If \( \cot\alpha \) and \( \cot\beta \) are the roots of the equation \( x^{2} + bx + c = 0 \) with \( b \neq 0 \), then the value of \( \cot(\alpha + \beta) \) is
The sum of the roots of the equation \( x^{2} + bx + c = 0 \) (where b and c are non-zero) is equal to the sum of the reciprocals of their squares. Then \( \frac{1}{c} \), b, \( \frac{c}{b} \) are in
The sum of the roots of the equation \( ax^{2} + x + c = 0 \) (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, \( ca^{2} \), \( c^{2} \) are in
The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word ‘EQUATION’ is
