CAT2004 SECTION - MATHS _ CAT4MBA

0 b 1 c 2 d no n e o f th e a b o ve e no t atte mp te

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Unformatted text preview: mp te d 9. If f(x) = x3 - 4x + p, and f(0) and f(1) are of oppos ite s igns , then which of the following is neces s arily true? ra h u l n e m a re fre sh a . -1 < p < 2 b. 0 < p < 3 c. -2 < p < 1 d . -3 < p < 0 e .No t Atte mp te d 10. Suppos e n is an integer s uch that the s um of the digits of n is 2, and 101 0 < n < 101 1 . The num ber of different values for n is a . 11 b . 10 c. 9 d. 8 e .No t Atte mp te d 11. If a/(b+c) = b/(c+a) = c/(a+b) = r , then r cannot take any value except a . 1 /2 b . -1 c. 1 /2 o r -1 d . -1 /2 o r -1 e .No t Atte mp te d 12. Let What is the value of y? a . (√1 3 +3 )/2 b . (√1 3 -3 )/2 c. (√1 5 +3 )/2 d . (√1 5 -3 )/2 e .No t Atte mp te d 13. Let f(x) = ax2 - b |x|, where a and b are cons tants . Then at x = 0, f(x) is a . ma ximiz e d w h e n e ve r a > 0 , b >0 b . ma ximiz e d w h e n e ve r a > 0 , b < 0 c. min imiz e d w h e n e ve r a > 0 , b > 0 d . min imiz e d w h e n e ve r a > 0 , b < 0 e .No t Atte mp te d 14. Two boats , traveling at 5 and 10 km s per hour, head directly towards each other. They begin at a dis tance of 20 km s from each other. How far apart are they (in km s ) one m inute before they collide? a . 1 /1 2 b . 1 /6 c. 1 /4 d . 1 /3 e .No t Atte mp te d 15. Each fam ily in a locality has at m os t two adults , and no fam ily has fewer than 3 children. Cons idering all the fam ilies together, there are m ore adults than boys , m ore boys than girls , and m ore girls than fam ilies . Then the m inim um pos s ible num ber of fam ilies in the locality is a. 4 b. 5 c. 2 d. 3 e . No t Atte mp te d 16. In Nuts And Bolts factory, one m achine produces only nuts at the rate of 100 nuts per m inute and needs to be cleaned for 5 m inutes after production of every 1000 nuts . Another m achine produces only bolts at the rate of 75 bolts per m inute and needs to be cleaned for 10 m inutes after production of every 1500 bolts . If both the m achines s tart production at the s am e tim e, what is the m inim um duration required for producing 9000 pairs of nuts and bolts ?...
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