Matrices & Determinants · JEE Main previous year questions

2017 3 questions

1. Q42017 · 9 Apr 2017 · Shift 1

   For two $3\times 3$ matrices A and B, let $\mathrm{A}+\mathrm{B}=2{\mathrm{B}}^{\mathrm{T}}$ and $3\mathrm{A}+2\mathrm{B}={\mathrm{I}}_3$, where ${\mathrm{B}}^{\mathrm{T}}$ is the transpose of B and ${\mathrm{I}}_3$ is $3\times 3$ identity matrix. Then :

   1. A.$5\mathrm{A}+10\mathrm{B}=2{\mathrm{I}}_3$
   2. B.$10\mathrm{A}+5\mathrm{B}=3{\mathrm{I}}_3$
   3. C.$\mathrm{B}+2\mathrm{A}={\mathrm{I}}_3$
   4. D.$3\mathrm{A}+6\mathrm{B}=2{\mathrm{I}}_3$
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   Answer: B

2. Q222017 · 9 Apr 2017 · Shift 1

   The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is $60^{\circ }$. If the area of the quadrilateral is $4\sqrt{3}$, then the perimeter of the quadrilateral is :

   1. A.$12.5$
   2. B.$13.2$
   3. C.$12$
   4. D.$13$
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   Answer: C

3. Q52017 · 8 Apr 2017 · Shift 1

   Let $A$ be any $3\times 3$ invertible matrix. Then which one of the following is not always true ?

   1. A.$\mathrm{adj}(A)=|A|\cdot A^{-1}$
   2. B.$\mathrm{adj}(\mathrm{adj}(A))=|A|\cdot A$
   3. C.$\mathrm{adj}(\mathrm{adj}(A))=|A{|}^2\cdot (\mathrm{adj}(A){)}^{-1}$
   4. D.$\mathrm{adj}(\mathrm{adj}(A))=|A|\cdot (\mathrm{adj}(A){)}^{-1}$
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   Answer: D