BUET Admission Test 2021-2022 (Written)

1. Among three circles, the biggest circle's radius is 4 unit and medium circle's radius is 2 unit. A straight line is tangent to all three circles. Each circle touches the other two circles externally. What is the radius of the third circle?

2. Two forces of 4 and $5 \mathrm{~kg}$-wt acting parallel to the length and base of a frictionless inclined plane, respectively, can singly support an object of weight on the plane. Find the value of $w$.

3. Find the integrate: $\int(\sqrt{\tan \theta}+\sqrt{\cot \theta}) d \theta$

4. $50 \mathrm{ml} 6.0 \times 10^{-3} \mathrm{M} \mathrm{CaCl}_{2}$ solution is mixed with $30 \mathrm{ml} 0.04 \mathrm{M} \mathrm{NaF}$ solution. Show calculations to determine whether precipitation of $\mathrm{CaF}_{2}$ will form or not. $\left(\mathrm{K}_{\mathrm{sp}}, \mathrm{CaF}_{2}=4.0 \times 10^{-11}\right)$

5. In the circuit shown in Fig. 3, what is the base current $\left(\mathrm{I}_{\mathrm{b}}\right)$ if the value of current gain $(\beta)$ is 100 ? Also, find potential drops across collector-emitter $\left(V_{c e}\right)$, base-emitter $\left(V_{b e}\right)$ and base-collector $\left(V_{b c}\right)$. Collector current $\mathrm{I}_{\mathrm{c}}=1.5 \mathrm{~mA}$.