Determinants Test

Determinants

This is Determinants Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
\(\left| {\begin{array}{*{20}{c}} {a - b - c}&{2a}&{2a} \\ {2b}&{b - c - a}&{2b} \\ {2c}&{2c}&{c - a - b} \end{array}} \right| = \)
  • A
    \(4{\left( {a + b + c} \right)^3}\)
  • B
    \(2{\left( {a + b + c} \right)^2}\)
  • C
    \( - 2{\left( {a + b + c} \right)^3}\)
  • D
    none of these
    Correct
2
The roots of the equation det. \(\left| {\begin{array}{*{20}{c}} {1 - x}&2&3 \\ 0&{2 - x}&0 \\ 0&2&{3 - x} \end{array}} \right| = 0\) are
  • A
    none of these.
  • B
    1 , 2, and 3
    Correct
  • C
    2, and 3
  • D
    1 and 3
3
If \({\text{A}} + {\text{B}} + {\text{C }} = {\text{ }}\pi \), then the value of \(\left| {\begin{array}{*{20}{c}} {\sin (A + B + C)}&{\sin B}&{\cos C} \\ { - \sin B}&0&{\tan A} \\ {\cos (A + B)}&{ - \tan A}&0 \end{array}} \right|\)
  • A
    none of these
  • B
    0
    Correct
  • C
    1
  • D
    2
4
If \(\Delta = \left| {\begin{array}{*{20}{c}} 0&a&b \\ { - a}&0&c \\ { - b}&{ - c}&0 \end{array}} \right|\) , then equals
  • A
    0
    Correct
  • B
    none of these.
  • C
    –abc
  • D
    2abc
5
If the entries in a 3 x 3 determinant are either 0 or 1 , then the greatest value of this determinant is :
  • A
    0
  • B
    none of these.
  • C
    1
  • D
    2
    Correct
6
If \(\left| {\begin{array}{*{20}{c}} 1&3&9 \\ 1&x&{{x^2}} \\ 4&6&9 \end{array}} \right| = 0\) , then x =
  • A
    3 or 3/2
    Correct
  • B
    3 or 6
  • C
    3
  • D
    none of these
7
The determinant \(\left| {\begin{array}{*{20}{c}} {a - b}&{b - c}&{c - a} \\ {x - y}&{y - z}&{z - x} \\ {p - q}&{q - r}&{r - p} \end{array}} \right|\) is equal to
  • A
    1
  • B
    0
    Correct
  • C
    none of these
  • D
    –1
8
If 1/a+1/b+ 1/c = 0 , then \(\left| {\begin{array}{*{20}{c}} {1 + a}&1&1 \\ 1&{1 + b}&1 \\ 1&1&{1 + c} \end{array}} \right| = \)
  • A
    –abc
  • B
    none of these
  • C
    abc
    Correct
  • D
    0
9
A determinant is unaltered , if
  • A
    Two rows are interchanged
  • B
    To each element of any row is added the corresponding element of the other row multiplied by a given factor
    Correct
  • C
    Two columns are interchanged
  • D
    Every element in a column is multiplied by the same factor
10
If \(\left| {\begin{array}{*{20}{c}} a&b&c \\ m&n&p \\ x&y&z \end{array}} \right| = k,\,\,\,then\,\,\,\left| {\begin{array}{*{20}{c}} {6a}&{2b}&{2c} \\ {3m}&n&p \\ {3x}&y&z \end{array}} \right| = \)
  • A
    6/k
  • B
    6k
    Correct
  • C
    2k
  • D
    3k
11
If \(A = \left| {\begin{array}{*{20}{c}} { - 1}&2&4 \\ 3&1&0 \\ { - 2}&4&2 \end{array}} \right|\,\,\& \,\,\,\,B = \left| {\begin{array}{*{20}{c}} { - 2}&4&2 \\ 6&2&0 \\ { - 2}&4&8 \end{array}} \right|\) , then B is given by
  • A
    B = 6 A
  • B
    B = 4A
  • C
    B = –4A
    Correct
  • D
    B = – A
12
Find the area of triangle with vertices ( 1 ,1 ) , (2 ,2 ) and ( 3, 3 ).
  • A
    3
  • B
    1
  • C
    0
    Correct
  • D
    2
13
Find the area of triangle with vertices ( 0 ,0 ),(4 , 2) and ( 1,1).
  • A
    0
  • B
    1
    Correct
  • C
    5
  • D
    2
14
A(adj A) is equal to
  • A
    I
  • B
    none of these
  • C
    O
  • D
    \(\left| A \right|I\)
    Correct
15
The inverse of the matrix \(\left[ {\begin{array}{*{20}{c}} 0&1&0 \\ 1&0&0 \\ 0&0&1 \end{array}} \right]\)\(\) is
  • A
    A’
  • B
    A
    Correct
  • C
    \(\left[ {\begin{array}{*{20}{c}} 1&1&0 \\ 1&1&0 \\ 0&0&1 \end{array}} \right]\)
  • D
    none of these.