Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.

The standard deviation is ______to the mean deviation taken from the arithmetic mean.

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.

Evaluate the following limit.

`lim_(x -> pi) (sin(pi - x))/(pi (pi - x))`

Evaluate the following limit.

`lim_(x ->0) cos x/(pi - x)`

Evaluate the following limit.

`lim_(x -> 0) (cos 2x -1)/(cos x - 1)`

Evaluate the following limit.

`lim_(x -> 0) (ax +  xcos x)/(b sin x)`

Evaluate the following limit.

`lim_(x → 0) x sec x`

Evaluate the following limit.

`lim_(x -> 0) (sin ax + bx)/(ax + sin bx) a, b, a+ b != 0`

Evaluate the following limit.

`lim_(x -> 0) (cosec x -  cot x)`

Evaluate the following limit.

`lim_(x -> (pi)/2) (tan 2x)/(x - pi/2)`

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.

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.

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.

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.

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.

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).

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).

Write the following statement in five different ways, conveying the same meaning.

p: If triangle is equiangular, then it is an obtuse angled triangle.

Find the mean and variance for the following frequency distribution.