SSC CPO 4th Oct 2023 Shift 2

Tom can do a piece of work in 7 days, whereas Jay can do the same work in 14 days.
How long will they take to finish the work if both work together?

Two trains of lengths 200 m and 250 m are running on parallel rail tracks at speeds of 68 km/h and 50 km/h, respectively. In how much time (in seconds) will they cross each other if they are running in the same direction?

Travelling a distance of 1000 km, a train slowed down due to repairs of the tracks. Its average speed for the trip reduced by 75 km/h and the time of travel increased by 3 hours. The original duration of the travel is:

$$7 \sin^{2} A+3 \cos^{2} A=4$$, then find $$\cot A$$:

If $$\sec A - \tan A = p$$, then find the value of $$\sec A$$.

$$2(\sin 1^{\circ} \times \sec 89^{\circ} ) + 3 (\cos 11^{\circ} \times \cosec 79^{\circ}) + 5 (\tan 21^{\circ} \times \tan 69^{\circ}) = ?$$

A person has three iron bars whose lengths are 20, 30 and 40 metres, respectively. He wants to cut pieces of the same length from each of the three bars. What is the least number of total pieces if he cuts without any wastage?

In a $$\triangle PQR, \angle P : \angle Q : \angle R = 3 ∶ 4 ∶ 8. The shortest side and the longest side of the triangle, respectively, are:

In a triangle ABC, if $$\angle B = 90^{\circ}, \angle C = 45^{\circ}$$ and AC = 4 cm, then the value of BC is:

Study the given pie-chart and answer the question that follows.
The pie-chart shows the number of boys studying in play group of various schools (A, B, C).

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What is the average number of boys studying in schools A and C?