HSC Science (General) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Construct the matrix A = [a_ij]_{3 × 3} where a_ij = i − j. State whether A is symmetric or skew-symmetric.

If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A² – 4A is a scalar matrix 

If A = `[(1, 0),(-1, 7)]`, find k so that A² – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.

If A = `[(3, 1),(-1, 2)]`, prove that A² – 5A + 7I = 0, where I is unit matrix of order 2

Select the correct option from the given alternatives:

Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______

Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?

Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A

Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C

Answer the following question:

If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.

Answer the following question:

If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices

Answer the following question:

If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix

If odds in favour of X solving a problem are 4:3 and odds against Y solving the same problem are 2:3. Find probability of: X solving the problem

If odds in favour of X solving a problem are 4:3 and odds against Y solving the same problem are 2:3. Find probability of: Y solving the problem

The odds against John solving a problem are 4 to 3 and the odds in favor of Rafi solving the same problem are 7 to 5. What is the chance that the problem is solved when both them try it?

The odds against student X solving a statistics problem are 8:6 and odds in favour of student y solving the same problem are 14:16. Find is the chance that the problem will be solved if they try it independently

The odds against student X solving a statistics problem are 8:6 and odds in favour of student y solving the same problem are 14:16. Find is the chance that neither of them solves the problem

The odds against a husband who is 60 years old, living till he is 85 are 7:5. The odds against his wife who is now 56, living till she is 81 are 5:3. Find the probability that at least one of them will be alive 25 years hence

The odds against a husband who is 60 years old, living till he is 85 are 7:5. The odds against his wife who is now 56, living till she is 81 are 5:3. Find the probability that exactly one of them will be alive 25 years hence

There are three events A, B and C, one of which must, and only one can happen. The odds against the event A are 7:4 and odds against event B are 5:3. Find the odds against event C

In a single toss of a fair die, what are the odds against the event that number 3 or 4 turns up?