HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

If f(x) = a sin x – b cos x, `"f'"(pi/4) = sqrt(2) and "f'"(pi/6)` = 2, then find f(x)

If f(2) = 4, f′(2) = 1 then find `lim_(x -> 2) [(x"f"(2) - 2"f"(x))/(x - 2)]`

Prove the following identity:

`(1 - sec theta + tan theta)/(1 + sec theta - tan theta) = (sec theta + tan theta - 1)/(sec theta + tan theta + 1)`

Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.

Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

If A = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.

If A = `[(7,1), (2,5)]` and B = `[(1,2), (3,-1)]` then verify that |AB| = |A|  |B|.

Find the value of `sin  (19pi^"c")/3`.

Find the value of :

cos 1140°

Find the values of:

`cot  (25pi^"c")/3`

Select the correct option from the given alternatives:

If secθ = m and tanθ = n, then `1/"m"{("m + n") + 1/(("m + n"))}` is equal to

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?