Two stones are thrown vertically upwards with equations of motion $s_1 = 19.6t - 4.9t^2$ and $s_2 = 9.8t - 4.9t^2$ respectively. The maximum height of the first stone is $h$. When the first stone is at its maximum height,the height of the second stone is:

The number of distinct real roots of $x^{4}-4x+1=0$ is

The minimum value of $4e^{2x} + 9e^{-2x}$ is:

Let $f(x) = x^3 + px + 1$ and consider the following three statements:
$(i)$ For $p \geqslant 0$,$f(x) = 0$ has one negative root and $f(x)$ is monotonic.
$(ii)$ For $-1 < p < 0$,$f(x) = 0$ has one negative root and $f(x)$ is non-monotonic.
$(iii)$ For $p < -3/\sqrt[3]{4}$,$f(x) = 0$ has three real and distinct roots.
Which of the following is correct?

$A$ tank with a rectangular base and rectangular sides,open at the top,is to be constructed such that its depth is $2 \ m$ and volume is $8 \ m^{3}$. If the cost of building the tank is Rs $70$ per square metre for the base and Rs $45$ per square metre for the sides,what is the minimum cost of the tank?

If the function $y = a \log x + bx^2 + x$ has extreme values at $x = 1$ and $x = 2$,then $(a, b) = \dots$