MATHEMATICS-04-06- 11th (PQRS) Space

EXTRA PAGE  2 3 4 Q.19 Let S = sec 0 + sec + sec + sec + sec and P = tan  · tan 2 · tan 4 then prove 5 5 5 5 9 9 9 S + P = 2 2 sin 7 [6] 12 tan  1 cot  Q.18 If tan   tan 3 = 3 , find the value of cot   cot 3 . [6] Q.17 Suppose that x and y are positive numbers for which log9x = log12y = log16(x + y). If the value of y x = 2 cos , where   (0,  2) find . [6]  1 2   1  Q.15 If log25 = a and log 225 = b, then find the value of log   + log  in terms of a and  9    2250  b (base of the log is 10 everywhere). [5] Q.13 Prove the identity cot A + cosec A 1 = cot A . [4] cot A  cosec A +1 2 PART-B cos3  + cot(3 + ) sec(  3) cosec 3   Q.11 Simplify     tan2 (  ) sin(  2)     . [4] Q.9 Let x = (0.15)20. Find the characteristic and mantissa in the logarithm of x, to the base 10. Assume log102 = 0.301 and log103 = 0.477. [3] Q.7 If the tangent of DAB is expressed as a ratio of positive integers a b in lowest term, then find the value of (a + b). [3] Q.5 tan  = 1 2 + 1 2 + 1 where   (0, 2), find the possible value of . [3] 2 +O  Q.3 If logx–3(2x – 3) is a meaningful quantity then find the interval in which x must lie. [3] PART-A Q.1 Find the number of real solution(s) of the equation logx9 – log3x2 = 3. [3]