Delhi Police SI 2024 June 27 Shift 2 Question Paper

Find the fourth proportion to $10$, $12$, and $15$.

Two circles with centers $B$ and $D$ have radii $DA=8\text{cm}$ and $BC=x\text{cm}$, respectively. $AC$ is tangent to both circles. If $DB$ and $AC$ intersect at the point $E$, $AE=12\text{cm}$ and $EC=18\text{cm}$, then find the value of $x$ (in $\text{cm}$).

Simplify the following expression:
$$5\times [14÷13\times \{13\times 14÷(14\times 14)\}]$$

If $\alpha +\beta +\gamma =0$, then find the value of $\frac{3{\beta }^2+{\alpha }^2+{\gamma }^2}{2{\beta }^2-\alpha \gamma }$.

In an election, the winner was supported by $46\%$ of all the voters in the list, and he got $410$ votes more than his only rival. $10\%$ of the voters on the voters' list did not cast their votes, and $60$ voters cast their ballot papers blank. How many voters were on the list?