If \( p, q, r, s \) are in A.P. and
\( f(x)=\left|\begin{array}{llc}p+\sin x & q+\sin x & p-r+\s... VIDEO
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\[
\begin{array}{l}
\lambda x-y+(\cos \theta) z=0 \\
3 x+y+2 z=0 \\
(\cos \... 2023-06-08 \( \Delta=\left|\begin{array}{ll}a_{1} & a_{2} \\ a_{3} & a_{4}\end{array}\right| \) and \( a_{i... 2023-06-08 In triangle \( A B C \), if \( \left|\begin{array}{ccc}1 & 1 & 1 \\ \cot \frac{A}{2} & \cot \fra... 2023-06-08 If \( x, y, z \) are natural numbers such that \( \left|\begin{array}{ccc}x^{4}+x & x^{3} y & x^... 2023-06-08 If \( \left|\begin{array}{lll}(\beta+\gamma-\alpha-\delta)^{4} & (\beta+\gamma-\alpha-\delta)^{2... 2023-06-08 \( \mathrm{P}(x, y, z) \) satisfies the equations \( x+\left(\log _{a} b\right) y+\left(\log _{\... 2023-06-08 If \( \alpha, \beta, \gamma \) are the angles of a triangle and the system of equations
\[
\begi... 2023-06-08 If \( a_{1}, a_{2}, a_{3}, 5,4, a_{6}, a_{7}, a_{8}, a_{9} \) are in H.P. and \( \Delta=\left|\b... 2023-06-08 \( \alpha, \beta \) are are the, maximum and minimum values of \( f(x)=\left|\begin{array}{ccc}1... 2023-06-08 If \( p, q, r, s \) are in A.P. and
\( f(x)=\left|\begin{array}{llc}p+\sin x & q+\sin x & p-r+\s... 2023-06-08 Suppose \( a_{1}, a_{2}, \ldots \) real numbers, with \( a_{1} \neq 0 \). If \( a_{1}, a_{2}, a_... 2023-06-08 If \( f(\theta)=\left|\begin{array}{lll}\sin \theta & \cos \theta & \sin \theta \\ \cos \theta &... 2023-06-08 If the value of the determinant
\[
\left|\begin{array}{ccc}
\sqrt{(13)}+\sqrt{3} & 2 \sqrt{5} & ... 2023-06-08 Let \( a=\operatorname{Lim}_{x \rightarrow 1} \frac{x}{\ln x}-\frac{1}{x \ln x} ; b=\operatornam... 2023-06-08 The value of the determinant \( \left|\begin{array}{ccc}-\left(2^{5}+1\right)^{2} & 2^{10}-1 & \... 2023-06-08 If \( \Delta=\left|\begin{array}{cc}f(x) & f\left(\frac{1}{x}\right)+f(x) \\ 1 & f\left(\frac{1}... 2023-06-08 The value of \( \Delta=x y z\left|\begin{array}{ccc}1 / x & 1 / y & 1 / z \\ p & 2 q & 3 r \\ 1 ... 2023-06-08 If \( xm, yn, zr(x, y, z0) \) such that \( \left|\begin{array}{lll}x & n & r \\ m & y & r \\ m &... 2023-06-08 If \( x^{2 a} y^{3 b}=e^{5 m}, x^{3 c} y^{4 d}=e^{2 n}, \Delta_{1}=\left|\begin{array}{cc}5 m & ... 2023-06-08 If \( 0 \leq \theta \leq \pi / 2 \), find the number of roots of
\[
\Delta(\theta)=\left|\begin{...
0