## Tuesday, May 26, 2020

RE-109'AP'

SEE 2075 (2019)
Compulsory Mathematics
Time: 3 hrs.                                                     FM: 100
Group 'A'
1.
a.    If initial population of any place is PO, population after T years is PT and annual rate of population growth is Q% then express PT in terms of PO, T and Q.
b.    Write the area of an isosceles triangle having length of equal sides x cm and third side 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 XY and between the same parallel lines XY and 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 Rs.2000 after levying 13%, Value Added Tax? Find it.
b.    The present price of a Television is Rs. 40,000. If its price reduces every year by after how many years its price will be Rs. 29,160? Find it.
5.
a.    In the given figure, find the area of ΔXYZ.
b.    If the volume of a hemisphere is 9216π cubic cm, then find its radius.
c.    In the given figure, AB= 10 cm, AA' =20 cm, AC= 8 cm and the area of rectangular surfaces of prism is 480 square cm, find the length of BC.
6.
a.    Prove that:
b.    Rationalize the denominator of:
7.
a.
c.    If the sum of two consecutive even numbers is 42, find the numbers.
8.
a.    In the given figure, WXYZ is a parallelogram. If XAY= 90°, AY=12 cm and the area of parallelogram WXYZ is 120 sq. cm, find the length of AX.
b.    In the given figure, O is the centre of the circle. If MPN= 6x° and PMN=3x°, find the size of PQN.
c.    In the given figure O is the centre of the circle, PQ and PR are two tangents. If QOR= 120°, find the value of QPR.
9.
a.    In ΔPQR, PQ = 9 cm and PR = 12cm. If the area of ΔPQR is 27√3 sq. cm, find the value of RPQ.
b.    In a continuous series the average weight of some students is 45 kg and the sum of their weights is 540 kg. Find the number of students.
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 52 cards in succession without replacement. Show the probabilities of possible outcomes of getting and not getting a queen card in a tree diagram.
Group ’C’
11. In a survey of a group of people, it was found that 70% of the people liked folk songs, 60% liked modern songs and 4000 people liked both of them. If 10% liked none of them then,
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 Rs. 840000 into pound sterling at the rate of £1= Rs. 140. After one day Nepali currency is revaluated by 5% and he exchanged the pounds which he had into Nepali currency again. What is his gain or loss? Find it.
13. The given figure is combined solid made up of a cylinder and a cone. The diameter of the base of the object is 16 cm, length of the cylindrical part is 75 cm and the total length of the solid object is 90 cm. Find the total surface area of the combined solid.
14. Find the H.C.F of:
b2(b2+4bc+4c2), b5 + 8b2c3 and 3b4 + b 3c - 10b2c2
15. Simplify:
17. Construct a ΔMNQ equal in area to the quadrilateral MNOP having NO= OP= 5.5 cm, PM= 4.5 cm and MNO=75°.
18. Verify experimentally that the relationship between centre angle MAN and circumference angle MIN standing on the same arc NIN of the circle. (Two circles having radii at least 3 cm are necessary)
19. The angle of depression of the top of a tree as observed from the roof of a house 30 ft. high is found to be 30°. If the distance between the house and tree is 10√3 ft., find the height of the tree.
20. Calculate the median from the data given below.
Group 'D'
21. A person deposited Rs. 50,000 in bank ‘M' for two years at 10% 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.
22. Two pillars of height 8 feet each where its four faces are shown in the gate of a stadium have one-one pyramid of height 4 feet each having the same base on their tops. The base of each pillars is 6 ft x 6 ft. If the pillar with pyramid are painted at the rate of Rs. 60 per square feet, what will be the total cost? Find it.
23. The area of a rectangular field is 1440 sq. metre and perimeter is 152 metre. Out of length or breadth, which one is to be decreased by what percentage to make it a square? Find it.
24. Points S, O, M and I are concyclic such that arc SO = arc IM. If the chords SM and IO are intersected at the point K, prove that:
i.              Area of ΔSOK  = Area of ΔIMK.
ii.            SM=IO
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