Math Puzzle 11

This math puzzle 11 is on real numbers,arithmetic progression etc.
1) If 'a' and 'b' are real numbers such that b < a, then which of the following inequalities is true?
I a < (a + b)/2 < b
II b < (b + a)/2 < a
III a < ab < b
A. I only B. II only C. III only D. I and II only E. II and III only
2) If a/b is multiplied by a² /b ³ and the product is divided by -a² /b² the result is:
A. -1 B. -a²/b² C. a² / b² D. -a / b² E.-a / b
3) The simplest form of (ab/ (a² - b ² )) - ((b/ (2a - 2b)) is
A. 2ab /(a - b) B. 2ab / (a + b) C. 2 /(a² - b²)
D. b / 2(a - b) E. b / 2(a + b)
4) For what value of 'a' do the numbers 1, a and (14-a) taken in order, make an arithmetic progression?
A. 3 B. 4 C. 5 D. 6 E. 15
5) A sequence is given by a_n = n² - 2n. Which of the following gives the (n-1) th term?
A. (n - 1)² B. (n - 1)(n - 3) C. (n - 1)² - 2
D. (n - 1)(n - 2) E. 2(n - 1)²
6) In a group of persons, each knows either French or German. If 100 know French, 50 know German and 20 know both, how many persons are there in the group?
A. 100 B. 120 C. 130 D. 150 E. 180
7) In a group of 70 persons, 32 drink coke but not coffee and 47 drink coke. How many drink coffee but not coke?
A. 19 B. 23 C. 32 D. 42 E. 47
8) If x*y = x^3y for all positive integers, what is (4*3)* 1/9?
A. 4 B. 4³ C. 4⁶ D. 4⁹ E. 4¹⁸
9) The symbols @ and # are defined as A @ B = (A + B) 2 and
A # B = (A - B) 2 , when A and B are real numbers. Each of the following is true except
A. (A @ B)+(A # B)=2(A² +B² ) B. (A @ B)-(A # B)= 4AB
C. (A @ B)(A # B)=( A² - B² ) D. A @ 0=A² E. (A # B)#0 = 0
10) If f(x) = | |x| - 5|, what is the value of f(1)?
A. 5 B. 4 C. -4 D. -5 E. -6

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Math Puzzle 11

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