HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following equations by using inversion method.

x + y + z = −1, x − y + z = 2 and x + y − z = 3

If A = `[(1, -1, 2),(3, 0, -2),(1, 0, 3)]`, verify that A(adj A) = (adj A)A

Solve the following system of equations by using inversion method

x + y = 1, y + z = `5/3`, z + x = `4/3`

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is ₹ 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is ₹ 90. Whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is ₹ 70. Find the cost of each item per dozen by using matrices

sin⁻¹x − cos⁻¹x = `pi/6`, then x = ______

The principal value of sin⁻¹`(1/2)` is ______

The principal value of cos⁻¹`(-1/2)` is ______

`tan^-1(tan  (7pi)/6)` = ______

If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______

Evaluate cot(tan⁻¹(2x) + cot⁻¹(2x))

Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`

Evaluate:

`sin[cos^-1 (3/5)]`

Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`

Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`

If tan⁻¹x + tan⁻¹y + tan⁻¹z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1

Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1

Prove that cot⁻¹(7) + 2 cot⁻¹(3) = `pi/4`

Show that `sin^-1(3/5)  + sin^-1(8/17) = cos^-1(36/85)`

Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`

Find the distance between the parallel lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 1)/2`