HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?

How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?

Find the sum `sum_("r" = 1)^"n"("r" + 1)(2"r" - 1)`.

Find \[\displaystyle\sum_{r=1}^{n} (3r^2 - 2r + 1)\].

Find \[\displaystyle\sum_{r=1}^{n}\frac{1 + 2 + 3 + ... + r}{r}\]

Find `sum_("r" = 1)^"n" (1^3 + 2^3 + ... + "r"^3)/("r"("r" + 1)`.

Find the sum 5 × 7 + 9 × 11 + 13 × 15 + ... upto n terms.

Find the sum 2² + 4² + 6² + 8² + ... upto n terms.

Find (70² – 69²) + (68² – 67²) + ... + (2² – 1²)

Find the sum 1 x 3 x 5 + 3 x 5 x 7 + 5 x 7 x 9 + ... + (2n – 1) (2n + 1) (2n + 3) 

Find n, if `(1 xx 2 + 2 xx 3 + 3 xx 4 + 4 xx 5 + ... + "upto n terms")/(1 + 2 + 3 + 4 + ... + "upto n terms")= 100/3`.

If S₁, S₂ and S₃ are the sums of first n natural numbers, their squares and their cubes respectively, then show that: 9S₂² = S₃(1 + 8S₁).

Find \[\displaystyle\sum_{r=1}^{n}(5r^2 + 4r - 3)\].

Find \[\displaystyle\sum_{r=1}^{n}r(r-3)(r-2)\].

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^2 + 2^2 + 3^2+...+r^2}{2r + 1}\]

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^3 + 2^3 + 3^3 +...+r^3}{(r + 1)^2}\]

Find 2 x + 6 + 4 x 9 + 6 x 12 + ... upto n terms.

Find 12² + 13² + 14² + 15² + … + 20².

Find (50² – 49²) + (48² –47²) + (46² – 45²) + .. + (2² –1²).

Find `sum_(r=1)^n(1 + 2 + 3 + . . .  + r)/r`