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11th Standard Maths Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. If aij =\({1\over2}(3i-2j)\) and A=[aij]2x2 is

    (a)

    \(\begin{bmatrix} {1\over 2}& 2 \\ -{1\over2} & 1 \end{bmatrix}\)

    (b)

    \(\begin{bmatrix} {1\over 2}& -{1\over2} \\ 2& 1 \end{bmatrix}\)

    (c)

    \(\begin{bmatrix} 2& 2\\ {1\over 2}& -{1\over2} \end{bmatrix}\)

    (d)

    \(\begin{bmatrix} -{1\over 2}& {1\over2} \\ 1& 2 \end{bmatrix}\)

  2. 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

  3. The value of x, for which the matrix A=\(\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}\) is singular is

    (a)

    9

    (b)

    8

    (c)

    7

    (d)

    6

  4. If \(\triangle\)=\(\begin{vmatrix} a&b &c \\ x & y & z \\ p &q &r \end{vmatrix}\) ,then \(\begin{vmatrix} ka&kb &kc \\ kx & ky & kz \\k p &kq &kr \end{vmatrix}\)is

    (a)

    \(\triangle\)

    (b)

    k\(\triangle\)

    (c)

    3k\(\triangle\)

    (d)

    k3\(\triangle\)

  5. 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

  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. 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

  8. If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is

    (a)

    5

    (b)

    6

    (c)

    4

    (d)

    3

  9. On using elementary row operation R1⟶R1-3R2 in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

    (a)

    \(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

    (b)

    \(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)

    (c)

    \(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

    (d)

    \(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

  10. The value of\(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+sin\theta & 1 \\ 1 & 1 & 1+cos\theta \end{matrix} \right| \) is

    (a)

    3

    (b)

    1

    (c)

    2

    (d)

    \(\frac{1}{2}\)

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