If A 2i3jk B I2j 5k C3i5jk Then A Vector Perpendicular To A And In The Plane Containing B And C Is 1) -17i + 21j - 97k 2) 17i + 21j - 123k 3) -17i -21j + 97k 4) -17i -21j -97k Answer: (4) -17i -21j -97k Solution: Let the required vector be... View Article
If Abc Are Unit Vectors Such That A B C 0 Find The Value Of Vector A B B C Ca 1) 1/2 2) 0 3) 1 4) -3/2 Answer: (4) -3/2 Solution: Given, a+ b+ c=0 Squaring both the sides, |a + b + c|2 = 0 (a+b+a) (a+b+c) = 0... View Article
If A B B C And C A Are Coplanar Then A B C Is 1) 0 2) 1 3) a.b 4) b.c Answer: (1) 0 Solution: Given, vectors (a + b), (b + c) and (c + a) are coplanar Therefore, (a+b) [(b+c) x (c +... View Article
Let A B And C Be Non Zero Vectors Such That A B C 1 4b C A If Theta Is The Acute Angle 1) 2π/3 2) π/4 3) π/3 4) π/2 Answer: (4) π/2 Solution: Given, (a × b) × c = –1/4|b| |c| a ⇒ (c.a)b - (c.b)a = ¼ |b| |c| a ⇒ (c.a) b = 0... View Article
If A B And C Be Three Unit Vectors Such That A B C 12 B B And C Being Non Parallel If Theta1 Is The Angle 1) θ1 = π/6, θ2 = π/3 2) θ1 = π/3,θ2 = π/6 3) θ1 = π/2,θ2 = π/3 4) θ1 = π/3,θ2 = π/2 Answer: (3) θ1 = π/2,θ2 = π/3 Solution: Given,... View Article
Let U And V Are Unit Vectors And W Is A Vector Such That U X V U W And W X U V Then Find The Value Of U V W 1) 0 2) 1 3) |w| 4) 2 |w| Answer: (2) 1 Solution: Given, u x v + u = w Multiply both sides with vector u → (u x v + u) x u = w x u → (u x... View Article
If 3 Sec Square Theta Plus Tan Square Theta 5 Then 1) 2nπ + π/6 2) 2nπ ± π/6 3) nπ ± π/6 4) nπ ± π/3 Answer: (3) nπ ± π/6 Solution: Given, 3(sec2θ + tan2θ) = 5 sec2θ + tan2θ = 5/3... View Article
If 1 Minus Cos 2theta 1 Plus Cos 2theta 3 Then 1) 2nπ ± π/6 2) nπ ± π/6 3) 2nπ ± π/3 4) nπ ± π/3 Answer: (4) nπ ± π/3 Solution: Given, (1 - cos 2θ)/(1 + cos 2θ) = 3 1 - cos 2θ... View Article
If Plus Cot Theta Cosec Theta Then The General Value Of Theta 1) nπ + π/2 2) 2nπ - π/2 3) 2nπ + π/2 4) None of these Answer: (3) 2nπ + π/2 Solution: Given, 1 + cot θ = cosec θ 1 + (cos θ/sin... View Article
If Tan 2theta Tan Theta 1 Then The General Value Of Theta 1) (n + 1/2) π/3 2) (n + 1/2) π 3) (2n ± 1/2) π/3 4) None of these Answer: (4) None of these Solution: Given, tan 2θ tan θ = 1... View Article
If Root3 Tan 2theta Plus Root3 Tan 3theta Plus Tan 2 Theta 1) nπ + π/5 2) (n + 1/6) π/5 3) (2n ± 1/6) π/5 4) (n + 1/3) π/5 Answer: (2) (n + 1/6) π/5 Solution: Given, √3 tan 2θ + √3 tan 3θ +... View Article
If 2 Sin Theta Plus Tan Theta 0 Then The General Values Of Theta 1) 2nπ ± π/3 2) nπ, 2nπ ± 2π/3 3) nπ, 2nπ ± π/3 4) nπ, nπ + 2π/3 Answer: (2) nπ, 2nπ ± 2π/3 Solution: Given, 2 sin θ + tan θ = 0... View Article
If 2 Tan Square Theta Sec Square Theta Then 1) nπ + π/4 2) nπ - π/4 3) nπ ± π/4 4) 2nπ ± π/4 Answer: (2) nπ ± π/4 Solution: Given, 2 tan2θ = sec2θ 2(sin2θ/cos2θ) = 1/cos2θ... View Article
If Sin Square Theta Minus 2 Cos Theta Plus 1 4 0 Then 1) nπ ± π/3 2) 2nπ ± π/3 3) 2nπ ± π/6 4) nπ ± π/6 Answer: (2) 2nπ ± π/3 Solution: Given, sin2θ - 2 cos θ + 1/4 = 0 Using the... View Article
If Sec Square Theta 4 3 Then The General Value Of Theta Is 1) 2nπ ± π/6 2) nπ ± π/6 3) 2nπ ± π/3 4) nπ ± π/3 Answer: (2) nπ ± π/6 Solution: Given, sec2θ = 4/3 sec θ = √(4/3) sec θ = ±2/√3... View Article
If Sin Square Theta Is 1 4 Then The Most General Value Of Theta 1) 2nπ ± (-1)n π/6 2) (nπ/2) ± (-1)n π/6 3) nπ ± π/6 4) 2nπ ± π/6 Answer: (3) nπ ± π/6 Solution: Given, sin2θ = 1/4 sin θ =... View Article
Tanh Inverse 1 2 Plus Tanh Inverse 1 3 Is 1) tanh-1(5/7) 2) tanh-1(7/5) 3) tanh-1(1/6) 4) tanh-1(5/6) Answer: (1) tanh-1(5/7) Solution: We know that, tanh-1(x) + tanh-1(y)... View Article
If Tan Theta Plus I Phi Sin X Plus Iy Then The Value Of 1) tan x cot 2θ 2) tan x sin 2θ 3) cot x sin 2θ 4) None of these Answer: (3) cot x sin 2θ Solution: Given, tan(θ + iΦ) = sin(x +... View Article
The Value Of Cosech Pi I 6 Is 1) -2 2) 2 3) -2i 4) 2i Answer: (3) -2i Solution: We know that cosech(ix) = -i cosec x cosech(Ï€i/6) = -i cosec(Ï€/6) = -i(2)... View Article
If F X Cosh X Minus Sinh X Then F X1 Plus X2 1) f(x1).f(x2)...f(xn) 2) f(x1) + f(x2) + ... +f(xn) 3) 0 4) 1 Answer: (1) f(x1).f(x2)...f(xn) Solution: Given, f(x) = cosh x -... View Article