HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Answer the following:

If p, q, r are in G.P. and `"p"^(1/x) = "q"^(1/y) = "r"^(1/z)`, verify whether x, y, z are in A.P. or G.P. or neither.

Find n, if ⁿP₆ : ⁿP₃ = 120 : 1

Find m and n, if ^(m+n)P₂ = 56 and ^(m-n)P₂ = 12

Find r, if ¹²P_r–2 : ¹¹P_r–1 = 3 : 14

Show that (n + 1) (ⁿP_r) = (n – r + 1) [⁽ⁿ⁺¹⁾P_r]

A code word is formed by two different English letters followed by two non-zero distinct digits. Find the number of such code words. Also, find the number of such code words that end with an even digit.

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object never occurs

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x)⁻⁴

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 - x)^(1/3)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 – x²)^–3

State, by writing first four terms, the expansion of the following, where |x| < 1

`(1 + x)^(-1/5)`

State, by writing first four terms, the expansion of the following, where |x| < 1

(1 + x²)^–1

State, by writing first four terms, the expansion of the following, where |b| < |a|

(a − b)⁻³ 

State, by writing first four terms, the expansion of the following, where |b| < |a| 

(a + b)⁻⁴ 

State, by writing first four terms, the expansion of the following, where |b| < |a| 

`("a" + "b")^(1/4)`

State, by writing first four terms, the expansion of the following, where |b| < |a| 

`("a" - "b")^(-1/4)`

State, by writing first four terms, the expansion of the following, where |b| < |a| 

`("a" + "b")^(-1/3)`

Simplify first three terms in the expansion of the following

(1 + 2x)^–4 

Simplify first three terms in the expansion of the following

`(1 + 3x)^(-1/2)`