Match the statements/expressions given in List I with the values given in List II. (JEE Advanced 2015)
List I | List II | ||
(A) | In , if the magnitude of the projection vector of the vector on is and if , then possible value(s) of is (are) | (P) | 1 |
(B) | Let and be real numbers such that the function
all . Then possible value(s) of is(are) | (Q) | 2 |
(C) | Let be a complex cube root of unity. If , then possible value(s) of is (are) | (R) | 3 |
(D) | Let the harmonic mean of two positive real numbers and be 4. If is a positive real number such that is an arithmetic progression, then the value(s) of is (are) | (S) | 4 |
(T) | 5 |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Let vector 
and vector 
.
Therefore, magnitude of projection of vector a on
Therefore, 
is differentiable 
. So
,
Also,
Hence, from Eqs. (1) and (2),
HM of ' a ' and ' b ' 
, where 
.
Now, 
are in AP, where 
.
Therefore
Also 
and 
Therefore, from Eqs. (3), (4) and (5),
or 
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