Mathematics_Today_-_October_2016

8. The number of seven digit integers, with sum of the
   digits equal to 10 and formed by using any of the
   digits 1, 2 and 3 only, is
   (a) 55 (b) 66
   (c) 77 (d) 88


9. A man has 10 friends among whom two are married
   to each other. Then the number of different ways in
   which he can invite 5 people to a dinner party if
   married couple refuse to attend separately is
   (a)^10 C 5 – 2 (b)^10 C 5 – 2 ×^8 C 4
   (c) 2 ×^8 C 3 (d) 112


10. If (1 + 2x + 3x^2 )^10 = a 0 + a 1 x + a 2 x^2 + ... + a 20 x^20 ,
    then
    (a) a 1 = 20 (b) a 2 = 210
    (c) a 3 = 8085 (d) a 20 = 2^2 · 3^7 · 7


11. Let S = {1, 2, ...., n}. If X denotes the set of all subsets
    of S containing exactly two elements, then the value
    of (min )A
    AX∈

∑ is given by

(a) n + 1C 3 (b)

1

6

()nn^2 − 1

(c) nC 3 (d)

1

6

()n− 1 n

12. If the third term in the expansion of ()xx+ log^10 x^5
    is 10^6 , then x is
    (a) 10–1/3 (b) 10
    (c) 10–5/2 (d) 10^2


13. In the expansion of (x^2 + 2x + 2)n, (where n is a
    positive integer) then coefficient of
    (a) x is 2n · n (b) x^2 is n^2 · 2n – 1
    (c) x^3 is 2n · n + 1C 3 (d) none of these
    Comprehension Type

A committee of 12 is to be formed from 9 women and
8 men such that atleast 5 women have to be included in
the committee.

14. The number of ways of forming the committee is
    (a) 6000 (b) 6060
    (c) 6062 (d) 6080


15. The number of committee in which women are in
    majority is
    (a) 1008 (b) 2410
    (c) 2700 (d) 2702
    Matrix Match Type


16. Match the columns:
    Column I Column II
    P The sum of the two middle
    coefficients of (1 + x)^9 is

119

Q The coefficient of x^4 in the

expansion of (1 + x + x^2 )^4 is

235

R The value of

0

8

1

8

2

8

3

8

4

8

()−()+()−()+()is

3 252

P Q R

(a) 1 2 3

(b) 1 3 2

(c) 2 3 1

(d) 3 1 2

Integer Answer Type

17. If k Pk k k

k

+ + = +P

−

(^51) × 3
11 1
2
()
, then value of k
greater than 6 is

18. If x x px
    x

+=^11 and =^4000 + 40001 and q be the

digit at unit place in the number 212

n

+ , n ∈ N and

n > 1, then p + q =

19. The number of terms which are free from radical
    signs in the expansion of (y1/5 + x1/10)^55 is


20. A student is allowed to select at most n books from
    a collection of (2n +1) books. If the total number of
    ways in which he can select a book is 63, then the
    value of n is ””
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