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What is the difference between the mean, median and mode

Mean is the sum of all the numbers divided by the total number of numbers. Example, the mean of the... View Article

What is the charge stored on each capacitor?

The charge stored in the capacitor is given by the expression Q = C/V Q is the charge stored C... View Article

What is the meaning of Harmonic?

Harmonics is defined as the integer (whole number) multiple of the fundamental frequency. Open cylindrical columns, vibrating strings will vibrate... View Article

What are types of motion

In mechanics there are four types of motions. It is oscillatory motion, linear motion, rotational motion and circular motion. Oscillatory... View Article

Let the function g : (- ∞, ∞) → (- π / 2, π / 2) be given by g (u) = 2 tan^-1 (e^u) – (π / 2). Then g is

1) Even and is strictly increasing in (0, ∞) 2) Odd and is strictly decreasing in (–∞,∞) 3) Odd and... View Article

If f (x) = kx³ – 9x² + 9x + 3 is monotonically increasing in each interval, then

1) k < 3 2) k ≤ 3 3) k > 3 4) None of these Solution: (3) k >... View Article

The function f (x) = cos x – 2px is monotonically decreasing for

1) p < 1 / 2 2) p > 1 / 2 3) p < 2 4) p > 2... View Article

For which value of x, the function f (x) = x² – 2x is decreasing

1) x > 1 2) x > 2 3) x < 1 4) x < 2 Solution: (3) x <... View Article

The function f (x) = 2x³ – 9x² + 12x – 6 is monotonic decreasing, when

1) 1 < x < 2 2) x > 2 3) x < 1 4) None of these Solution: (1)... View Article

Let y = x²e^-x, then the interval in which y increases with respect to x is

1) (- ∞, ∞) 2) (- 2, 0) 3) (2, ∞) 4) (0, 2) Solution: (4) (0, 2) y =... View Article

The range in which y = – x² + 6x – 3 is increasing is

1) x < 3 2) x > 3 3) 7 < x < 8 4) 5 < x < 6... View Article

If f (x) = sin x – (x / 2) is increasing function, then

1) 0 < x < π / 3 2) – π / 3 < x < 0 3) – π... View Article

For what values of a, f (x) = – x³ + 4ax² + 2x – 5 is decreasing ∀ x

1) (1, 2) 2) (3, 4) 3) R 4) No value of a Solution: (4) No value of a f... View Article

For the every value of x the function f (x) = 1 / 5^x is

1) Decreasing 2) Increasing 3) Neither increasing nor decreasing 4) Increasing for x > 0 and decreasing for x <... View Article

If f’(x) is zero in the interval (a, b) then in this interval it is

1) Increasing function 2) Decreasing function 3) Only for a > 0 and b > 0 is increasing function 4)... View Article

For every value of x function f (x) = e^x is

1) Decreasing 2) Increasing 3) Neither increasing nor decreasing 4) None of the above Solution: (2) Increasing f (x) =... View Article

Function f (x) = x⁴ – (x³ / 3) is

1) Increasing for x > 1 / 4 and decreasing for < 1 / 4 2) Increasing for every value... View Article

The function f (x) = [x (x – 2)]² is increasing in the set

1) (- ∞, 0) ⋃ (2, ∞) 2) (- ∞, 1) 3) (0, 1) ⋃ (2, ∞) 4) (1, 2)... View Article

The function f defined by f (x) = x³ – 6x² – 36x + 7 is increasing, if

1) x < 2 and also x > 6 2) x > 2 and also x < 6 3) x... View Article

The which interval the given function f (x) = – 2x³ – 9x² – 12x + 1 is decreasing

1) (- 2, ∞) 2) [- 2, – 1] 3) (- ∞, – 1) 4) (- ∞, – 2) and... View Article

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