Question

Find the equation of tangent to the curve $y={\frac{x-7}{x^{2}-5x+6}}$ at the point, where it cuts the x-axis.

Find the particular solution of the differential equation ${\frac{d y}{d x}}={\frac{x\left(2\log x+1\right)}{\sin y+y\cos y}}$ given that $y={\frac{\pi}{2}}$ where x = 1.

A and B throw a pair of dice alternately. A wins the game if he gets a total of 9 and B wins if he gets a total of 7. If A starts the game, find the probability of winning the game by B.

Find the equation of the tangent to the curve y = x⁴ – 6x³ + 13x² – 10x + 5 at point x = 1, y = 0.

Find the particular solution of the following differential equation given that at x = 2, y = 1 $x\,{\frac{d y}{d x}}\,+\,2y=x^{2},\,(x\,\neq\,0).$

Using properties of determinants, prove that : $\begin{vmatrix}a+b+2c & a & b \\ c & b+c+2a & b \\ c & a & c+a+2b\end{vmatrix}$ = $2(a+b+c)^{3}.$

Using properties of determinants, solve for x : $\begin{vmatrix}a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x\end{vmatrix}$ = 0