Delhi Police SI 2024 June 27 Shift 1 Question Paper

What will be the possible value of $x$ that satisfies the given equation?
$$\frac{(143÷13\times x-3\times 3)}{(6^2-7\times 5+x^2)}=1$$

Simplify the following expression:
$$(1+{\tan }^{2}A)+\left(1+\frac{1}{{\tan }^{2}A}\right)$$

$57\%$ of Ranita's weekly income is equal to $76\%$ of Bhaskar's weekly income. If Ranita's weekly income is decreased by $\text{₹}400$ while Bhaskar's weekly income remains unchanged, the ratio of the weekly incomes of Ranita and Bhaskar becomes $6:5$ respectively. What is the weekly income of Bhaskar (in $\text{₹}$)?

A alone can complete a work in $200$ days, while B alone can complete the same work in $100$ days. In each three-day cycle, on the first day both A and B work together, on the second day only A works, and on the third day only B works. This cycle continues until the work is completed. How many days will they take together to complete the work?

Simplify the following expression:
$$3\frac{1}{5}\text{ of }2\frac{3}{4}÷\frac{11}{3}+\left(2\frac{1}{5}÷1\frac{2}{5}\text{ of }1\frac{3}{7}-2\frac{1}{3}\right)$$