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Question 1:

Points $\mathrm{A}$ and $\mathrm{B}$ are on a circle with centre $\mathrm{O}$. $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle from an external point $\mathrm{P}$. If $\mathrm{PA}$ and $\mathrm{PB}$ are inclined to each other at $42^{\circ}$, then find the measure of $\angle O A B$.

Question 2:

In a village, $55 \%$ of the total population are males and the rest are females. If $27.27 \%$ males are illiterate and $44.44 \%$ of the females are literate. If literate males are more than illiterate females by 2730 , then total population of the village is______.

Question 3:

The income of $A$ and $B$ are in the ratio $5: 6$ and their expenditure are in the ratio $4: 3$. If A saves Rs. 8000 and B saves Rs. 12000 , then find the income of B?

Question 4:

A can plough a field in $10 \frac{1}{2}$ days, while B can plough the same field in $17 \frac{1}{2}$ day. Along with $\mathrm{C}$ they did the job in $5 \frac{1}{4}$ days. In how many days can $\mathrm{C}$ alone ploygh the same field?

Question 5:

A, B and C started a business. Twice the investment of $\mathrm{A}$ is equal to thrice the investment of $B$ and also equal to five times the investment of $\mathrm{C}$. If $\mathrm{B}^{\prime}$ s share out of total profit is Rs. 1590 , then total profit is (in rupees)

Question 6:

If $\sec \theta-\tan \theta=\frac{x}{y}$,then find the value of $\sin \theta$.

Question 7:

The marked price of an article is $35 \%$ more than its cost price. If a certain discount is given on the marked price, then the profit made is $14 \frac{3}{4} \%$. What is the percentage Discount offered?

Question 8:

If a solid cone of volume $27 \pi \mathrm{cm}^{3}$ is kept inside a hollow cylinder whose radius and height are that of the cone, then the volume of water needed to fill the empty space is:

Question 9:

In $\Delta \mathrm{ABC}, \mathrm{BC}$ is produced to $\mathrm{D}$. If $\angle \mathrm{A} \underline{\mathrm{C}} \mathrm{D}=$ $112^{\circ}$ and $\angle \mathrm{B}=\frac{3}{4} \angle \mathrm{A}$ then find out the $\angle \mathrm{A}$ is:

Question 10:

If $x+\frac{1}{x}=\frac{\sqrt{3}+1}{2}$, then what is the value of $x^{4}+\frac{1}{x^{4}}$?