HSC Science (Electronics) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Express the following as a sum or difference of two trigonometric function:

2 cos 35° cos 75°

Prove the following :

`(sin2x + sin2y)/(sin2x - sin2y) = (tan(x + y))/(tan(x - y))`

Prove the following :

sin 6x + sin 4x – sin 2x = 4 cos x sin 2x cos 3x

Prove the following :

`(sinx - sin3x + sin5x - sin7x)/(cosx - cos3x - cos5x + cos7x)` = cot2x

Prove the following :

sin 18° cos 39° + sin 6° cos 15° = sin 24° cos 33°

Prove the following :

cos 20° cos 40° cos 60° cos 80° = `1/16`

Prove the following :

sin 20° sin 40° sin 60° sin 80° = `3/16`

Prove the following:

cos 12°+ cos 84° + cos 156° + cos 132° = `-1/2`

Prove the following:

`(cos9x - cos5x)/(sin17x - sin3x) = - (sin2x)/(cos10x)`

Prove the following:

3(sin x – cos x)⁴ + 6(sin x + cos x)² + 4(sin⁶x + cos⁶x) = 13

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = `(("i" - "j")^2)/(5 - "i")`

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = i – 3j

Construct a matrix A = [a_ij]_{3 × 2} whose element a_ij is given by

a_ij = `(("i" + "j")^3)/5`

Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82

Find the coefficient of variation of a sample which has mean equal to 25 and standard deviation of 5

A group of 65 students of class XI have their average height is 150.4 cm with coefficient of variance 2.5%. What is the standard deviation of their height?

Two workers on the same job show the following results:

1. Regarding the time required to complete the job, which worker is more consistent?
2. Which worker seems to be faster in completing the job?

A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively: Which department has a larger bill?

A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively: Which department has larger variability in wages?

The following table gives weights of the students of two classes. Calculate the coefficient of variation of the two distributions. Which series is more variable?