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11th Business Maths Monthly Test - 1 ( Algebra )

MABS Institution

11th Business Maths Monthly Test - 1 ( Algebra )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

2
6
20
24

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 \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\)

156
165
162
160

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

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

If nC₃ = nC₂, then the value of nC₄ is

2
3
4
5

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

120
240
720
6

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

nC₂
nC₂ - 2
nC₂ - n
nC₂ - 1

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

4
5
6
7

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

9
11
5
7

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

7!
3!
8!
5!

Part - B

Generic 2 - Answer All Question

a) In how many ways can 8 identical beads be strung on a necklace?
b) In how many ways can 8 boys form a ring?

Using 9 digits from 1,2,3,……9, taking 3 digits at a time, how many 3 digits numbers can be formed when repetition is allowed?

Find the co-efficient of x⁴⁰ in (1+2x+x²)²⁷

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.
Resolve into partial fractions for the following
\(\frac { 3x+7 }{ { x }^{ 2 }-3x+2 } \)

In how many ways 7 pictures can be hung from 5 picture nails on a wall ?

Find 8C₂

If 15C_3r = 15C_r+3 , find r

In a railway compartment, 6 seats are vacant on a bench. In how many ways can 3 passengers sit on them?

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

Part - C

Generic 3 - Answer All Question

Find the middle terms in the expansion of \({ \left( 3x+\frac { { x }^{ 2 } }{ 2 } \right) }^{ 8 }\)

Find the Coefficient of x¹⁰ in the binomial expansion of \({ \left( 2x^2-\frac { 3 }{ { x }^{ } } \right) }^{ 11 }\)

Find n, if \(\frac{1}{9!}+\frac{1}{10!}=\frac{n}{11!}\)

Resolve into partial fractions for the following:
\(\frac { 1 }{ (x-1)(x+2)^{ 2 } } \)

Find the Co-efficient of x¹¹ in the expansion of \({ \left( x+\frac { 2 }{ { x }^{ 2 } } \right) }^{ 17 }\)
Find the number of arrangements that can be made out of the letters of the word "ASSASSINATION".

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?

It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

Show that the middle term in the expansion of (1 +x)²ⁿ is \(\frac { 1.3.5....(2n-1){ 2 }^{ n }.{ x }^{ n } }{ n! } \)

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

Part - D

Generic 5 - Answer All Question

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.
4+8+12+......+4n=2n(n+1), for all \(n\in N\).

If 22P_r+1:20P_r+2=11: 52, find r.

Resolve into partial fractions:\(\frac{2x+1}{(x-1)(x^2+1)}\)

By the principle of mathematical induction, prove the following.
aⁿ-bⁿ is divisible by a-b, for all \(n\in N\) .
Show by the principle of mathematical induction that 2^3n–1 is a divisible by 7, for all n∈N.

How many numbers are there between 100 and 1000 such that atleast one of their digits is 7?

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?

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

Find the middle term in the expansion of \((\frac{x}{3}+9y)^2\)

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