Question 1 :
If {tex} A ^ { 2 } - A + I = 0 , {/tex} then the inverse of {tex} A {/tex} is
Question 2 : If ω be a complex cube root of unity, then <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f87c19f8d44d3a17ec75' height='68' width='97' > is equal to-
Question 3 :
Consider the system of linear equation in x, y, z (sin3θ) x - y + z = 0, (cos2θ) x + 4y + 3z = 0 2x + 7y + 7z = 0 If the system has non-trivial solution then, θ∈ [0, π] are -
Question 4 : If A<sub>r</sub> = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f89e19f8d44d3a17ecac' height='41' width='72' > where r ∈ N then the value of |A<sub>1</sub>| + |A<sub>2</sub>| + |A<sub>3</sub>| + ...........+|A<sub>2006</sub>| is -
Question 5 :
For the determinant {tex} \Delta = \left| \begin{array} { c c c } { - 1 } & { a } & { a ^ { 2 } } \\ { \sin x } & { \cos y } & { \sin x } \\ { \cos y } & { \sin x } & { \cos y } \end{array} \right| ( a \in R ) {/tex}
Question 6 :
If A and B are square matrices of same order and A is non-singular, then for a positive integer n(A<sup>-1</sup>BA)<sup>n</sup> is equal to-
Question 7 :
Let {tex} P {/tex} and {tex} Q {/tex} be {tex} 3 \times 3 {/tex} matrices with {tex} P \neq Q . {/tex} If {tex} P ^ { 3 } = Q ^ { 3 } {/tex} and {tex} P ^ { 2 } Q = Q ^ { 2 } P , {/tex} then determinant of {tex} \left( P ^ { 2 } + Q ^ { 2 } \right) {/tex} is equal to
Question 8 :
If the value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be
Question 9 : If A = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa2ce6d3604eaa92e0fb' height='63' width='67' >, then adj. (adj. A) is equal to
Question 10 : If a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, ............., a<sub>n</sub>, ........ are in GP, then the value of the determinant <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ec8e39014bbd053c6532bee" width=148 height=57 /> is
Question 11 : If the three digit numbers A28, 3B9 and 62C when A, B and C are integers between 0 and 9 which are divisible by λ, then Δ = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f965e6d3604eaa92dff1' height='63' width='67' > is divisible by -
Question 12 : If A(θ) =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f8cf75ed294f2c7c3396' height='41' width='89' > and AB = I, then (sec<sup>2</sup>θ) B is equal to-
Question 13 : If A<sub>r</sub> = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f89e19f8d44d3a17ecac' height='41' width='72' >where r is a natural number then |A<sub>1</sub>| + |A<sub>2</sub>| + |A<sub>3</sub>| +......+ |A<sub>2006</sub>| must be equal to-
Question 14 : The determinant <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f94a19f8d44d3a17eda4' height='63' width='183' >is independent of -
Question 15 :
If {tex} a , b {/tex} and {tex} c {/tex} are sides of a {tex} \Delta A B C {/tex} and {tex}\left| \begin{array} { c c c } { a ^ { 2 } } & { b ^ { 2 } } & { c ^ { 2 } } \\ { ( a + 1 ) ^ { 2 } } & { ( b + 1 ) ^ { 2 } } & { ( c + 1 ) ^ { 2 } } \\ { ( a - 1 ) ^ { 2 } } & { ( b - 1 ) ^ { 2 } } & { ( c - 1 ) ^ { 2 } } \end{array} \right| = 0 , {/tex} then<br>
Question 16 : The value of determinant <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f88019f8d44d3a17ec7b' height='63' width='77' > is:
Question 18 :
If {tex} A {/tex} is any square matrix then which of the following is not symmetric?
Question 19 : In the det. <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9b419f8d44d3a17ee3d' height='63' width='77' >the value of C<sub>23</sub> is-
Question 20 :
If A and B are square matrices of same size and |B| ≠ 0, then (B<sup>-1</sup> AB)<sup>4</sup> =
Question 21 : If U = [2 -3 4], V = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa2275ed294f2c7c3562' height='63' width='28' >, X = [0 2 3] and Y = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa2219f8d44d3a17eec5' height='63' width='28' >, then UV + XY is equal to :
Question 22 : The matrix <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa0019f8d44d3a17ee91' height='68' width='91' > is a -
Question 23 :
Let P be a non-singular matrix 1 + P + P<sup>2</sup> +..... + P<sup>n</sup> = O(O denotes the null matrix), then P<sup>-1</sup> is-
Question 24 :
If {tex} l _ { r } ^ { 2 } + m _ { r } ^ { 2 } + n _ { r } ^ { 2 } = 1 , {/tex} where {tex} r = 1,2,3 {/tex} and {tex} l _ { 1 } l _ { 2 } + m _ { 1 } m _ { 2 } + n _ { 1 } n _ { 2 } = 0 {/tex} ...... etc, then, {tex}\Delta = \left| \begin{array} { c c c } {l_1} & { m_1 } & { n_1 } \\ { l_2 } & {m_2} & { n_2 } \\ {l_3 } & { m_3 } & { n_3} \end{array} \right| ^2 {/tex} is equal to
Question 25 :
Let {tex} A {/tex} and {tex} B {/tex} are the non-singular square matrices, then which of the following is always correct?
Question 26 :
If {tex} A {/tex} is a {tex} 3 \times 3 {/tex} non-singular matrix such that {tex} A A ^ { \prime } = A ^ { \prime } A {/tex} and {tex} B = A ^ { - 1 } A ^ { \prime } , {/tex} then {tex} B B ^ { \prime } {/tex} equals
Question 27 : If the matrix A= <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa0b19f8d44d3a17eea0' height='63' width='91' > is singular, then λ equal to -
Question 28 :
If {tex} A = \left[ \begin{array} { l l } { a } & { b } \\ { b } & { a } \end{array} \right] {/tex} and {tex} A ^ { 2 } = \left[ \begin{array} { l l } { \alpha } & { \beta } \\ { \beta } & { \alpha } \end{array} \right] , {/tex} then
Question 29 :
If A, B are symmetric matrices of the same order then (AB - BA) is -
Question 30 : If a, b, & c are sides of a ΔABC and <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f84fe6d3604eaa92de57' height='71' width='168' >, then
Question 31 :
Let A and B be 3 × 3 matrices, then AB = O implies:
Question 32 :
If {tex} A = \left[ \begin{array} { l l l } { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } \\ { 0 } & { 1 } & { 0 } \end{array} \right] , {/tex} then {tex} A {/tex} is
Question 33 :
If A and B are square matrices of order 3, then
Question 34 :
Let A be the set of all 3 × 3 symmetric matrix all of whose entries are either 0 or 1 five of these entries are 1 and four of them are zero. Find the number of matrix in A are-
Question 35 : If A = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86fa06e6d3604eaa92e0bf' height='41' width='88' > is symmetric, then x =
Question 36 :
The inverse of a skew symmetric matrix (if it exists) is -
Question 38 : If A = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f89519f8d44d3a17ec9d' height='63' width='71' >, I = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f896e6d3604eaa92dec5' height='63' width='61' > and A<sup>-1</sup> = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f89675ed294f2c7c3340' height='37' width='15' > (A<sup>2</sup> + cA + d) then the values of c and d are respectively -
Question 39 : If X = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f8c819f8d44d3a17ecec' height='41' width='37' >, then X<sup>n</sup>, for n ∈ N, is equal to -
Question 41 :
In a symmetric matrix of order '12' maximum number of different elements are -
Question 42 : If a, b, c are non zero real numbers then <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f98b75ed294f2c7c349c' height='68' width='104' > is equal to
Question 43 :
If A<sup>2</sup> - A + I = 0, then the inverse of A is -
Question 44 :
Let {tex} x _ { 1 } y _ { 1 } z _ { 1 } , x _ { 2 } y _ { 2 } z _ { 2 } {/tex} and {tex} x _ { 3 } y _ { 3 } z _ { 3 } {/tex} be three 3 -digit even numbers and {tex} \Delta = \left| \begin{array} { l l l } { x _ { 1 } } & { y _ { 1 } } & { z _ { 1 } } \\ { x _ { 2 } } & { y _ { 2 } } & { z _ { 2 } } \\ { x _ { 3 } } & { y _ { 3 } } & { z _ { 3 } } \end{array} \right| . {/tex} Then, {tex} \Delta {/tex} is
Question 45 :
If {tex} A {/tex} is a square matrix such that {tex} A ^ { 3 } = l {/tex} then {tex} A ^ { - 1 } {/tex} is equal to
Question 46 : The rank of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9c4e6d3604eaa92e07d' height='63' width='61' > is equal to
Question 47 : If Δ = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e86f9b519f8d44d3a17ee3e' height='63' width='79' > then value of b<sub>1</sub>B<sub>1</sub> + b<sub>2</sub>B<sub> 2</sub> + b<sub>3</sub>B<sub> 3</sub> is where B<sub>1</sub>, B<sub>2</sub>, B<sub>3</sub> are co-factor of a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub> respectively-
Question 48 :
If the matrices A, B, (A + B) are non-singular, then [A (A + B)<sup>-1</sup> B]<sup>-1</sup>, is equal to -
Question 49 :
If A and B are square matrices of order 3 such that |A| = - 1, |B| = 3 then |3AB| = ...
Question 50 :
If {tex} A = \left[ \begin{array} { c c } { 1 } & { 0 } \\ { - 1 } & { 7 } \end{array} \right] {/tex} and {tex} A ^ { 2 } = 8 A + K I _ { 2'} {/tex} then find the value of {tex} | k | {/tex}
