HSC Commerce: Marketing and Salesmanship ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Evaluate the following:

`lim_(x->0)[((25)^x - 2(5)^x + 1)/x^2]`

Evaluate the following:

`lim_(x->0)[((25)^x -2(5)^x +1)/(x^2)]`

Evaluate the following:

`lim_(x->0) [((25)^x - 2(5)^x + 1)/x^2]`

Solve the following quadratic equation.

8x² + 2x + 1 = 0

A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is solved?

A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is not solved

A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, exactly two students solve the problem?

The probability that a 50-year old man will be alive till age 60 is 0.83 and the probability that a 45-year old woman will be alive till age 55 is 0.97. What is the probability that a man whose age is 50 and his wife whose age is 45 will both be alive after 10 years?

One-shot is fired from each of the three guns. Let A, B, and C denote the events that the target is hit by the first, second and third guns respectively. assuming that A, B, and C are independent events and that P(A) = 0.5, P(B) = 0.6, and P(C) = 0.8, then find the probability that at least one hit is registered.

An urn contains four tickets marked with numbers 112, 121, 122, 222 and one ticket is drawn at random. Let A_i (i = 1, 2, 3) be the event that i^th digit of the number of the ticket drawn is 1. Discuss the independence of the events A₁, A₂, and A₃.

The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.

The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 20 years hence.

The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that at least one of them will be alive 20 years hence.

The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the chance that the problem will be solved, if they try independently?

The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the probability that neither solves the problem?

If `omega` is a complex cube root of unity, show that `(2 - omega)(2 - omega^2)` = 7

If ω is a complex cube root of unity, show that (2 + ω + ω²)³ - (1 - 3ω + ω²)³ = 65

If ω is a complex cube root of unity, show that `(("a" + "b"omega + "c"omega^2))/("c" + "a"omega + "b"omega^2) = omega^2`.

If ω is a complex cube root of unity, find the value of `omega + 1/omega`

If ω is a complex cube root of unity, find the value of ω² + ω³ + ω⁴.