Determinants Test

Determinants

This is Determinants Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The value of the determinant \(\left| {\begin{array}{*{20}{c}} 1&a&{b + c} \\ 1&b&{c + a} \\ 1&c&{a + b} \end{array}} \right|\) is
  • A
    none of these
  • B
    1+a+b+c
  • C
    a+b+c
  • D
    0
    Correct
2
If\(\left| {\begin{array}{*{20}{c}} 1&3&9 \\ 1&x&{{x^2}} \\ 4&{16}&{64} \end{array}} \right| = 0\)\( \Rightarrow \) , then
  • A
    x = 2
  • B
    x = 2 or 6
  • C
    x = 4 or 3
    Correct
  • D
    none of these
3
\(\left| {\begin{array}{*{20}{c}} 1&1&1 \\ 4&3&2 \\ {{4^2}}&{{3^2}}&{{2^2}} \end{array}} \right|\)is equal to
  • A
    0
  • B
    2
  • C
    -2
    Correct
  • D
    1
4
\(\left| {\begin{array}{*{20}{c}} {x + 1}&{x + 2}&{x + 3} \\ {x + 2}&{x + 4}&{x + 6} \\ {x + 4}&{x + 9}&{x + 14} \end{array}} \right| = \)
  • A
    0
    Correct
  • B
    x+2
  • C
    –2
  • D
    none of these
5
The value of determinant \(\left| {\begin{array}{*{20}{c}} x&a&a&a \\ a&x&a&a \\ a&a&x&a \\ a&a&a&x \end{array}} \right|\) is
  • A
    0
  • B
    \({a^4}\)
  • C
    none of these
  • D
    (x+3a) \({\left( {x - a} \right)^3}\)
    Correct
6
If D = \(\left| {\begin{array}{*{20}{c}} 1&2&3 \\ 2&{ - 1}&0 \\ 3&4&5 \end{array}} \right|\), then\(\left| {\begin{array}{*{20}{c}} 1&6&3 \\ 4&{ - 6}&0 \\ 3&{12}&5 \end{array}} \right|\) is equal to
  • A
    3D
  • B
    6D
    Correct
  • C
    2D
  • D
    0
7
\(\left[ {\begin{array}{*{20}{c}} {1 + x}&2&3&4 \\ 1&{2 + x}&3&4 \\ 1&2&{3 + x}&4 \\ 1&2&3&{4 + x} \end{array}} \right]\)
  • A
    \((x + 10){x^2}\)
  • B
    0
  • C
    \({x^3}(x + 10)\)
    Correct
  • D
    None of these
8
The only integral root of the equation det. \(\left| {\begin{array}{*{20}{c}} {2 - y}&2&3 \\ 2&{5 - y}&6 \\ 3&4&{10 - y} \end{array}} \right| = 0\)is
  • A
    3
  • B
    1
    Correct
  • C
    2
  • D
    4
9
Solution set of the equation \(\left| {\begin{array}{*{20}{c}} x&{ - 6}&{ - 1} \\ 2&{ - 3x}&{x - 3} \\ { - 3}&{2x}&{x + 2} \end{array}} \right| = 0\) is
  • A
    { 2 , 0 ,1 }
  • B
    { –3 , 1, 5 }
  • C
    { 2 , –3 ,1}
    Correct
  • D
    { 2 , 1, 5 }
10
Solution set of the equation \(\left| {\begin{array}{*{20}{c}} x&3&7 \\ 2&x&2 \\ 7&6&x \end{array}} \right| = 0\) is
  • A
    { –9 ,2 , 7 }
    Correct
  • B
    { 1, 2 ,7 }
  • C
    none of these
  • D
    { 2 , 5, 6 }
11
\(\left| {\begin{array}{*{20}{c}} 1&2&3 \\ 3&5&7 \\ 8&{14}&{20} \end{array}} \right|\) is equal to
  • A
    a negative real number
  • B
    a positive real number
  • C
    none of these.
  • D
    0
    Correct
12
If f(x) = \(\left| {\begin{array}{*{20}{c}} {2\cos x}&1&0 \\ 1&{2\cos x}&1 \\ 0&1&{2\cos x} \end{array}} \right|\) then , f (\(\frac{\pi }{3}\)) =
  • A
    1
  • B
    2
  • C
    0
  • D
    –1
    Correct
13
\(\left| {\begin{array}{*{20}{c}} { - a + b + c}&{ - 2a}&{ - 2a} \\ { - 2b}&{ - b + c + a}&{ - 2b} \\ { - 2c}&{ - 2c}&{ - c + a + b} \end{array}} \right|\)is
  • A
    a perfect square
  • B
    none of these
  • C
    0
  • D
    a perfect cube
    Correct
14
If D =\(\left| {\begin{array}{*{20}{c}} {x + \lambda }&x&x \\ x&{x + \lambda }&x \\ x&x&{x + \lambda } \end{array}} \right|\) , then D is equal to
  • A
    \({\lambda ^2}({\text{x }} + {\text{ 3}}\;)\)
  • B
    \({x^2}({\text{ x }} + {\text{ 3}}\;)\)
  • C
    \({\lambda ^2}\left( {3x{\text{ }} + \lambda \;} \right)\)
    Correct
  • D
    none of these
15
One of the factors of \(\left| {\begin{array}{*{20}{c}} a&b&c&d \\ b&c&d&a \\ c&d&a&b \\ d&a&b&c \end{array}} \right|\) is
  • A
    none of these.
  • B
    abcd
  • C
    ab+bc+cd+da
  • D
    a+b+c+d
    Correct