1
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=⎡⎢
⎢
⎢⎣(r−1)1r11(r−1)2⎤⎥
⎥
⎥⎦. Then limn→∞(detM2+detM3+⋯+detMn)lnn equals (P)16(B) If ∣∣
∣
∣∣1cosαcosβcosα1cosγcosβcosγ1∣∣
∣
∣∣=∣∣
∣
∣∣0cosαcosβcosα0cosγcosβcosγ0∣∣
∣
∣∣, then sin2α+sin2β+sin2γ equals (Q)4(C) If A=[31−11] and a matrix C is defined as C=(BAB−1)(B−1ATB), where |B|≠0,(R)2 then detC is a square of natural number equal to (D) If A=[11−11] and A4=−λI, then λ equals (S)1
Which of the following is a CORRECT combination?
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=⎡⎢
⎢
⎢⎣(r−1)1r11(r−1)2⎤⎥
⎥
⎥⎦. Then limn→∞(detM2+detM3+⋯+detMn)lnn equals (P)16(B) If ∣∣
∣
∣∣1cosαcosβcosα1cosγcosβcosγ1∣∣
∣
∣∣=∣∣
∣
∣∣0cosαcosβcosα0cosγcosβcosγ0∣∣
∣
∣∣, then sin2α+sin2β+sin2γ equals (Q)4(C) If A=[31−11] and a matrix C is defined as C=(BAB−1)(B−1ATB), where |B|≠0,(R)2 then detC is a square of natural number equal to (D) If A=[11−11] and A4=−λI, then λ equals (S)1
Which of the following is a CORRECT combination?
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Solution
The correct option is B (C)→(Q), (D)→(Q)
(C)
C=(BAB−1)(B−1ATB)
⇒|C|=|A|2 (∵|AB|=|A||B|,|AT|=|A|)
⇒|C|=42
(D)
Compute A2 and then A4 to get the result
A2=[11−11][11−11]=[02−20]⇒A4=A2A2=[02−20][02−20]=[−400−4]=−4I
Hence, λ=4
(C)
C=(BAB−1)(B−1ATB)
⇒|C|=|A|2 (∵|AB|=|A||B|,|AT|=|A|)
⇒|C|=42
(D)
Compute A2 and then A4 to get the result
A2=[11−11][11−11]=[02−20]⇒A4=A2A2=[02−20][02−20]=[−400−4]=−4I
Hence, λ=4
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