Match of the column.
Column –IColumn –II(i) Fundamental period of f(x) = [x] + [2x] + [3x] +… … +[n…

Question

Match of the column.
Column –IColumn –II(i) Fundamental period of f(x) = [x] + [2x] + [3x] +… … +[nx] – x is (where [.] isrepresent greatest integerfunction)[A] sin2 x – cos2 x when x = π/4(ii)   is[B] sin2x + cos2 x when x = π/4(iii) Let A and B are square matrices of order 3 × 3 whichsatisfy AB = A and BA = B. If(A – B)5 = k(A –B) then k =[C]  (iv) If A =  and AA' = I, then x2 + y2 + z2 =[D] HCF of (3, 4)

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [B]; (ii) [B]; (iii) [A]; (iv) [B]. Ans.
(i) [B],[C],[D]
(ii) [B],[C],[D]
(iii) [A]
(iv) [B],[C],[D]
Sol.
(i) f(x) = – [{x} + {2x} + …. {nx}]
period of f(x) = LCM {1, 1/2, …….. 1/n} = 1
(ii)   =  
=   .  = 1
(iii) AB = A and BA = B
A 2 = A B 2 = B
There (A – B) 2 = A 2 – AB – BA + B 2
= A – A – B + B = 0
(iv)  
=  = 
2x 2 = 6y 2 = 3z 2 = 1
x 2 + y 2 + z 2 = 1/2 + 1/6 + 1/3 = 1

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Column –I	Column –II
(i) Fundamental period of f(x) = [x] + [2x] + [3x] +… … + [nx] – x is (where [.] is represent greatest integer function)	[A] sin2 x – cos2 x when x = π/4
(ii) is	[B] sin2x + cos2 x when x = π/4
(iii) Let A and B are square matrices of order 3 × 3 which satisfy AB = A and BA = B. If (A – B)5 = k(A –B) then k =	[C]
(iv) If A = and AA' = I, then x2 + y2 + z2 =	[D] HCF of (3, 4)

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