If F Of X Is Cosh X Plus Sinh X And F Of P 1) xy 2) x - y 3) x + y 4) None of these Answer: (3) x + y Solution: Given, f(x) = cosh x + sinh x From this, we can write f(y)... View Article
Cosech X Root Of Cosech Square X Plus 1 Equals 1) tanh x 2) coth x 3) sech x 4) cosh x Answer: (3) sech x Solution: cosech x/√(cosech2x + 1) Using the identity coth2x - cosech2x... View Article
1 Plus Tanh X 1 Minus Tanh X Is 1) e2x 2) e-2x 3) i 4) -1 Answer: (1) e2x Solution: We know that tanh x = (ex - e-x)/ (ex + e-x) (1 + tanh x)/(1 - tanh x) = [1... View Article
The Value Of E Power 2 Theta Minus 1 1) coth θ 2) coth 2θ 3) tanh θ 4) tanh 2θ Answer: (3) tanh θ Solution: (e2θ - 1)/(e2θ + 1) = (eθ eθ - 1)/(eθ eθ - 1) = [eθ(eθ -... View Article
Tanh X Plus Y Equals 1) (tanh x + tanh y)/(1 - tanh x tanh y) 2) (tanh x + tanh y)/(1 + tanh x tanh y) 3) (tanh x - tanh y)/(1 - tanh x tanh y) 4) (tanh x -... View Article
Sinh 3z Equals 1) 2 sinh z - 4 sinh3z 2) 4 sinh3z - 3 sinh z 3) 3 sinh z + 4 sinh3z 4) None of these Answer: (3) 3 sinh z + 4 sinh3z Solution:... View Article
Find The Real Part Of Tan Inverse 1 Plus I 1) -(1/2) tan-1(2) 2) 12 tan-1(2) 3) -(1/2) tan-1(1/2) 4) 0 Answer: (1) -(1/2) tan-1(2) Solution: Let a + ib = tan-1(1 + i) a - ib... View Article
Value Of Tan Inverse Sin 2 Minus 1 Cos 2 Is 1) (Ï€/2) - 1 2) 1 - (Ï€/4) 3) 2 - (Ï€/2) 4) (Ï€/4) - 1 Answer: (2) 1 - (Ï€/4) Solution: We know that sin 2A = 2 sin A cos A cos 2A =... View Article
Tan 2 Tan Inverse 1 5 Minus Pi 4 Equals 1) 17/7 2) -17/7 3) 7/17 4) -7/17 Answer: (4) -7/17 Solution: 2 tan-1(1/5) = tan-1(1/5) + tan-1(1/5) Using the formula tan-1(x) +... View Article
Tan 2 Cos Inverse 3 5 Equals 1) 7/25 2) 24/25 3) -24/7 4) 8/3 Answer: (3) -24/7 Solution: Let cos-1(3/5) = A....(i) cos A = 3/5 Using the identity sin2A +... View Article
If Sin Inverse 1 X Plus 2 Sin Inverse X Pi 2 Then X 1) (0, -1/2) 2) (1/2, 0) 3) {0} 4) (-1, 0) Answer: (2) (1/2, 0) Solution: Given, sin-1(1 - x) + 2 sin-1(x) = π/2 sin-1(1 - x) =... View Article
If Cos Of 2 Sin Inverse X 1 9 Then X Equal To 1) only 2/3 2) only -2/3 3) 2/3, -2/3 4) Neither 2/3 nor -2/3 Answer: (3) 2/3, -2/3 Solution: Given, cos[2 sin-1(x)] = 1/9 Let... View Article
If A Equal To Tan Inverse X Then Sin 2a 1) 2x/√(1 - x2) 2) 2a/(1 - x2) 3) 2x/(1 + x2) 4) None of these Answer: (3) 2x/(1 + x2) Solution: Given, A = tan-1(x) tan A = x... View Article
Tan 1 2 Sin Inverse 2a 1 Plus A Square Plus 1 2 1) 2a/(1 + a2) 2) (1 - a2)/(1 + a2) 3) 2a/(1 - a2) 4) None of these Answer: (3) 2a/(1 - a2) Solution: tan[(1/2) sin-1{2a/(1 + a2)}... View Article
Cot Inverse Cos Alpha Power 1 2 Minus Tan Inverse Cos Alpha 1) tan2(α/2) 2) cot2(α/2) 3) tan α 4) cot α/2 Answer: (1) tan2(α/2) Solution: Given, cot-1[(cos α)1/2] - tan-1[(cos α)1/2] = x... View Article
If Cos Inverse Root P Plus Cos Inverse Root 1 Minus P 1) 1 2) 1/√2 3) 1/3 4) 1/2 Answer: (4) 1/2 Solution: Given, cos-1√p + cos-1√(1 - p) + cos-1√(1 - q) = 3π/4 cos-1√p + cos-1√[1 -... View Article
The Equation Of Particle Is X T 3 9t 2 3t 1 And V 24 Then A 1) 3 2) 2 3) 1 4) 0 Solution: (4) 0 Velocity of the ball (v) = ds/ dt = u - 9.8t Terminal velocity v = 0 and t = 3 seconds u = 9.8 (3) =... View Article
A Particle Is Moving On A Straight Line Where Its Position S In Metre Is A Function 1) –1 m / s2 2) (5 / 4) m / s2 3) (1 / 2) m / s2 4) (- 5 / 4) m / s2 Solution: (2) (5 / 4) m / s2 s = at2 + bt + 6 v = 2at + b... View Article
If Y X 3 5 And X Changes From 3 To 2 99 Then The Approximate Change In Y Is 1) 2.7 2) –0.27 3) 27 4) None of these Solution: (2) –0.27 y = x3 + 5 dy = 3x2 dx = 3 (3)2 - 0.01 = - 0.27... View Article
A Triangular Park Is Enclosed On Two Sides On Two Sides By A Fence 1) (3 / 2) x2 2) √x3 / 8 3) (1 / 2) x2 4) πx2 Solution: (3) (1 / 2) x2 Area of triangle = (1 / 2) base * height = (1 / 2) (2x2... View Article
