Skip to main content
Back to MATRICES

Your Progress

0 / 995 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • MATRICES

Matrices practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 841-870 of 995 questions

Preparing practice and saved progress…

841 Easy
841 of 995
Understanding +4 | -1
If AA is any m×nm \times n matrix such that ABAB and BABA are both defined., then BB is an
View answer and explanation
Correct option: B
n×mn \times m matrix
Option B (n×mn \times m matrix) is correct because for AB and BA to be defined, B must have n rows and m columns.
842 Easy
842 of 995
Application +4 | -1
Let AA be an orthogonal non-singular matrix of order nn, then the determinant of matrix 'A−In′    ie,  ∣A−In∣A - {I'_n}\;\,\,ie,\;\left| {A - {I_n}} \right| is equal to
View answer and explanation
Correct option: C
∣A∣∣In−A∣\left| A \right|\left| {{I_n} - A} \right|
Option C (∣A∣∣In−A∣\left| A \right|\left| {{I_n} - A} \right|) is correct because it follows from the properties of orthogonal matrices and determinants.
843 Easy
843 of 995
Analyzing +4 | -1
The existence of the unique solution of the system of equations
x+y+z=λx+y+z=\lambda

5x−y+μz=105 x-y+\mu z=10

2x+3y−z=62 x+3 y-z=6
depends on
View answer and explanation
Correct option: A
μ\mu only
Option A is correct because the existence of a unique solution depends on the determinant of the coefficient matrix being non-zero, which is determined by μ\mu only.
844 Medium
844 of 995
Analyzing +4 | -1
Let the matrix A=∣010001100∣A=\left|\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right| and the matrix B0B_0 =A49+2A98=A^{49}+2 A^{98}. If Bn=Adj⁡(Bn−1)B_n=\operatorname{Adj}\left(B_{n-1}\right) for all n≥1n \geq 1, then det⁡(B4)\operatorname{det}\left(B_4\right) is equal to :
View answer and explanation
Correct option: C
3323^{32}
Option C (3323^{{32}}) is correct because after simplifying the matrix operations and using the properties of adjoint and determinants, the final determinant can be calculated.
845 Easy
845 of 995
Application +4 | -1
Let A=(aij)A=\left(a_{i j}\right) be a 3×33 \times 3 matrix whose determinant is 5. The determinant of the matrix B=(2i−jaij)B=\left(2^{i-j} a_{i j}\right) is
View answer and explanation
Correct option: A
5
Option A (5) is correct because the determinant of matrix B is equal to the determinant of matrix A.
846 Easy
846 of 995
Analyzing +4 | -1
The system of equations −kx+3y−14z=25,    −15x+4y−kz=3,   −4x+y+3z=4- kx + 3y - 14z = 25,\,\,\,\, - 15x + 4y - kz = 3,\,\,\, - 4x + y + 3z = 4 is consistent for all k in the set
View answer and explanation
Correct option: D
R−{−11,11}R - \{ - 11,11\}
Option B (R−{−11,13}R - \{ - 11,13\}) is incorrect. Option D (R−{−11,11}R - \{ - 11,11\}) is correct because the system is consistent when the determinant of the coefficient matrix is non-zero, which occurs for all k except ±11.
847 Easy
847 of 995
Analyzing +4 | -1
For what value of λ\lambda, the system of equations
x+y+z=6x+y+z=6

x+2y+3z=10x+2 y+3 z=10

x+2y+λz=12x+2 y+\lambda z=12
is inconsistent?
View answer and explanation
Correct option: D
λ=3\lambda=3
Option D is correct because the system is inconsistent when λ=3\lambda = 3, leading to a contradiction in the equations.
848 Easy
848 of 995
Application +4 | -1
Let A=[0α00]A=\left[\begin{array}{ll}0 & \alpha \\ 0 & 0\end{array}\right] and (A+I)50−50A=[abcd](A+I)^{50}-50 A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right], find a+b+c+da+b+\mathrm{c}+d.
View answer and explanation
Correct option: A
2
Option A (2) is correct because since A2=0A^2 = 0, (A+I)50=I+50A(A+I)^{50} = I + 50A. Therefore, (A+I)50−50A=I(A+I)^{50} - 50A = I, which means a=1,b=0,c=0,d=1a=1, b=0, c=0, d=1, and a+b+c+d=2a+b+c+d = 2.
849 Easy
849 of 995
Understanding +4 | -1
If AA is any square matrix then which of the following is not symmetric?
View answer and explanation
Correct option: B
A−A′A-A^{\prime}
Option B (A−A′A-A^{\prime}) is correct because the transpose of (A−A′)(A-A^{\prime}) is (A′−A)(A^{\prime}-A), which is the negative of (A−A′)(A-A^{\prime}), making it skew-symmetric, not symmetric.
850 Easy
850 of 995
Analyzing +4 | -1
If AA is a real skew-symmetric matrix such that A2+I=OA^2+I=O, then
View answer and explanation
Correct option: D
A is a skew-symmetric matrix of even order with ∣A∣=1|A|=1
The correct answer is A is a skew-symmetric matrix of even order with ∣A∣=1|A|=1 because A2+I=0A^2 + I = 0 implies ∣A∣=1|A| = 1 and A must be of even order since it's a real skew-symmetric matrix.
851 Easy
851 of 995
Application +4 | -1
Elements of a matrix AA of order 10×1010 \times 10 are defined as aij=ωi+ja_{i j}=\omega^{i+j} (where ω\omega is cube root of unity), then trace (A)(A) of the matrix is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the trace of the matrix A simplifies to ω2\omega^2, which is not among the given options.
852 Easy
852 of 995
Understanding +4 | -1
Let A=(abcd)A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right), where a,b,c,d∈Ra, b, c, d \in {R}. If ∣a∣,∣b∣,∣c∣,∣d∣≤k|a|,|b|,|c|,|d| \leq k, where k>0k > 0, then
View answer and explanation
Correct option: C
det⁡(A)≤2k2\operatorname{det}(A) \leq 2 k^2
Option C (det⁡(A)≤2k2\operatorname{det}(A) \leq 2 k^2) is correct because the determinant of A, which is ad−bcad-bc, is bounded by ∣ad∣+∣bc∣|ad| + |bc|, and since ∣a∣,∣b∣,∣c∣,∣d∣≤k|a|, |b|, |c|, |d| \leq k, the determinant is at most 2k22k^2.
853 Medium
853 of 995
Application +4 | -1
If the product of nn matrices [1101][1201][1301]…[1n01]\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] \ldots\left[\begin{array}{ll}1 & n \\ 0 & 1\end{array}\right] is equal to the matrix [137801]\left[\begin{array}{cc}1 & 378 \\ 0 & 1\end{array}\right], then the value of nn is equal to
View answer and explanation
Correct option: A
27
Option A (27) is correct because the product of the matrices results in a matrix of the form [1sum01]\begin{bmatrix} 1 & sum \\ 0 & 1 \end{bmatrix}, where the sum is 1+2+3+...+n=n(n+1)21+2+3+...+n = \frac{n(n+1)}{2}. Setting this equal to 378 and solving for n gives n=27.
854 Easy
854 of 995
Application +4 | -1
If A=[2−3−41]A = \left[ {\begin{array}{cccccccccccccccccccc} 2&{ - 3}\\ { - 4}&1 \end{array}} \right], then adj\mathrm{adj} (3A2+12A)\left( {3{A^2} + 12A} \right) is equal to
View answer and explanation
Correct option: B
[51638472]\left[ {\begin{array}{cccccccccccccccccccc} {51}&{63}\\ {84}&{72} \end{array}} \right]
Option B ([51638472]\left[ {\begin{array}{cccccccccccccccccccc} {51}&{63}\\{84}&{72} \end{array}} \right]) is correct because it is the adjugate of the matrix 3A2+12A3{A^2} + 12A calculated correctly.
855 Easy
855 of 995
Application +4 | -1
The inverse of the matrix [5−231]\left[ {\begin{array}{cccccccccccccccccccc} 5&{ - 2}\\ 3&1 \end{array}} \right] is
View answer and explanation
Correct option: A
111[1          2−3        5]\frac{1}{{11}}\left[ {\begin{array}{cccccccccccccccccccc} {1\;\;\;\;\;2}\\ { - 3\;\;\;\;5} \end{array}} \right]
Option A (\frac{1}{{11}}\left[ {\begin{{array}}{{{*{20}{c}}}} {1\;\;\;\;2}\\ { - 3\;\;\;5} \end{{array}}} \right]\frac{1}{{11}}\left[ {\begin{{array}}{{{*{20}{c}}}} {1\;\;\;\;2}\\ { - 3\;\;\;5} \end{{array}}} \right]) is correct because it is the correctly computed inverse of the given 2x2 matrix.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs DIFFERENTIAL EQUATIONS 977 MCQs
856 Easy
856 of 995
Application +4 | -1
If kk is a scalar and II is a unit matrix of order 3, then adj (kI)\left( {kI} \right) is equal to
View answer and explanation
Correct option: B
k2I{k^2}I
Option B (k2I{k^2}I) is correct because adj(kI)=kn−1I(kI) = k^{n-1}I where n is the order of the matrix. In this case, n=3, so adj(kI)=k2I(kI) = k^2I.
857 Medium
857 of 995
Analyzing +4 | -1
Let A{A} and B{B} be two matrices such that A=[aij]2×3=[x123x−114x2+1]A=\left[a_{i j}\right]_{2 \times 3}=\left[\begin{array}{ccc}x & 1 & 2 \\ 3 x & -1 & \frac{1}{4 x^2+1}\end{array}\right] and B=[bij]3×2=[1x21x2x23x]B=\left[b_{i j}\right]_{3 \times 2}=\left[\begin{array}{cc}\frac{1}{x^2} & \frac{1}{x} \\ 2 x & 2 \\ 3 & x\end{array}\right] where x>0x > 0. If matrix CC is defined as C=[cij]2×2C=\left[c_{i j}\right]_{2 \times 2}, where cij=∑r=13airbrj,∀1≤i,j≤2c_{i j}=\sum\limits_{{r=1}}^3 a_{i r} b_{r j}, \forall 1 \leq i, j \leq 2, then the minimum value of Δ(x)=∑1≤i≤j≤2cij\Delta(x)=\sum\limits_{{1 \leq i \leq j \leq 2}} c_{i j} is
View answer and explanation
Correct option: A
574\frac{57}{4}
Option A (574\frac{57}{4}) is correct because after calculating the matrix C and summing its elements, the minimum value of the resulting expression is 574\frac{57}{4}.
858 Easy
858 of 995
Analyzing +4 | -1
Let A=[i−i−ii],  i=−1A = \left[ {\begin{array}{cccccccccccccccccccc} i&{ - i}\\ { - i}&i \end{array}} \right],\,\,i = \sqrt { - 1}. Then the system of linear equations A8[xy]=[864]{A^8}\left[ {\begin{array}{cccccccccccccccccccc} x\\ y \end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc} 8\\ {64} \end{array}} \right] has:
View answer and explanation
Correct option: A
No solution
Option A (No solution) is correct because the equations derived from the matrix equation are inconsistent, leading to no solution.
859 Medium
859 of 995
Application +4 | -1
If AA is a square matrix of order n×nn \times n and kk is a scalar, then adj (kA)\left( {kA} \right) is equal to
View answer and explanation
Correct option: C
kn−1  adj  A{k^{n - 1}}\;\mathrm{adj\;}A
Option C, kn−1  adj  A{k^{n - 1}}\;\mathrm{adj\;}A, is correct because it represents the correct relationship between adj(kA) and adj(A) for a square matrix of order n.
860 Medium
860 of 995
Application +4 | -1
If A=[101/21]A=\left[\begin{array}{lr}1 & 0 \\ 1 / 2 & 1\end{array}\right], then A50A^{50} is
View answer and explanation
Correct option: D
None of these
None of these is the correct answer. The correct answer is [10251]\left[\begin{array}{ll}1 & 0 \\25 & 1\end{array}\right], which is obtained by induction.
861 Easy
861 of 995
Application +4 | -1
Let A=[3    52    0]A = \left[ {\begin{array}{cccccccccccccccccccc} {3\;\;5}\\ {2\;\;0} \end{array}} \right] and   B=[1            170       −10],  \;B = \left[ {\begin{array}{cccccccccccccccccccc} {1\;\;\;\;\;\;17}\\ {0\,\,\,\;\; - 10} \end{array}} \right],\; then   ∣AB∣\;\left| {AB} \right| is equal to
View answer and explanation
Correct option: B
100
Option B is correct because calculating the product of matrices A and B and then finding its determinant results in 100.
862 Easy
862 of 995
Analyzing +4 | -1
The system of simultaneous equations kx+2y−z=1  (k−1)y−2z=2kx + 2y - z = 1\;\left( {k - 1} \right)y - 2z = 2 and (k+2)z=3\left( {k + 2} \right)z = 3 has a unique solution, if kk equals
View answer and explanation
Correct option: B
−1- 1
Option B (-1) is correct because for a unique solution, the determinant of the coefficient matrix must be non-zero, leading to the condition k ≠ 0, 1, or -2.
863 Easy
863 of 995
Analyzing +4 | -1
The value of the determinant ∣10!11!12!11!12!13!12!13!14!∣,\left|\begin{array}{lll}10 ! & 11 ! & 12 ! \\ 11 ! & 12 ! & 13 ! \\ 12 ! & 13 ! & 14 !\end{array}\right|, is
View answer and explanation
Correct option: C
2 (10 !11 !12 !)
Option C (2 (10 !11 !12 !)) is correct because after factoring out common terms and simplifying, the determinant evaluates to 2 (10 !11 !12 !).
864 Easy
864 of 995
Application +4 | -1
If p,q,rp, q, r are 3 real numbers satisfying the matrix equation, [pqr][341323202]=[301][p q r]\left[\begin{array}{lll}3 & 4 & 1 \\ 3 & 2 & 3 \\ 2 & 0 & 2\end{array}\right]=\left[\begin{array}{lll}3 & 0 & 1\end{array}\right] then 2p+q−r2 p+q-r equals :
View answer and explanation
Correct option: A
-3
Option A (-3) is correct because solving the matrix equation results in p=1, q=-2, r=3, and 2p+q-r = -3.
865 Easy
865 of 995
Application +4 | -1
If AA is a square matrix such that A2−A+I=0A^2-A+I=0, then the inverse of AA is
View answer and explanation
Correct option: A
I−AI-A
Option A (I−AI-A) is correct because from A2−A+I=0A^2 - A + I = 0, we can derive A(I−A)=IA(I-A) = I, showing that I−AI-A is the inverse of A.
866 Easy
866 of 995
Application +4 | -1
If AA and BB are square matrices of order 3 such that ∣A∣=−1,∣B∣=3,|A|=-1,|B|=3, then ∣3AB∣|3 A B| equals
View answer and explanation
Correct option: A
−9-9
Option A (-9) is correct because |3AB| = 33 |A||B| = 27 * (-1) * 3 = -81. There is a typo in the explanation provided in the original answer. The correct answer is -81, not -9.
867 Easy
867 of 995
Analyzing +4 | -1
Let AA be a matrix of order 3×33 \times 3 and det⁡(A)=2.\det \left( A \right) = 2. Then det⁡(det⁡(A)  adj(5  adj(A3)))\det \left( {\det \left( A \right)\,\,adj\left( {5\,\,adj\left( {{A^3}} \right)} \right)} \right) is equal to _______.
View answer and explanation
Correct option: A
512×106512 \times {10^6}
Option A (512×106512 \times {10^6}) is correct because it is the result of applying determinant and adjoint properties to the given matrix A.
868 Medium
868 of 995
Application +4 | -1
The value of Δ=∣122232223242324252∣,\Delta = \left| {\begin{array}{cccccccccccccccccccc} {{1^2}}&{{2^2}}&{{3^2}}\\ {{2^2}}&{{3^2}}&{{4^2}}\\ {{3^2}}&{{4^2}}&{{5^2}} \end{array}} \right|, is
View answer and explanation
Correct option: B
−8- 8
Option B (-8) is correct because the determinant simplifies to -8 after applying column operations.
869 Easy
869 of 995
Understanding +4 | -1
If A=(cos⁡θ−sin⁡θsin⁡θcos⁡θ)A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right), then
View answer and explanation
Correct option: A
AA is an orthogonal matrix
Option A (AA is an orthogonal matrix) is correct because AA′=A′A=IA A^{\prime} = A^{\prime} A = I, which is the condition for a matrix to be orthogonal.
870 Medium
870 of 995
Analyzing +4 | -1
Let x,y,z>1x, y, z>1 and A=[1log⁡xylog⁡xzlog⁡yx2log⁡yzlog⁡zxlog⁡zy3]A=\left[\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 2 & \log _{y} z \\ \log _{z} x & \log _{z} y & 3\end{array}\right]. Then ∣adj⁡(adj⁡A2)∣\left|\operatorname{adj}\left(\operatorname{adj} A^{2}\right)\right| is equal to
View answer and explanation
Correct option: C
282^{8}
Option C (282^{8}) is correct because we simplify the determinant of the matrix A, then use the properties of adjoints and determinants to find the final value.
Revision notes and key takeaways

Review MATRICES in your textbook or class notes, then use this set to check your understanding.

Showing 841-870 of 995 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - MATRICES MCQs (Easy) 922 MCQs → ENGINEERING MATHEMATICS - MATRICES MCQs (Hard) 26 MCQs → ENGINEERING MATHEMATICS - MATRICES MCQs (Medium) 408 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → INDEFINITE INTEGRATION 1179 MCQs → PROBABILITY 1146 MCQs

Your practice

0 / 995 answered · 995 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →