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

Let x₁, x₂, ..., x_n be n observations and `barx` be their arithmetic mean. The formula for the standard deviation is given by ______.

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is ______.

Let x₁, x₂, x₃, x₄, x₅ be the observations with mean m and standard deviation s. The standard deviation of the observations kx₁, kx₂, kx₃, kx₄, kx₅ is ______.

Let x₁, x₂, ... xn be n observations. Let wi = lx_i + k for i = 1, 2, ...n, where l and k are constants. If the mean of x_i’s is 48 and their standard deviation is 12, the mean of w_i’s is 55 and standard deviation of w_i’s is 15, the values of l and k should be ______.

Standard deviations for first 10 natural numbers is ______.

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is ______.

If the variance of a data is 121, then the standard deviation of the data is ______.

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.