Determinant

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #41

Without expanding, prove that: $ \begin{vmatrix} 0 & 2016 & -2017 \\ -2016 & 0 & 2018 \\ 2017 & -2018 & 0 \end{vmatrix} = 0 $
Ans: N.A.
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Question No: #42

Without expanding prove that: $ \begin{vmatrix} a+1 & a+4 & a+2 \\ a+2 & a+5 & a+4 \\ a+3 & a+6 & a+6 \end{vmatrix} = 0 $

Question No: #43

Without expanding prove that: $ \begin{vmatrix} a+b & 2a+b & 3a+b \\ 2a+b & 3a+b & 4a+b \\ 4a+b & 5a+b & 6a+b \end{vmatrix} = 0 $

Question No: #44

Show that the value of $ \begin{vmatrix} x+1 & x+2 & x+4 \\ x+3 & x+5 & x+8 \\ x+5 & x+8 & x+12 \end{vmatrix} $ , is not depend on `x`.

Question No: #45

If `a, b, c` are in Arithmetic Progression (A.P.) , then show that $ \begin{vmatrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{vmatrix} = 0 $

Question No: #46

Prove that $ \begin{vmatrix} 1 & 1 & 1 \\ C_1^m & C_1^{m+1} & C_1^{m+2} \\ C_2^m & C_2^{m+1} & C_2^{m+2} \end{vmatrix} = 1 $

Question No: #47

Prove that $ \begin{vmatrix} 1 & \log_xy & \log_xz \\ \log_yx & 1 & \log_yz \\ \log_zx & \log_zy & 1 \end{vmatrix} = 0 $

Question No: #48

Without expanding prove that: $ \begin{vmatrix} \log_x\ xyz & \log_x\ y & \log_x\ z \\ \log_y\ xyz & 1 & \log_y\ z \\ \log_z\ xyz & \log_z\ y & 1 \end{vmatrix} = 0 $

Question No: #49

If `p^{th}`, `q^{th}` and `r^{th}` terms of a geometric series are `a`, `b`, `c` respectively, then show that $ \begin{vmatrix} \log a & p & 1 \\ \log b & q & 1 \\ \log c & r & 1 \end{vmatrix} = 0 $ where `a, b, c` are positive.

Question No: #50

Find the value of $ \begin{vmatrix} 1+x & y & z \\ x & 1+y & z \\ x & y & 1+z \end{vmatrix} $