" /> -->

Matrices and Determinants Model Question Paper

11th Standard

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:30:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. If A=\(\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}\) ,then for what value of \(\lambda\), A2 = O?

    (a)

    0

    (b)

    \(\pm 1\)

    (c)

    -1

    (d)

    1

  2. If A is a square matrix, then which of the following is not symmetric?

    (a)

    A+ AT

    (b)

    AAT

    (c)

    AT A

    (d)

    A− AT

  3. If A and B are symmetric matrices of order n, where (A \(\neq\) B), then

    (a)

    A + B is skew-symmetric

    (b)

    A + B is symmetric

    (c)

    A + B is a diagonal matrix

    (d)

    A + B is a zero matrix

  4. If the points (x,−2), (5, 2), (8,8) are collinear, then x is equal to

    (a)

    -3

    (b)

    \({1\over 3}\)

    (c)

    1

    (d)

    3

  5. If A is skew-symmetric of order n and C is a column matrix of order n × 1, then CT AC is

    (a)

    an identity matrix of order n

    (b)

    an identity matrix of order 1

    (c)

    a zero matrix of order 1

    (d)

    an identity matrix of order 2

  6. 7 x 2 = 14
  7. Suppose that a matrix has 12 elements. What are the possible orders it can have? What if it has 7 elements?

  8. If A=\(\begin{bmatrix} 0 &c &b \\ c & 0 &a \\ b & a & 0 \end{bmatrix}\),compute A2

  9. Construct an m × n matrix A= [aij], where a ij is given by
    \(a_{ij}={|3i-4j|\over 4}with \ m=3,n=4\)

  10. If A=\(\begin{bmatrix} 4 & 2 \\ -1 & x \end{bmatrix}\) and such that (A- 2I)(A-3I)=O, find the value of x.

  11. Show that the points (a, b + c), (b, c + a), and (c, a + b) are collinear

  12. If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k.

  13. In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section of Express the given information as a column matrix. Using sclar multiplication find the total number ofp of each kind in all the colleges.

  14. 7 x 3 = 21
  15. Solve for x if [x 2 -1] \(\begin{bmatrix} 1&1 &2 \\ -1 & -4 &1 \\ -1 &-1 &-2 \end{bmatrix}\)\(\begin{bmatrix} x \\ 2 \\ 1 \end{bmatrix}\)=0

  16. A fruit shop keeper prepares 3 different varieties of gift packages. Pack-I contains 6 apples, 3 oranges, and 3 pomegranates. Pack-II contains 5 apples, 4 oranges, and 4 pomegranates and Pack –III contains 6 apples, 6 oranges, and 6 pomegranates. The cost of an apple, an orange, and a pomegranate respectively are Rs. 30, Rs. 15 and Rs. 45. What is the cost of preparing each package of fruits?

  17. If A =\(\begin{bmatrix} 4 & 6 & 2 \\ 0 & 1 & 5 \\ 0 & 3 & 2 \end{bmatrix}\) and B= \(\begin{bmatrix} 0 & 1 & -1 \\ 3 & -1 & 4 \\ -1 & 2 & 1 \end{bmatrix}\)
    verify(AB)T=BTAT

  18. If A =\(\begin{bmatrix} 4 & 6 & 2 \\ 0 & 1 & 5 \\ 0 & 3 & 2 \end{bmatrix}\) and B= \(\begin{bmatrix} 0 & 1 & -1 \\ 3 & -1 & 4 \\ -1 & 2 & 1 \end{bmatrix}\)
    verify(A-B)T=AT-BT

  19. If AT=\(\begin{bmatrix} 4 & 5 \\ -1 & 0 \\ 2 & 3 \end{bmatrix}\) and B= \(\begin{bmatrix} 2 & -1&1 \\7 & 5&-2 \end{bmatrix}\),verify (A+B)T=AT+BT=BT+AT

  20. Identify the singular and non-singular matrices:\(\begin{bmatrix} 0&a-b &k \\ b-a & 0 &5 \\ -k & -5 & 0 \end{bmatrix}\)

  21. If A=\(\left[ \begin{matrix} \alpha & 0 \\ 1 & 1 \end{matrix} \right] \) and B=\(\left[ \begin{matrix} 1 & 0 \\ 5 & 1 \end{matrix} \right] \) find the values of \(\alpha\) for which A2=B.

  22. 2 x 5 = 10
  23. If A=\(\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ x & 2 & y \end{bmatrix}\) is a matrix such that AAT =9I, find the values of x and y.

  24. If \(\lambda =-2\) , determine the value of \(\begin{vmatrix} 0& 2\lambda &1 \\ \lambda^2 &0 &3\lambda^3+1 \\ -1 &6\lambda-1 &0 \end{vmatrix}\) .

*****************************************

TN 11th Standard Maths free Online practice tests

Reviews & Comments about 11th Standard Maths - Matrices and Determinants Model Question Paper

Write your Comment