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The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.
Concept: undefined >> undefined
The standard deviation is ______to the mean deviation taken from the arithmetic mean.
Concept: undefined >> undefined
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The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> pi) (sin(pi - x))/(pi (pi - x))`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x ->0) cos x/(pi - x)`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> 0) (cos 2x -1)/(cos x - 1)`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> 0) (ax + xcos x)/(b sin x)`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x → 0) x sec x`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> 0) (sin ax + bx)/(ax + sin bx) a, b, a+ b != 0`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> 0) (cosec x - cot x)`
Concept: undefined >> undefined
Evaluate the following limit.
`lim_(x -> (pi)/2) (tan 2x)/(x - pi/2)`
Concept: undefined >> undefined
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
p: Each radius of a circle is a chord of the circle.
Concept: undefined >> undefined
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
q: The centre of a circle bisects each chord of the circle.
Concept: undefined >> undefined
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
r: Circle is a particular case of an ellipse.
Concept: undefined >> undefined
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
s: If x and y are integers such that x > y, then –x < –y.
Concept: undefined >> undefined
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
t`sqrt11` is a rational number.
Concept: undefined >> undefined
Check the validity of the statements given below by the method given against it.
p: The sum of an irrational number and a rational number is irrational (by contradiction method).
Concept: undefined >> undefined
Check the validity of the statements given below by the method given against it.
q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).
Concept: undefined >> undefined
Write the following statement in five different ways, conveying the same meaning.
p: If triangle is equiangular, then it is an obtuse angled triangle.
Concept: undefined >> undefined
Find the mean and variance for the following frequency distribution.
| Classes | 0 - 30 | 30 - 60 | 60 - 90 | 90 - 120 | 120 - 150 | 150 - 180 | 180 - 210 |
| Frequencies | 2 | 3 | 5 | 10 | 3 | 5 | 2 |
Concept: undefined >> undefined
