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Question 1:

X, Y and Z can do a piece of work in 46 days, 92 days and 23 days respectively. X started work. Y joined him after 2 days. If Z joins them after 8 days from the start, then for how many days did X work?

Question 2:

In a circle with centre $\mathrm{O}$, chords $\mathrm{PR}$ and $\mathrm{QS}$ meet at the point $\mathrm{T}$, when produced, and $\mathrm{PQ}$ is a diameter. If $\angle R O S=42^{\circ}$, then the measure of $\angle \mathrm{PTQ}$ is

Question 3:

How many such numbers are there from 500 to 650 (inclusive of both) which are not divisible by both 3 and 7?

Question 4:

A vertical pole and a vertical tower are placed on a flat ground such that the angle of elevation of the top of the tower from the top of the pole is $60^{\circ}$ and the angle of depression of the base of the tower  from the top of the pole is $30^{\circ}$. If the height of the tower is $76 \mathrm{~m}$, then find the height of the pole (in $\mathrm{m}$).

Question 5:

The run rate in the first 10 overs of a cricket match was only $7.2$. What should be the average run rate in the remaining 40 overs to chase the target of 272 runs?

Question 6:

Find the greatest number by which dividing 108, 124 and 156 gives the same remainder.

Question 7:

If $\cos (A-B)=\frac{\sqrt{3}}{2}$ and $\sec A=2,0^{\circ} \leq A \leq 90^{\circ}, 0^{\circ} \leq B \leq 90^{\circ}$, then what is the measure of B?

Question 8:

What is the value of:

$8 \sqrt{3} \sin 30^{\circ} \tan 60^{\circ}-3 \cos 0^{\circ}+3 \sin ^{2} 45^{\circ}+2 \cos ^{2} 30 ?$

Question 9:

A car runs first $275 \mathrm{~km}$ at an average speed of $50 \mathrm{~km} / \mathrm{h}$ and the next $315 \mathrm{~km}$ at an average speed of $70 \mathrm{~km} / \mathrm{h}$. What is the average speed (in $\mathrm{km} / \mathrm{h}$ ) for the entire journey?

Question 10:

If $(4 x+2 y)^{3}+(4 x-2 y)^{3}=16\left(A x^{3}+B x y^{2}\right)$, then what is the value of $\frac{1}{2}\left(\sqrt{A^{2}+B^{2}}\right) ?$