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

If some or all of n objects are taken at a time, the number of combinations is 2ⁿ – 1.

Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.

To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is ⁵C₃ × ²⁰C₉.

There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:

There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:

Find the middle term in the expansion of `(2ax - b/x^2)^12`.

Find the middle term (terms) in the expansion of `(p/x + x/p)^9`.

Find numerically the greatest term in the expansion of (2 + 3x)⁹, where x = `3/2`.

The ratio of the coefficient of x¹⁵ to the term independent of x in `x^2 + 2^15/x` is ______.

Find the term independent of x, x ≠ 0, in the expansion of `((3x^2)/2 - 1/(3x))^15`

If the term free from x in the expansion of `(sqrt(x) - k/x^2)^10` is 405, find the value of k.

Find the term independent of x in the expansion of `(3x - 2/x^2)^15`

Find the middle term (terms) in the expansion of `(x/a - a/x)^10`

Find the middle term (terms) in the expansion of `(3x - x^3/6)^9`

Find the coefficient of `1/x^17` in the expansion of `(x^4 - 1/x^3)^15`

Find the value of r, if the coefficients of (2r + 4)^th and (r – 2)^th terms in the expansion of (1 + x)¹⁸ are equal.

If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.

Show that the middle term in the expansion of `(x - 1/x)^(2x)` is `(1 xx 3 xx 5 xx ... (2n - 1))/(n!) xx (-2)^n`

Find n in the binomial `(root(3)(2) + 1/(root(3)(3)))^n` if the ratio of 7^th term from the beginning to the 7^th term from the end is `1/6`