11Ans is (c) 6
Ques 1) If 0 ≤ x ≤ 3 π , 0 ≤ y ≤ 3 π and cosx . siny = 1 , then the possible number of ordered pairs (x,y) is:-
(a) 4 (b) 8 (c) 6 (d) 12
Ques 2) The no. of points inside or on the circle x2 + y2 = 4 satisfying tan 4 x + cot 4 x + 1 = 3 sin 2 y is :-
(a) 1 (b) 2 (c) 4 (d) none of these
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UP 0 DOWN 0 0 6
6 Answers
1sorryy made a silly mistake !!!!
answer is c only
see tushar
1.1 =1
-1 . -1 =1
now how many times sin achieves 1or -1 in 0 - 3 pi ?
at pi/2 (1) ,3 pi/2 (-1),5pi/2 (1)
now come to cosine
now how many times cosin achieves 1 or -1 in 0 - 3 pi ?
at 0 (1),pi(-1),2pi(1),3pi(-1)
now do permutation of possible cases
in 2 ways i can choose 1 fom cosine
and 2 ways from sin
so
simultaneously the events can be done in
2*2=4
now in 2 ways i can chose -1 from cosine
and 1 way from sin
so
simultaneously the events can be done in
2*1 =2
adding up the cases
2+4 = 6
hence answer is 6
12 one ....
we observe the min value of l.h.s = max of r.h.s
so
tan4x=1
sin2y=1
possible values are
x=pi/4,-pi/4
y=pi/2,-pi/2
so answer is 4
