InstaQB

Home
Institutions
- Institutions
  
  Polytechnic Colleges
  
  Medical Colleges
  
  Arts & Science Colleges
  
  Universities
  
  Engineering Colleges
  
  Agricultural Colleges
  
  Research Institute
  
  Law Colleges
  
  Audiology and Speech Colleges
  
  Business & Management colleges
  
  Nursing colleges
  
  Hotel Management institutes
  
  Aeronautical Colleges
  
  Bachelor's Degree
Syllabus
Courses
Stateboard
- 12th Standard English Medium
  
  Maths
  
  Physics
  
  Chemistry
  
  Biology
  
  Computer Science
  
  Business Maths
  
  Economics
  
  Commerce
  
  Accountancy
  
  History
  
  Computer Applications
  
  Computer Technology
  12th Standard Tamil Medium
  
  உயிரியல்
  
  கணினி பயன்பாடுகள்
  
  கணினி அறிவியல்
  
  வணிகக் கணிதம்
  
  வணிகவியல்
  
  பொருளியல்
  
  கணிதவியல்
  
  வேதியியல்
  
  இயற்பியல்
  
  கணினி தொழில்நுட்பம்
  
  வரலாறு
  
  கணக்குப்பதிவியல்
  11th Standard English Medium
  
  Maths
  
  Commerce
  
  Economics
  
  Biology
  
  Business Maths
  
  Accountancy
  
  Computer Science
  
  Physics
  
  Chemistry
  
  Computer Applications
  
  History
  
  Computer Technology
  
  Bio - Zoology
  11th Standard Tamil Medium
  
  கணிதவியல்
  
  உயிரியல்
  
  பொருளியல்
  
  இயற்பியல்
  
  வேதியியல்
  
  வணிகக் கணிதம்
  
  கணினி அறிவியல்
  
  கணக்குப்பதிவியல்
  
  வணிகவியல்
  
  கணினி பயன்பாடுகள்
  10th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  9th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  8th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  7th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
ICSE/ISC
- Class XII
  
  Mathematics
  
  Physics
  
  Accountancy
  
  Biology
  
  History
  
  Geography
  
  Psychology
  
  chemistry
  
  Economics
  
  Computer Science
  
  Political Science
  
  Business Studies
  Class XI
  
  Accountancy
  
  Chemistry
  
  Mathematics
  
  Biology
  
  Geography
  
  Physics
  
  History
CBSE
- 12Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Geography
  
  Socialogy
  
  Business Studies
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  
  Home Science
  11Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Socialogy
  
  Business Studies
  
  Geography
  
  Home Science
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  10Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  Mathematics
  
  Economics
  
  Geography
  
  History & Civics
  
  Computer Application
  9Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  mathematics
  
  Computer Application
  
  Economics
  
  Geography
  
  History & Civics

12th Maths Weekly Test-3 (Applications Of Matrices And Determinants)

St. Britto Hr. Sec. School - Madurai

12th Maths Weekly Test-3 (Applications Of Matrices And Determinants)-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If |adj(adj A)| = |A|⁹, then the order of the square matrix A is

3
4
2
5

If A = \(\left[ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} \right] \), B = adj A and C = 3A, then \(\frac { \left| adjB \right| }{ \left| C \right| } \) =

\(\frac { 1 }{ 3 } \)
\(\frac { 1 }{ 9 } \)
\(\frac { 1 }{ 4 } \)
1

If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I - A =

A^-1
\(\frac { { A }^{ -1 } }{ 2 } \)
3A^-1
2A^-1

If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

15
12
14
11

If (AB)^-1 = \(\left[ \begin{matrix} 12 & -17 \\ -19 & 27 \end{matrix} \right] \) and A^-1 = \(\left[ \begin{matrix} 1 & -1 \\ -2 & 3 \end{matrix} \right] \), then B^-1 =

\(\left[ \begin{matrix} 2 & -5 \\ -3 & 8 \end{matrix} \right] \)
\(\left[ \begin{matrix} 8 & 5 \\ 3 & 2 \end{matrix} \right] \)
\(\left[ \begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix} \right] \)
\(\left[ \begin{matrix} 8 & -5 \\ -3 & 2 \end{matrix} \right] \)

If A is a non-singular matrix such that A^-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (A^T)⁻¹ =

\(\left[ \begin{matrix} -5 & 3 \\ 2 & 1 \end{matrix} \right] \)
\(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \)
\(\left[ \begin{matrix} -1 & -3 \\ 2 & 5 \end{matrix} \right] \)
\(\left[ \begin{matrix} 5 & -2 \\ 3 & -1 \end{matrix} \right] \)

If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I , then B =

\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A\)
\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }\)
\(\left( \cos ^{ 2 }{ \theta } \right) I\)
(Sin²\(\frac { \theta }{ 2 } \))A

If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA⁻¹ =A, then λ is

17
14
19
21

The rank of the matrix \(\left[ \begin{matrix} 1 \\ \begin{matrix} 2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 2 \\ \begin{matrix} 4 \\ -2 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} 6 \\ -3 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} 8 \\ -4 \end{matrix} \end{matrix} \right] \) is

1
2
4
3

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λⁿ adj(A).
(iv) A(adjA) = (adjA)A = |A|I

Only (i)
(ii) and (iii)
(iii) and (iv)
(i), (ii) and (iv)

Let A = \(\left[ \begin{matrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{matrix} \right] \) and 4B = \(\left[ \begin{matrix} 3 & 1 & -1 \\ 1 & 3 & x \\ -1 & 1 & 3 \end{matrix} \right] \). If B is the inverse of A, then the value of x is

2
4
3
1

The system of linear equations x + y + z = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if

λ = 8
λ = 8, μ ≠ 36
λ ≠ 8
none

Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

±2
±4
±8
±12

If A is a square matrix that IAI = 2, than for any positive integer n, |Aⁿ| =

0
2n
2ⁿ
n²

If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2. is inconsistent then k is

-3, -\(\frac{1}{2}\)
-\(\frac{1}{2}\)
1
2

If \(\rho\)(A) = \(\rho\)([A/B]) = number of unknowns, then the system is

consistent and has infinitely many solutions
consistent
inconsistent
consistent and has unique solution

If \(\rho\)(A) = r then which of the following is correct?

all the minors of order n which do not vanish
'A' has at least one minor "of order r which does not vanish and all higher order minors vanish
'A' has at least one (r + 1) order minor which vanish
all (r + 1) and higher order minors should not vanish

Cramer's rule is applicable only when ______

Δ ≠ 0
Δ = 0
Δ =0, Δ_x =0
Δ_x = Δ_y = Δ_z =0

If A = [2 0 1] then the rank of AA^T is ______

1
2
3
0

In a square matrix the minor M_ij and the' co-factor A_ij of and element a_ij are related by _____

A_ij = -M_ij
A_ij = M_ij
A_ij = (-1)^i+j M_ij
A_ij =(-1)^i-j M_ij

Part - B

Generic 2 - Answer All Question

Find the adjoint of the following:
\(\left[ \begin{matrix} -3 & 4 \\ 6 & 2 \end{matrix} \right] \)

If A = \(\left[ \begin{matrix} 5 & 3 \\ -1 & -2 \end{matrix} \right] \), show that A² - 3A - 7I₂ = O₂. Hence find A⁻¹.

If A = \(\left[ \begin{matrix} 8 & -4 \\ -5 & 3 \end{matrix} \right] \), verify that A(adj A) = |A|I₂.

Find adj(adj A) if adj A = \(\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 0 \\ -1 & 0 & 1 \end{matrix} \right] \).

Given A = \(\left[ \begin{matrix} 1 & -1 \\ 2 & 0 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 3 & -2 \\ 1 & 1 \end{matrix} \right] \) and C = \(\left[ \begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix} \right] \), find a matrix X such that AXB = C.

Find the rank of the following matrices by minor method:
\(\left[ \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right] \)

Solve the following system of linear equations by matrix inversion method:
2x + 5y = −2, x + 2y = −3

The prices of three commodities A, B and C are Rs.x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C . Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C . In the process, P, Q and R earn Rs.15,000, Rs.1,000 and Rs.4,000 respectively. Find the prices per unit of A, B and C . (Use matrix inversion method to solve the problem.)

A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution ? (Use Cramer’s rule to solve the problem).

Solve the following systems of linear equations by Gaussian elimination method:
2x − 2y + 3z = 2, x + 2y − z = 3,3x − y + 2z = 1

Part - C

Generic 3 - Answer All Question

Solve: 2x + 3y = 10, x + 6y = 4 using Cramer's rule.

Verify (AB)^-1 =B^-1 A^-1 for A=\(\left[ \begin{matrix} 2 & 1 \\ 5 & 3 \end{matrix} \right] \) and B=\(\left[ \begin{matrix} 4 & 5 \\ 3 & 4 \end{matrix} \right] \).

Find,the rank of the matrix math \(\left[ \begin{matrix} 4 \\ -2 \\ 1 \end{matrix}\begin{matrix} 4 \\ 3 \\ 4 \end{matrix}\begin{matrix} 0 \\ -1 \\ 8 \end{matrix}\begin{matrix} 3 \\ 5 \\ 7 \end{matrix} \right] \).

If the rank of the matrix \(\left[ \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right] \) is 2, then find ⋋.

Verify the property (A^T)^-1 = (A^-1) with A = \(\left[ \begin{matrix} 2 & 9 \\ 1 & 7 \end{matrix} \right] \).

If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)^-1 = B^-1A^-1

Find the rank of the matrix \(\left[ \begin{matrix} 2 \\ \begin{matrix} -3 \\ 6 \end{matrix} \end{matrix}\begin{matrix} -2 \\ \begin{matrix} 4 \\ 2 \end{matrix} \end{matrix}\begin{matrix} 4 \\ \begin{matrix} -2 \\ -1 \end{matrix} \end{matrix}\begin{matrix} 3 \\ \begin{matrix} -1 \\ 7 \end{matrix} \end{matrix} \right] \) by reducing it to an echelon form.

Find the inverse of the non-singular matrix A = \(\left[ \begin{matrix} 0 & 5 \\ -1 & 6 \end{matrix} \right] \), by Gauss-Jordan method.

Solve the system of linear equations, by Gaussian elimination method 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1.

Solve the following system:
x + 2y + 3z = 0, 3x + 4y + 4z = 0, 7x + 10y + 12z = 0.

Comment

Add Comment

Tamilnadu Stateboardszs - Class