The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

If the pairs of straight lines $x^2-2 q x y-y^2=0$ and $x^2-2 p x y-y^2=0$ bisect the angles between each other,then which of the following is correct?

The $pH$ value of which one of the following is not equal to $1$?

The equation of the line passing through the point $(-1, 3, -2)$ and perpendicular to each of the lines $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ and $\frac{x+2}{-3} = \frac{y-1}{2} = \frac{z+1}{5}$ is

If the system of equations $ax + y + z = 0$,$x + by + z = 0$,and $x + y + cz = 0$ $(a, b, c \neq 1)$ has a non-trivial solution,then the value of $\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$ is:

To determine the different types of gametes produced by a pea plant with the genotype $AaBb$,it should be crossed with a plant of which genotype?