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If y = cot^-1 x², then dy/dx is equal to

(1) 2x/(1 + x4) (2) 2x/√(1 + 4x) (3) -2x/(1 + x4) (4) -2x/√(1 + x2) Solution: Given y = cot-1 x2 Differentiate w.r.t.x dy/dx =... View Article

If y = log tan √x, then the value of dy/dx is

(1) 1/2√x (2) sec2√x/(√x tan √x) (3) 2sec2√x (4) sec2√x/(2√x tan √x) Solution: Given y = log tan √x Differentiate w.r.t.x dy/dx... View Article

If y = sec x^o, then dy/dx =

(1) sec x tan x (2) sec xo tan xo (3) (π/180) sec xo tan xo (4) (180/π) sec xo tan xo Solution: Given y = sec xo We know π... View Article

If [latex]y = \cot^{-1}\left [ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \right ][/latex], then dy/dx =

(1) 1/2 (2) 2/3 (3) 3 (4) 1 Solution: Given y = cot-1 [ √(1 + sin x) + √(1 - sin x)]/[√(1 + sin x) - √(1 - sin x)] Multiply... View Article

If f(x) = e^x g(x), g(0) = 2, g’(0) = 1, then f’(0) is

(1) 1 (2) 2 (3) 3 (4) 0 Solution: Given f(x) = ex g(x) f’(x) = ex g(x) + ex g’(x) f’(0) = e0g(0) + e0 g’(0) = 2 + 1 = 3 Hence... View Article

For the function f(x) = x² -6x+8, 2 ≤ x ≤ 4, then the value of x for which f’(x) vanishes is

(1) 9/4 (2) 5/2 (3) 3 (4) 7/2 Solution: Given f(x) = x2 -6x+8 Differentiate w.r.t.x f’(x) = 2x-6 f’(x) = 0=> 2x-6 = 0 2x =... View Article

If y = e^{(1 + log x)}, then the value of dy/dx =

(1) e (2) 1 (3) 0 (4) log x elog x Solution: y = e(1 + log x) = e.elog x = e. x Differentiate w.r.t.x dy/dx = e Hence... View Article

d/dx (1/x) = ..; x ≠ 0

(1) -1/x2 (2) 1/x2 (3) not possible (4) 1 Solution: Let y = 1/x = x-1 Differentiate w.r.t.x dy/dx = -x-2 = -1/x2 Hence... View Article

[latex]\frac{d}{dx}\frac{2}{\pi }\sin x^{o}=[/latex]

(1) (π/180) cos xo (2) (1/90) cos xo (3) (π/90) cos xo (4) (2/90) cos xo Solution: Let y = (2/π) sin xo We know 1o = π/180... View Article

Why is iodine less reactive than bromine?

Iodine has 5 shells whereas bromine has 4 shells. Since bromine has less number of shells, the outer shell is closer to the nucleus and there is... View Article

Is liquid oxygen diamagnetic?

Liquid oxygen is paramagnetic. It gets attracted by the magnetic field but once the magnetic field is removed it does not remain magnetic.... View Article

Why is aluminum used to make airplanes?

Aluminium is a strong and lightweight metal. This weight of aluminium is almost ⅓ rd the weight of steel. This allows the aircraft to carry more... View Article

Do capacitors have voltage?

Like batteries, capacitors can also be used to supply voltage to the circuit. They supply voltage to the circuit in the same way. The capacitors... View Article

How fast can a capacitor charge?

A capacitor will charge upto 63% of the supply voltage in one time constant. After 5 time constants the capacitor will be charged to 99% of the... View Article

What is the difference between capacitor start and capacitor run motor?

The capacitance of the start capacitor is more than the run capacitor. The start capacitor is found in the start windings of the motor.The start... View Article

Can I use a 440v capacitor instead of a 370v?

440 V capacitor cannot be used in place of 370 V capacitor. The voltage rating on the capacitor displays should not be exceeded. This means 440 V... View Article

How big is a 1 farad capacitor?

The size of the 1 farad capacitor depends on the potential difference we are taking. If the value of voltage is high the 1 farad capacitor will... View Article

What are the signs of a bad capacitor?

The following symptoms shows that the capacitor is bad in the air conditioner Smoke or burning smell from the components Noise from AC The... View Article

What is the SI unit of a capacitor?

Capacitor is a device and it does not have a unit. The capacitance of the capacitor is the ratio of the charge stored in either one of the... View Article

When should you use a capacitor?

The capacitors have a wide range of uses. It can be used as power stores, filters, timers, voltage stabilizers, oscillation, digital storage... View Article

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