If Tan Inverse A Plus X A Plus Tan Inverse A Minus X 1) 2√3a 2) √3a 3) 2√3a2 4) None of these Answer: (1) 2√3a Solution: Given, tan-1[(a + x)/a] + tan-1[(a - x)/a] = π/6 Using the... View Article
Cot Inverse Xy Minus 1 X Minus Y Plus Cot Inverse Yz 1) 0 2) 1 3) cot-1(x) + cot-1(y) + cot-1(z) 4) None of the above Answer: (1) 0 Solution: cot-1[(xy + 1)/(x - y)] + cot-1[(yz +... View Article
Tan Inverse X Plus Cot Inverse 1 X 1 1) tan-1(x2 + 1) 2) tan-1(x2 + x) 3) tan-1(x + 1) 4) tan-1(x2 + x + 1) Answer: (4) tan-1(x2 + x + 1) Solution: tan-1(x) + cot-1(x +... View Article
Cos Tan Inverse 1 3 Plus Tan Inverse 1 2 1) 1/√2 2) √3/2 3) 1/2 4) π/4 Answer: (1) 1/√2 Solution: tan-1(1/3) + tan-1(1/2) Using the formula tan-1(x) + tan-1(y) = tan-1[(x... View Article
2 Sin Inverse 3 5 Plus Cos Inverse 24 25 Equal To 1) π/2 2) 2π/3 3) 5π/3 4) None of these Answer: (1) π/2 Solution: Let 2 sin-1(3/5) = A sin-1(3/5) = A/2 sin A/2 = 3/5 Using the... View Article
If Cot Inverse X Plus Tan Inverse 3 Pi 2 Then X 1) 1/3 2) 1/4 3) 3 4) 4 Answer: (3) 3 Solution: Given, cot-1(x) + tan-1(3) = π/2 We know that tan-1(x) + cot-1(x) = π/2... View Article
The Equation Of The Normal To The Curve Y 1 X Y Sin 1 Sin 2 X At X 0 1) x + y = 2 2) x + y = 1 3) x - y = 1 4) x2 - y2 = 2 Solution: (2) x + y = 1 y = (1 + x)y + sin-1 (sin2 x) (dy / dx) = y ∙ (1 +... View Article
If F X X 1 And G X F F F X The Value For X 2 G X 1) 1 for all x > 2 2) 1 for 2 < x < 3 3) -1 for 2 < x < 3 4) Not defined Solution: (3) -1 for 2 < x < 3 For x... View Article
The Minimum Value Of Sec 2 X Cosec 2 X Equation Maximum Value Of 1) a = b 2) a = 2b 3) a = 3b 4) a = 4b Solution: (4) a = 4b y = tan2 x + cot2 x and Z = a sin2 x + b cos2 x y = (√ɑ tanx - √β... View Article
In 0 1 Mean Value Theorem Is Not Applicable To 1) f (x) = [(1 / 2) - x), x < 1 / 2] 2) f (x) = sinx / x, x = 0 3) f (x) = x |x| 4) f (x) = |x| Solution: (1) f (x) = [(1 / 2) -... View Article
In A B C 0 Then The Equation 3ax 2 2bx C 0 Has In The Interval 0 1 1) At least one root 2) At most one root 3) No root 4) Exactly one root exists Solution: (1) At least one root f’ (x) = 3ax2 + 2bx... View Article
If M Tan X Is The Slope Of The Tangent To The Curve E Y 1 X 2 Then 1) |tan x| > 1 2) |tan x| < 1 3) 1 ≤ tan x < 1 4) -1 ≤ |tan x| ≤ 1 Solution: (4) -1 ≤ |tan x| ≤ 1 dy / dx = m = 2x / [1 +... View Article
At Any Point Of A Curve Sub Tangent Sub Normal Is Equal To The Square Of The 1) Slope of the tangent at the point 2) Slope of the normal at the point 3) Abscissa of the point 4) Ordinate of the point Solution:... View Article
If The Curves 2x 2 3y 2 6 And Ax 2 4y 2 4 Intersect Orthogonally Then A 1) 2 2) 1 3) 3 4) –3 Solution: (1) 2 2x2 + 3y2 = 6 2 ∙ 2x + 6y (dy / dx) = 0 4x + 6y (dy / dx) = 0 (dy / dx) = [(– 4x) / 6y] =... View Article
Two Measurement Of A Cylinder Are Varying In Such A Way That The Volume Is Kept Constant 1) r = 2h 2) h = 2r 3) h = r 4) h = 4r Solution: (1) r = 2h Volume of cylinder = v = πr2h Volume is constant ⇒ (dv / dt) = 0 (dv... View Article
Prove That The Condition X Cos Alpha Y Sin Alpha P Touches The Curve 1) m + n 2) m - n 3) n - m 4) m2 - n2 Solution: (1) m + n nm . yn = am+n, m log x + n log y = (m + n) log x (dy / dx)(x1, y1) =... View Article
Function F X X 1 2 X 1 Tanx How Many Points Are Not Differentiable In 0 2 1) 1 2) 2 3) 3 4) 4 Solution: (3) 3 f (x) = |x - (1 / 2)| + |x - 1| + tanx g (x) = |x - (1 / 2)| at x = 1 / 2, g (x) is not... View Article
The Length Of Line Segment When Tangent Of The Curve Intersect To Both Axes 1) a 2) |a| 3) a2 4) a3 Solution: (1) a (x / a)⅔ = cos2 θ and (y / a)⅔ = sin2 θ (x / a)⅓ = cos θ, (y / b)⅓ = sin θ x = a cos3 θ,... View Article
If X 13y 7 X Y 20 Then Xy 1 Y 1) 7 2) 13 3) 20 4) 0 Solution: (4) 0 x13y7 = (x + y)20 13 log x + 7 log y = 20 log (x + y) (13 / x) + (7 / y) (dy / dx) = [20... View Article
If Y X X And D 2y Dx 2 Y X 1 Y Dy Dx 2 Then 1) xy 2) xx 3) yx 4) x Solution: (2) xx y = xx, log y = x . log x [d2y / dx2] (y / x) (1 / xx) (dy / dx)2 dy / dx = xx [1 + log x]... View Article