C. Mathematics
1. In a survey of 400 tourists, it is found that
the ratio of the tourists who visited Pokhara to Lumbini was 2:3, 120 of them
visited both places and 60 of them didn’t visit any of the two places.
a.
Represent the above the information in a
Venn-diagram.[1]
b.
Find the number of tourists who visited only one
place.[3]
c.
Find the number of tourists who visited at least
one place.[1]
d.
Find the number of tourists who visited at most
one place.[1]
Answer:
2. Chandra deposited Rs.2, 00,000 in a bank for 2
years at the rate of 10% annual compound interest. But after one year, the bank
has changed the policy & decided to pay semiannual compound interest at the
same rate.
a.
What is the relation between principal, interest
and amount?[1]
b.
Find the interest of first year. [2]
c.
Find the interest for second year.[2]
Answer:
2a. CA = P+I
3. The population of a town increases every year by
10%. At the end of two years, the total population of the town became 30,000.
In this population, 5800 people are also added who were migrated from other
places.
a.
How is the population growth rate related to
birth rate & death rate?[1]
b.
What was the initial population of the town?[2]
c.
How much will be the population of the town
after 1 year?[1]
Answer:
4. Raju exchanges some Nepali rupees into American
dollars at the rate of $1=NRs. 132. After 5 days Nepali currency is devaluated
by 10% in comparison to US dollars & he exchange those dollars into Nepali
rupees bearing a loss of Rs.1, 32,000.
a.
Find the new exchange rate.[1]
b.
How much Nepali currency was exchanged into US
dollars by Raju in the beginning? [2]
c.
If Nepali currency was devaluated instead of
revaluation, what would be the new exchange rate? [1]
Answer:
5. Sophiya has a pot in the shape of a square based pyramid, in which she has filled water. The height of the pot is 25cm &length of the side of the base is 30cm.
a. Which formula is used for finding volume of given pyramid? [1]
i. V = (1/3) πr2 h ii. V = (1/3) a2 h iii. V = l*b*h iv. V = (4/3) πr3 h
b.
Find the volume of the pot.[2]
c.
How much water does the pot contain?[1]
Answer:
6. In
the alongside figure, AB=29cm & OB=20cm.
a.
Find the height of hemisphere. [1]
b.
Find the surface area of the solid. [2]
c. Find the cost of silver plating the surface of the solid at the rate of 50 Paisa per sq.cm. [1]
Answer:
7. In
the gate of a house, there are two pillars of height 6 ft. On the top of each
pillar a pyramid of height 1 ft. is made. The base of each pillar is a square
of side 1 ft.
a.
Draw one figure according to given to given
information & find the slant height of the pyramid. [2]
b.
Find the surface area of both pillars & find
the cost of painting at Rs. 20 sq.ft [3]
Answer:
8. In
a geometric series, the second term is 24 & the fifth term is 81.
a.
Write the formula to find the general term of
G.S. [1]
b.
Find the common ratio of the series. [2]
c.
Find the sum of first five terms of the series.
[2]
Answer:
10. When
a group of people went for a picnic, the total bus fare was Rs. 1800 which was
to be paid by equally by them. If there were 6 people more the bus fare for
each would be Rs.50 less.
a.
Write the above statement into mathematical
equation. [1]
b. Find the number of people & the bus fare of each people .[2]
c. If the number of people is half of the original number, how much more fare each would have to pay? Find in percent. [2]
Answer:
10 a. Simplify : [2]
10 b. Solve: [3]
Answer:
11. In the given figure, ABCD & EFGC are two parallelograms.
a. Write the relation between the area of a triangle & a parallelogram standing on same base & between same parallel lines? [1]
b. Prove that the Ar. ABCD & EFGC are equal. [2]
c. What will be the area of parallelogram ABCD, each side of ABEC formed by joining BE is 10 cm? [2]
Answer:
12 . In the adjoining figure, O is the center of the circle angles PRT & PST are drawn on the same arc.
a. What is the relation of ∡ PRT & ∡ PST?[1]
b. By making two different figures with different radii not less than 3 cm, examine the relation of ∡ PRT & ∡ PST experimentally. [2]
c. If the measurement of ∡ POT is (3X+70) &∡ PRT is (X+45), find the value of ∡ PST. [2]
Answer:
13. A square PQRS is given
a. Write the ration of angles & sides of a square. [1]
b. Construct a square PQRS with PQ = 5cm. Also construct a triangle SPX equal in area to the square PQRS. [3]
Answer:
14. The
distance between a tower & a house is one third of the height of the tower.
The distance between the tower & the house is 20m & the angle of
depression of the root of the house from the top of the tower is 30
.
a.
What type of angle is called angle of
depression?[1]
b.
Show the above relation in figure. [1]
c.
Find the height of the house. [1]
d.
If the angle of depression was 45 , what would be the height of the house? [1]
Answer:
15. Study
the data
|
Marks
Obtained |
0-10 |
0-20 |
0-30 |
0-40 |
0-50 |
|
No.
of Studs. |
4 |
12 |
24 |
44 |
62 |
a.
What type of data is this? [1]
b.
Write formula of finding median of the
data. [1]
c.
Find the median of the data. [2]
d.
Find the mean of the data. [2]
Answer:
16. A box contains 2 white, 3 red & 5 black balls of same type & size. From
the box, one ball is drawn then without replacing it another ball is drawn.
a.
Show the above events in a tree diagram.
[1]
b.
Find the probability of getting both
balls of the same colour. [1]
c.
Find the probability of getting both
white balls. [1]
d.
If the first balls is replaced & the
second ball is drawn, what is the probability of getting both red balls?
[1]
Answer:
1.In a survey of 200
game lovers, it was found that 130 liked football 90n liked cricket and 20 did
not like both of them.
a. How many sets are
related to the above information?
b. Represent the above
information in venn diagram.
c. Find the number of people
who like both
d. Compare the number
of people who like both and only one game.
Answer:
1. 
2. Rs 1200 is
deposited in a bank for 1 year at 10% p.a
a. Write the formula
for finding compound interest.
b. What is the
compound interest of the same sum compound half yearly?
c. How many copies
costing rs 41 per copy can be purchased by the obtained interest?
Answer:
3. Answer the
following
a. What is Vo in the
formula Vt = V0(1-R/100) t?
b. What is the growth
rate 5% In how many years the population of a town reach to 44100 from 40000?
c. The value of the
machine depreciates at the rate of 10% pea What will be the value of machine
after 1 year if the present value is Rs 300000?
Answer:
3.a. Vo = Initial value
b. Vt = V0 [(1+R/100)T]
= 2 years
c. Vt = V0 [(1+R/100)T] = 270000
4. In Jetha 15 2080
105 dollar is exchange to Nrs 130 & 1 pound is equal to Rs 160
a. Which organization
issue the money exchange rate in Nepal?
b. Which suitcase is
expensive in Nepal by what amount of two costing 24 dollar and 20 pound in
Nepal?
c. How many dollars is
paid for a cap costing Nrs. 650?
Answer:
4. a. Nepal Rastra Bank
b. here cost of suit case costing $24 in Nrs. = Rs. 3120
here cost of suit case costing £ in Nrs. = Rs. 3200
cost of the suit case is expensive by Rs 80
c. cost of a cap = 650/130 = $5
5. A tent is formed by
a cylinder and a cone whose diameter of the base is 8 m height of the
cylindrical part is 6m and the total height is 9m.
a. To find CSA of the tent
which one of the following is used?
i. πrl+2πrh ii. 2 πrl+ πr2
Answer:
5. a. 2πrh + πrl
b. CSA of a solid = 2πrh + πrl
= 213.71 cm3
c. Base area = πr2 =50.29cm2
6. An umbrella is made
by stitching 8 triangular pieces of cloth. The sides of each triangle piece of
cloth are 50cm, 50cm, and 60cm respectively
a. Find the area of
each triangular piece of cloth.
b. How much money is
required to make the umbrella if the cost of the cloth is 20 paisa per sqm.
Answer:
7. a.Write the formula
for sum of geometric series.
b. Find the arithmetic
mean between 35 and 65.
c. Find the sum of
geometric series 3+9+27+…….+729
Answer:
Answer:
9.a. Rs 250 is divided
equally among a certain number of students if there are 25 student s more each
would have received 50 paisa each less.
a. Write the equation
in standard form.
c. Find the total
number of students.
Answer:
9. a let the no of student be x
250/x – 50/100 = 250/ x+25
b. x2 + 25x -12500=0
c. not possible
10. a Simplify
1/1-x+x2 –
1/1-x+x2 – 2x/ 1+x2+x4
b. Solve
52x- 6*5x+1
+125 =0
Answer:
Answer:
Answer:
13. a. Construct a
parallelogram WXYZ in which WX = 5cm XY=4cm and angleWXY =750
b. Construct a
traingleVEW with VW =6 cm and equal in area to the parallelogram WXYZ.
c. How does the area
of parallelogram WXYZ and triangleVEW equal ? Give reason
Answer:
14. A tree is 18m high
which is broken by wind so that its top touches the ground and makes an angle
300 with the ground
a. Represent the above
information in diagram .
b. Find the length of
broken part.
c. Find the height of
remaining part.
d. If the broken part
and remaining part are equal what will be the angle made by the ground?
Answer:
15. Study the data and
answer the following
|
30-40 |
40-50 |
50-60 |
60-70 |
70-80 |
|
4 |
16 |
10 |
14 |
6 |
Marks obtained
No of stds
a. What type of data is given?
b. Find the first quartile.
c. Construct CF table of the data.
d. IN which class interval does the mode lie?
Answer:
16. From the deck of
cards are drawn one after another without replacement
a. Draw a tree diagram
to show all the possibilities of getting
or not getting spade cards.
b. Find the
probability of getting both face card
and both ace cards.
c. Compare the
probability of getting both face and both ace cards.
Answer:
1) In a class of 65 students, the number
of students who like coke is three times the number of students who like Pepsi.
12 students like both of them and 5 like none.
a. Illustrate the above information in a
Venn-diagram.[1]
b. Find the no. of students who like at
least one drink.[1]
c. Find the number of students who like
coke only.[3]
d. Find the ratio of students who like
coke & both of drinks.[1]
Answer:
2) The population of a city is 10000.
Every year, the birth rate & death of people in the city are 5% & 3%
respectively.
a. What is the population growth
rate?[1]
b. What will be the population of the
city after 2 years?[1]
c. At the end of 2 years, if 204 people
will migrate to other places, then what will be the population of the city at
the end of 3 years?[2]
Answer:
3) The population of a city is 10000.
Every year, the birth rate & death of people in the city are 5% & 3%
respectively.
a. What is the population growth
rate?[1]
b. What will be the population of the
city after 2 years?[1]
c. At the end of 2 years, if 204 people
will migrate to other places, then what will be the population of the city at
the end of 3 years?[2]
Answer:
4) Ramesh returned from Saudi Arab to
Nepal with SAR 10000. He exchanged SAR to Nepali with 2% commission. (1
SAR=Rs.34.89). He bought motorcycle using this money. After 2 years he sold his
motorcycle with 10% p.a. compound depreciation.
a. How much commission would he need to
pay?[1]
b. How much Nepali currency would he get
after commission.[1]
c. What is the value of motorcycle after
2years?[2]
d. What percent of investment did he get
back after 2 years.[1]
Answer:
5) 
In the adjoining figure, the diameter
of the cylinder is 6cm & length is 40cm. The
length of the whole solid is 44cm
a. Find the total surface area of the
object.[2]
b. Find the volume of the object.[2]
Answer:
6) A girl plans to construct a temporary
tunnel in the shape of square pyramid by using plywood. She needs the height of
the tunnel 4m and length of side on ground 6m.
a. Write the relation between height slant
height & base of pyramid.[1]
b. Find the L.S.A. of the tunnel.[2]
c. How much quantity of air is contained
in it?[1]
Answer:
7)
The given shape PQRS is the open
ground.
a. Find the perimeter of the ground.[1]
b. If the ground if around by fence 5
times, how long fence
is needed.[1]
c. The cost of the fence is Rs.50 per m. & a labor takes Rs.1450 per day. If the work is completed in 4 days, find the total cost for it.[3]
Answer:
8)
There
are n arithmetic means between 12 & 84 such that first mean: Last mean =
5:19.
a. Find the common difference.[2]
b. Find the value of n.[1]
c. Find the sum of first seven terms of
the series.[2]
Answer:
9)
The
present ages of father & his son are 40 years & 5years & 8years
respectively x years ago, the product of their ages was 105.
a. Express the given condition in
mathematical order.[1]
b. Find the value of x.[3]
c. Find the sum of their ages after five
years.[1]
Answer:
Answer:
11)
In the adjoining figure, ABCD is a //gm.
a. If the area of triangle ABQ is 30cm2.
What is the area of //gm ABCD?[1]
b. Prove that: ΔAPQ = ΔPCD
[2]
c. In trapezium ABCD, AD=10cm, AB=18cm,DC=12cm, DC//AB &
BC AD,
Calculate the area of ΔBDC. [1]
Answer:
12)
a. O
is the center of the circle given in the diagram. If OPQR is a //gm, find
the value of ∡OPQ.[1]
b. Write the relation two are made by two parallel
chord.[1]
c. Experimentally verify the relation between center angle & circumference
angle
standing on same arc.[2]
Answer:
13)
a. Construct a
triangle ABC having sides a=6.4cm, b=6cm, & c=5.6. Also construct a
parallelogram inside the triangle having one side 7cm & equal in area to ΔABC.[2]
b. Prove the area of triangle is half of the area of
parallelogram standing on same base &between same parallel lines.
Answer:
14) A pillar of 60 high was fixed in the center of a circular
meadow. The angle of education of its top was found to be 30o , when observed from a point of the
circumference.
a) Find the diameter of the meadow.[2]
b) Find the circumference of the
meadow.[1]
c) If the height of the pole is 180m,
what is the angle of elevation.[1]
Answer:
Answer:
16) Two cards are drawn from a well
shuffled pack of 52 cards without replacement.
a. If A&B are non-mutually exclusive
events, find formula to calculate p(AUB).[1]
b. Find the probability of getting both
black cards.[1]
c. Show the result of getting with king
& without king in tree diagram.[2]
d. If two cards are replaced one after
another, what is the ratio of the probability of getting both Aces & that
of getting both face cards.[1]
Answer:
