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Question

Match List I with the List II and select the correct answer using the code given below the lists :

List I List II(A)Mr is defined as Mr=⎢ ⎢ ⎢(r1)1r11(r1)2⎥ ⎥ ⎥. Then limn(detM2+detM3++detMn)lnn equals (P)16(B) If ∣ ∣ ∣1cosαcosβcosα1cosγcosβcosγ1∣ ∣ ∣=∣ ∣ ∣0cosαcosβcosα0cosγcosβcosγ0∣ ∣ ∣, then sin2α+sin2β+sin2γ equals (Q)4(C) If A=[3111] and a matrix C is defined as C=(BAB1)(B1ATB), where |B|0,(R)2 then detC is a square of natural number equal to (D) If A=[1111] and A4=λI, then λ equals (S)1

Which of the following is a CORRECT combination?

A
(C)(P), (D)(S)
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B
(C)(Q), (D)(Q)
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C
(C)(Q), (D)(R)
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D
(C)(R), (D)(P)
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Solution

The correct option is B (C)(Q), (D)(Q)
(C)
C=(BAB1)(B1ATB)
|C|=|A|2 (|AB|=|A||B|,|AT|=|A|)
|C|=42

(D)
Compute A2 and then A4 to get the result
A2=[1111][1111]=[0220]A4=A2A2=[0220][0220]=[4004]=4I
Hence, λ=4

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