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Question 1:

Find the value of $3+\left\{1+\frac{1}{3}-(3-4 \div 3)+\frac{1}{4}+\frac{2}{3}\right\}$.

Question 2:

The population of a town increases $4 \%$ annually but is decreased by migration annually to the extent of $\frac{1}{2} \%$. What will be the increase percent in three years ?

Question 3:

A man travelled a distance of $47 \mathrm{~km}$ in 6 hours. He travelled partly on foot at a speed of $6 \frac{1}{2} \mathrm{~km} / \mathrm{h}$ and the rest on a bicycle at a speed of $8 \frac{1}{2} \mathrm{~km} / \mathrm{h}$. The distance travelled (in $\mathrm{km}$ ) on bicycle is

Question 4:

A and B can build a wall in 9 days and 12 days respectively, While C can destroy the whole wall in 15 days. What is the number of days required to build 86 such walls if A is joined by B and then C on alternate days?

Question 5:

The sum of the cost price of two bikes is Rs. 50,000 . The first bike was sold at a profit of $20 \%$, and the second bike at a loss of $20 \%$. If the selling prices are the same, what is the cost price (in Rs.) of the first bike that was sold?

Question 6:

A sum invested at 8 % p.a. amounts to ₹ 20,280 at the end of one year, when the interest is compounded half yearly. What will be the compound interest (in ₹) on the same sum for 2 years if the interest rate is the same as earlier and interest is compounded annually?

Question 7:

Two chords $A B$ and $C D$ of a circle are produced to intersect each other at a point $P$ outside the circle. If $A B=7 \mathrm{~cm}$, $B P=4.2 \mathrm{~cm}$ and $P D=2.8 \mathrm{~cm}$, then find length of CD is.

Question 8:

In $\triangle A B C$, D and $\mathrm{E}$ are the points on sides $\mathrm{AB}$ and $\mathrm{AC}$, respectively such that $\angle A D E=\angle B$. If $A D=7 \mathrm{~cm}, B D=5 \mathrm{~cm}$ and $\mathrm{BC}=9 \mathrm{~cm}$, then $\mathrm{DE}$ (in $\mathrm{cm}$ ) is equal to:

Question 9:

If $\cos 63^{\circ}=\mathrm{x}$, then the value of $\tan 27^{\circ}$ is:

Question 10:

If $x+\frac{1}{x}=3$, then find the value of $\mathrm{x}^{5}+\frac{1}{x^{5}} ?$