Attempt
all the questions compulsorily:
1. In a
group of 150 people, 120 like to play volleyball, 85 like to play football and
25 like to play none of the games.
a. If F
and V denote the set of people who likes to play football and volleyball
respectively, write the cardinality of
b. Show
the above information in Venn – diagram. (1)
c. How
many people like to play volleyball only. (3)
d. Prove
that the percentage of people who like to play football only is 12.5 % of the
people like to play volleyball only. (1)
2.
In a group of
students, 45 read Nepali, 40 read mathematics, and 35 read Science, 20 read
Nepali and Mathematics, 10 read Mathematics and Science, 15 read Science and
Nepali. 5 read all three subjects and 20 don’t read all three subjects.
a. Find
the number of students who read at least one subject. (1)
b. Find
the total number of students. (1)
c. Find
the number of students who read Mathematics and
Science
only. (3)
d. What
is the total number of students if 10 people don’t read all three subjects? (1)
3. Krishna
borrowed Rs 50,000 from Radha at the rate of 10 % p.a. At the end of 1 year.
a. The
annual compound amount on a sum P in T years at R % p. a. is CA respectively.
Write down the relation between, P, T, R, and CA. (1)
b. How
much semi – annual compound interest has to be paid? (1)
c. Find
the difference between semi – annual and quarterly compound interest. (2)
d. Which
interest system is good for lending money? Give reason. (1)
4. The
population of a village is 20,000. The population increases by 2 % annually in
the village.
a. If
the initial population is P, growth rate is R % per annum and population after
T years is PT, then write the formula to find PT. (1)
b. After
how many years the population of the village will be 20,808? (2)
c. If
the population of the village increases at the rate of 3 % p.a., by what number
will the population of the village be increased in 2 years? (2)
5. The
initial price of a machine was Rs 8,00,000. If the price of the machine in the
first year increased by 10 % and then depreciated in the following years by 4 %
and 5 % respectively.
a. Which
formula is used to calculate the price after increment? (1)
b. Find
the price of the machine at the end of first year. (1)
c. Find
the price of the machine at the end of the second year. (1)
d. If
the machine was sold at the end of the third year, what is the profit or loss? (1)
6.
|
|
|
3 m |
A
temple resembles the combined solid made up of a prism and a square based
pyramid.a. What
is the formula to calculate the area of the
base
of the temple? (1)
b. Find
the volume of the pyramidal part. (1)
c. How
much space in the air is occupied by the temple? (2)
7. A
carpenter made a wooden square – based pyramid having slant height 10 cm and vertical height 8 cm.
a. How
many faces are there in a square – based pyramid. (1)
b. Find
the length of the base side. (1)
c. Find
the total surface area of the pyramid. (2)
8. There
are 20 terms in an arithmetic series. If the sum of the first 3 terms of the
arithmetic series is 42 and that of the first 5 terms is 80,
a. Find
the common difference of the series. (2)
b. Compute
the first term of the series. (1)
c. Calculate
the 20th term of the series. (2)
9. A
metallic solid made up of cylinder and cone is shown in the figure. The radii
of the base of the cone and cylinder is 7 cm each. The height of the cylinder
is 40 cm and the height of the cone is 24 cm.
a.
|
24 cm |
If
the radius of the base and slant height of the cone are given, then write the
formula to find the curved surface area of the cone. (1)b. Find
the volume of the object. (2)
c. Compare
the volume of the cylindrical part and the volume of conical part. (1)
10. The
total height of a toy made up of cone and hemisphere is 42 cm. If the diameter
of the toy is also 42 cm, then answer the following questions.
a. Find
the volume of the toy. (3)
b. If
the surface of the toy is colored at the rate of 50 paisa per cm2,
find the total cost. (2)
11. Answer
the following questions:
a. What
value of y makes the expression
b. Simplify:
12. Answer
the following questions:
a. If ax
+ 1 = a1 + y, then write the relation between x and y.(1)
b. Prove
that the value of x obtained by solving 4 X 3x + 1 – 9x =
27 also satisfy the equation 32x – 4 X 3x + 1 + 27 = 0. (3)
|
A E D |
|
B C |
13. Parallelograms
EBCD and triangle ABC are on the same base BC and between the same parallels AD
and BC.
a. Write
the relation between ∠ AEB
and ∠ ADC with reason. (1)
b. Prove
that the area of parallelograms EBCD is twice the area of △ ABC. (2)
14.
|
P |
|
Q |
|
R |
|
S |
a. Write
the relation between
b. Find
the value of x when
c. Prove
experimentally that
15. The
given data shows the marks obtained by students in an examination of
mathematics out of 100 marks are given below.
|
Marks |
0 – 20 |
20 – 40 |
40 – 60 |
60 – 80 |
80 - 100 |
|
No. of students |
2 |
5 |
4 |
6 |
3 |
a. Write
the formula to find the third quartile of a continuous data. (1)
b. Find
the median. (2)
c. Find
the modal class. (1)
d. If
the marks obtained is converted to 50 full marks, then what will be the new
average. (2)
16. A box contains 5 white and 4 red balls of same
shape and size.
a. Define
the multiplication law of probability. (1)
b. Two
balls are drawn randomly one after another from the box without replacement.
Show the probability of all the possible outcomes in a tree diagram. (2)
c. Find
the probability of first ball white second ball red. (1)
d. If
two white balls are added in the box and two balls are drawn randomly without
replacement, what will be the probability of getting the first ball white and
second ball red? (1)
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