 4) y = 3 Solution: (4) y = 3 Slope of the line parallel to x-axis = 0 y = x + 4 / x2 y’ = 1 + (-2)... View Article

Let F R Be A Continuous Function Defined By F X 1 E X 2e X

Statement I : f (c) = 1 / 3, for some c ∈ R Statement II : 0 < f (x) ≤ 1 / (2√2), ∀ x ∈ R 1) Statement I is correct, Statement II is also... View Article

The Length Of The Normal To The Curve Y A Cosh X A At Any Point Varies As

1) ordinate 2) abscissa 3) Square of the abscissa 4) square of the ordinate Solution: (4) square of the ordinate y = a cosh (x/a)... View Article

F X X 2 1 X 2 1 For Every Real Number X Then Minimum Value Of F Is

1) -1 2) does not exist 3) 0 4) 1 Solution: (1) -1 f (x) = [x2 - 1] / [x2 + 1] = 1 - [2 / (x2 + 1)] f (x) will be minimum when 2... View Article

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