Is hydrogen harmful to humans?
Yes, hydrogen is harmful to humans. If hydrogen is inhaled in small concentrations it can cause symptoms like headache, nausea,... View Article
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What are the sources of radiation?
We are surrounded by the sources of radiations. The cosmic rays enter the earth’s atmosphere from outer space. The largest... View Article
Can a black hole kill you?
Although gravity is infinite in a black hole the stretching force is weak. Therefore, there are chances that the person... View Article
Why the Carnot cycle is not practically possible
The Carnot cycle is reversible whereas the real engines are not reversible due to different reasons like friction, heat transfer... View Article
Can entropy be reversed?
The entropy of a closed system cannot be reversed, meaning it cannot be decreased. According to the second law of... View Article
What is meant by Poisson’s ratio?
Poisson’s ratio is the ratio of lateral strain to the longitudinal strain within the elastic limit. The lateral strain is... View Article
Is coffee a base or acid
Most of the coffee varieties are acidic in nature. The acidity is determined by the pH value. Any solution with... View Article
Is Tea acidic or basic?
Most of the tea is mildly acidic. The levels of acidity vary based on the type of tea, brewing time... View Article
Is water an acid or base
Pure water is neither an acid nor a base. Water is neutral. In water, there is a balance between the... View Article
How do you create a truth table?
A truth table is a basic method to describe the Boolean function. The Boolean variables can either be 0 or... View Article
Do electrons have a size?
The electrons are extremely small and nobody has determined its size but the radius of the electron was calculated to... View Article
For the function f (x) = ecosx, Rolle’s theorem is
1) applicable when π / 2 ≤ x ≤ 3π / 2 2) applicable when 0 ≤ x ≤ π... View Article
The function f(x) = (x – 3)2 satisfies all the conditions of mean value theorem in [3, 4]. A point on y = (x – 3)2, where the tangent is parallel to the chord joining (3, 0) and (4, 1) is
1) (7 / 2, 1 / 2) 2) (7 / 2, 1 / 4) 3) (1, 4) 4) (4, 1)... View Article
The abscissa of the points of the curve y = x3 in the interval [–2, 2], where the slope of the tangents can be obtained by mean value theorem for the interval [–2, 2], are
1) ± 2 / √3 2) ± √3 3) ± √3 / 2 4) 0 Solution: (1) ± 2 /... View Article
If the mean value theorem is f (b) – f (a) = (b – a) f’ (c). Then for the function x2 – 2x + 3 in [1, (3 / 2)], the value of c is
1) 6 / 5 2) 5 / 4 3) 4 / 3 4) 7 / 6 Solution: (2) 5 /... View Article
If the function f (x) = x3 – 6x2 + ax + b satisfies Rolle’s theorem in the interval [1, 3] and f’ [(2√3 + 1) / √2] = 0, then
1) a = – 11 2) a = – 6 3) a = 6 4) a = 11 Solution: (4)... View Article
If f (x) satisfies the conditions of Rolle’s theorem in [1, 2] and f (x) is continuous in [1, 2] then integral from 1 to 2 f’ (x) dx is =
1) 3 2) 0 3) 1 4) 2 Solution: (2) 0 ∫12 f’ (x) dx = [f (x)]12 = f... View Article
Let f (x) = √x – 1 + √x + 24 – 10 √x – 1; 1 < x < 26 be real valued function. Then f’ (x) for a < x < 26
1) 0 2) 1 / √x – 1 3) 2√x – 1 – 5 4) None of these Solution: (1)... View Article
A function f is defined by f (x) = ex sin x in [0, π]. Which of the following is not correct
1) f is continuous in [0, π] 2) f is differentiable in [0, π] 3) f(0) = f(π) 4) Rolle’s... View Article
A function f (x) = 1 + (1 / x) is defined on the closed interval [1, 3]. A point in the interval, where the function satisfies the mean value theorem, is
1) x = 1 / 3 2) x = 1 / √3 3) x = √3 4) None of these... View Article
