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JEE Advanced

Matrices and Determinants

Mathematics

Previous Years Questions

MCQ (Single Correct Answer)

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If $M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of ...
JEE Advanced 2022 Paper 2 Online
Let $$p, q, r$$ be nonzero real numbers that are, respectively, the $$10^{\text {th }}, 100^{\text {th }}$$ and $$1000^...
JEE Advanced 2022 Paper 1 Online
Let $$M = \left[ {\matrix{ {{{\sin }^4}\theta } \cr {1 + {{\cos }^2}\theta } \cr } \matrix{ { - 1 - {{\si...
JEE Advanced 2019 Paper 1 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...
JEE Advanced 2017 Paper 2 Offline
Let $$P = \left[ {\matrix{ 1 & 0 & 0 \cr 4 & 1 & 0 \cr {16} & 4 & 1 \cr } } \right]$$ and I be the iden...
JEE Advanced 2016 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 identi...
IIT-JEE 2012 Paper 2 Offline
Let $$P = [{a_{ij}}]$$ be a 3 $$\times$$ 3 matrix and let $$Q = [{b_{ij}}]$$, where $${b_{ij}} = {2^{i + j}}{a_{ij}}$$ f...
IIT-JEE 2012 Paper 1 Offline
Let $$\omega$$ $$\ne$$ 1 be a cube root of unity and S be the set of all non-singular matrices of the form $$\left[ {\ma...
IIT-JEE 2011 Paper 2 Offline
Let b = 6, with a and c satisfying (E). If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation ax2 + bx + c...
IIT-JEE 2011 Paper 1 Offline
Let $$\omega$$ be a solution of $${x^3} - 1 = 0$$ with $${\mathop{\rm Im}\nolimits} (\omega ) > 0$$. If a = 2 with b and...
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

Numerical

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Let $\beta$ be a real number. Consider the matrix $$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & ...
JEE Advanced 2022 Paper 2 Online
The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 $$ \times $$ 2 matrix such th...
JEE Advanced 2020 Paper 2 Offline
Suppose det$$\left| {\matrix{ {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \cr {\...
JEE Advanced 2019 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 ma...
JEE Advanced 2018 Paper 2 Offline
For a real number $$\alpha $$, if the system$$\left[ {\matrix{ 1 & \alpha & {{\alpha ^2}} \cr \alpha &...
JEE Advanced 2017 Paper 1 Offline
Let $$z = {{ - 1 + \sqrt 3 i} \over 2}$$, where $$i = \sqrt { - 1} $$, and r, s $$\in$$ {1, 2, 3}. Let $$P = \left[ {\ma...
JEE Advanced 2016 Paper 1 Offline
The total number of distinct x $$\in$$ R for which $$\left| {\matrix{ x & {{x^2}} & {1 + {x^3}} \cr {2x} & {4{x^...
JEE Advanced 2016 Paper 1 Offline
Let M be a 3 $$\times$$ 3 matrix satisfying $$M\left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right] = \left[ ...
IIT-JEE 2011 Paper 2 Offline

MCQ (More than One Correct Answer)

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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...
JEE Advanced 2021 Paper 1 Online
For any 3 $$\times$$ 3 matrix M, let | M | denote the determinant of M. Let$$E = \left[ {\matrix{ 1 & 2 & 3 ...
JEE Advanced 2021 Paper 1 Online
Let M be a 3 $$ \times $$ 3 invertible matrix with real entries and let I denote the 3 $$ \times $$ 3 identity matrix. I...
JEE Advanced 2020 Paper 1 Offline
$${P_1} = I = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \r...
JEE Advanced 2019 Paper 2 Offline
Let x $$ \in $$ R and let $$P = \left[ {\matrix{ 1 & 1 & 1 \cr 0 & 2 & 2 \cr 0 & 0 &amp...
JEE Advanced 2019 Paper 2 Offline
Let $$M = \left[ {\matrix{ 0 & 1 & a \cr 1 & 2 & 3 \cr 3 & b & 1 \cr } } \right...
JEE Advanced 2019 Paper 1 Offline
Let S be the set of all column matrices $$\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \rig...
JEE Advanced 2018 Paper 2 Offline
Which of the following is(are) NOT the square of a 3 $$ \times $$ 3 matrix with real entries?
JEE Advanced 2017 Paper 1 Offline
Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations ax + 2y = $$\lambda$$ 3x $$-$$ 2y = $$\mu$$ Whi...
JEE Advanced 2016 Paper 2 Offline
Let $$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$...
JEE Advanced 2016 Paper 1 Offline
Which of the following values of $$\alpha$$ satisfy the equation $$\left| {\matrix{ {{{(1 - \alpha )}^2}} & {{{(1 + 2...
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, no...
JEE Advanced 2015 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 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 $$\omega$$ be a complex cube root of unity with $$\omega$$ $$\ne$$ 1 and P = [pij] be a n $$\times$$ n matrix with p...
JEE Advanced 2013 Paper 2 Offline
For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?
JEE Advanced 2013 Paper 1 Offline
If the ad joint of a 3 $$\times$$ 3 matrix P is $$\left[ {\matrix{ 1 & 4 & 4 \cr 2 & 1 & 7 \cr 1 & 1 & 3 \...
IIT-JEE 2012 Paper 2 Offline
Let M and N be two 3 $$\times$$ 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of...
IIT-JEE 2011 Paper 1 Offline

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