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If tan^-1 (a / x) + tan^-1 (b / x) = π / 2, then x is equal to

1) √ab 2) √2ab 3) 2ab 4) ab Solution: (1) √ab tan-1 (a / x) + tan-1 (b / x) = π / 2 tan-1 [(a / x) + (b / x)] / [1 - (ab / x2)]... View Article

If cos^-1 x > sin^-1 x, then

1) (1 / √2) < x ≤ 1 2) 0 < x < 1 / √2 3) - 1 ≤ x < 1 / √2 4) x > 0 Solution: (3) - 1 ≤ x < 1 / √2 cos-1 x >... View Article

The greatest and least values of (sin^-1 x)² + (cos^-1 x)² are respectively

1) π4 / 4 and 0 2) π / 2 and - π / 2 3) 5π2 / 4 and π2 / 8 4) π2 / 4 and - π2 / 4 Solution: (3) 5π2 / 4 and π2 / 8 (sin-1 x)2 +... View Article

For the function f (x) = (4 / 3) x³ – 8x² + 16x + 5 is a point of

1) Local maxima 2) Local minima 3) Point of inflexion 4) None of these Solution: (3) Point of inflexion f (x) = (4 / 3) x3 - 8x2 +... View Article

Can two identical and independent sodium lamps act as coherent sources?

No, the two identical and independent sodium lamps do not act as coherent sources because the phase difference between waves emitted will change... View Article

Can two different bulbs similar in all respects act as coherent sources?

No, the two independent bulbs will not act as coherent sources because they won’t possess stable constant phase difference.... View Article

At what point will the electric field of a charged object be strongest?

The electric field of a charged object will be strongest where the electric field lines are the closest.... View Article

Can you measure latent heat with a thermometer?

The latent heat cannot be measured with a thermometer. A thermometer measures only the sensible heat. Similar Reading: Latent Heat of Water... View Article

Which earthquake wave is more dangerous?

S waves have greater amplitude and produce vertical and horizontal motion of the ground surface and are more dangerous than P waves.... View Article

What is the range of voltmeter?

The range of practical voltmeter ranges between 1000 to 3000 volts. Understand what makes the voltmeter different from the ammeter by reading... View Article

Which has more surface tension oil or water?

Water has higher surface tension. Water has a surface tension of 72 dynes/cm, and oil has a surface tension of 30–35 dynes/cm.... View Article

Which of the following produces uniform electric field?

a) Linear Charge b) Point Charge c) Two Parallel Plates d) Charge distributed on a circular plot Answer: c) Two parallel plates. Read More:... View Article

Which state of matter is most affected by temperature change?

Gases are most affected by temperature change. Among all the states of matter, gases have the highest kinetic energy and occur at the highest... View Article

The point in the interval [0, 2π], where f (x) = e^x sin x has maximum slope, is

1) π / 4 2) π / 2 3) π 4) 3π / 2 Solution: (2) π / 2 f (x) = ex sin x f’ (x) = ex cosx + sinx ex f’’ (x) = – ex sinx + cosx ex... View Article

The displacement of a particle at time t is x, where x = t⁴ – kt³. If the velocity of the particle at time t = 2 is minimum, then

1) k = 4 2) k = – 4 3) k = 8 4) k = – 8 Solution: (1) k = 4 x = t4 – kt3 dx / dt = t4 – kt3 dv / dt = 12t2 - 6kt at t = 2... View Article

If f (x) = Integral from 0 to x e^{-x^2/2} (1 – t²) dt, minimum at x =

1) 1 2) –1 3) 2 4) –2 Solution: (2) –1 f (x) = ∫0x e-x^2/2 (1 - t2) dt f’ (x) = e-x^2/2 (1 - x2) f (x) = 0 ⇒ (1 - x2) = 0 ⇒ x =... View Article

The minimum value of f (x) = |3 – x| + 7 is

1) 0 2) 6 3) 7 4) 8 5) 10 Solution: (3) 7 f (x) = |3 – x| + 7 f (x) = {(3 - x + 7), (3 - x) ≥ 0 and - (3 - x) + 7, when 3 - x... View Article

The value of a for which the function f (x) = a sin x + (1 / 3) sin 3x has an extremum at x = π / 3 is

1) 1 2) –1 3) 0 4) 2 Solution: (4) 2 f (x) = a sin x + (1 / 3) sin 3x f’ (x) = 0 f’ (x) = a cos x + cos 3x f’ (π / 3) = 0 (a /... View Article

Let f’’R → R be defined by f (x) = {k – 2x, if x ≤ – 1 and 2x + 3, if x > – 1. If f has a local minimum at x = – 1, then a possible value of k is

1) 1 2) 0 3) - 1 / 2 4) –1 Solution: (4) –1 f (x) = {k - 2x, if x ≤ - 1 and 2x + 3, if x > - 1 limx→1+ f (x) = 1 As f (-1) =... View Article

f (x) = x⁵ – 5x⁴ + 5x³ + 1 has

1) Two maximum and two minimum value 2) Two maximum and one minimum value 3) One maximum and one minimum value 4) None of the above... View Article

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