Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 11 TN Board chapter 2 - Algebra [Latest edition]

Resolve into partial fraction for the following:

`(3x + 7)/(x^2 - 3x + 2)`

Resolve into partial fraction for the following:

`(4x + 1)/((x - 2)(x + 1))`

Resolve into partial fraction for the following:

`1/((x - 1)(x + 2)^2)`

Resolve into partial fraction for the following:

`1/(x^2 - 1)`

Resolve into partial fraction for the following:

`(x - 2)/((x + 2)(x - 1)^2)`

Resolve into partial fraction for the following:

`(2x^2 - 5x - 7)/(x - 2)^3`

Resolve into a partial fraction for the following:

`(x^2 - 6x + 2)/(x^2 (x + 2))`

Resolve into partial fraction for the following:

`(x^2 - 3)/((x + 2)(x^2 + 1))`

Resolve into a partial fraction for the following:

`(x + 2)/((x - 1)(x + 3)^2)`

Resolve into a partial fraction for the following:

`1/((x^2 + 4)(x + 1))`

Find x if `1/(6!) + 1/(7!) = x/(8!)`

Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.

If (n+2)! = 60[(n–1)!], find n

How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?

How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?

If nP₄ = 12(nP₂), find n.

In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?

How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?

Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.

1. In how many ways can 8 identical beads be strung on a necklace?
2. In how many ways can 8 boys form a ring?

Find the rank of the word ‘CHAT’ in the dictionary.

If ⁿP_r = 1680 and ⁿC_r = 70, find n and r.

Verify that ⁸C₄ + ⁸C₃ = ⁹C₄.

How many chords can be drawn through 21 points on a circle?

How many triangles can be formed by joining the vertices of a hexagon?

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?

If a polygon has 44 diagonals, find the number of its sides.

In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?

1. There is no restriction on the selection.
2. A particular player is always chosen.
3. A particular player is never chosen.

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

1. atleast two ladies are included.
2. atmost two ladies are included.

By the principle of mathematical induction, prove the following:

1³ + 2³ + 3³ + ….. + n³ = `("n"^2("n + 1")^2)/4` for all x ∈ N.

By the principle of mathematical induction, prove the following:

1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` for all n ∈ N.

By the principle of mathematical induction, prove the following:

4 + 8 + 12 + ……. + 4n = 2n(n + 1), for all n ∈ N.

By the principle of mathematical induction, prove the following:

1 + 4 + 7 + ……. + (3n – 2) = `("n"(3"n" - 1))/2`  for all n ∈ N.

By the principle of mathematical induction, prove the following:

3²ⁿ – 1 is divisible by 8, for all n ∈ N.

By the principle of mathematical induction, prove the following:

aⁿ – bⁿ is divisible by a – b, for all n ∈ N.

By the principle of mathematical induction, prove the following:

5²ⁿ – 1 is divisible by 24, for all n ∈ N.

By the principle of mathematical induction, prove the following:

n(n + 1) (n + 2) is divisible by 6, for all n ∈ N.

By the principle of mathematical induction, prove the following:

2ⁿ > n, for all n ∈ N.

Expand the following by using binomial theorem.

(2a – 3b)⁴

Expand the following by using binomial theorem.

`(x + 1/y)^7`

Expand the following by using binomial theorem.

`(x + 1/x^2)^6`

Evaluate the following using binomial theorem:

(101)⁴

Evaluate the following using binomial theorem:

(999)⁵

Find the 5th term in the expansion of (x – 2y)¹³.

Find the middle terms in the expansion of

`(x + 1/x)^11`

Find the middle terms in the expansion of

`(3x + x^2/2)^8`

Find the middle terms in the expansion of

`(2x^2 - 3/x^3)^10`

Find the term independent of x in the expansion of

`(x^2 - 2/(3x))^9`

Find the term independent of x in the expansion of

`(x - 2/x^2)^15`

Find the term independent of x in the expansion of

`(2x^2 + 1/x)^12`

Prove that the term independent of x in the expansion of `(x + 1/x)^(2n)` is `(1*3*5...(2n - 1)2^n)/(n!)`.

Show that the middle term in the expansion of is (1 + x)²ⁿ is `(1*3*5...(2n - 1)2^nx^n)/(n!)`

If nC₃ = nC₂ then the value of nC₄ is:

The value of n, when np₂ = 20 is:

The number of ways selecting 4 players out of 5 is

If nP_r = 720(nC_r), then r is equal to:

The possible outcomes when a coin is tossed five times:

The number of diagonals in a polygon of n sides is equal to

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:

If n is a positive integer, then the number of terms in the expansion of (x + a)ⁿ is:

For all n > 0, nC₁ + nC₂ + nC₃ + …… + nC_n is equal to:

The term containing x³ in the expansion of (x – 2y)⁷ is:

The middle term in the expansion of `(x + 1/x)^10` is

The constant term in the expansion of `(x + 2/x)^6` is

The last term in the expansion of (3 + √2 )⁸ is:

If `(kx)/((x + 4)(2x - 1)) = 4/(x + 4) + 1/(2x - 1)` then k is equal to:

The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:

There are 10 true or false questions in an examination. Then these questions can be answered in

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅) is:

The total number of 9 digit number which has all different digit is:

The number of ways to arrange the letters of the word “CHEESE”:

Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:

The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:

Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:

The number of permutation of n different things taken r at a time, when the repetition is allowed is:

Sum of the binomial coefficients is

Resolve into Partial Fractions:

`(5x + 7)/((x-1)(x+3))`

Resolve into Partial Fractions:

`(x - 4)/(x^2 - 3x + 2)`

Decompose into Partial Fractions:

`(6x^2 - 14x - 27)/((x + 2)(x - 3)^2)`

Decompose into Partial Fractions:

`(5x^2 - 8x + 5)/((x - 2)(x^2 - x + 1))`

Evaluate the following.

`(3! xx 0! + 0!)/(2!)`

Evaluate the following.

`(3! + 1!)/(2^2!)`

Evaluate the following.

`((3!)! xx 2!)/(5!)`

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters

1. cannot be repeated
2. can be repeated
3. cannot be repeated but must begin with E
4. cannot be repeated but end with CAB.

From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?

In how many different ways, 2 Mathematics, 2 Economics and 2 History books can be selected from 9 Mathematics, 8 Economics and 7 History books?

Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?

Find the Co-efficient of x¹¹ in the expansion of `(x + 2/x^2)^17`