**RE-109'AP'**

**SEE 2075 (2019)**

**Compulsory Mathematics**

**Time: 3 hrs. FM: 100**

**Answer all the questions.**

**To Download the Question Paper, Click Here.**

**To Download the Answer Key, Click Here.**

**Group 'A'**

1.

a. If initial population of any place is

**, population after***P*_{O}**years is***T***and annual rate of population growth is***P*_{T}**then express***Q%***in terms of***P*_{T}*P*,_{O}**and***T**Q.*
b. Write the area of an isosceles triangle having length
of equal sides

**and third side***x cm***.***y cm*
2.

a. What is the value of

**?***(7x)*^{2}
b. Write the name of the quartile which divides the
continuous data below

*25%.*
3.

a. Write down the relation between the area of a square
and a triangle standing on the same base

**and between the same parallel lines***XY***and***XY**MN.*
b. Write the relation between the opposite angles of a
cyclic quadrilateral.

**Group ‘B’**

4.

a.
What is the price of an article costing

**after levying***Rs.2000***Value Added Tax? Find it.***13%,*
b.
The present price of a Television is

**. If its price reduces every year by after how many years its price will be***Rs. 40,000***? Find it.***Rs. 29,160*
5.

a.
In the given figure, find the area of

*Î”XYZ.*
b.
If the volume of a hemisphere is

*9216Ï€***, then find its radius.***cubic cm*
c.
In the given figure,

**and the area of rectangular surfaces of prism is***AB= 10 cm, AA' =20 cm, AC= 8 cm***, find the length of***480 square cm***.***BC*
6.

a.
Prove that:

b.
Rationalize the denominator of:

7.

c.
If the sum of two consecutive even numbers is

**, find the numbers.***42*
8.

a.
In the given figure,

**is a parallelogram. If***WXYZ**∠***and the area of parallelogram***XAY= 90°, AY=12 cm***is***WXYZ***, find the length of***120 sq. cm**AX.*
b.
In the given figure,

**is the centre of the circle. If***O**∠***and***MPN= 6x°**∠***find the size of***PMN=3x°,**∠**PQN.*
c.
In the given figure

**is the centre of the circle,***O***and***PQ***are two tangents. If***PR**∠***find the value of***QOR= 120°,**∠**QPR**.*
9.

a.
In

**and***Î”PQR, PQ = 9 cm***. If the area of***PR = 12cm***is***Î”PQR***, find the value of***27√3 sq. cm**∠**RPQ.*
b.
In a continuous series the average weight of
some students is

**and the sum of their weights is***45 kg***. Find the number of students.***540 kg*
10.

a.
If a dice is rolled and a coin is tossed at the
same time, find the probability of occurring prime number on the dice and head
on the coin.

b.
Two cards are drawn randomly from a well
shuffled deck of

**cards in succession without replacement. Show the probabilities of possible outcomes of getting and not getting a queen card in a tree diagram.***52***Group ’C’**

11. In a
survey of a group of people, it was found that

**of the people liked folk songs,***70%***liked modern songs and***60%***people liked both of them. If***4000***liked none of them then,***10%*
i.
draw a venn-diagram to illustrate the above
information.

ii.
find the total number of people in the survey.

iii.
find the number of people who like folk song
only.

12.
A businessman exchanged

**into pound sterling at the rate of***Rs. 840000***. After one day Nepali currency is revaluated by***£1= Rs. 140***and he exchanged the pounds which he had into Nepali currency again. What is his gain or loss? Find it.***5%*
13.
The given figure is combined solid made up of a
cylinder and a cone. The diameter of the base of the object is

**, length of the cylindrical part is***16 cm***and the total length of the solid object is***75 cm***Find the total surface area of the combined solid.***90 cm.*
14.
Find the H.C.F of:

*b*^{2}(b^{2}+4bc+4c^{2}), b^{5}+ 8b^{2}c^{3}and 3b^{4}+ b^{3}c - 10b^{2}c^{2}
15.
Simplify:

17.
Construct a

**equal in area to the quadrilateral***Î”MNQ***having***MNOP***and***NO= OP= 5.5 cm, PM= 4.5 cm***∠****MNO=75°.**
18.
Verify experimentally that the relationship
between centre angle

**and circumference angle***MAN***standing on the same arc***MIN***of the circle. (Two circles having radii at least***NIN***are necessary)***3 cm*
19.
The angle of depression of the top of a tree as
observed from the roof of a house

**. high is found to be***30 ft***If the distance between the house and tree is***30°*.**find the height of the tree.***10√3 ft.,*
20.
Calculate the median from the data given below.

**Group 'D'**

21.
A person deposited

**in bank***Rs. 50,000***for two years at***‘M'***compound interest annually. But after one- year bank has changed the policy and decided to pay semi-annual compound interest at the same rate. What is the percentage difference between compound interests of first and second year? Give reason with calculation.***10%*
22.
Two pillars of height

**each where its four faces are shown in the gate of a stadium have one-one pyramid of height***8 feet***each having the same base on their tops. The base of each pillars is***4 feet***. If the pillar with pyramid are painted at the rate of***6 ft x 6 ft***, what will be the total cost? Find it.***Rs. 60 per square feet*
23.
The area of a rectangular field is

**and perimeter is***1440 sq. metre***Out of length or breadth, which one is to be decreased by what percentage to make it a square? Find it.***152 metre.*
24.
Points

**and***S, O, M***are concyclic such that arc***I***= arc***SO***If the chords***IM.***and***SM**are intersected at the point***IO****, prove that:***K*
i.
Area of

*Area of***Î”SOK**=*Î”IMK.*
ii.

*SM=IO***----------- 0 -----------**

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