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Question

Column Matching:

Column (I)Column (II)(A)  In R2, if the magnitude of the projectionvector of the vector α^i+β^j on 3^i+^j3 and if α=2+3β, then possiblevalue(s) of |α| is (are)(P)     1(B)  Let a and b be real numbers such thatthe functionf(x)={3ax22,  x<1bx+a2,       x1 is differentiable for all xR. Thenpossible value(s) of a is (are) (Q)     2(C)  Let ω1 be a complex cube root ofunity. If (33ω+2ω2)4n+3+(2+3ω3ω2)4n+3+(3+2ω+3ω2)4n+3=0,then possible value(s) of n is (are)(R)     3(D)  Let the harmonic mean of two positive realnumbers a and b be 4. If q is a positive realnumber such that a,5,q,b is an arithmeticprogression, then the value(s) of |qa| is (are)(S)     4(T)     5
Option (D) matches with which of the elements of right hand column?
  1. P
  2. Q
  3. R
  4. S
  5. T


Solution

The correct options are
A P
B Q
Function is continuous.
So limx1f(x)=f(1)
3a2=b+a2     (1)
For function to be differentiable, 
6a=b     (2)
From (1) and (2), we get
3a2=6a+a2
a23a+2=0a=1,2  

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