# Matrices and Determinants · Mathematics · JEE Advanced

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## MCQ (More than One Correct Answer)

JEE Advanced 2023 Paper 2 Online
Let $M=\left(a_{i j}\right), i, j \in\{1,2,3\}$, be the $3 \times 3$ matrix such that $a_{i j}=1$ if $j+1$ is divisible by $i$, otherwise $a_{i j}=0$....
JEE Advanced 2021 Paper 1 Online
For any 3 $$\times$$ 3 matrix M, let | M | denote the determinant of M. Let$$E = \left[ {\matrix{ 1 & 2 & 3 \cr 2 & 3 & 4 \cr... JEE Advanced 2021 Paper 1 Online For any 3$$\times$$3 matrix M, let |M| denote the determinant of M. Let I be the 3$$\times$$3 identity matrix. Let E and F be two 3$$\times$$3 m... JEE Advanced 2020 Paper 1 Offline Let M be a 3$$ \times $$3 invertible matrix with real entries and let I denote the 3$$ \times $$3 identity matrix. If M$$-$$1 = adj(adj M), then w... JEE Advanced 2019 Paper 2 Offline Let x$$ \in $$R and let$$P = \left[ {\matrix{ 1 & 1 & 1 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$,$$Q...
JEE Advanced 2019 Paper 2 Offline
$${P_1} = I = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right],\,{P_2} = \left[ {\matri... JEE Advanced 2019 Paper 1 Offline Let$$M = \left[ {\matrix{ 0 & 1 & a \cr 1 & 2 & 3 \cr 3 & b & 1 \cr } } \right]$$andadj$$M = \left[ {\matr...
JEE Advanced 2018 Paper 2 Offline
Let S be the set of all column matrices $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]$$ such that $${b_1},{b_2},... JEE Advanced 2017 Paper 1 Offline Which of the following is(are) NOT the square of a 3$$ \times $$3 matrix with real entries? JEE Advanced 2016 Paper 2 Offline Let a,$$\lambda$$, m$$\in$$R. Consider the system of linear equations ax + 2y =$$\lambda$$3x$$-$$2y =$$\mu$$Which of the following statements... JEE Advanced 2016 Paper 1 Offline Let$$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where$$\alpha\in$$R. ... JEE Advanced 2015 Paper 1 Offline Let X and Y be two arbitrary, 3$$\times$$3, non-zero, skew-symmetric matrices and Z be an arbitrary 3$$\times$$3, non-zero, symmetric matrix. Then... JEE Advanced 2015 Paper 1 Offline Which of the following values of$$\alpha$$satisfy the equation$$\left| {\matrix{ {{{(1 - \alpha )}^2}} & {{{(1 + 2\alpha )}^2}} & {{{(1 + 3\alph...
JEE Advanced 2014 Paper 1 Offline
Let M be a 2 $$\times$$ 2 symmetric matrix with integer entries. Then, M is invertible, if
JEE Advanced 2014 Paper 1 Offline
Let M and N be two 3 $$\times$$ 3 matrices such that MN = NM. Further, if M $$\ne$$ N2 and M2 = N4, then
JEE Advanced 2013 Paper 2 Offline
Let $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with pij = $$\omega$$i + j. Then P2 ...
JEE Advanced 2013 Paper 1 Offline
For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
IIT-JEE 2012 Paper 2 Offline
If the ad joint of a 3 $$\times$$ 3 matrix P is $$\left[ {\matrix{ 1 & 4 & 4 \cr 2 & 1 & 7 \cr 1 & 1 & 3 \cr } } \right]$$, then the ...
IIT-JEE 2011 Paper 1 Offline
Let M and N be two 3 $$\times$$ 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2(MTN)$$-$$1(MN$$-... ## Numerical JEE Advanced 2023 Paper 2 Online Let R=\left\{\left(\begin{array}{lll}a & 3 & b \\ c & 2 & d \\ 0 & 5 & 0\end{array}\right): a, b, c, d \in\{0,3,5,7,11,13,17,19\}\right\}. Then the ... JEE Advanced 2022 Paper 2 Online Let \beta be a real number. Consider the matrix$$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right) $$If ... JEE Advanced 2020 Paper 2 Offline The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2$$ \times $$2 matrix such that the trace of A is 3 and the... JEE Advanced 2019 Paper 2 Offline Suppose det$$\left| {\matrix{ {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \cr {\sum\limits_{k = 0}^n {{}^n{C_k...
JEE Advanced 2018 Paper 2 Offline
Let P be a matrix of order 3 $$\times$$ 3 such that all the entries in P are from the set {$$-$$1, 0, 1}. Then, the maximum possible value of the de...
JEE Advanced 2017 Paper 1 Offline
For a real number $$\alpha$$, if the system$$\left[ {\matrix{ 1 & \alpha & {{\alpha ^2}} \cr \alpha & 1 & \alpha \cr ... JEE Advanced 2016 Paper 1 Offline The total number of distinct x$$\in$$R for which$$\left| {\matrix{ x & {{x^2}} & {1 + {x^3}} \cr {2x} & {4{x^2}} & {1 + 8{x^3}} \cr {3...
JEE Advanced 2016 Paper 1 Offline
Let $$z = {{ - 1 + \sqrt 3 i} \over 2}$$, where $$i = \sqrt { - 1}$$, and r, s $$\in$$ {1, 2, 3}. Let $$P = \left[ {\matrix{ {{{( - z)}^r}} & {{z^... IIT-JEE 2011 Paper 2 Offline Let M be a 3$$\times$$3 matrix satisfying$$M\left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right] = \left[ {\matrix{ { - 1} \cr 2...

JEE Advanced 2023 Paper 1 Online
Let $\alpha, \beta$ and $\gamma$ be real numbers. Consider the following system of linear equations \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=1... JEE Advanced 2022 Paper 2 Online If M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right), then which of the following matrices is equa... JEE Advanced 2022 Paper 1 Online Letp, q, r$$be nonzero real numbers that are, respectively, the$$10^{\text {th }}, 100^{\text {th }}$$and$$1000^{\text {th }}$$terms of a har... JEE Advanced 2019 Paper 1 Offline Let$$M = \left[ {\matrix{ {{{\sin }^4}\theta } \cr {1 + {{\cos }^2}\theta } \cr } \matrix{ { - 1 - {{\sin }^2}\theta } \cr {{{\co...
JEE Advanced 2017 Paper 2 Offline
How many 3 $$\times$$ 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?
JEE Advanced 2016 Paper 2 Offline
Let $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right]$$ and I be the identity matrix of order 3. If $$Q... IIT-JEE 2012 Paper 2 Offline If P is a 3$$\times$$3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3$$\times$$3 identity matrix, then there exists a... IIT-JEE 2012 Paper 1 Offline Let$$P = [{a_{ij}}]$$be a 3$$\times$$3 matrix and let$$Q = [{b_{ij}}]$$, where$${b_{ij}} = {2^{i + j}}{a_{ij}}$$for$$1 \le i,j \le 3$$. If the... IIT-JEE 2011 Paper 1 Offline If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is IIT-JEE 2011 Paper 1 Offline Let$$\omega$$be a solution of$${x^3} - 1 = 0$$with$${\mathop{\rm Im}\nolimits} (\omega ) > 0$$. If a = 2 with b and c satisfying (E), then the va... IIT-JEE 2011 Paper 1 Offline Let b = 6, with a and c satisfying (E). If$$\alpha$$and$$\beta$$are the roots of the quadratic equation ax2 + bx + c = 0, then$$\sum\limits_{n = ...
IIT-JEE 2011 Paper 2 Offline
Let $$\omega$$ $$\ne$$ 1 be a cube root of unity and S be the set of all non-singular matrices of the form $$\left[ {\matrix{ 1 & a & b \cr \o... IIT-JEE 2009 Paper 1 Offline The number of matrices in A is IIT-JEE 2009 Paper 1 Offline The number of matrices A in A for which the system of linear equations$$A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\m...
IIT-JEE 2009 Paper 1 Offline
The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{ x \cr y \cr z \cr } } \right] = \left[ {\m... IIT-JEE 2008 Paper 1 Offline Consider the system of equations:$$x-2y+3z=-1-x+y-2z=kx-3y+4z=1$$Statement - 1 : The system of equations has no solution for$$k\ne3. an...
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