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Question 1:

$\mathrm{BC}$ is the chord of a circle with centre O. A is a point on major arc $\mathrm{BC}$ as shown in the given figure. What is the value of $\angle B A C+\angle O B C=$ ?

Question 2:

If $a+\frac{1}{a+2}=0$, then the value of $(a+2)^{3}+\frac{1}{(a+2)^{3}}$:

Question 3:

Milk contains 5% water, what quantity of pure milk should be added to 10 liters of milk to reduce this to 2%?

Question 4:

If $\tan \theta+\cot \theta=2$, then the value of $\tan ^{100} \theta^{+}$ $\cot ^{100} \theta$ is:

Question 5:

Two trains A and B, start from stations $\mathrm{X}$ and $\mathrm{Y}$ towards $\mathrm{Y}$ and $\mathrm{X}$ respectively. After passing each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach $\mathrm{Y}$ and $\mathrm{X}$ respectively. If train $A$ is moving at $45 \mathrm{~km} /$ hr then the speed of the train $\mathrm{B}$ is:

Question 6:

The students in three classes are in the ratio $4: 6: 9 .$ If 12 students are increased in each class, the ratio changes to $7: 9: 12 .$ Then the total number of students in the three classes before the increase is :

Question 7:

A swimming pool has 3 drain pipes. The first two pipes $A$ and $B$ operating simultaneously can empty the pool in half the time then that C the 3 rd pipe alone takes to empty it. Pipe $A$ working alone takes half the time taken by pipe $B$. Together they all take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool in hours is:

Question 8:

A tank can be filled by pipe $A$ in 2 hours and pipe $\mathrm{B}$ in 6 hours. At 10 a.m pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 a.m?

Question 9:

If $\mathrm{a}=25, \mathrm{~b}=15, \mathrm{c}=-10$, then the value of $\frac{\alpha^{3}+b^{3}+c^{3}-3 a b c}{(a-b)^{2}+(b-c)^{2}+(c-a)^{2}}$ is:

Question 10:

A motor-boat can travel at $10 \mathrm{~km} / \mathrm{h}$ in still water. It travelled $91 \mathrm{km}$ downstream in a river and then return to the same place, taking altogether 20 hours. Find the rate of flow of river.