Archives

If 0 Theta Pi 0 Phi Pi And Cos Theta Cos Phi Cos Theta Plus Phi Is 1 8 Then

1) θ = π/4, Φ = π/3 2) θ = π/3, Φ = π/4 3) θ = Φ = π/3 4) θ = Φ = π/4 Answer: (3) θ = Φ = π/3 Solution: Given, 0 < θ < π, 0... View Article

Sin Power 2n X Plus Cos Power 2n X Lies Between

1) -1 and 1 2) 0 and 1 3) 1 and 2 4) None of these Answer: (2) 0 and 1 Solution: sin2nx + cos2nx The powers of sin and cos are the... View Article

If A Greater Than 0 B Greater Than 0 And A Plus B Is Pi 3 Then

1) 1/2 2) 1/3 3) 1/4 4) 1/6 Answer: (2) 1/3 Solution: Given, A > 0, B > 0 and A + B = π/3 That means, tan A > 0, tan B... View Article

If 2 Sin Alpha 1 Cos Alpha Sin Alpha Equal To X Then

1) 1/x 2) x 3) 1 - x 4) 1 + x Answer: (2) x Solution: Given, [(2 sin α)/ (1 + cos α + sin α)] = x....(i) Now, [(1 - cos α + sin... View Article

If A B C Are Acute Positive Angles Then Sin A Sin B Sin B Sin C Sin C Sin A

1) > 1 2) ≤ 1 3) = 2 4) None of these Answer: (4) None of these Solution: Given, A, B, C are acute positive angles. Therefore,... View Article

If Cosec A Sec A Cosec B Sec B Then Tan A Tan B Is

1) tan(A + B)/2 2) cot(A + B)/2 3) sin(A + B)/2 4) cos(A + B)/2 Answer: (2) cot(A + B)/2 Solution: Given, cosec A + sec A = cosec... View Article

Let A And B Denote The Statements A Cos Alpha Cos Beta Cos Gamma 0

1) A is correct and B is incorrect 2) A is incorrect and B is correct 3) both A and B are correct 4) both A and B are incorrect... View Article

If Alpha Plus Beta Plus Gamma Is 2pi Then

1) tan α/2 + tan β/2 + tan γ/2 = tan α/2 tan β/2 tan γ/2 2) tan α/2 tan β/2 + tan β/2 tan γ/2 + tan γ/2 tan α/2 = 1 3) tan α/2 + tan β/2 + tan... View Article

If Cot Beta Equal To Sin Alpha Sin Gamma Cos Gamma Cos Alpha Then

1) A.P 2) G.P 3) H.P 4) None of these Answer: (1) A.P Solution: cot β = (sin α – sin γ)/ (cos γ – cos α) Using the formulas sin x... View Article

If Tan K Plus 1 Theta Tan Theta Then Theta Belongs To

1) {nπ : n ϵ I} 2) {nπ/2 : n ϵ I} 3) {nπ/k : n ϵ I} 4) {nπ/2k : n ϵ I} Answer: (3) {nπ/k : n ϵ I} Solution: Given, tan (k + 1)θ =... View Article

Which One Of The Following Equations Has No Solution

1) cosec θ - sec θ = cosec θ . sec θ 2) cosec θ . sec θ = 1 3) cos θ + sin θ = √2 4) √3 sin θ - cos θ = 2 Answer: (2) cosec θ . sec θ... View Article

The General Solution Of Sin X Cos X Root2 For Any Integer N Is

1) nπ 2) 2nπ + 3π/4 3) 2nπ 4) (2n + 1)π Answer: (2) 2nπ + 3π/4 Solution: Given, sin x - cos x = √2 Dividing by √2 on both sides,... View Article

The Number Of Values Of X In The Interval 0 3pi Satisfying The Equation

1) 6 2) 1 3) 2 4) 4 Answer: (4) 4 Solution: Given, 2 sin2x + 5 sin x - 3 = 0 2 sin2x + 6 sin x - sin x - 3 = 0 2 sin x(sin x +... View Article

The Set Of Values Of Theta Satisfying The Equation 2 Sin 2 Theta 5 Sin Theta 2 Greater Than 0

1) (0, π/6) ⋃ (5π/6, 2π) 2) [0, π/6) ⋃ [5π/6, 2π] 3) [0, π/3] ⋃ [2π/3, 2π] 4) None of these Answer: (1) (0, π/6) ⋃ (5π/6, 2π)... View Article

The Solution Of Tan 2theta Tan Theta 1 Is

1) π/3 2) (6n ± 1)π/6 3) (4n ± 1)π/6 4) (2n ± π)π/6 Answer: (2) (6n ± 1)π/6 Solution: tan 2θ tan θ = 1 [(2 tan θ)/ (1 - tan2θ)]... View Article

The General Value Of Theta Is The Equation Cos Theta 1 Root2 Tan Theta 1 Is

1) 2nπ + π/6, n ∈ I 2) 2nπ + 7π/4, n ∈ I 3) 2nπ + (-1)n π/3, n ∈ I 4) 2nπ + (-1)n π/4, n ∈ I Answer: (2) 2nπ + 7π/4, n ∈ I Solution:... View Article

The Equation 3 Sin 2 X 10 Cos X 6 0 Is Satisfied If

1) x = nπ ± cos-1(1/3) 2) x = 2nπ ± cos-1(1/3) 3) x = nπ ± cos-1(1/6) 4) x = 2nπ ± cos-1(1/6) Answer: (2) x = 2nπ ± cos-1(1/3)... View Article

If Sin 3theta Sin Theta How Many Solutions Exist Such That 0 Theta 2pi

1) 8 2) 9 3) 5 4) 7 Answer: (3) 5 Solution: Given, sin 3θ = sin θ 3 sin θ - 4 sin3θ - sin θ = 0 2 sin θ - 4 sin3θ = 0 2 sin θ(1... View Article

Number Of Solutions Of Y E X And Y Sin X Is

1) 0 2) 1 3) 2 4) infinite Answer: (4) infinite Solution: Given, y = ex y = sin x Let us draw the graphs of these two... View Article

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

M	T	W	T	F	S	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30	31