BASIC MATHS & LOGARITHM Exercise # 1 1. 1 log abc bc + [Single Correct Choice Type Questions] 1 log ca abc (A) 1/2 2. (B) 6. (D) 4 (C) 0 (D) 1 (C) –1 < x < 0 (D) none of these (C) 3 (D) 4 Given system of simultaneous equations 2x. 5y = 1 and 5x+1 . 2y = 2. Then (A) x = log105 and y = log102 (B) x = log102 and y = log105 1 (C) x = log10   and y = log102 5 1 (D) x = log105 and y = log10   2 The value of 3 log 4 5  4 log 5 3  5 log 4 3  3log 5 4 is (B) 1 (C) 2 (D) none of these The natural number n for which the expression y = 5(log3n)2 – log3n12 + 9, has the minimum value is (B) 3 The ratio 2 log 1/4 a 2 7 log 27 ( a 2  1)3 3 4log 49 a  2a  a 1 (C) 36/5 (D) 4 (C) a2 – a + 1 (D) a2 + a + 1 simplifies to - (B) a2 + a – 1  x2  The value of the expression, log4   – 2 log4(4x4) when x = – 2 is  4  (A) – 6 10. 1 abc (B) 2 (A) a2 – a – 1 9. (C) 2 The number of real solution of the equation log10 (7x – 9)2 + log10 (3x – 4)2 = 2 is - (A) 2 8. has the value equal to - (B) –1 < x < 1 (A) 0 7. abc Value of x satisfying log10 1  x  3 log10 1  x  log 10 1  x 2  2 is (A) 1 5. ab 1 1 1   is equal to1  log b a  log b c 1  log c a  log c b 1  log a b  log a c (A) 0 < x < 1 4. 1 log (B) 1 (A) abc 3. + (B) – 5 (C) – 4 (D) meaningless Which one of the following denotes the greatest positive proper fraction ? 1 (A)   4 log 2 6 1 (B)   3 log3 5  log 2 (C) 3 3 (D) 8   1   log 2  3 11. 12. The equation, log2(2x2) + (log2x). x + 1 log24 (x4) + 2 3log1/2 (log 2 x ) = 1 has 2 (A) exactly one real solution (B) two real solutions (C) 3 real solutions (D) no solution If p = s , then n equals (1  k)n (A) log 13. log x (log 2 x 1) s p(1  k ) (B) log(s / p) log(1  k ) (C) log s log p(1  k ) (D) log p(1  k ) log(s / p) A = { x | x2 + (m – 1)x – 2(m + 1) = 0, x  R} Let B = { x | (m – 1)x2 + mx + 1 = 0, x  R} Number of values of m such that A  B has exactly 3 distinct elements, is (A) 4 14. 15. (A) 1 (C) 3 (B) 2   (B) 20.   (C)    (D)    If  and  are the roots of the equation (log2x)2 + 4(log2x) – 1 = 0 then the value of log + log equals (B) – 16 logAB ,where B  12 3 5  8 (C) 14 (D) – 18 and A  1  2  5  1 0 is - (B) a prime integer (C) a positive integer (D) an even–natural If logc2 . logb625 = log1016 . logc10 where c > 0 ; c  1 ; b > 1 ; b  1 determine b (A) 25 19. (D) 1/2 Given that logpx =  and logqx = then value of logp/q x equals - (A) a negative integer 18. (D) 7 log bc a  log cb a (b + c  1, c – b  1) equals log bc a·log cb a (A) 18 17. (C) 6 Let ABC be a triangle right angled at C. The value of (A) 16. (B) 5 (B) 5 (C) 625 (D) 16 The value of p for which both the roots of the quadratic equation, 4x2  20 px + (25p2 + 15p  66) are less than 2 lies in : (A) (4/5, 2) (B) (2, ) (C) ( 1, 4/5) (D) (,  1) 5 Number of cyphers after decimal before a significant figure comes in   3 (A) 21 (B) 22 (C) 23 100 is (D) none EXERCISE - 1 1. B 14. B 2. D 15. A 3. D 16. D 4. B 17. C 5. C 18. B 6. A 19. D 7. D 20. B 8. D 9. A 10. C 11. D 12. B 13. D

Basic Maths & Logarithm Exercise # 1

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