If the normal to the curve $y^2 = 5x - 1$ at the point $(1, -2)$ is of the form $ax - 5y + b = 0$,then $a$ and $b$ are:

$A$ particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ along two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by