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Algebra PrevQ - Set 0001

  • The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

    (1) 7

    (2) 13

    (3) 14

    (4) 18

    (5) 20        

    (CAT 2006)        

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  • Let f (x) = max (2x + 1, 3 − 4x), where x is any real number. Then the minimum possible value of f(x) is:

    (1) 1/3

    (2) 1/2

    (3) 2/3

    (4) 4/3

    (5) 5/3       

    (CAT 2006)

  • A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

    (1) –119

    (2) –159

    (3) –110

    (4) -180

    (5) -105       

     (CAT 2007)

  • Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight member joint family is nearest to:

    (1) 23 years

    (2) 22 years

    (3) 21 years

    (4) 25 years

    (5) 24 years        

    (CAT 2007)

  • A function f (x) satisfies f (1) = 3600, and f (1) + f (2) + ... + f (n) = n² f(n), for all positive integers n >1. What is the value of f (9) ?

    (1) 80

    (2) 240

    (3) 200

    (4) 100

    (5) 120         

    (CAT 2007)          

  • Let g (x) be a function such that g (x + 1) + g (x – l) = g (x) for every real x. Then for what value of p is the relation g (x + p) = g (x) necessarily true for every real x ?

    (1) 5

    (2) 3

    (3) 2

    (4) 6        (CAT 2005)

  • Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f (5) = −3f (2) and that 3 is a root of f(x) = 0.

    What is the other root of f(x) = 0?

    (1) −7

    (2) − 4

    (3) 2

    (4) 6

    (5) cannot be determined    

    What is the value of a+b+c?

    (1) 9

    (2) 14

    (3) 13

    (4) 37

    (5) cannot be determined         

    (CAT 2008)

  • Let f(x) = ax2 – b|x| , where a and b are constants. Then at x = 0, f(x) is:

    1. maximized whenever a > 0, b > 0

    2. maximized whenever a > 0, b < 0

    3. minimized whenever a > 0, b > 0

    4. minimized whenever a > 0, b < 0     

    (CAT 2004)    

  • If f (x) = x3 – 4x + p, and f (0) and f (1) are of opposite signs, then which of the following is necessarily true?

    1. –1 < p < 2

    2. 0 < p < 3

    3. –2 < p < 1

    4. –3 < p < 0     

    (CAT 2004)