79147 If \(a>0, b>0, c>0\) are respectively the pth, qth, rth terms of G.P., then the value of the
\(\text { determinant }\left|\begin{array}{lll}
\log a & p & 1 \\ \log b & q & 1 \end{array}\right| \text { is }\)
\(\begin{array}{lll}
\log c & \mathbf{r} & 1 \end{array}\)

79148 The determinant \(1 \quad(x-4) \quad(x-4)^{2}\) vanishes
\(1 \quad(x-5) \quad(x-5)^{2}\)
for

79149 If [ ] denotes the greatest integer less than or equal to the real number under consideration and \(-1 \leq \mathrm{x}<0 ; 0 \leq \mathrm{y}<1 ; 1 \leq \mathrm{z}<2\), then the value of the determinant
\(\left|\begin{array}{ccc}{[x]+1} & {[y]} & {[z]} \\ {[x]} & {[y]+1} & {[z]} \\ {[x]} & {[y]} & {[z]+1}\end{array}\right|\) is

79150 Let \(\omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}\). Then, the value of the determinant \(\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|\) is

79151 The points represented by the complex numbers \(1+i,-2+3 i, 5 / 3 i\) on the argand plane are

79147 If \(a>0, b>0, c>0\) are respectively the pth, qth, rth terms of G.P., then the value of the
\(\text { determinant }\left|\begin{array}{lll}
\log a & p & 1 \\ \log b & q & 1 \end{array}\right| \text { is }\)
\(\begin{array}{lll}
\log c & \mathbf{r} & 1 \end{array}\)

79148 The determinant \(1 \quad(x-4) \quad(x-4)^{2}\) vanishes
\(1 \quad(x-5) \quad(x-5)^{2}\)
for

79149 If [ ] denotes the greatest integer less than or equal to the real number under consideration and \(-1 \leq \mathrm{x}<0 ; 0 \leq \mathrm{y}<1 ; 1 \leq \mathrm{z}<2\), then the value of the determinant
\(\left|\begin{array}{ccc}{[x]+1} & {[y]} & {[z]} \\ {[x]} & {[y]+1} & {[z]} \\ {[x]} & {[y]} & {[z]+1}\end{array}\right|\) is

79150 Let \(\omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}\). Then, the value of the determinant \(\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|\) is

79151 The points represented by the complex numbers \(1+i,-2+3 i, 5 / 3 i\) on the argand plane are

79147 If \(a>0, b>0, c>0\) are respectively the pth, qth, rth terms of G.P., then the value of the
\(\text { determinant }\left|\begin{array}{lll}
\log a & p & 1 \\ \log b & q & 1 \end{array}\right| \text { is }\)
\(\begin{array}{lll}
\log c & \mathbf{r} & 1 \end{array}\)

79148 The determinant \(1 \quad(x-4) \quad(x-4)^{2}\) vanishes
\(1 \quad(x-5) \quad(x-5)^{2}\)
for

79149 If [ ] denotes the greatest integer less than or equal to the real number under consideration and \(-1 \leq \mathrm{x}<0 ; 0 \leq \mathrm{y}<1 ; 1 \leq \mathrm{z}<2\), then the value of the determinant
\(\left|\begin{array}{ccc}{[x]+1} & {[y]} & {[z]} \\ {[x]} & {[y]+1} & {[z]} \\ {[x]} & {[y]} & {[z]+1}\end{array}\right|\) is

79150 Let \(\omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}\). Then, the value of the determinant \(\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|\) is

79151 The points represented by the complex numbers \(1+i,-2+3 i, 5 / 3 i\) on the argand plane are

79147 If \(a>0, b>0, c>0\) are respectively the pth, qth, rth terms of G.P., then the value of the
\(\text { determinant }\left|\begin{array}{lll}
\log a & p & 1 \\ \log b & q & 1 \end{array}\right| \text { is }\)
\(\begin{array}{lll}
\log c & \mathbf{r} & 1 \end{array}\)

79148 The determinant \(1 \quad(x-4) \quad(x-4)^{2}\) vanishes
\(1 \quad(x-5) \quad(x-5)^{2}\)
for

79149 If [ ] denotes the greatest integer less than or equal to the real number under consideration and \(-1 \leq \mathrm{x}<0 ; 0 \leq \mathrm{y}<1 ; 1 \leq \mathrm{z}<2\), then the value of the determinant
\(\left|\begin{array}{ccc}{[x]+1} & {[y]} & {[z]} \\ {[x]} & {[y]+1} & {[z]} \\ {[x]} & {[y]} & {[z]+1}\end{array}\right|\) is

79150 Let \(\omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}\). Then, the value of the determinant \(\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|\) is

79151 The points represented by the complex numbers \(1+i,-2+3 i, 5 / 3 i\) on the argand plane are

79147 If \(a>0, b>0, c>0\) are respectively the pth, qth, rth terms of G.P., then the value of the
\(\text { determinant }\left|\begin{array}{lll}
\log a & p & 1 \\ \log b & q & 1 \end{array}\right| \text { is }\)
\(\begin{array}{lll}
\log c & \mathbf{r} & 1 \end{array}\)

79148 The determinant \(1 \quad(x-4) \quad(x-4)^{2}\) vanishes
\(1 \quad(x-5) \quad(x-5)^{2}\)
for

79149 If [ ] denotes the greatest integer less than or equal to the real number under consideration and \(-1 \leq \mathrm{x}<0 ; 0 \leq \mathrm{y}<1 ; 1 \leq \mathrm{z}<2\), then the value of the determinant
\(\left|\begin{array}{ccc}{[x]+1} & {[y]} & {[z]} \\ {[x]} & {[y]+1} & {[z]} \\ {[x]} & {[y]} & {[z]+1}\end{array}\right|\) is

79150 Let \(\omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}\). Then, the value of the determinant \(\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|\) is

79151 The points represented by the complex numbers \(1+i,-2+3 i, 5 / 3 i\) on the argand plane are