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Where Is Diamond Found

Diamonds are found in the Earth's mantle at depths between 150 to 250 kilometres. Diamonds originate under extremely high pressure. Visit BYJU'S... View Article

If Sin Theta 24 25 And Theta Lies In The Second Quadrant Then

1) -3 2) -5 3) -7 4) -9 Answer: (3) -7 Solution: Given, sin θ = 24/25 θ lies in the second quadrant. In the second quadrant sec and tan are... View Article

If Sin Theta Cos Theta M And Sec Theta Cosec Theta N Then N M 1

1) m 2) n 3) 2m 4) 2n Answer: (3) 2m Solution: Given, sin θ + cos θ = m sec θ + cosec θ = n n(m + 1)(m - 1) = n(m2 - 1) = (sec θ + cosec θ)... View Article

If Sin Theta Cos Theta Is 2 Then Sin 2 Theta Cosec 2 Theta

1) 1 2) 4 3) 2 4) None of these Answer: (3) 2 Solution: Given, sin θ + cosec θ = 2 sin θ + (1/sin θ) = 2 sin2θ + 1 = 2 sin θ sin2θ - 2 sin θ... View Article

Which Of The Following Relations Is Correct

1) sin 1c < sin 1° 2) sin 1c > sin 1° 3) sin 1° = sin 1° 4) (π/180°) sin 1c = sin 1° Answer: (2) sin 1c > sin 1° Solution: We know... View Article

If Sin Theta Plus Cos Theta Is 1 Then Sin 2theta

1) 0 2) 1/2 3) 1 4) 2 Answer: (1) 0 Solution: Given, sin θ + cos θ = 1 Squaring on both sides, sin2θ + cos2θ + 2 sin θ cos θ = 1 Using the... View Article

The Incorrect Statement Is

1) sin θ = -1/5 2) cos θ = 1 3) sec θ = 1/2 4) tan θ = 20 Answer: (3) sec θ = 1/2 Solution: 1) sin θ = -1/5 = -0.2 As we know the range of sin x... View Article

If For Real Value Of X Cos Theta X 1 X Then

1) θ is an acute angle 2) θ is a right angle 3) θ is an obtuse angle 4) No value of θ is possible Answer: (4) No value of θ is possible... View Article

If Cos Theta Alpha A Sin Theta Beta B Then

1) sin2(α - β) 2) cos2(α - β) 3) 1 4) 0 Answer: (2) cos2(α - β) Solution: Given, cos(θ - α) = a, sin(θ - β) = b α - β = (θ - β) - (θ - α)... View Article

If X Not Equal To Npi 2 And Cos Power Sin 2 X 3 Sin X 2 1 Then

1) 2nπ + π/2 2) (2n + 1)π - π/2 3) nπ + (-1)n π/2 4) None of these Answer: (3) nπ + (-1)n π/2 Solution: (cos x)^(sin2x - 3 sin x + 2) = 1... View Article

For N Belongs To Z The General Solution Of Root3 1 Sin Theta Root3 1 Cos Theta 2 Is

1) θ = 2nπ ± π/4 + π/12 2) θ = nπ + (-1)n π/4 + π/12 3) θ = 2nπ ± π/4 - π/12 4) θ = nπ + (-1)n π/4 - π/12 Answer: (1) θ = 2nπ ± π/4 + π/12... View Article

If 4 Sin 2 X 8 Sin X 3 Less Than Or Equal 0 Then

1) [0, π/6] 2) [0, 5π/6] 3) [5π/6, 2π] 4) [π/6, 5π/6] Answer: (4) [π/6, 5π/6] Solution: Given, 4 sin2x – 8 sin x + 3 ≤ 0 4 sin2x - 6 sin x -... View Article

The Set Of Values Of X For Which Sin X Cos 3 X Greater Than Cos X Sin 3 X

1) (0, π/4) 2) (π/2, 3π/4) 3) (π, 5π/4) 4) (3π/2, 7π/4) Answer: (1) (0, π/4) Solution: Given, sin x cos3x > cos x sin3x, 0 ≤ x ≤ π sin x... View Article

The Most General Solutions Of 2 Sin X 2 Cos X 2 1 1 Root2 Are

1) nπ - π/4 2) nπ + π/4 3) nπ + (-1)n π/4 4) 2nπ ± π/4 Answer: (4) 2nπ ± π/4 Solution: Given, 2sin x + 2cos x = 21 - 1-/√2 2sinx + 2cosx = 2... View Article

The Number Of Real Solutions Of Sin E X Cos E X

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

If Cos Sin X Is 1 Root2 Then X Must Lies In The Interval

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

A Solution Of The Equation 1 Tan Theta 1 Tan Theta Sec 2 Theta 2 Tan 2 Theta

1) θ = 0 2) θ = π/3 or -π/3 3) θ = -π/6 4) θ = π/6 Answer: (2) θ = π/3 or -π/3 Solution: Given, (1 - tan θ)(1 + tan θ)sec2θ + 2^(tan2θ) = 0... View Article

If X Sin Alpha Y Cos Alpha Then X Sec 2alpha Y Cosec 2alpha Is

1) x 2) y 3) x + y 4) x - y Answer: (1) x Solution: Given, x sin α = y cos α....(i) (x/sec 2α) + (y/cosec 2α) = x cos 2α + y sin 2α = x(1 - 2... View Article

If X Sin 6 Theta Cos 6 Theta Then X Belongs To The Interval

1) [3/4, 5/4] 2) [1/2, 3/4] 3) [1/4, 1] 4) None of these Answer: (3) [¼, 1] Solution: Given, x = sin6θ + cos6θ = (sin2θ)3 + (cos2θ)3 Using... View Article

If Cos Alpha Beta Sin Gamma Delta Is Cos Alpha Beta Sin Gamma Delta Then

1) cot α cot β = cot γ cot δ 2) cot α cot β cot γ = cot δ 3) cot α = cot β cot γ cot δ 4) None of these Answer: (2) cot α cot β cot γ = cot δ... View Article

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