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Which One Of The Following Vectors Is Of Magnitude 6 And Perpendicular Both A4ij3k And B2ij2k

1) 2i-jk2k 2) 2(2i-j+2k) 3) 3(2i-j-2j) 4) -2i+4j+4k Answer: (4) -2i+4j+4k Solution: Given, a=4i-j+3k and b=-2i+j-2k So, =i (2−3)−j... View Article

1) {1, 2} 2) {-1, 2} 3) {-1, 1, 0} 4) {1, 1/2, 0} Answer: (3) {-1, 1, 0} Solution: We know that, sin 2A = 2 tan A/(1 + tan2A)... View Article

1) π/3 2) π/2 3) 2π/3 4) -2π/3 Answer: (1) π/3 Solution: Given, θ = sin-1[sin(-600°)] sin θ = sin(-600°) = -sin 600° =... View Article

1) (π, π/2) 2) (-π/2, π/2) 3) (-π, π) 4) (0, π) Answer: (2) (-π/2, π/2) Solution: The graph of tan-1x (or) arctan x is given as:... View Article

1) cosec(sec-1x) 2) cot x 3) π 4) None of these Answer: (1) cosec(sec-1x) Solution: Let cosec-1x = A cosec A = x sin A = 1/x... View Article

1) 3 2) -3 3) 1/3 4) -1/3 Answer: (1) 3 Solution: Given, tan-1x = sin-1(3/√10)....(i) Let A = sin-1(3/√10) sin A = 3/√10 Using... View Article

1) 5π/3 2) -5π/3 3) -π/3 4) 4π/3 Answer: (3) -π/3 Solution: Let θ = sin-1(sin 5π/3) sin θ = sin 5π/3 sin θ = sin(2π - π/3) sin θ... View Article

1) 0 2) tan-1x 3) π/4 4) π/2 Answer: (3) π/4 Solution: Let cosec-1(√41/4) = A cosec A = √41/4 sin A = 4/√41 Using the identity... View Article

1) cos-1√(1 - x2) 2) -cos-1√(1 - x2) 3) cos-1√(x2 - 1) 4) π - cos-1√(1 - x2) Answer: (2) -cos-1√(1 - x2) Solution: Let x = sin... View Article

1) 0, π 2) 0, π/4 3) -π/4, π/4 4) π/4, π/2 Answer: (2) 0, π/4 Solution: Let x = tan A....(i) Now, f(x) = tan-1[(1 - x)/(1 + x)]... View Article

1) 10 2) 10 - 3π 3) 3π - 10 4) None of these Answer: (3) 3π - 10 Solution: As we know sin-1(sin x) = x when -π/2 ≤ x ≤ π/2 From... View Article

1) 25/24 2) 25/7 3) 24/25 4) None of these Answer: (4) None of these Solution: Let cos-1(7/25) = A cos A = 7/25 Using the... View Article

1) 3/17 2) 4/17 3) 5/17 4) 6/17 Answer: (4) 6/17 Solution: cot[cosec-1(5/3) + tan-1(2/3)]....(i) Let cosec-1(5/3) = A cosec A =... View Article

1) (-π, π) 2) [-1, 1] 3) (0, 2π) 4) (-∞, ∞) Answer: (2) [-1, 1] Solution: The graph of sin-1(x) or arcsin x is given as:... View Article

1) [√(1 - x2)]/x 2) x/(1 + x2) 3) [√(1 + x2)]/x 4) √(1 + x2) Answer: (1) [√(1 - x2)]/x Solution: Let cos-1(x) = θ x = cos θ... View Article

1) 0 2) (√5 - 4√2)/9 3) (√5 + 4√2)/9 4) π/2 Answer: (3) (√5 + 4√2)/9 Solution: Given, sin-1(1/3) + sin-1(2/3) = sin-1(x) Using... View Article

1) sin2θ + sin2β 2) sin2θ + cos2β 3) cos2θ + cos2β 4) cos2θ + sin2β Answer: (2) sin2θ + cos2β Solution: Given, sin-1(x) = θ + β... View Article

1) 1 2) 0 3) 4/5 4) 1/5 Answer: (4) 1/5 Solution: Given, sin[sin-1(1/5) + cos-1(x)] = 1 sin-1(1/5) + cos-1(x) = sin-1(1)... View Article

1) 1 2) 2 3) -1 4) -2 Answer: (1) 1 Solution: Given, A, B, C are the angles of a triangle. A + B + C = 180° ⇒ tan A + tan B +... View Article

1) A ≥ 1 2) 0 < A ≤ 1 3) 1 < 2A ≤ 3 4) None of these Answer: (2) 0 < A ≤ 1 Solution: Given, A = sin8θ + cos14θ We know that, 0... View Article