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

Which of the following is the conditional p → q?

The negation of the statement “The product of 3 and 4 is 9” is ______.

Which of the following is not a negation of “A natural number is greater than zero”?

Which of the following statement is a conjunction?

State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?

Show that the two formulae for the standard deviation of ungrouped data.

`sigma = sqrt((x_i - barx)^2/n)` and `sigma`' = `sqrt((x^2_i)/n - barx^2)` are equivalent.

Life of bulbs produced by two factories A and B are given below:

The bulbs of which factory are more consistent from the point of view of length of life?

A set of n values x₁, x₂, ..., x_n has standard deviation 6. The standard deviation of n values x₁ + k, x₂ + k, ..., x_n + k will be ______.

Find the standard deviation of the first n natural numbers.

The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results:
Number of observations = 25, mean = 18.2 seconds, standard deviation = 3.25 seconds. Further, another set of 15 observations x₁, x₂, ..., x₁₅, also in seconds, is now available and we have `sum_(i = 1)^15 x_i` = 279 and `sum_(i  = 1)^15 x^2` = 5524. Calculate the standard derivation based on all 40 observations.

The mean and standard deviation of a set of n₁ observations are `barx_1` and s₁, respectively while the mean and standard deviation of another set of n₂ observations are `barx_2` and  s₂, respectively. Show that the standard deviation of the combined set of (n₁ + n₂) observations is given by

S.D. = `sqrt((n_1(s_1)^2 + n_2(s_2)^2)/(n_1 + n_2) + (n_1n_2 (barx_1 - barx_2)^2)/(n_1 + n_2)^2)`

Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.

The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.

If for distribution `sum(x - 5)` = 3, `sum(x - 5)^2` = 43 and total number of items is 18. Find the mean and standard deviation.

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is ______.

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 ______.