NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...

## MCQ (More than One Correct Answer)

More
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$$E = \left[ {\matrix{ 1 &amp; 2 &amp; 3 ... JEE Advanced 2021 Paper 1 Online Let M be a 3$$ \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 &amp; 0 &amp; 0 \cr 0 &amp; 1 &amp; 0 \cr 0 &amp; 0 &amp; 1 \cr } } \r...
JEE Advanced 2019 Paper 2 Offline
Let x $$\in$$ R and let $$P = \left[ {\matrix{ 1 &amp; 1 &amp; 1 \cr 0 &amp; 2 &amp; 2 \cr 0 &amp; 0 &amp... JEE Advanced 2019 Paper 2 Offline Let$$M = \left[ {\matrix{ 0 &amp; 1 &amp; a \cr 1 &amp; 2 &amp; 3 \cr 3 &amp; b &amp; 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$$3 non-singular skew symmetric matrices such that MN = NM. If PT denotes the transpose of... IIT-JEE 2011 Paper 1 Offline ## Numerical More The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2$$ \times $$2 matrix such th... JEE Advanced 2020 Paper 2 Offline Suppose det$$\left| {\matrix{ {\sum\limits_{k = 0}^n k } &amp; {\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$$\left[ {\matrix{ 1 &amp; \alpha &amp; {{\alpha ^2}} \cr \alpha &... JEE Advanced 2017 Paper 1 Offline Let$$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 $$\left| {\matrix{ x & {{x^2}} & {1 + {x^2}} \cr {2x} & {4{x^... JEE Advanced 2016 Paper 1 Offline Let M be a 3$$\times$$3 matrix satisfying$$M\left[ {\matrix{ 0 \cr 1 \cr 0 \cr } } \right] = \left[ ...
IIT-JEE 2011 Paper 2 Offline

More
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

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12