Matrices & Determinants · JEE Main previous year questions

2019 9 questions

1. Q142019 · 12 Apr 2019 · Shift 1

   If A is a symmetric matrix and B is a skew-symmetric matrix such that $A+B=\left[\begin{array}{cc}2& 3\\ 5& -1\end{array}\right]$, then AB is equal to :

   1. A.$\left[\begin{array}{cc}4& -2\\ 1& -4\end{array}\right]$
   2. B.$\left[\begin{array}{cc}-4& -2\\ -1& 4\end{array}\right]$
   3. C.$\left[\begin{array}{cc}-4& 2\\ 1& 4\end{array}\right]$
   4. D.$\left[\begin{array}{cc}4& -2\\ -1& -4\end{array}\right]$
   Show answer

   Answer: D

2. Q162019 · 12 Apr 2019 · Shift 1

   If $B=\left[\begin{array}{ccc}5& 2\alpha & 1\\ 0& 2& 1\\ \alpha & 3& -1\end{array}\right]$ is the inverse of a $3\times 3$ matrix A, then the sum of all values of $\alpha$ for which $\det (A)+1=0$, is :

   1. A.2
   2. B.-1
   3. C.0
   4. D.1
   Show answer

   Answer: D

3. Q132019 · 10 Apr 2019 · Shift 2

   Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is :

   1. A.180
   2. B.210
   3. C.170
   4. D.190
   Show answer

   Answer: C

4. Q112019 · 9 Apr 2019 · Shift 2

   The total number of matrices $A=\left(\begin{array}{ccc}0& 2y& 1\\ 2x& y& -1\\ 2x& -y& 1\end{array}\right)$ $(x,y\in \mathbb{R},x\ne y)$ for which $A^{T}A=3I_3$ is :-

   1. A.3
   2. B.4
   3. C.2
   4. D.6
   Show answer

   Answer: B

5. Q92019 · 8 Apr 2019 · Shift 2

   Let the number 2,b,c be in an A.P. and $A=\left[\begin{array}{ccc}1& 1& 1\\ 2& b& c\\ 4& b^2& c^2\end{array}\right]$. If $\det (A)\in [2,16]$, then c lies in the interval :

   1. A.[2, 3)
   2. B.[4, 6]
   3. C.$(2+2^{3/4},4)$
   4. D.$[3,2+2^{3/4}]$
   Show answer

   Answer: B

6. Q202019 · 12 Jan 2019 · Shift 1

   Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $Q=[q_{ij}]$ be two $3\times 3$ matrices such that $Q-P^5=I_3$. Then $\frac{q_{21}+q_{31}}{q_{32}}$ is equal to :

   1. A.15
   2. B.9
   3. C.135
   4. D.10
   Show answer

   Answer: D

7. Q132019 · 12 Jan 2019 · Shift 2

   If $A=\left[\begin{array}{ccc}1& \sin \theta & 1\\ -\sin \theta & 1& \sin \theta \\ -1& -\sin \theta & 1\end{array}\right]$; then for all $\theta \in \left(\frac{3\pi }{4},\frac{5\pi }{4}\right)$, $\det (A)$ lies in the interval :

   1. A.$(\frac{3}{2},3]$
   2. B.$(0,\frac{3}{2}]$
   3. C.$[\frac{5}{2},4)$
   4. D.$(1,\frac{5}{2}]$
   Show answer

   Answer: A

8. Q252019 · 11 Jan 2019 · Shift 2

   Let A and B be two invertible matrices of order $3\times 3$. If $\det (\mathrm{AB}{\mathrm{A}}^{\mathrm{T}})=8$ and $\det (\mathrm{A}{\mathrm{B}}^{-1})=8$, then $\det (\mathrm{B}{\mathrm{A}}^{-1}{\mathrm{B}}^{\mathrm{T}})$ is equal to :

   1. A.$\frac{1}{4}$
   2. B.16
   3. C.$\frac{1}{16}$
   4. D.1
   Show answer

   Answer: C

9. Q122019 · 9 Jan 2019 · Shift 1

   If $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$, then the matrix $A^{-50}$ when $\theta =\frac{\pi }{12}$, is equal to :

   1. A.$\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& -\frac{1}{2}\\ \frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right]$
   2. B.$\left[\begin{array}{cc}\frac{1}{2}& -\frac{\sqrt{3}}{2}\\ \frac{\sqrt{3}}{2}& -\frac{1}{2}\end{array}\right]$
   3. C.$\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& \frac{1}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right]$
   4. D.$\left[\begin{array}{cc}\frac{1}{2}& \frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2}& \frac{1}{2}\end{array}\right]$
   Show answer

   Answer: C