11th Business Maths Monthly Test - 2 ( Algebra )

MABS Institution

11th Business Maths Monthly Test - 2 ( Algebra )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

n
n + 1
n-1
2n

The constant term in the expansion of \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\)

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is

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

3^rd
4^th
5^th
6^th

The possible out comes when a coin is tossed five times

2⁵
5²
10
\(\frac { 5 }{ 2 } \)

The total number of 9 digit number which have all different digit is

10!
9!
9\(\times\)9!
10\(\times\)10!

If nC₃ = nC₂, then the value of nC₄ is

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to

The number of ways to arrange the letters of the word "CHEESE" is

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is

81
16
8\(\sqrt{2}\)
27\(\sqrt{3}\)

Part - B

Generic 2 - Answer All Question

If (n + 2)C_n = 45, find n

Resolve into partial fractions for the following
\(\frac { 3x+7 }{ { x }^{ 2 }-3x+2 } \)

Evaluate the following expression.\(\frac { 8! }{ 5! } \)

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
If a polygon has 44 diagonals, find the number of its sides.

Find the rank of the word 'CHAT' in dictionary.

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

Part - C

Generic 3 - Answer All Question

Resolve into Partial Fractions:\(\frac { x-4 }{ { x }^{ 2 }-3x+2 } \)

In an examination, Yamini has to select 4 questions from each part. There are 6, 7 and 8 questions is Part I, Part II and Part III respectively. What is the number of possible combinations in which she can choose the questions?

Find the value of tan \(\left( {{\pi}\over{8}} \right).\)

Resolve into partial fractions for the following:
\(\frac { 2x^{ 2 }-5x-7 }{ (x-2)^3 } \)

Decompose into Partial Fractions \(\frac { { 6 }x^{ 2 }-14x-27 }{ (x+2){ (x-3) }^{ 2 } } \):
How many 3 digits numbers can be formed if the repetition of digits is not allowed?

In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

Part - D

Generic 5 - Answer All Question

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n², for all n∈N.

How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

Show by the principle of mathematical induction that 2^3n–1 is a divisible by 7, for all n∈N.

How many code symbols can be formed using 5 out of 6 of the letters of A, B, C, D, E, F so that the letters
a) cannot be repeated
b) can be repeated
c) cannot be repeated but must begin with E
d) cannot be repeated but end with CAB.

By the principle of mathematical induction, prove the following.
1³+2³+3³+.......+n³=\(\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 } \) for all \(n\in N\).

Prove that the term independent of x in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! } \)

In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

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11th Business Maths Monthly Test - 2 ( Algebra )

MABS Institution

11th Business Maths Monthly Test - 2 ( Algebra )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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

The constant term in the expansion of \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\)

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is

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

The possible out comes when a coin is tossed five times

The total number of 9 digit number which have all different digit is

If nC3 = nC2, then the value of nC4 is

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to

The number of ways to arrange the letters of the word "CHEESE" is

The last term in the expansion of (3 +\(\sqrt{2}\) )8 is

Part - B

Generic 2 - Answer All Question

If (n + 2)Cn = 45, find n

Resolve into partial fractions for the following \(\frac { 3x+7 }{ { x }^{ 2 }-3x+2 } \)

Evaluate the following expression.\(\frac { 8! }{ 5! } \)

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

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

Find the rank of the word 'CHAT' in dictionary.

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

Part - C

Generic 3 - Answer All Question

Resolve into Partial Fractions:\(\frac { x-4 }{ { x }^{ 2 }-3x+2 } \)

In an examination, Yamini has to select 4 questions from each part. There are 6, 7 and 8 questions is Part I, Part II and Part III respectively. What is the number of possible combinations in which she can choose the questions?

Find the value of tan \(\left( {{\pi}\over{8}} \right).\)

Resolve into partial fractions for the following: \(\frac { 2x^{ 2 }-5x-7 }{ (x-2)^3 } \)

Decompose into Partial Fractions \(\frac { { 6 }x^{ 2 }-14x-27 }{ (x+2){ (x-3) }^{ 2 } } \):

How many 3 digits numbers can be formed if the repetition of digits is not allowed?

In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

Part - D

Generic 5 - Answer All Question

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n2, for all n∈N.

How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

Show by the principle of mathematical induction that 23n–1 is a divisible by 7, for all n∈N.

How many code symbols can be formed using 5 out of 6 of the letters of A, B, C, D, E, F so that the letters a) cannot be repeated b) can be repeated c) cannot be repeated but must begin with E d) cannot be repeated but end with CAB.

By the principle of mathematical induction, prove the following. 13+23+33+.......+n3=\(\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 } \) for all \(n\in N\).

Prove that the term independent of x in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! } \)

In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

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

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

If nC₃ = nC₂, then the value of nC₄ is

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is

If (n + 2)C_n = 45, find n

Resolve into partial fractions for the following
\(\frac { 3x+7 }{ { x }^{ 2 }-3x+2 } \)

Resolve into partial fractions for the following:
\(\frac { 2x^{ 2 }-5x-7 }{ (x-2)^3 } \)

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n², for all n∈N.

Show by the principle of mathematical induction that 2^3n–1 is a divisible by 7, for all n∈N.

How many code symbols can be formed using 5 out of 6 of the letters of A, B, C, D, E, F so that the letters
a) cannot be repeated
b) can be repeated
c) cannot be repeated but must begin with E
d) cannot be repeated but end with CAB.

By the principle of mathematical induction, prove the following.
1³+2³+3³+.......+n³=\(\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 } \) for all \(n\in N\).