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11th Business Maths Weekly Test - 1 ( Algebra )

MABS Institution

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

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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!

The number of ways selecting 4 players out of 5 is

4!
20
25
5

The value of n, when nP₂ = 20 is

3
6
5
4

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

206
133
216
300

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

156
165
162
160

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

4
5
6
7

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

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

Sum of the binomial co-efficients is

2ⁿ
n²
2n
n + 17

Sum of Binomial co-efficient in a particular expansion is 256, then number of terms in the expansion is

8
7
6
9

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

In how many ways 8 students can be arranged along a circle

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 4(nC₂) = (n+2)C₃ , find n

Verify that 8C₄+8C₃=9C₄

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?

Part - C

Generic 3 - Answer All Question

Resolve into Partial Fractions:\(\frac { x-4 }{ { x }^{ 2 }-3x+2 } \)
Evaluate: \(\frac { n! }{ r!(n-r)! } \) when n=5 and r=2

How may different numbers between 100 and 1000 can be formed using the digits 0, 1,2,3,4, 5, 6 assuming that in any number, the digits are not repeated.

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

If tan \(\alpha={{1}\over{7}},\sin\beta{{1}\over{\sqrt{10}}},\) Prove that \(\alpha+2\beta{{\pi}\over4{}}\) where \(0<\alpha<{{\pi}\over{2}}\) and \(0<\beta<{{\pi}\over{}2}.\)

Part - D

Generic 5 - Answer All Question

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

By the principle of mathematical induction, prove the following.
aⁿ-bⁿ is divisible by a-b, for all \(n\in N\) .

By the principle of mathematical induction, prove the following.
5²ⁿ-1 is divisible by 24, for all \(n\in N\) .

How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?
Find the 11^th term from the end in \({ \left( 2x-\frac { 1 }{ { x }^{ 2 } } \right) }^{ 25 }\)

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