HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions

How many numbers between 100 and 1000 have 4 in the units place?

How many numbers between 100 and 1000 have the digit 7 exactly once?

How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?

How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be repeated?

A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?

How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?

Select the correct answer from the given alternatives.

A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening

Select the correct answer from the given alternatives.

A college has 7 courses in the morning and 3 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is -

How many words can be formed by writing letters in the word CROWN in different order?

Answer the following:

A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

Prove by method of induction, for all n ∈ N:

2 + 4 + 6 + ..... + 2n = n (n+1)

Prove by method of induction, for all n ∈ N:

3 + 7 + 11 + ..... + to n terms = n(2n+1)

Prove by method of induction, for all n ∈ N:

1² + 2² + 3² + .... + n² = `("n"("n" + 1)(2"n" + 1))/6`

Prove by method of induction, for all n ∈ N:

1² + 3² + 5² + .... + (2n − 1)² = `"n"/3 (2"n" − 1)(2"n" + 1)`

Prove by method of induction, for all n ∈ N:

1³ + 3³ + 5³ + .... to n terms = n²(2n² − 1)

Prove by method of induction, for all n ∈ N:

1.2 + 2.3 + 3.4 + ..... + n(n + 1) = `"n"/3 ("n" + 1)("n" + 2)`

Prove by method of induction, for all n ∈ N:

1.3 + 3.5 + 5.7 + ..... to n terms = `"n"/3(4"n"^2 + 6"n" - 1)`

Prove by method of induction, for all n ∈ N:

`1/(1.3) + 1/(3.5) + 1/(5.7) + ... + 1/((2"n" - 1)(2"n" + 1)) = "n"/(2"n" + 1)`

Prove by method of induction, for all n ∈ N:

`1/(3.5) + 1/(5.7) + 1/(7.9) + ...` to n terms = `"n"/(3(2"n" + 3))`