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11th Standard English Medium Maths Subject Matrices and Determinants Book Back 1 Mark Questions with Solution Part - II

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 10

    1 Marks

    10 x 1 = 10
  1. A root of the equation \(\begin{vmatrix} 3-x&-6 &3 \\ -6 & 3-x & 3 \\ 3 &3 &-6-x \end{vmatrix}=0 \ is\)

    (a)

    6

    (b)

    3

    (c)

    0

    (d)

    -6

  2. The value of the determinant of A = \(\begin{bmatrix} 0&a &-b \\ -a & 0 & c \\ b & -c & 0 \end{bmatrix}is\)

    (a)

    -2abc

    (b)

    abc

    (c)

    0

    (d)

    a+ b+ c2

  3. If x1, x2, x3 as well as y1, y2, y3 are in geometric progression with the same common ratio, then the points (x1, y1 ), (x2, y2), (x3, y3 ) are

    (a)

    vertices of an equilateral triangle

    (b)

    vertices of a right angled triangle

    (c)

    vertices of a right angled isosceles triangle

    (d)

    collinear

  4. If a \(\neq\) b, b, c satisfy \(\begin{vmatrix} a&2b &2c \\3 & b & c \\ 4 & a & b \end{vmatrix}=0,\) then abc =

    (a)

    a + b + c

    (b)

    0

    (c)

    b3

    (d)

    ab + bc

  5. If A = \(\begin{vmatrix}-1 & 2 &4 \\ 3 &1 &0 \\ -2& 4 &2 \end{vmatrix}\) and B = \(\begin{vmatrix}-2 & 4 &2 \\ 6 &2 &0 \\ -2& 4 &8 \end{vmatrix}\), then B is given by

    (a)

    B = 4A

    (b)

    B = -4A

    (c)

    B = -A

    (d)

    B = 6A

  6. If \(\left\lfloor . \right\rfloor \) denotes the greatest integer less than or equal to the real number under consideration and −1\(\le\) x < 0, 0 \(\le\) y < 1, 1 \(\le\) z < 2, then the value of the determinant \(\begin{vmatrix} \left\lfloor x \right\rfloor +1& \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor +1& \left\lfloor z \right\rfloor \\ \left\lfloor x \right\rfloor & \left\lfloor y \right\rfloor & \left\lfloor z \right\rfloor +1\end{vmatrix}\) is

    (a)

    \(\left\lfloor z \right\rfloor \)

    (b)

    \(\left\lfloor y \right\rfloor \)

    (c)

    \(\left\lfloor x \right\rfloor \)

    (d)

    \(\left\lfloor x \right\rfloor \)+1

  7. If A is skew-symmetric of order n and C is a column matrix of order n \(\times\) 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

  8. The matrix A satisfying the equation \(\begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}\) A = \(\begin{bmatrix} 1 & 1 \\ 0 & -1 \end{bmatrix}\) is

    (a)

    \(\begin{bmatrix} 1 & 4 \\ -1 & 0 \end{bmatrix}\)

    (b)

    \(\begin{bmatrix} 1 & -4 \\ 1 & 0 \end{bmatrix}\)

    (c)

    \(\begin{bmatrix} 1 & 4 \\ 0 & -1 \end{bmatrix}\)

    (d)

    \(\begin{bmatrix} 1 & -4 \\ 1 & 1 \end{bmatrix}\)

  9. If A + I =\(\begin{bmatrix} 3& -2 \\ 4 & 1 \end{bmatrix}\)then (A + I )(A - I) is equal to

    (a)

    \(\begin{bmatrix} -5& -4 \\ 8 & -9 \end{bmatrix}\)

    (b)

    \(\begin{bmatrix} -5& 4 \\ -8 & 9 \end{bmatrix}\)

    (c)

    \(\begin{bmatrix} 5& 4 \\ 8 & 9 \end{bmatrix}\)

    (d)

    \(\begin{bmatrix} -5& -4 \\ -8 & -9 \end{bmatrix}\)

  10. Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

    (a)

    A + B is a symmetric matrix

    (b)

    AB is a symmetric matrix

    (c)

    AB = (BA)T

    (d)

    AT B = ABT

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