BUET Admission Test 2022-2023 (Written)

1. If $y=\left(x+\sqrt{1+x^{2}}\right)^{20}, \left.\frac{d^{2} y}{d x^{2}} \right\rvert\, x=0$ ?

2. If area of the points $A(4,2 k+1), B(k, 4) \& C(3 k+2,2 k)$ is 3 square unit, determine the orthocenter of the triangle. [Let, $\mathrm{K}$ is an integer]

3.

4. If $\left|\begin{array}{ccc}x-4 & 2 x & 2 x \\ 2 x & x-4 & 2 x \\ 2 x & 2 x & x-4\end{array}\right|=(B x+A)(x-A)^{2}$, what is the value of $A \& B$ ?

5. The radius of a semicircular tunnel is $12 \mathrm{~m}$. Find the height at $10 \mathrm{~m}$ distance from the mid-point.