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Which of the following is a neutral oxide?

Which of the following is a neutral oxide? SrO Al2O3 CO2 CO Answer : (d) CO Reason: Carbon monoxide dissolves in water without... View Article

What alkali mean?

Alkalis are bases that can be dissolved in water. Few examples of alkalis are potassium hydroxide, sodium hydroxide etc. The pH value of a... View Article

What cannot be changed in Charles Law

The pressure is kept constant in Charles law. According to Charles law, the volume of the gas is proportional to the temperature if the pressure... View Article

What is the temperature coefficient of copper?

The temperature coefficient of copper is 0.393 percentage per degree celsius. In other words, if the temperature increases by 10C then the... View Article

Why is Aluminium a bad conductor?

We cannot truly say Aluminium is a bad conductor because firstly it is a metal compound and secondly it contains free moving delocalized... View Article

d/dx cos^-1 √cos x =

(1) (½) √(sec x + 1) (2) √(sec x + 1) (3) -(½) √(sec x + 1) (4) -√(sec x + 1) Solution: Let y = cos-1 √cos x dy/dx = -1/√(1-cos... View Article

If y = cos (sin x²), then at x = √(π/2), dy/dx =

(1) -2 (2) 2 (3) 0 (4) none of these Solution: Given y = cos (sin x2) dy/dx = -sin (sin x2). cos x2. 2x At x = √(π/2) dy/dx =... View Article

(d/dx)x² sin (1/x)

(1) cos (1/x) + 2x sin (1/x) (2) 2x sin (1/x) - cos (1/x) (3) cos (1/x) - 2x sin (1/x) (4) none of these Solution: Let y = x2 sin... View Article

(d/dx)[cos (1-x²)²] =

(1) -2x(1-x2)sin (1-x2)2 (2) -4x(1-x2)sin (1-x2)2 (3) 4x(1-x2)sin (1-x2)2 (4) none of these Solution: Let y = cos (1-x2)2 dy/dx... View Article

(d/dx)(x²e^xsin x)

(1) xex (2 sin x + x sin x + x cos x) (2) xex (2 sin x + x sin x - cos x) (3) xex (2 sin x + x sin x + cos x) (4) none of these... View Article

If y = x sin x, then

(1) (1/y)(dy/dx) = 1/x + cot x (2) dy/dx = 1/x + cot x (3) y(dy/dx) = 1/x - cot x (4) none of these Solution: Given y = x sin x... View Article

If y = 1/(a-z), then dz/dy =

(1) (a-z)2 (2) -(z-a)2 (3) (z+a)2 (4) -(z+a)2 Solution: Given y = 1/(a-z) ay-yz = 1 yz = ay-1 z = a - 1/y Differentiate... View Article

If y = log_a x, x>0, then dy/dx =

(1) 1/x (2) 1/ax (3) (1/x)logx a (4) (1/x)loge a Solution: y = loga x =log x/log a dy/dx = (1/x)×(1/log a) = (1/x)×(log e/log... View Article

(d/dx)(1/x⁴ sec x) =

(1) [4 cos x - x sin x]/x5 (2) -[x sin x + 4 cos x]/x5 (3) [4 cos x + x sin x]/x5 (4) none of these Solution: Let y = 1/x4 sec x... View Article

If y = x + 1/x, then

(1) x2(dy/dx) + xy = 0 (2) x2(dy/dx) + xy + 2 = 0 (3) x2(dy/dx) - xy + 2 = 0 (4) none of these Solution: Given y = x + 1/x dy/dx =... View Article

[latex]\frac{d}{dx}\left ( \sqrt{x}+\frac{1}{\sqrt{x}} \right )^{2}=[/latex]

(1) 1 - 1/x2 (2) 1 + 1/x2 (3) 1 - 1/2x (4) none of these Solution: Let y = (√x + 1/√x)2 = x + 1/x + 2 dy/dx = 1 - 1/x2... View Article

If u = sin^-1 ((x²+y²)/(x+y)) , then x ∂u/∂x + y ∂u/∂y is equal to

(1) sin u (2) tan u (3) cos u (4) cot u Solution: u = sin-1 ((x2+y2)/(x+y)) sin u = (x2+y2)/(x+y)) = x2(1+y2/x2)/x(1+y/x) =... View Article

(d/dx)log tan x =

(1) 2 sec 2x (2) 2 cosec 2x (3) sec 2x (4) cosec 2x Solution: Let y = log tan x dy/dx = (1/tan x) sec2x = cos x/sin x cos2 x =... View Article

If z = log (tan x + tan y), then sin 2x(∂z/∂x) + sin 2y(∂z/∂y) is equal to

(1) 1 (2) 2 (3) 3 (4) 4 Solution: Given z = log (tan x + tan y) Take antilog on both sides ez = (tan x + tan y) ez ∂z/∂x =... View Article

If z = tan (y + ax) – √(y-ax), then z_xx-a²z_yy is equal to

(1) 0 (2) 2 (3) zx+zy (4) zxzy Solution: Given z = tan (y + ax) - √(y-ax) Differentiate partially w.r.t.x zx = sec2(y + ax) a -... View Article

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