HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following equation for x, y ∈ R:

2x + i⁹ y (2 + i) = x i⁷ + 10 i¹⁶ 

Verify whether the following sequence is H.P.:

`1/3, 1/5, 1/7, 1/9`, ...

Verify whether the following sequence is H.P.:

`1/3, 1/6, 1/9, 1/12`, ... 

Verify whether the following sequence is H.P.:

`1/7, 1/9, 1/11, 1/13, 1/15`, ...

Find the n^th term and hence find the 8^th term of the following H.P.s:

`1/2, 1/5, 1/8, 1/11`, ...

Find the n^th term and hence find the 8^th term of the following H.P.s:

`1/4, 1/6, 1/8, 1/10`, ... 

Find the n^th term and hence find the 8^th term of the following H.P.s:

`1/5, 1/10, 1/15, 1/20`, ...

Insert two numbers between `1/7 and 1/13` so that the resulting sequence is a H.P.

By using determinant, show that the following points are collinear: P(5, 0), Q(10, –3), R(–5, 6)

Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`

Evaluate the following: `lim_(x -> 0)[(5^x + 3^x - 2^x - 1)/x]`

Evaluate the following: `lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`

Evaluate the following: `lim_(x -> 0) [(3^x + 3^-x - 2)/x^2]`

Evaluate the following: `lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`

Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`

Evaluate the following: `lim_(x -> 0) [("a"^(3x) - "b"^(2x))/(log 1 + 4x)]`

Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + x))]`

Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`

Evaluate the following: `lim_(x -> 2) [(3^(x/2) - 3)/(3^x - 9)]`

Evaluate the following:

`lim_(x ->0)[((25)^x - 2(5)^x + 1)/x^2]`