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0807 QM (CFA530)

# 0807 QM (CFA530) - Question Paper Quantitative...

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1 Question Paper Quantitative Methods (CFA530): July 2008 Answer all 73 questions. Marks are indicated against each question. Total Marks : 100 1. If the letters of the word VICTORY are arranged in a row at random, the probability that the two vowels do not come together is (a) 2 7 (b) 3 7 (c) 4 7 (d) 5 7 (e) 6 7 . (1mark) <Answer > 2. The sum of the series 2 3 4 2 3 log log log log .... a a a a b b b up to n terms is (a) (n/2) [ n log ab log (a/b)] (b) (n/2) [ log ab n log (a/b)] (c) (n/2) [ n log ab + log (a/b)] (d) (n/2) [ log ab + n log (a/b)] (e) (n/2) [ log (a/b) – n log ab]. (1mark) <Answer > 3. The ratio between the sum of n terms of two A.P.’s is (3n + 8) : (7n + 15). The ratio between their twelfth terms is (2 marks ) <Answer > 4. If m 1 n n 1 m m x = n , 1 n m m 3 n n y= m and 5 n 1 2n m m z = n , then the value of xyz is (a) m n m n (b) n m m n (c) m n n m (d) n m n m (e) n m m n . (1mark) <Answer >

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2 5. Consider the following simultaneous equations. 2x 3y 3z 7 x y z 5 2x 2y z 2 The value of x in the above equations is (1mark) <Answer > 6. How many committees of five members each can be formed from 8 official and 4 non-official members when these committees would require at least 2 non-official members? (1mark) <Answer > 7. If 2 1 x 2x f(x) log , then f 1 x 1 x (a) 0 (b) 1 (c) f (x) (d) 2 f (x) (e) 3 f (x). (1mark) <Answer > 8. The logarithm of a number (a) Is always expressed with respect to base 10 (b) Is always expressed with respect to base 1 (c) Is always expressed with respect to base e (d) Is equal to the base which must be raised to a given exponent in order to get the number (e) Is equal to the exponent to which a given base must be raised in order to get the number. (1mark) <Answer > 9. Differentiation of log (a bx) with respect to x is (1mark) <Answer >
3 10. x 2 3 1, for 1 x<0 Let f (x) = x ,for 0 x 6 x 2 The value of f(1) is (1mark) <Answer > 11. An investment of Rs.1000 is earning 4% interest per annum compounded annually. If the value, V, of the investment after t years is given by V = 1000(1.04) t then t, written as a function of V, is 10 10 log V log (1.04) 3 10 10 log V 3log (1.04) 3 t = 10 10 log V 3 log (1.04) t = 10 10 log V 3 log (1.04) . (2 marks ) <Answer >

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0807 QM (CFA530) - Question Paper Quantitative...

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