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  Single Choice Correct Q.1 If the value of    1 142 11 3 tan 8.3tan108 tan8 .1 3tan 8.3 r r o or r   x y       Then the value of    x y   equals. (All angles are in degrees) (A) 8 (B) 9 (C*) 10 (D) None of these Q.2   21 12 9 136 nn r r  S t n n n        , then 1 1. r  r  r t     equals (A*) 1  (B) 2  (C) 32  (D) 12  Q.3 If , , a b c  are in G.P, , , a b c a b c     are in HP, then the value 4 a b c    is (A) 12 (B*) 0 (C) 11 (D) 2 Q.4 If 1 2 3 2 1 , , ..... n  H H H H    are in H.P then   2111 1 nii ii ii  H H  H H      is equal to (A) 2n -1 (B) 2n + 1 (C*) 2n (D) 2n + 2 Q.5 Solve the inequality          23 3 3log 4 2log2  x x  x      (A)     3, 2 2,3  x      (B)     5 53, ,32 2  x      (C*)     5 5, 2 2,2 2  x      (D) None  More than one option correct Q.1 If a, b & c are positive integers such that  16 2 abc    and the value of 4 4 2 a b c    is minimum. Then (A) 2 2 c    (B*) 4 2 c    (C)  2 2 a    (D) 8 2 ac    Q.2. Solve the inequality 1 32 log log 1  x x    (A*) 3 1log 2 1 0,2         (B)  2 1log 3 1 0,3         (C*) 23 log 3 0,2      (D*)  2 11 log 3 0,3         Q.37 If   n a  is a sequence such that 1 r r  a ra    then the value of 221 1 nr r  r r a      = (A*)   2 2 11 n na a    (B)   1 1 12 1 n a n a   (C*)   1 1 12 2 n a n a   (D) None of these Integer Type Questions Q.1 Three friends whose ages form a G.P. divide a certain sum of money in proportion to their ages. If they do that three years later, when the youngest is half the age of the oldest, then he will receive Rs. 1050/  –   more than he gets now, and the middle friend will get Rs. 150 more than now, then the age of the middle friend minus the age of the youngest is __6_____ Q.2 If the value of     21722 11 2 n n n pqn n n       , where p and q are relatively coprime 3-digit numbers, then the difference of the sum of the digits in the denominator and the sum of the digits in the numerator is ____8______ Q.3 If the solution to the following inequality   20.50.5 log  log2 2.5  x  x x   is of the form     0, ,  x a b     then the values baba   is _____5____.    Q.4 The solution set of the inequality   23 3 3log 2 log 12  x x        is of the form     , , a b c d    then the value of abcd     _____8_______. Q.5. If the number of solutions to the equation   4 1 2 6 2  x x  x x       are ‘a’ and the number of solutions to the equation 2 1  x  x     are ‘b’ then the value of a b   is __3__ Comprehenesion Type If a, b, c are in A.P and x, y, z are in G.P where a, b, c  R   , and x, y, z  R   . Q1. If , , a b c x y z   are in H.P, then (A*) c a   (B) 2 c a   (C) 3 c a   (D) c y   Q.2 If , ,  x y z a b c  are in H.P &  x z    then (A) a xc z    (B*) a xc z    (C) a xc z    (D) ax cz     Matrix Match (A) Let N =        2 4 32 2 1 2 1 2 1 .... 2 1 1       then 256 log  N is  (P) 16 (B) If , , a b c  are the sides of a triangle and 2 a b c s    , then the least value of     2 abc s a s b s c     is (Q) 17 (C) If ‘n’ is any integer such that 181 4  x ne   then number of possible values of n can be (R) 18 (D) If the sum of first 84 terms of the series 4 3 8 15 12 35.....1 3 3 5 5 7         is 524k, then k+14 is equal to (S) None of these (A)->(S) (B)->(P) (C)->(Q) (D)->(P)
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