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If Npr 720 Ncr Then R Is Equal To

1) 6 2) 5 3) 4 4) 7 Answer: (1) 6 Solution: Given, nPr = 720. nCr n!/(n-r)! = 720. [n!/(n-r)!.r!] r!=720 r!=6.5.4.3.2.1 r!=6! r = 6... View Article

1) CD 2) CD/(C2 + D2) 3) (C2 + D2)/2CD 4) 2CD/(C2 + D2) Answer: (4) 2CD/(C2 + D2) Solution: sin A + sin B = C....(i) cos A + cos B... View Article

1) 4 2) -2 3) -4 4) 0 Answer: (3) -4 Solution: Given, (cos A)/3 = (cos B)/4 = 1/5 cos A = 3/5, cos B = 4/5 Also, given that -π/2... View Article

1) 0 2) 1 3) -1 4) None of these Answer: (4) None of these Solution: Given, x = 5π/6 2 sin 3x + 3 cos 3x = 2 sin(15π/6) + 3... View Article

1) (1 + cos A)/sin A 2) (1 + sin A)/cos A 3) (1 - cos A)/(1 + cos A) 4) (1 + sin A)/(1 - sin A) Answer: (2) (1 + sin A)/cos A... View Article

1) 4 2) 5 3) 2 4) 9 Answer: (4) 9 Solution: Given, 3 sin A + 5 cos A = 5....(i) Let 3 cos A - 5 sin A = x....(ii) Squaring and... View Article

1) √2 2) 1/√2 3) 0 4) 1 Answer: (3) 0 Solution: Given, A = 5π/4 cos A - sin A = cos 5π/4 - sin 5π/4 = cos(π + π/4) - sin(π +... View Article

1) sin B 2) sin 2B 3) sin 3B 4) None of these Answer: (2) sin 2B Solution: Given, tan A = 1/2, tan B = 1/3 cos 2A = (1 -... View Article

1) -1 2) -2 3) -3 4) -4 Answer: (1) -1 Solution: tan( - 945°) = tan(- 3 × 360° + 135°) = tan(135°) = tan(180° - 45°) = -tan 45° = -1... View Article

1) 1 2) -1 3) 0 4) 2 Answer: (4) 2 Solution: sin²(π/8) + sin²(3π/8) + sin²(5π/8) + sin²(7π/8) = sin²(π/8) + sin²(3π/8) + sin²(π/2... View Article

1) sec A 2) 2 sec A 3) 0 4) 2 Answer: (3) 0 Solution: (sec A + tan A - 1)(sec A - tan A + 1) - 2 tan A = [sec A + (tan A - 1)]... View Article

1) 1 2) 0 3) 1/√2 4) None of these Answer: (4) None of these Solution: We know that, sin(π/2 + θ) = cos θ cos(π/2 - θ) = sin θ... View Article

1) 0 2) 2 tan A 3) 2 cot A 4) 2(tan A - cot A) Answer: (1) 0 Solution: We know that, cot(180° + x) = cot x (quadrant III) cot(90°... View Article

1) -1 2) 0 3) 1 4) ∞ Answer: (3) 1 Solution: cot(45° + θ) cot(45° - θ) = [(cot 45 cot θ - 1)/ (cot 45 + cot θ)] [(cot 45 cot θ +... View Article

1) 1 2) -1 3) sin θ 4) -sin θ Answer: (2) -1 Solution: sin(π + θ) sin(π - θ) cosec2θ = (-sin θ)(sin θ) cosec2θ = -sin2θ cosec2θ... View Article

1) 2 tan 2θ 2) 2 cot θ 3) tan 2θ 4) cot 2θ Answer: (1) 2 tan 2θ Solution: tan(π/4 + θ) - tan(π/4 - θ) = [(tan π/4 + tan )/(1 - tan... View Article

1) -1 2) 0 3) 1 4) None of these Answer: (2) 0 Solution: We know that, sin(270° + x) = -cos x sin(270° - x) -cos x cos(180° + x)... View Article

1) x > 0 2) x < 0 3) x = 0 4) x ≤ 0 Answer: (1) x > 0 Solution: Given, A = 130° x = sin A + cos A x = sin 130° + cos... View Article

1) 2 2) 4 3) 8 4) 16 Answer: (3) 8 Solution: x sin 45° cos260° = (tan260° cosec 30°)/(sec 45° cot230°) x (1/√2) (1/2)2 = [(√3)2... View Article

1) 1/2 2) -1/2 3) 1/4 4) 1 Answer: (3) 1/4 Solution: we know that sin 18° = (√5 - 1)/4, cos 36° = (√5 + 1)/4 sin(π/10) sin(3π/10)... View Article