CAT4MBA

Q1) For which of the values of g(x) can f(x) be expressed as f1(x) + f2(x) where f1(x) & f2(x) are any two function of x?

a) g (x) = e^x   b)   g (x)=x²  c) g (x) =log(x)  d) None of these

Q2) If 0<x<1000 & [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,
a) 34   b) 32   c)  33   d) None of these

Q3) (x²-1) is a factor of f(x)=(x⁵+ax⁴+bx³+cx²+x+d).The graph of f(x) intersects Y axis at (0,-3). Find the value of (a+c).
a)  0    b)   3    c) -3    d)   -1

Q4)  Let f(x) =ax²+bx+c,where a,b,c are rational & f:z->,where z is the set of integers,which of the following best describes the value of a+b

a) a negative integer
b) an integer
c) not integral ratonal number
d) None of these

Q5) If f(x+1)+f(x-1)=2f(x) & f(0) =0,then f(x),n is a natural number is
a) nf(1)   b)  {f(1)}^n    c)  0   d) None of these

Q6) The domainof the function f(x) =^16-xC_2x-1 + ^20-3xP_4x-5,
is the set
a) [1,2,3,4,5]    b) {2,3,4}    c)  {2,3}  d) None of these

Q7)  The domain of the function f(x)=loge[x-mod(x)] where [.] denotes the greatest integeral function is
a) R    b)   R-Z    c)   (0,infinity)   d)   None of these

Q8)If f(x) =x^n, n is a natural number g of (x) =n g(x),then g(x) can be
a) n[mod(x)]   b) 3(cube rootx)  d) e^x   d) log [mod(x)]

Q9)If f(x) =4^x/(4^x+2),find the value of f(1/1999)+f(2/1999)+...+f(1998/1999)
a) 1998   b) 1999   c) 998   d)999

Q10) If f(x)=2x²+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

Q11) Find f(111)
a) 1  b) -1  c) 2   d) None of these

Q12) f(1)+f(2)+...+f(25)
a) -26   b)  -24    c) -22   d) None of these

Q13) Let y=f(x)=loga x and a>1. Then only one of the solution is

a) If x=1 then y=0

b) If x<1 then y<0
c) If x=1/2 then y=1/2
d) If x=1 then y=1.

14) A function H is defined for all positive integers that satisfy the following condition
a) 2/2005  b)2/2006 c)  2/2006!   d)2/2005!