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Question 1:

An equilateral triangle $\mathrm{ABC}$ is inscribed in a circle with centre $\mathrm{O} . \mathrm{D}$ is a point on the minor arc $\mathrm{BC}$ and $\angle C B D=40^{\circ}$. Find the measure of $\angle B C D$.

Question 2:

Water flows into a tank $180 \mathrm{~m} \times 140 \mathrm{m}$ through a rectangular Pipe of $1.2 \mathrm{~m} \times 0.75 \mathrm{~m}$ at a rate of $45 \mathrm{~km} / \mathrm{h}$. In what time Will the water rise by $4 \mathrm{~m}$?

Question 3:

A batsman has a certain average in 59 innings. In the next three innings he scored with an average of 84 thereby increasing his overall average by $1 \frac{1}{2}$ runs. What is his average after 62 innings?

Question 4:

Three bottles of orange juice contains orange and water in the ratio of 4: 3, 3: 2 and 9 : 7 respectively.  21 litres from first bottle and 20 litres form second  bottle is mixed with x litres from third bottle to get a new juice in which orange and water are in the ratio of 15: 11, then find the value of x.

Question 5:

If $x^{4}+\frac{1}{x^{4}}=14159$, then the value of $x+\frac{1}{x}$ is:

Question 6:

Ratio of monthly incomes of A and B is $5: 8$ and that of their monthly expenditure is 4 : 7 . If the income of $A$ is equal to expenditure of $B$, then what is the ratio of savings of $B$ to savings of A?

Question 7:

Two friends Amit and Bipeen invest in a business in partnership. Bipeen borrows $20 \%$ of Amit 's salary, combines it with $60 \%$ of his salary and invests with Amit , who puts all of his remaining salary. One year later the ratio of profit of Amit and Bipeen is 5: 3 respectively and returns Rs. 21000 to $A$ mit which he borrowed from him. What is the difference between salary of Amit and Bipeen?

Question 8:

A contractor engaged 100 labourers for a construction work to be completed in 96 days. But only $\frac{1}{7}$ of the work was done in $\frac{1}{6}$ of the scheduled time. The additional number of labourers that will be required to complete the work in time is:

Question 9:

If $\sec x+\cos x=4$ then $\tan ^{2} x-\sin ^{2} x$ is equal to:

Question 10:

If the sides of a quadrilateral ABCD touch a circle and $\mathrm{AB}=8 \mathrm{~cm}, \mathrm{CD}=7 \mathrm{~cm}, \mathrm{BC}=9 \mathrm{~cm}$, then the length of $\mathrm{AD}$ in $\mathrm{cm}$ is: