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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+^j√3 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)={−3ax2−2, x<1bx+a2, x≥1 is differentiable for all x∈R. Thenpossible value(s) of a is (are) (Q) 2(C) Let ω≠1 be a complex cube root ofunity. If (3−3ω+2ω2)4n+3+(2+3ω−3ω2)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 |q−a| is (are)(S) 4(T) 5Option (D) matches with which of the elements of right hand column?

Answer»

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+^j√3 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)={−3ax2−2, x<1bx+a2, x≥1 is differentiable for all x∈R. Thenpossible value(s) of a is (are) (Q) 2(C) Let ω≠1 be a complex cube root ofunity. If (3−3ω+2ω2)4n+3+(2+3ω−3ω2)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 |q−a| is (are)(S) 4(T) 5

Option (D) matches with which of the elements of right hand column?


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