CAT4MBA

1) If the mth term of a HP is n and the nth term is m,what is the value of (m+n) th term?

2) If (x^n+1+y^n+1)/(x^n++y^n) is the harmonic mean of x and y .Find the value of n.

3) In the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8....where n consecutive terms have the value n,the 1025 th term is?

4) If the pth,qth,rth term of an AP are in GP then the common ratio of the GP is?

5)The ratio of the sum of nth terms of 2 AP is (3n-13):(5n+21).Find the ratio of their 25th term.

6) If a,b,c are in AP then,a+1/b,b+1/ca,c+1/ab are in which series?

7)If a GP of alternatively positive and negative terms ,any term is the AM of the next two terms.Then the common ratio is?

8)A group of friends have some money which was in increasing GP. The total money with the 1st and the last friend is Rs.66 and the product of the money that the second friend had and the last but one friend has was Rs.128. If the total money with all of them together was Rs.126,then how many friends were there?

9) Let a1,a2,a3 be in AP and ap,aq,ar be in GP.Then, aq:ap=?

10)The coefficient of n^15 in the product (1-x)(1-2x)(1-2^2.x)....(1-2^15.x)=?

11)The AM of two given positive number is 2 .If the larger number is increased by 1,the GM of the number becomes equal to the AM of the given numbers.Then the HM of the given numbers is ?

12) Let tn=n(n!).Then summation tn, n=1 to 15 =?

13) If the roots of x^3-12x^2+39x-28=0 are in an AP then their common ratio is ?

14)For each of the positive integer n consider the set sn defined as follows:
s1={1},s2={2,3},s3{4,5,6}... and in general ,s_(n+1) consists of (n+1) consecutive integers then the smallest of which is one more than the largest integer in s_n .Then the sum of all the integer in s21 =?

15)Find the sum of 37th bracket of the following series:
(1)+(7+7²+7³)+(7⁴+7⁵+...+7⁸)+(7⁹+7¹⁰+...+7¹⁵)....

16)An infinite GP has the 1st term X and the sum S,then X belongs to which range of values?

17)Find the sum of the series:
1+2.2+3.2^2+4.2^3+...+100.2^99

18)The mid-point of the adjacent sides of a square are joined. Again the mid-point of the adjacent sides of the newly formed figure is connected and this process is repeated again and again.Calculate the sum of the area of all such figures.Given that the disgonal of the outermost square is 6sqrt(2) cm?

19)The sum of the 1st n terms of an AP is n(n-1) .Then the sum of the squares of these terms is=?

20) If m times the mth term of an AP is equal to p times the pth term,then the (m+p)th term =?

21) In how many ways can we select 3 natural numbers out of the 1st 10 natural number,so that they are in GP with common ratio >1.

22) There are three numbers in an AP .if the two larger number are increased by 1 ,then the resulting numbers are prime.The product of these two primes and the smallest of the original numbers is 598. Find the sum of the three numbers.

23)A function f(x) is defined asf(x)=log[g(x)] where g(x) is any function of x.Then ,for which values of g(x),can f(x) be expressed as f1(x)+f2(x),where f1(x) and f2(x) are any two functions of x?
a) g(x)=e^x  b) g(x) =x^2  c) g(x)=log (x)  d) None of these

24)Let f(x) be defined in[-1,1] in such a way that the area of the equation of triangle with two of its vertices at (0,0) and{x,f(x)} is sqrt(3)/4 units.Which of the following can be f(x)
i) sqrt(1-x^2)   ii) -sqrt(1-x^2)
a) i correct,ii wrong
b)ii correct,i wrong
c) both right
d) both wrong

25)If 0<x<1000 and [x/2]+[x/3]+[x/5]=31x/30, where[x] is the greatest integer less than or equal to x,the number of possible values of x is?

26)A function is defined as fⁿ(x)=f{f^n-k(x)}.
If n is odd ,k=1
n is even ,k=2 and f⁰(x)=1.Find f⁷ (x) at x=1,if f(x) =x²+1

27) (x^-1) is a factor of f(x) =(x^5+ax^4+bx^3+cx^2+x+d). the graph intersect Y axis at (0,-3). Find the value of (a+c).

28) Let f(x) =ax^2+bx+c,where a,b,c are rational, and f:z->z,where z is the set of integers. Which of the following best describes the value of a+b? a) a -ve integer b) non integer rational c) an integer  d) None of these.

29) If f(x+1)+f(x-1)=2f(x) and f(0)=0,then f(n),n is the element of N is=?

30) The domain of the function f(x) =^16-x _C2x-1 +^20-3x P _4x-5; where the symbols have their usual meaningin the set?

31) The domain of the function f(x) =log_e (x-[x]),where [.] denotes the greatest integer function is?

32)If f(x) =x^n,g(x)=ng(x),then g(x) can be?

33) The inverse function of the following,f(x)=(e^x-e^-x)/(e^x+e^-x) is?

34)If f(x) =4^x/(4^x+2) ;find the value of
f(1/1999)+f(12/1999)+...+(1998/1999)?

35) If f(x) =2x^2+6x-1;then the value of [f(3/4)+1]/[f(3/4)-1]?
a) 11/13    b)35/3   c)  45/29  d) None of these

36) Let {x}& [x] denotes the fraction and integral part of real no. x respectively.Solve 4{x}=x+[x]?

37) Let f be the greatest integers function and g be the mod. function then what i sthe value of (gof)(-5/3)+(fog)(-5/3)?

38) If f(x) =x^2+x+7; then find [f(x1)+f(x2)]/x1-x2; x1=! x2?

39)A function H is defined for all the positive integers that satisfy the following condition;
If H(1) +H(2)+H(3)+..+H(x)=n^2 H(x).If H(1) =2006;find the value of H(2005)?

40)if f(x) =max(4x+3,3x+6) for x is the element of [-6,10],find the maximum value of f(x)?

41)What is the maximum value of f(x) =min(4-9x,x-3) for every x is the element of (0,4)?
a) -1 b)2  c)4  d) None of these

42) A(x,y,z)=min(x+y,y+z,z+x)
B(x,y,z)=min(x-y,y-z,z-x)
C(x,y,z)=max[A(x,y,z),B(x,y,z)]
D(x,y,z)=min[A(x,y,z),B(x,y,z)]
I) D(o,1,2)=?
II) Value of A(2,3,4)+B(2,3,4)=?
III) D[1,2,C(0,1,2))]=?

43) Fill in th blanks
The graph of y=(x+y)^2-3 is the graph of y=x^2-
shift _____ units ________(right/left/up/down)towards_____(+ve/-ve) X axis and ____units _____(right/left/up/down) towards ____(+ve/-ve) Y axis.

44)The minimum value of 4^x+4^(1-x);x is the element of R is?

45)If 2[log(x+y)-log5]=logx+logy;then what is the value of x^2+y^2?

ANSWERS:
1) (mn/m)+m
2)-1
3)2^10
4)(r-1)/(q-p)
5)1:2
6)AP
7)-2
8)6
9)(r-1)/(q-p)
10)2^105-2^121
11)3/2
12)16!-1
13)3,-3
14)4641
16)0<x<10
17)99x2100+1
18)72 cm^2
19)2n(n-1_(2n-1)/3
20)0
22)42
23) d
25)33
27)3
28) c
29)nf(1)
30){2,3}
31)R-Z
32)logIxI
33)1/2  log(1+x)/(1-x)
34)999
35) d
36)5/3
37)3
38)x1+x2+1
39)2/2005
40)6
41) d
42) I)1
II)7
III)1
43)2,left,-ve,3,down,-ve
44)4
45)25-xy