HSC Science (Computer Science) 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 4θ cos 2θ

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?