PM: 40
Attempt all
the questions
Group –A 6×1=6
1. (a) The present population of a town is P. If
the population increases by R% every year, what will be the population of the
town after T years?
(b) What is
the area of the equilateral triangle whose each side is ‘2a’ cm?
2. (a)
Express 3√2 into pure surd.
3. (a) What is the relation between
the area of rectangle and parallelogram standing on same base and between same
parallels?
Group –B17×2=34
4. (a) A watch is bought at $30 and
sold it at £20. If $1 = Rs 89 and there was a profit of Rs 100. What was the
exchange rate of pound sterling with Nepali rupees?
(b) A machine which was bought two
years ago is sold for Rs 8,464 after depreciation at the rate of 8% per annum.
At what price was it bought?
5.
(a) The area of an isosceles triangle is 120 cm2 and its base
is 16 cm. find its equal sides.
(b) A bowl in the form of hemisphere
has capacity of 2425.50 ml. Find its radius.
(c) Calculate lateral surface area of
the given prism.
6. (a) Find the LCM of : x3
–xy2 and x3- 2x2y +xy2
(B) Simplify:
7. (a) simplify: 3x+2 + 3x
-28=0
:
(c) The sum of two consecutive even numbers is
38. Find their difference.
8. (a) In the given figure. AB
EC,
ADBC
and M is the mid-point of AE. If the area of ∆EMB is 12 cm2, find
the area of parallelogram ABCD.
EC,
ADBC
and M is the mid-point of AE. If the area of ∆EMB is 12 cm2, find
the area of parallelogram ABCD.
(b) In the given figure, O is the
centre of the circle. AED is a straight line and AB is a diameter of circle if
ADB=650,
find the value of COE.
ADB=650,
find the value of COE.
(c) In the given figure, O is the
centre of the circle. PQ is tangent and P is the point of contact. If OP=3 cm,
QP = 4 cm. Find the length of QR.
9. (a) In the given 
, AC =4cm , BC=7cm , CAB=1100and
ABC=400.
Find the area of.
, AC =4cm , BC=7cm , CAB=1100and
ABC=400.
Find the area of.
(b) In a continuous series, mean 
= 40, 
and
calculate the value of a.
= 40, and
calculate the value of a.
10. (a) A card is drawn randomly from
a pack of number of cards, numbered from 3 to 32 find the probability that the
card is multiple of 5 or 7.
(b) A box contains 5 red, 4 green and
3 blue balls. A ball is drawn randomly (without replacement) and another ball
is drawn randomly. By drawing a tree-diagram, show all the probabilities of
possible outcomes.
Group – C 10×4=40
11.
In a group of 95 students, the ratio of students who like mathematics
and science is 4:5. If 10 of them like both subjects and 15 of them like none
of the subjects then by drawing a Venn-diagram find how many of them like only
one subject.
12. The sum of simple interest and
compound interest on a sum of money at the rate of 10% per annum after 3 years
is Rs 504.80. Find the principal.
13.
Find the total surface area of given combined solid.
14.
Find the HCF of: a4 + a2 + 1, a3+1 and
a3 – a2 + a
15.
Simplify: 
+ 
+ 
+ +
16.
“O ‘is the centre of a circle and AB is an arc. If P and Q are any point
on the circumference of the circle in the major arc AB. Prove that: APB=AQB.
APB=AQB.
17.
Verify experimentally that the opposite angles of a cyclic quadrilateral
PQRS are supplementary. (Two circles of radiinot less than 3cm are necessary).
18.
Construct a rectangle having equal area to the parallelogram ABCD having
AB=6cm,BC =7.5cm and ABC
=60o.
ABC
=60o.
19.
The angle of elevation from the roof of a house to the top of a tree is
found to be 30o.If the height of the house and tree are 8m and 20m
respectively, find the distance between the house and the tree.
20.
Find third quartile (Q3) from the following data.
Marks obtained
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
No of students
|
3
|
7
|
15
|
10
|
5
|
Group-D 4×5=20
21.
Pujan paid Rs 15,255 for a smart phone with 10% discount and 13% VAT.
Find the marked price of that smart phone. Also, find by what percent VAT
amount is more than discount amount?
22. In a rice-feeding ceremony of Raju’s
son Marwin he has to make an arrangement for accommodation of 25 persons.For
this purpose he plans to build a square based pyramid shaped tent in such a way
that each person has 4 m2 of the surface on ground and 96m3
of air to breath. What should be the height of the tent? Also find total cost
of clothes required to make the tent at the rate of Rs40 per m2?
23.
The length of hypotenuse of a right angled triangle exceeds the length
of the base by 2cm and exceeds twice the length of altitude by 1cm. Find the
area of the triangle.
24.
ABCD is a parallelogram and P is any Point within it. Prove that the sum
of the area of the triangles PAD and PBC is equal to half of the area of
parallelogram.
 The present population of a town is P...){kind=link}
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