HSC Commerce (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following quadratic equation:

x² – (5 – i)x + (18 + i) = 0

Solve the following quadratic equation:

(2 + i) x² – (5 – i) x + 2(1 – i) = 0

Find a and b if the following function is continuous at the point indicated against them.

`f(x) = (32^x - 1)/(8^x - 1) + a` , for x > 0
         = 2                      , for x = 0
         = x + 5 − 2b       , for x < 0
is continuous at x = 0

Solve the following equation for x, y ∈ R:

(4 – 5i) x + (2 + 3i) y = 10 – 7i

Solve the following equation for x, y ∈ R:

(1 – 3i) x + (2 + 5i) y = 7 + i

Solve the following equation for x, y ∈ R:

`(x + "i"y)/(2 + 3"i")` = 7 – i

Solve the following equation for x, y ∈ R:

(x + iy)(5 + 6i) = 2 + 3i

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]`