79169 If the value of third order determinant be 11 , then what is the value of the square of determinant formed by its cofactors?

79170 If \(f(x), g(x), h(x)\) are three polynomials of degree 2 , what is the degree of the polynomial
\(\varphi(x)\) where \(\varphi(x)=\left|\begin{array}{lll}f^{\prime}(x) & g(x) & h(x) \\ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \\ f^{\prime \prime}(x) & g^{\prime \prime}(x) & h^{\prime \prime}(x)\end{array}\right|\) ?

79171 The area of the triangle formed by the points \((a, b+c),(b, c+a)\) and \((c, a+b)\) will be

79172 Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c} \mathbf{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to

79169 If the value of third order determinant be 11 , then what is the value of the square of determinant formed by its cofactors?

79170 If \(f(x), g(x), h(x)\) are three polynomials of degree 2 , what is the degree of the polynomial
\(\varphi(x)\) where \(\varphi(x)=\left|\begin{array}{lll}f^{\prime}(x) & g(x) & h(x) \\ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \\ f^{\prime \prime}(x) & g^{\prime \prime}(x) & h^{\prime \prime}(x)\end{array}\right|\) ?

79171 The area of the triangle formed by the points \((a, b+c),(b, c+a)\) and \((c, a+b)\) will be

79172 Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c} \mathbf{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to

79169 If the value of third order determinant be 11 , then what is the value of the square of determinant formed by its cofactors?

79170 If \(f(x), g(x), h(x)\) are three polynomials of degree 2 , what is the degree of the polynomial
\(\varphi(x)\) where \(\varphi(x)=\left|\begin{array}{lll}f^{\prime}(x) & g(x) & h(x) \\ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \\ f^{\prime \prime}(x) & g^{\prime \prime}(x) & h^{\prime \prime}(x)\end{array}\right|\) ?

79171 The area of the triangle formed by the points \((a, b+c),(b, c+a)\) and \((c, a+b)\) will be

79172 Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c} \mathbf{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to

79169 If the value of third order determinant be 11 , then what is the value of the square of determinant formed by its cofactors?

79170 If \(f(x), g(x), h(x)\) are three polynomials of degree 2 , what is the degree of the polynomial
\(\varphi(x)\) where \(\varphi(x)=\left|\begin{array}{lll}f^{\prime}(x) & g(x) & h(x) \\ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \\ f^{\prime \prime}(x) & g^{\prime \prime}(x) & h^{\prime \prime}(x)\end{array}\right|\) ?

79171 The area of the triangle formed by the points \((a, b+c),(b, c+a)\) and \((c, a+b)\) will be

79172 Let \(a, b, c\) be three distinct real numbers, none equal to one. If the vectors \(\mathbf{a} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\mathbf{b} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{c} \mathbf{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to