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1 2
0
20
60
80
100
20X
Y
40
120
40 60 80 100 120 140
140
160
SET ISET ISET ISET I
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :1
1 a
x y +1
1 a
y x [Ans: 1]
(b) Evaluate :5
1024 [Ans: 2]
2. (a) Solve :1
3
2x 3
= 2 [Ans:25
16]
(b) The product of the ages of a man 10 years before and
10 years hence is 300. Find his present age. [Ans: 20]
3. (a) x 1, 2x + 1, x + 5 and 3x + 1 are in ascending order. If
its median is 18, find the value of x. [Ans: 10]
(b) Construct a cumulative frequency table represented by
the given ogive.
[Ans:
C.I. f
0 20 0
20 40 10
40 60 20
60 80 30
80 100 50
100 120
10
4. (a) A number card is drawn at random from a group of
number cards numbered from 2 to 13. Find the
probability of getting a prime numbered or even
numbered card. [Ans: 11/22]
(b) Three children are born in a family. Calculate the
probability of getting exactly two sons by drawing a
tree diagram. [Ans:
3
8]
5. (a) The area of the given parallelogram is
14 cm2. If SR = 4 cm, QR = 7cm, find
the value of QRS. [Ans : 30]
(b) Find the lateral surface area of the
given prism [Ans: 140 cm2]
6. (a) The radius and height of a right circular cone are in the
ratio 5 : 12 and its volume is 2512 cm3. Find the radius
of its base. [Ans: 10cm]
(b) Find the circumference of the sphere whose volume is1375
21 cm
3.
Ans:110
7cm
7. (a) A milkman bought 100 l of milk for Rs. 1500. 51
2 lof
milk was lost by leakage. If he sold the remaining milkfor Rs. 18 per litre, what was his gain or loss
percentage? [Ans: 13.4 %]
(b) Find the compound interest on Rs. 11250 for 3 years if
the rates of interest for the first, second and third year
are 4%, 5% and 6% respectively. [Ans: Rs. 1772.10]
8. (a) In the given figure if the areaof PQT is 50 cm
2. Find the
area of PRS. [Ans: 50 cm2]
Q R
SP
10 cm
4 cm6 cm
P Q
TSR
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3 4
(b) Find the value of x:
[Ans: 125]
9. (a) In the adjoining figure, O is the centre of
the circle. OPQ = 50. Calculate the
value of x and y. [Ans: x = 100, y =
130]
(b) In the adjoining figure, Aand B are the points of
contact of the tangents TA
and TB. O is the centre of
the circle and ATB =
50. Calculate the value of x. [Ans: 65]
Group 'B' [16 4 = 64]
10. In a survey of a group of 120 people, 90 use Everest
toothpaste, 72 use brighter toothpaste and 10 use neither of
the past.
(i) Construct a Venn-diagram to illustrate the above
information.(ii) How many people use both the toothpaste?
(iii) How many people use Everest toothpaste only?
(iv) How many people use exactly one toothpaste?
[Ans: 52, 38, 58]
11. Find the H.C.F. of
2x3 16, x
2 4x + 4, x
3 3x
2+ 2x [Ans: x 2]
12. Solve: 5x 5
+ 54 x
= 115 [Ans: 4,5]
13. Simplify :1
a b +
1
a + b +
2a
a2+ b
2 +4a
3
a4+ b
4 [Ans:8a
7
a8 b
8]
14. The sum of the digits of a two digit number is 6. If 18 issubtracted from the number, the digits in the number are
reversed, find the number.
[Ans: 42]
15. Calculate the lower quartile (Q1) from the following data
[Ans: 41.67]
Marks 20-40 40- 60-
80
80-100
No of
students
8 12 10 6
16. The angle of elevation from the roof of a house to the top of
a tree is found to be 45 . If the heights of the house and tree
are 12 m and 25m respectively, find the distance between
the house and the tree. [Ans:13m]
17. Find the total surface area and
volume of the given solidobject.
[Ans:6006cm2, 1950.67cm
3]
18. In the given figure, the total surface area
of the given square based pyramid is
384cm2
and the side of the square base is12 cm, find the slant height of the
pyramid . [Ans: 10 cm]
19. Santosh and Mandip can reap a field in 10 days . Mandip
and Roshan can reap a field in 12 days. Roshan and Santosh
can reap the same field in 15 days.
(i) In how many days will they complete to reap the field
if all of them reap together?
B
OxQ
A
T50
A
A'
O P24cm
12 cm
P
D
A B
C
x
35O
B
C
A
D
PQ
R
S
x yO
50
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5 6
0
51015
2025
3035
1020 30 40 506070
Class Interval
Y
X
40
(ii) How many days will each of them take to reap the field
completely ?[Ans; (i) 8days, (ii) 24 days, 171
7days , (iii) 40 days]
20. A merchant sells his goods marketing them 25% above the
cost price.
If he allows a discount of 12% on selling the goods, whatpercent profit does he make? [Ans:10%]
21. A person borrows Rs.10,000 for 1 year and 6 months at
10% p.a. compound interest payable yearly. But he
immediately lends the sum for the same time and same rate
of compound interest payable half yearly, How much does
he gain in his transaction? [Ans: Rs.781.25]22 Prove that the triangles standing on the same base and
between the same parallels are equal in area.
23. In the given figure ABCD is a square and AE
= AF Prove that BD // EF
24. Verify experimentally that the angle in the same segment ofa circle are equal. ( Two different figures are necessary but
the radii of the circles must not be less than 3 cm)
25. Construct a triangle equal in area to the quadrilateral ABCDin which AB = 5cm, BC = 4.5cm, CD = 3.4cm, AD =
4.2cm, and diagonal AC = 6cm.
SET ISET ISET ISET IIIII
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify: {(x-y)-3
}-n
{(x+y)n}
3
[Ans: (x2
- y2
)3n
]
(b) Evaluate:3
a6b
2c
3
4a
-8b
-8c
4 [Ans: a
5b
4/3]
2. (a) x+5 = x +1 [Ans: 4]
(b) The product of two positive numbers which are in the
ratio 2:3 is 96. Find the numbers. [Ams: 8 & 12]
3 (a) If x=50 and fx = 750, find the value of f. [Ans:15]
(b) Write down the frequency table corresponding to thealong side of frequency curve.
[Ans:
c.f. f
20 40 5
30 40 5
40 50 10
50 60 7
60 70 8
4. (a) A coin is tossed and a dice is rolled. Find the
probability of getting a head on the coin and a number
less than 3 on the dice. [Ans:
1
6]
(b) A bag contains 1 red ball, 1 white ball and 1 blue ball.
Two balls are drawn one after the other without
replacement. Show all the possible outcomes and
corresponding probabilities in a tree diagram.
5. (a) Calculate the area of parallelogram PQRS if PS = 3 2
cm, SR = 8 cm and PQR = 45. [Ans: 24 cm2]
BE
C
F
DA
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7 8
(b) The area of a parallelogram is 48 cm2. If the two
adjacent sides are 8cm and 6 cm, find the length of its
diagonal. [Ans: 10cm]
6. (a) The surface area of a marble is 2 cm2. What will be
the difference in the area if the radius is made
2
3 of its
original size? [Ans:10
9cm
2]
(b) The volume of a rectangular pyramid is 210 cm3. If the
area of its rectangular base is 105 cm2, find the height
of the pyramid.
[Ans: 6 cm]
7. (a) A fruit seller bought a basket containing 1 grossoranges for Rs. 432. But 14 oranges were rotten. He
then sold the good oranges for Rs. 3.50 per orange.
Find his profit or loss. [Ans: Rs. 23]
(b) In what time will the compound interest compounded
semi-annually on Rs. 4000 at 5% p.a. be Rs. 202.50?
[Ans: 1 year]
8. (a) ABCD is a square. If the diagonal BD = 3 3 cm, findthe area of ABCD. [Ans: 9 cm
2]
(b) Find the values of x and y [Ans: x = 35,
y = 55]
9. (a) In the adjoining figure, PQ is thediameter of the circle with centre O. If
ROS = 42, find the value of RTS.
[Ans:69]
(b) Find the values of x and y from the
given figure, where O is the centre ofthe circle and TAN is the tangent at
the point A. AP is the bisector of
OAN. [Ans: x = 90, y = 45]
Group 'B' [16 4 = 64]
10. In a class of 50 students, 25 students like to play football,
35 like to play cricket and 15 like to play both the games.
How many students donot like to play any games? Show the
above information in a Venn-diagram. [Ans: 5]
11. Find the L.C.M. of
8x3 + 1, 8x
4 x, 16x
4 + 4x
2+ 1 [Ans: x(8x
3 1) (8x
3 + 1)]
12. Solve: xx+
108
xx = 31 [Ans: 2,3]
13. Simplify :
1 + x
1 x +
1 x
1 + x +
4x
1 + x2 +
8x3
1 x4
Ans:
2(1 + x)
1 x
14. 6 years ago, Ram was six times his son, 4 years hence,
thrice his age will be equal to eight time his son's age. What
are their present ages?
[Ans: 36 yrs, 11 yrs]
15. Calculate the upper quartile (Q3) from the given data [Ans: 61.43]
Marks
obtained
20
30
50 60 30
40
60
70
40 -50 70
80
No. of
students
5 10 6 7 8 4
16. A tree of 14m height is broken by the wind so that its toptouches the ground and makes an angle of 60 with the
ground. Find the length of the broken part of the tree.[Ans: 7.50 m]
17. Find the slant height of the cone if the
volume of the given solid is660
7cm
3.
[Ans: 5 cm]
18. Given figure is a square pyramid is which
vertical height is 8 cm and length of base side
x
O
y70
A
B C
42
R T
S
Q
O
P
Ox y
AT N
P
B
C
O A3cm
12cm
12cm
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9 10
is 12cm. Find its total surface area and volume. [Ans: 384
cm2, 1152 cm
3]
19. Deekshyanta can do2
5 part of a work in 9 days. He calls
Samir to finish the remaining work. They work together and
finish it in 6 days. How many days will be taken by Samirto finish the work alone? [Ans: 18 days]
20. The marked price of an article is 25% above its selling price
and the cost price is 30% less than its marked price. Find
the discount percent and gain percent. [Ans: 20%, 142
7%]
21. In what time will a sum of Rs. 1280 at 121
2 % p.a.
compounded annually amount to Rs. 1620? [Ans: 2 years]
22. In the given figure, P is the mid point of
RC. Prove that area of RBC = area of
//gm ABCD.
23. Prove that a parallelogram inscribed in a circle is a
rectangle.
24. Verify experimentally that the angles in the conjugatesegments are supplementary, (Two different figures are
necessary but the radii of the circles must not be less than3cm)
25. Construct a triangle ABC in which BC = 7 cm, ABC =
45 and AC = 8.5 cm. Also construct a triangle equal in
area to the given ABC.
SET IIISET IIISET IIISET III
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :12
1
4
1
+ 3
1 [Ans: 1/7]
(b) Evaluate:(343)
2/3
5
(32)3
[Ans:1
112]
2. (a) Solve:4
6x + 5 =4
x + 30 [Ans: 5]
(b) The difference of the square of a number and 23 is 2.
FInd the number . [Ans: 5]
3. (a) The average temperature from Sunday to Friday is
28C and that of Sunday to Saturday is 30C. Find the
temperature on Saturday.
[Ans: 42 C]
(b) From the ogive given
alongside, find the median. [Ans: 55]
4. (a) The probability of solving a mathematical problem by
two students A and B is1
2 and
1
5 respectively. If the
problem is given to both the students find theprobability of the problem being solved.
[Ans:3
5]
(b) There are 30 students in a class of which2
3 are boys.
Three students are chosen from the class at random, one
after the other. Draw the probability tree diagram and
B C
DPA
R
0
510152025
3035
50 545862
Height (inch)
Y
X
40
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11 12
find the probability that there will be at least two boys
selected. [Ans:152
203]
5. (a) Find the area of the given
quadrilateral ABCD in which AB =
BC, AD = DC = 3cm, BD = 5cm andADB = 30. [Ans: 7.5 cm
2]
(b) Find the area of ABC in which AB = 105cm, BC =91cm and AC = 98 cm. [Ans: 4116 cm
3]
6. (a) A solid metallic sphere of radius 7cm is out into two
halves. Find the total surface area of each hemisphere
so formed [Ans: 462 cm2
](b) If the volume and height of a right circular cone are
1887 cm3and 37 cm respectively. Find the area of its
base. [Ans: 153 cm2]
7. (a) An electrician bought 50 balls at Rs. 15 per bulb. If 7
bulbs were defective and he has to make a profit of Rs.
67 on the total outlay, find the selling price of one bulb.[Ans: Rs. 19]
(b) Find the rate of compound interest when Rs. 5120amounts to Rs. 7290 in 1 year 6 months, if the interest
is compounded half yearly?
[Ans: 25 %]
8. (a) In adjoining figure NMRP is a
quadrilateral in which MN // PR.
NMR = PRM = 90, MR = 8cm
and PN = 10cm. Find the area of
quadrilateral NMRP.
[Ans: 120 cm2]
(b) Find the values of x and y: [Ans: x =
130, y = 115]
9. (a) If O is the centre of the circle, Calculate all the angle of
the rhombus OABC.
[Ans: A = C= 60, B = O = 120]
(b) PA and PB are the tangents from
an external point P to the circle
with centre at O. Calculate the
values of x and y if BAE =
106. [Ans: x = 32, y = 148]
Group 'B' [16 4 = 64]
10. In a class of 75 students, 28 like football but not cricket and
32 liked cricket but not football. If 7 students did not like
both games, find
(i) how many students liked both the games?(ii) how many students liked football?
(iii) how many students liked cricket?
(iv) illustrate the above information in Venn-diagram. [Ans: 8, 36, 40]
11. Find the H.C.F. of
2x3 5x
2+ 2x, 3x
3 8x
2+ 4x, 2x
4 16x [Ans: x(x 2)]
12. Solve:5x 1
5x + 1 = 1 +5x 1
2 [Ans:9
5]
13. Simplify:1
x 3
2
2x + 3 +
1
x + 3
2
2x 3[Ans:
54x
4x4+ 5x
2+ 81
]
14. A number of two digits is equal to four times the sum of its
digits. If 18 is added to the number, the digits are reserved.
Find the number.
[Ans: 24]
15. Compute the arithmetic mean of the following data:[Ans: 57.75]
A
D
C
B
N M
RP 18 cm
y
O
x
A
B
DC
65
OC
BA
y O
106A
E
Px
BD
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13 14
Marks
obtained
25
35
65 75 75
85
35
45
45
55
85
95
55
65
No. ofstudents
3 5 4 5 9 2 12
16. An observer finds an angle of depression of 60 when he
observes a car on the road from the roof of his house. If the
car is at a distance of 50m from the foot of the house, find
the height of the house. [Ans: 86.6m]
17. The volume of a cone is equal to the volume of cylinder
whose height is 9 cm and diameter 40cm. If the height of
the cone is 108 cm then find its radius of circular base.[Ans: 10cm]
18. Find the total surface area of the solidobject given in the figure. [Ans: 92.5m
2]
19. Praful can do as much work in 4 days as Safal can do it in 5
days. If they work together, they can finish it in 20 days.
What time will each take to finish the work? [Ans: 45 days, 36 days]20. If a tourist paid Rs. 5610 for a carved window made of
wood with a discount of 15% including 10% VAT, what is
the marked price of the window? [Ans: Rs. 6000]
21. Deepa has invested a certain sum of money at compound
interest added annually. She gets an interest of Rs. 225
added in her investment at the end of second year. Find the
sum invested and the rate of compound interest.[Ans: Rs. 3750, 6%]22. In the given figure, rectangle ABCD
and parallelogram EBCF are on the
same base BC and between the same
parallels AF and BC. Prove that
(i) ABE DCF
(ii) Area of the rectangle ABCD = Area of the
parallelogram EBCF.
23. In the given figure, CD is the
angular bisector of BDE of a
cyclic quad. ABCD. Prove that
ABC is an isosceles triangle.
24. Verify experimentally that the angle at the centre of a circle
is double of the angle at the circumference standing on the
ame arc (Two different figures are necessary but the radii of
the circles must not be less than 3cm)
25. Construct a trapezium ABCD in which AD//BC, AB = 4.6cm, BC = 2.5cm, DAB = 60 and BCD = 90. Also
construct a triangle equal in area to the trapezium.
2.5m
A D E F
CB
A
B C
D E
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15 16
SET IVSET IVSET IVSET IV
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :x
5m + 3n x
3m 2n
x
2m + n [Ans: x4n
]
(b) Evaluate:
20
a5
10
a51 5
a5 [Ans: 1]
2. (a) Solve:5
x + 9 = 1 [Ans: 8]
(b) If 11 is added to the square of a number the result is
47. Find the number. [Ans: 6]
3. (a) If the lower quartile class is 20 30, cumulative
frequency of pre-lower quartile class is 6, the frequency
of quartile class is 14 and the total number of data is 30
then find the value of lower quartile.
[Ans: 31.7]
(b) Find the value of p and q in the following table:
C.I. f c.f.
0 4 5 5
4 8 7 12
8 12 p 20
12 16 10 q
[Ans: p = 8, q = 30]
4. (a) Two coins are tossed at the same time. Find the
probability of getting the same event in both the toss.[Ans:1
2]
(b) There are 9 white and 11 black balls of the same shape
and size in a bag. If two balls are drawn randomly in
succession without replacement from the bag. Show the
probability of all the possible outcomes in a tree
diagram.
5. (a) In the given figure, find the length AB if
the area of ABC is 27 cm2
[Ans: 9 cm]
(b) Find the total surface area of the
given triangular prism. [Ans: 768
cm2]
6. (a) The height and radius of base of a
cylinder are in the ratio 3 : 1. If its volume is 1029
cm3, find its height. [Ans: 7 cm]
(b) Find the total surface area of the solid cone obtained by
revolving the given right angles ABC about BC. [Ans:
942 cm2]
7. (a) A watch is priced at Rs. 1530 including
121
2% VAT. Calculate the price of the
watch without VAT. [Ans: Rs. 1360]
(b) The share of a bank depreciates every year by 2.5%. If
the amount depreciation of the share this year is Rs. 15,
find the present value of the share. [Ans: Rs. 600]8. (a) The area of the rhombus ABCD is 36 cm
2 and the
diagonal AC = 8cm. Find the length of the diagonal
BD. [Ans: 9 cm]
(b) O is the centre of the circle. Find the
value of x if OBA = 35 [Ans: 55]
9. (a) Find the values of x and y if BC{=
CD{ and DCE = 90
[Ans: x = 42, y = 45]
12 cm30
A C
B
B C5 cm
A
x
35
O
AB
C
32
xy
60
T
PQ
C
30 cm
A
B C
D
E
x
48y
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17 18
(b) Find the value of x and y where O is the centre of the
circle and PQ is the tangent. [Ans: x = 62, y = 59]
Group 'B' [16 4 = 64]
10. In a group of 150 music lovers, it was found that 90 people
liked folk songs, 70 people liked modern songs and 30 didnot like both songs.
(i) How many liked both songs?
(ii) Show the above information in a Venn-diagram.[Ans: 40]
11. Find the H.C.F. and L.C.M. of M
(x3+ 1) (x 1) and (x
4+ x
2+ 1) (x
2 3x + 2)
[Ans: H.C.F. = (x 1) (x2 x + 1), L.C.M. =(x 2) (x
3+ 1) (x
3 1)]
12. Solve : x + 7 + x =28
x + 7 [Ans: 9]
13. Simplify :
1
1 + xb a
+ xc a+
1
1 + xc b
+ xa b+
1
1 + xa c
+ xb c[Ans: 1]
14. One year ago, the father was 8 times as old as his son. Now,
his age is equal to the square of his son's age, find their
present ages.
[Anrs: 49 yrs, 7 yrs]
15. If the mean of the data is 30.75, find the value of x. [Ans: 7]
Class 0-10 10 - 20 20 30
30 40
40 50
50 60
No. of
students
5 x 6 9 8 5
16. From the top of the 40m hight house, the angles of
depression to the two points on the same side of the house
observed are 60 and 45 respectively. Find the distance
between two points. [Ans: 16.9 m]
17. Find the surface area and volume of given
cylinder with a hemisphere at one end.[Ans: 555.5cm
2, 859.83 cm
3]
18. Find the total surface area and volume of
the given solid. [Ans: 289.98 cm2, 384cm
3]
19. 4 boys and 6 girls can do a piece of work in
5
2 days. 8 boys
and 3 girls can do the same work in 2 days. In how many
days will 1 boy and 1 girl do the work separately? [Ans: 20 days, 30 days]
20. The marked price of an electric heater is R. 3200. If the
shopkeeper allows a certain discount and a customer bought
it for Rs. 2640 including 10% VAT, what is the discount
percent? [Ans: 25%]
21. A man borrowed a sum of money and paid back in 2 yearsin two equal installments. If the rate of compound interest
was 4% p.a. and if he paid back Rs. 676 annually, what sum
did he borrow? [Ans: Rs. 1275]
22. In the given parallelogram ABCD, P
and Q are the mid points of AB and
AD respectively. Prove that area of fig.
PQDCB =7
8(area of //gm ABCD)
23. In the adjoining figure, O is the centre of
the circle and AB is a diameter. If arc BC
= arc CD, prove that AD // OC.
24. In the cyclic quadrilateral ABCD, Verify experimentally
that ABC + ADC = 180 and BAD + BCD = 180
A Q D
CB
P
OA B
CD
20 cm
6cm
4cm
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19 20
(Two different figures are necessary but the radii of the
circles must not be less than 3cm)
25. Construct a triangle ABC in which AB = 5.7 cm, BC =
5.3cm and CA = 6.2 cm. Also construct a parallelogram
equal in area to the ABC if one side of the parallelogram
is 7.5 cm.
SET VSET VSET VSET V
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :
6n + 2
+ 7 6n
6n + 1 8 5 6n [Ans: 1]
(b) Evaluate:4
128 a3
42
1a
9 [Ans: 4a
3]
2. (a) Solve: 5x 1 = 2 x + 3 [Ans: 13]
(b) Divide 81 into two parts whose product is 1260.[Ans: 60,21]
3. (a) The mean of a,b,c,d is 9 and the
mean of a,b,c,d,e, f is 12. Find
the mean of e and f.[Ans: 18]
(b) From the given ogive, find the
median [Ans: 12]
4. (a) What is the probability that a leap year will have 53
Tuesdays? [Ans:2
7]
(b) Two cards are drawn from a well-suffled deck of 52
cards. Drawing a tree diagram find the probability that
both the cards are knaves. [Ans:1
221]
5. (a) The area of ABC is 12 cm2. If AC = 6 cm and AB =
8cm, find the value of BAC. [Ans: 30]
(b) Find the volume of given prism.
[Ans: 124.70 cm3]
6. (a) Find the volume of the following
square based pyramid. [Ans: 384
cm3]
(b) The circumference of the base of a cylinder is 132 cm
and the area of its curved surface is 1584 cm2. Find its
height. [Ans: 12 cm]
7. (a) The VAT on a crarte of beer is Rs. 90. If VAT was
levied at 10%, find the cost of the crate of beer
including VAT. [Ans: Rs.990]
(b) Calculate the population of a town three years ago ifthe present population is 83,65,427 and the annual
growth rate is 10%.
[Ans: 62,85,069]
8. (a) In the given figure ABCD is asquare and EBCF is a
parallelogram. If AB = 4cm,calculate the area of parallelogram
EBCF. [Ans: 16 cm2]
(b) O is the centre of the circle and OA //
BC. If reflex AOC = 230, find thevalues of x and y. [Ans: x = y = 50]
Y
X4O 8 12 16 20
4
8
12
10
20
Marks obtained
12 cm
P
A B
CD
A D E F
CB
y
230O
A
B
C
x
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23 24
AF and BC. Prove that area of //gm ABCD = area of //gm
EBCF.
23. In a circle with centre O, chords ABand CD intersect outside the circle at
E. Prove that AOC BOD =
2AEC.
24. Verify experimentally that the inscribed angle is half of the
angle at the centre standing on the same arc. (Two different
figures are necessary but the radii of the circles must not beless than 3cm)
25. Construct a parallelogram ABCD with AB = 3.6 cm, A =
60 and AD = 4.4 cm. Also construct a triangle with one
side = 5.5 cm and making its area equal to the area of the
parallelogram.
SET VISET VISET VISET VI
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :(a b) (b2
a2
)
Ans:a + b
a2b
2
(b) Evaluate:
34 27
3 9
5
816 33
Ans:
1
81
2. (a) Solve: 2a + 1 + a = 5. [Ans: 4]
(b) 10 pencil and 2 eraser cost Rs. 40 and 25 pencils and 4
erasers cost Rs. 90. Find the cost of a pencil and an
eraser.
[Ans: Rs. 2 and Rs. 10]
3. (a) The mean of 6 observations is
48 but one of the data was
misread as 43 instead of 34, find the correct mean.[Ans: 46.50]
(b) From the given ogive, find the modal class. [Ans: 60
80]
4. (a) The odds in favour of an event is 2 : 3. Find theprobability of occurance of this event. [Ans: 2/5]
(b) A bag contains 5 blue and x yellow balls. A ball is
taken out and without replacing the first ball another
ball is taken out. Draw a probability tree diagram and
find the value of x, if the probability getting both
yellow balls is3
28 [Ans: 3]
5. (a) Find BAD of a rhombus ABCD with sides 12cm and
area 72 cm2 [Ans: 30]
(b) Find the volume of the givensolid. [Ans: 1400 cm
3]
6. (a) If the surface area of a marble is1
4 cm
2, find its
volume
Ans:1
482cm
3
(b) Find the curved surface area of the given
cone. [Ans: 137.5 cm2]
7. (a) Find the percentage discount if an article labelled at Rs.
4200 is sold for Rs. 3822. [Ans: 9%]
E D C
A
B O
Y
X20O 40 60 80 100
10
20
30
4050
Marks
16 cm
5cm
7cm
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25 26
(b) The population of a place was 2000. Within a year the
population increased 3% by brith rate and 2% by
migration. Find the present population. [Ans: 2100]
8. (a) In the figure alongside PQRS is a
parallelogram, PX and PY are the
altitudes. If QR = 12cm, SR =10cm and area of PQRS = 96
cm2, calculate PX and PY .[Ans:
9.6 cm, 8 cm]
(b) Find the values of a, b, and c. [Ans: a =
22, b = c = 68]
9. (a) In the given figure, if DAB =
80, EDF = 15 and DF //
BC, find the value of ABC.[Ans: 115]
b) Find the values of a, b and c.
[Ans: a = 65, b = 130, c = 25]
Group 'B' [16 4 = 64]
10. A college awarded 38 medals in football, 15 in basketball
and 20 in cricket. If these medals went to a total of 58 men
and only three men got medals in all three games, howmany received medals in exactly two of the three games. [Ans: 9]
11. Find the H.C.F. of:
8a3 27, 8a
3 18a and 16a
2 16a 12 [Ans: (2a 3)]
12. Solve :
x + 2 x 2
x + 2 + x 2 =
1
2
Ans:5
2
13. Simplify:
x + 3
x2+ 3x + 9
+x 3
x2 3x + 9
54
x4+ 9x
2+ 81
Ans:2(x 3)
x2 3x + 9
14. Rs. 200 is divided equally among a certain number of
children. If there were 25 children more, each would have
received 40 paisa less, find the number of children.[Ans: 100]
15. Calculate the value of 'a' from the following data, if the
upper quartile (Q3) is 74 [Ans: a = 10]
Marks 20
40
40
60
60
80
80
100
No. ofstudents
8 12 a 6
16. A ladder 16m long leans against the wall of a house. If the
foot of the ladder is 8m from the house, (i) at what height
did the top of the ladder lean against the house from itsfoot? (ii) find the angle made by the ladder with the ground.
[Ans: 8 3 m, 60]
17. A cone is placed on a cylinder as shown in
the figure. The area of the base of the
cylinder is 125 cm2and height of the cylinderis 3cm. If the volume of the whole solid is
625 cm3, find the height of the solid. [Ans: 9
cm]
18. The given figure is a solid object made
of a pyramid and a prism. Find the
P
QY
X
R
S
22
ab
cC
B
A
O
10 cm
19 cm
80
E
F
D
C
B
A15
C
B
A
D
E
a
bO
c
65
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27 28
volume of the solid object. [Ans: 148 cm3]
19. A man undertakes to do a cerain job in 40 days. He hires
15men for the job. At the end of 10 days, only one-fifth ofthe work was completed. How many extra men must be
employed in order to complete the work in time?[Ans: 5 men]
20. A shopkeeper sold his goods for Rs. 16950 allowing 25%
discount and then levied 13% VAT. Find the amount of
discount. [Ans: Rs. 5000]
21. The compound amount of a sum of money in 2 years is Rs.
8820 and in 3 years is Rs. 9261. Find the sum and the rateof interest
[Ans: Rs. 8000, 5%]
22. On the given figure, AE // CD, AB
//EC//FD and CB //DA//FE. Prove that
area of //gm ABCG = area of //gm
EGDF.
23. O is the centre of the circle in which inscribed angle ABC
and central angle AOC are standing on the same arc. AC.
Prove that AOC = 2ABC.
24. Verify experimentally that the inscribed angles standing on
the same arc are equal (Two different figures are necessary
but the radii of the circles must not be less than 3cm)
25. Construct a parallelogram ABCD in which AB = 3.2 cm,
BC = 5cm and AC = 3.5cm. Also, construct a parallelogram
equal in area to the parallelogram ABCD whose one angle
is 60.
SET VIISET VIISET VIISET VII
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :(x1
+ y1
) (x2
y2
) (x1
y1
) [Ans: 1]
(b) Evaluate : 2
3
8
4
64
2
43 16
4 [Ans: 8192]
2. (a) Solve: x 3 = 2 x [Ans: 9]
(b) Find the two numbers such that 5 times the larger plus
3 times the smaller is 47 and 4 times the larger minus
twice the smaller is 20.
[Ans: 7, 4]
3. (a) The mean of a continuous serieswhich has 80 terms is 40. When
class 5 15 is included in the
series, the new mean is 30. Find
the frequency of the class
interval 5 15. [Ans: 10]
(b) Give the Q3class from the
adjoining figure. [Ans: 30 40]
4. (a) What is probability of giving a child birth by a pregnant
lady on a Tuesday? [Ans: 1/7]
(b) A coin is biased so that the probability that it lands
showing heads up is2
3. The coin is tossed three times.
Draw a tree diagram to show the possible outcomes andfind the probability that more heads than tails are
obtained. [Ans:20
27]
5. (a) In the given figure, ABCD is a
parallelogram. If BC = 5cm, and
DAB = 30. Find the length of
AB if the area of ABC = 15 cm2
.
Y
X10O 20 30 40 50
5
10
15
20
25
Class Interval
30
60
D C
BA
30
A E
F
DC
BG
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29 30
[Ans: 6cm]
(b) The perimeter of a triangular field is 540 m and its
sides are in the ratio 25 : 17 : 12. Find the area of the
triangle. [Ans: 9000 cm2]
6. (a) Find the area of the triangular
faces of the given pyramid if theheight of the pyramid is 5cm and
the base is a square of side 24 cm .
[Ans: 312 cm2]
(b) If the circumference of great circle of a sphere is cm,
find its volume.
Ans:
6cm
3
7. (a) Hari sold three bags for Rs. 645 bearing a loss of Rs.
51. At what rate did he buy the bags. [Ans: Rs. 232]
(b) What is the rate of compound depreciation of a
machine worth Rs. 1,00,000 which is sold after 2 yearsfor Rs. 81,000. [Ans: 10%]
8. (a) Calculate the area of the given quadrilateral.
Ans:1
2h(a + b)
h
a
b
(b) Find the values of a and b. [Ans: a = b = 60]
9. (a) In the given figure, O is the centre ofthe circle and ABCD is a cyclic
quadrilateral where BC is produced
to E. If AB = AD and ADB = 48
find the value of DCE. [Ans: 84]
(b) From the given figure, find the values ofa, b and c. [Ans: a= b = c= 45]
Group 'B' [16 4 = 64]
10. In a survey of a group of students, it was found that 40% of
the students like folk songs, 30% like modern songs and
20% like both songs. If 90 students like neither folk normodern songs, find the number of students in the school and
the number of students who like only folk songs.
[Ans: 180, 36]
11. Find the LCM of
1 + 4a + 4a2 16a
4and 1 + 2a 8a
3 16a
4.
[Ans: (1 + 2a)(1 2a) (1 + 2a 4a2) (1 + 2a + 4a
2)]
12. Solve: 4x+ 4
x= 16 1
16 [Ans: 2, 2]
13. Simplify:a 1
(2a 1)(a + 2) +
3
(a + 2) (a 1)
1
(1 a)(1 2a)
Ans:a + 4
(a + 2) (2a 1)
14. A year hence a father will be 5 times as old as his son. Two
years ago the father was 3 times as old as his son will be4years hence. Find their present ages. [Ans: 29 yrs, 5 yrs]
15. Calculate the median from the given data: [Ans: 11.83]
Marks
obtained
0
5
5 10 10
15
15
20
20
25
25
30
30
35
No. of
students
11 6 15 6 8 5 4
24 cm
P
A B
C
ba
O
30B
AD
C
a 2ac
O
b
OB
C
D
E
A
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31 32
16. A man 1.6 m tall is 30m away from a tower and he
observers the angle of elevation of the top of the tower to be
30. What is the height of the tower? [Ans: 18 .92m]
17. Find the volume of the given solid made up ofcone on both sides.[Ans: 2310 cm
3]
18. In the given solid, the upper part has a
pyramid of slant height 5cm and thelower part is a prism of side 8cm. If the
volume of the solid figure is 448 cm3,
find the height of the prism.
[Ans: 6 cm]
19. Amit and Ankit can do a piece of work in 16 days and 24
days respectively. Amit worked alone for 4 days and Ankit
worked alone for 6 days. In how many days will the
remaining work be finished if they work together?
Ans: 44
5days
20. A shopkeeper allows a discount of 10% and still makes a
profit of 15% on selling an article. If the marked price ofthe article is Rs. 15000, find its selling price, cost price and
profit.
[Ans: Rs. 13500, Rs.11739.13, Rs. 1760.87]
21. The difference between the compound interest and thesimple interest on a sum of money for 2 years at a rate of
10% interest per annum is Rs. 20. Find the sum.[Ans: Rs. 2000]
22. In the given tranpezium ABCD,
AD // BC and AP = PB. Prove that
PCD =1
2trap. ABCD.
23. In the cyclic quadrilateral ABCD, Prove that i) BAD +
BCD = 180 and (ii) ABC + ADC = 180.
24. Verify experimentally that the angle in the semi-circle a
right angle. (Two different figures are necessary but the
radii of the circles must not be less than 3cm)
25. Construct a quadrilateral ABCD in which AB = BC = 6cm,
AC = AD = 6.5 cm and BAD = 60. Also construct atriangle equal in area to the quadrilateral ABCD.
8 cm
P
A DMO
CB
A D
B C
P
14 cm
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33 34
SET VIII
S.L.C. Question 2065 CDR
2065 (2009)Attempt allthe questions.
Group'A' [9(2+2)]=36
1= (a) Simplify :132x+1+ 5 169x
9 169x [Ans: 2]
(b) Evaluate:4
216a9b
5
46
1a
3b [Ans: 6a
3b]
2= (a) Solve : 9x2
20 = 3x 2 [Ans: 2]
(b) If 6 is added to the square of a number, the result is 31.
Find the number. [Ans: +5, 5]
3. (a) The mean weight of some men is 56 kg and the sum of
their weight is 392 kg, find
the number of men. [Ans: 7]
(b) From the given graph, find
the third qnartile class. [Ans:
40 60]
4. (a) A number card is drawn
randomly from the set of
numbered cards, numbered from 6 to 39. Find the
probability that the card may be a prime number or a
cubed number. [Ans:5
7]
(b) An urn contains 7 green and 9 black balls of the same
shape and size. Two balls are drawn at random oneafter the other without replacement. Draw a tree
diagram showing all the probabilities and also find the
probability of getting both black balls. [Ans:3
10]
5. (a) In the given figure, PQRS is a
parallelogram in which QR is
produced to the point T. If the area ofthe parallelogram is 27 3 sq. cm, the
side QP = 6 cm and the side PS = 9 cm, determine the
measure of the SRT. [Ans: 60]
(b) Given figure is a triangular prism
whose volume is 1,800 cubic cm.
If AB = 15 cm, BC = 8 cm andABC = 90
o, find the length of
the prism. [Ans: 30 cm]
6. (a) Obtain the total surface area of a hemisphere having the
diameter 21 cm. [Ans: 1039.50 cm2]
(b) The curved surface area of the givencone is 8,800 sq. cm. If the slant height is
100 cm, determine the height PO of the
cone. [ Ans: 96 cm2]
7. (a) At 18% loss the selling price article of an article is Rs.
164. Calculate the cost price of the article. [Ans: 200]
(b) A radio costing Rs. 6,000 is depreciated per year and 2
years later its price becomes to Rs. 5,415. Find the rate
of depreciation in percent.
[An: 15%]
8. (a) In the given figure, ABCD is arhombus in which the
diagonal AC = 20 cm and the
diagonal BD = 28 cm. If AD is produced to E, find the
area of the BCE. [Ans: 140 cm2]
(b) In the given figure O is the centre of the
circle. If QOR = 110o, calculate the
value of the PSQ. [Ans: 35]
Y
X20O 40 60 80 100
50
100
150
200
250
Marks obtained
C'
A'A
B
C
B'
O R
P
Q
B C
EDA
P Q
R
S O 110
R Q
PS
T
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35 36
9. (a) In the given figure, ABCD is a cyclic
quadrilateral in which AB is produced
to F. If DC || BE, DAB = 92oandFBE = 10
o, evaluate the ADC.
[Ans: 98]
(b) In the given figure, PT is a tangent in
which T is the point of contant. If
PTQ= 75 and STQ = 35, calculatethe QST. [ Ans: 105]
Group 'B' [16 4 = 64]
10. If n(A) = 48, n(B) = 51, n(C) = 40, n(AB) = 11, n(BC) =
10, n(CA) = 9, n(ABC) = 4 and n(U) = 120, find the
values of n(ABC) and n (ABC). Present the above
information in a Venn diagram. [Ans: 113,7]
11. Find the H.C. F. of:
9x2
4y2 8yz 4z
2, 4z
2 4y
2 9x
2 12xy and 9x
2+ 12xz
+ 4z2
4y2
[Ans: 3x + 2y + 2z]
12. Solve : 7x+
343
7x = 56 [Ans: 1,2]
13. Simplify:x + 3
x2+ 3x + 9
+x 3
x2 3x + 9
54
x4+ 9x
2+ 81
[Ans:
2(x 3)
x23x + 9
]
14. A number consists of two digits whose sum is 9. It three
times the number is equal to eight times the number formed
by interchanging the digits, find the number. [Ans: 72]
15. Compute the median from the table given below: [Ans:
49.16]
Marks obtained 2535
3545
4555
5565
6575
7585
No. of students 5 10 12 8 3 2
16. From the roof of a house of 6m tall, the angle of elevation
of the top of a tower was observed and found to be 30. If
the distance between the house and the tower was 19 3 m,
determine the height of the tower.
[Ans: 63 m]
17. Given figure is s solid composed of a cylinder
with hemisphere at one end. If the total surface
area and the height of solid are 770 sq cm. and
14 cm respectively. Find the height of the
cylinder.[Ans: 7cm]
18. Given figure is a square based pyramid. If
the slant height of the pyramid is 17cm and
the side of the base 16 cm, determine the
volume of the pyramid.
[Ans: 1280 cm]
19. A man undertook a contract to finish a piece of work in 32
days and he immediately employed 28 labourers to do the
work. After 24 days only two third of the work was
finished. How many labours should be added to finish thework in time? [Ans: 14]
92
F
E
B
C
D
A10
T
P75
35
S
Q
16cm
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37 38
20. After allowing 16% discount on the marked price of an
article and levying 13% value added tax, then the price of
the article becomes to Rs. 9,492. Find the value added tax.
[Ans: Rs. 1092]
21. A person took a loan of Rs. 46,875. If the rate of compound
interest is 4 paisa per rupee per year, in how many yearswill the compound interest be Rs. 5,853. [Ans 3 yrs]
22. Prove that the centre angle MCN at the center C of a circle
is twice the angle MPN at the circumference standing on the
same arc MN.
23. In the given figure, ABCD is a
parallelogram. If M and N are any pointson CD and DA respectively, prove that
AMB = CDN + ANB.
24. Verify experimentally that the sum of the opposite angles of
a cyclic quadrilateral is two right angles (Two circles of
radii not less than 3cm are necessary).25. Construct a quadrilateral PQRS having PQ = 4.4 cm, QR =
4.9cm, RS = 4.2 cm, SP = 2.8 cm and SQ = 6.6 cm. Draw a
PST equal in area to the quadrilateral.
SET IX
Send-Up Test: 2009
SEDIPSSEDIPSSEDIPSSEDIPS
Answer all the questionsGroup 'A' [9 (2 + 2) = 36]
1. (a) Simplify :5
x + 2 45.5
x 1
16.5x [Ans: 1]
(b) Evaluate:3
24a7b
11
33a
4b
5 [Ans: 2ab
2]
2. (a) Solve: x + 16 = x + 2 [Ans: 9]
(b) Divide 25 into two parts such their product is 156.[Ans: 12, 13]3. (a) Find arithmetic mean from given data: [Ans: 2.94]
x 1 2 3 4 5
f 2 4 6 5 1
(b) Find the class and frequency of first quartile from the
following graph. [Ans: 2 4, 20]
0
20406080
100
120140
2 4 6 8 10 12
Marks
Y
X
4. (a) A card is drawn at a random from a well shuffled packof 52 cards. Find the probability that it is a king or red
card. [Ans:7
13]
(b) A bag contains 10 white and 15 black balls. Two balls
are drawn randomly one by one without replacement.
By drawing tree diagram, show all
the probabilities with possible
outcomes.
MD C
BA
N
S R
QP
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39 40
A
B C
FE
D
12cm
9cm
5. (a) The area of rhombus PQRS is 18 3 sq cm and side of
rhombus is 6cm. Find SPQ. [Ans: 60]
(b) Find the lateral surface area ofgiven triangular prism.
[Ans: 720 cm2]
6. (a) The total surface area of a hemisphere is 1848 sq cm,
find its radius. [Ans: 14 cm]
(b) If the area of the curved surface of a circular prism of
radius 5cm is 660 cm2, find its volume. [Ans: 1650 cm
3]
7. (a) A fruit seller bought 1200 oranges at Rs. 1.50 each . Ifhe sold them at Rs. 21.60 per dozen, find his profit or
loss percent.
[Ans: 20%]
(b) The cost of a motorbike after 3 years becomes Rs.92583 at the rate of depreciation of 10% per annum.
Calculate the original price of the motorbike.[Ans: 127000]
8. (a) In the adjoining figure, AB =
4cm, AC = 5cm and ABC =
90, find the area of
parallelogram ABDE.
[Ans: 12 cm2]
(b) In the given figure, AB is thediameter of a circle with
center O and BOD = 120,
find the value of x. [Ans: 30]
9. (a) In the given circle, O is the
centre of the circle. If QRS
= 130. Find the value of
QOS
[Ans: 100]
(b) In the given figure, ABE is atangent where B is the point
of contact. If AB = BC and
CBE = 50, find DBC. [Ans: 105]
Group 'B' [16 4 = 64]
10. In a class X, 20% students passed in all three subjects, 46%failed in Maths, 57% failed in English, 42% failed in
Science, 35% failed in Math and English, 25% failed in
English and Science, 15% failed in Science and Maths.
(a) Find the percentage of students who failed in all three
subjects.
(b) Draw a Venn -diagram to show the above information. [Ans: 10%]11. Find the HCF of :
8a3 1, 4a
3 2a
2+ 2a 1 and 6a
2+ 11a 7 [Ans: 2a 1]
12. Solve: 51 x
+ 5x 1
=26
5 [Ans: 2, 0]
13. Simplify :1
x 3
2
2x + 3+
1
x + 3
2
2x 3
Ans:54x
(x2 9)(4x
2 9)
14. The sum of the digits of a two digits number is 13. If thedigits are reversed, the new number is 9 less than the
original number. Find the number. [Ans: 76]
15. Find the median from the table given below: [Ans: 60]
Marks
obtained
35
45
45
55
55
65
65
75
75
85
No. of
students
7 8 10 9 6
DE
A B
C
xO
120
B
DA
C
O
S
P
Q
R
O
B
DA
C
E
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41 42
O
A B
CD
O
B
C
D
A
E
F
16. The upper part of the tree broken down by the wind makes
an angle of 30 with the ground and the distance from the
foot to the point where the top of the tree touches the
ground is 50m. What was the original height of the tree?[Ans: 86.6 = 50 3 m]
17. Find the volume of the given solid:
[Ans: 718.66 + 3080 + 616 = 4414.66 cm3]
14 cm
32 cm
12 cm
18. In the given figure, the total
surface area of the given square
based pyramid is 384 sq cm. and
the side of a square base is 12 cm,find the slant height of pyramid.[Ans: 10 cm]
19. Ram takes 16 days and Shyam takes 24 days to finish a
piece of work separately. Ram alone worked for 4 days and
Shyam alone for 6 days. In how many days will theremaining work be finished if they worked together?[Ans: 4.8 days ]
20. A shopeeer sells an article at 8% discount and gains Rs. 40.
If he does not allow any discount, he will gain Rs. 60. At
what price did the purchase the article?[Ans: MP = Rs. 250, CP = Rs. 190]
21. The compound amount of a sum of money in 3 years and 4
years are Rs. 3240 and Rs. 3888 respectively, find the rate
of interest compounded yearly and the sum.[Ans: R = 20%, Rs. 1875]
22. Prove that the parallelograms standing on the same base and
between same parallels are equal in area.
23. In the given figure, O is the
centre of a circle. AB is a
chord, C and D are two points
on AB. If AC = BD and arc
AE = arc BF, Prove that
ACE = BDF.
24. Verify experimentally that the opposite angles of a cyclic
quadrilateral are supplementary. (Two figures with radii of
circle more than 3 cm are necessary)25. Construct a quadrilateral ABCD in which AB = 6.1 cm, BC
= 5.4 cm, CD = 4.9cm, AD = 5.1cm and BD = 5.9 cm. Also
construct a triangle equal to the area of quadrilateral ABCD.
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43 44
O
B
D
A
C
O
BC
DA
SET X
Send-Up Test: 2009
SEDIPSSEDIPSSEDIPSSEDIPS
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :7. 3
a 9.3
a 2
3a+2
3a + 1 [Ans: 1]
(b) Evaluate:3
54a7b
9
34a
2b
3 [Ans: 6a
3b
4]
2. (a) Solve: x 4 = x 2 [Ans: 4]
(b) The sum of two numbers is 10 and their product is 21.
Find the numbers. [Ans: 7, 3]3. (a) Find the arithmetic mean from given data: [Ans: 5.06]
x 2 4 6 8
f 3 4 5 3
(b) Find the class and frequency of median from thefollowing graph
[Ans: 40 60, f = 10]
Y
X20O 40 60 80 100
10
20
30
40
50
Mark obtained
60
4. (a) Find the probability of having a number which is prime
or odd when a dice is thrown. [Ans:2
3]
(b) If three children are born in a family, calculate the
probability that all children are girls by drawing a tree
diagram. [Ans:1
8]
5. (a) ABCD is a parallelogramin which ABC = 30,
BC = 12cm and area of
parallelogram ABCD = 54
cm2. Find the measure of
AB. [Ans: 9 cm]
(b) Find the volume of the given prism.[Ans: 30 7 = 79.37cm3]
4 cm 4 cm
6 cm
E D
CB
A
F
6. (a) If the surface area of a sphere is 1386 sq cm, find its
radius.
[Ans: 10.5 cm]
(b) A cone has radius of base 7cm and its slant height is25cm. Find its volume. [Ans: 1232 cm
3]
7. (a) Pravin bought a second hand bike for Rs. 45000. He
spent Rs. 3260 on its repair. If he sold it for Rs. 44520,
find his gain or loss percent. [Ans: 7.74 %](b) The price of a machine is depreciated from Rs. 50000
to Rs. 40500 in two years. Find the rate of depreciation.[Ans: 10%]
8. (a) PQRS is a parallelogram in which the altitude SM on
the side PQ is 6 cm, the altitude SN on the side QR is
5cm and its area is 45 sq cm. Find the sides of the
parallelogram.
[Ans: QR = 9cm, PQ = 7.5 cm]
(b) In the given figure, O is the
centre of the circle. If ACB
= 30, find the value of
DBA. [Ans: 60]
30B C
DA
9 ( ) I h i i l O i h 16 A b h i 1 5 ll i fl i ki Wh h l h f
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45 46
O
B
DA
C
E O
P
C
A
B
E FNM
9. (a) In the given circle, O is the
centre and ABCD is a cyclic
quadrilateral. If ADB = 30,
what will be the value of
BCD? [Ans: 120]
(b) In the given figure, ABE is a
tangent where B is the point
of contact. If AB = BC and
DBC = 105, find DBA .[Ans: 25]
Group 'B' [16 4 = 64]10. In the class IX, 58% students failed in Account, 39% in
English and 25% in Statistics, 32% in Account and English,
19% in Account and Statistics, 17% in English and
Statistics, 13% in all the three subjects.
(a) Draw a Venn -diagram to show above information.
(b) What percent passed in all three subjects. [Ans: 33%]
11. Find HCF of :m
6 1, m
5 + m
3+ m and m
3+ 2m
2+ 2m + 1[Ans: m
2+ m + 1]
12. Solve : 4. 3x + 1
9x= 27 [Ans: 2,1]
13. Simplify:1
x + 1+
2
x2+ 1
+4
x4+ 1
+8
x8 1
Ans:1
x 1
14. A number of two digits is 36 less than the number with the
digits reversed. If the unit digit exceeds twice the tens digit
by 1, find the number [Ans: 37]
15. Find the first quartile from the table given below:[Ans: 88.75]
Wages (Rs.) 50
70
70
90
90
110
110
130
130
150
No. of
workers
5 8 15 12 10
16. A boy who is 1.5m tall is flying a kite. When the length of
the string of kite is 200m, it makes an angle of 30 with
horizontal. At what height is the kite from the ground [Ans: 101.5m]
17. Find the total surface area of
given solid made ofhemisphere and cone.
[Ans: 858 cm2]
24 cm
O
C
C
31 cm
18. The figure is the squarepyramid in which vertical
height OP is 8 cm, and length
of base side is 12 cm, find its
total surface area.[Ans: 384 cm2]
19. A and B can do a piece of work in 24 days. A takes 40 days
to complete the same work. After they work for 8 days, A
leaves. If B completes the remaining work, in how many
days was the whole work completed?
[Ans: 48 days]
20. A shopkeeper sells an article at 5% discount and makes a
profit of Rs. 15. If he does not allow any discount, he will
gain Rs. 25. At what price did he purchase the article?[Ans: MP = Rs. 200,
21. Find the difference between interest compounded yearly
and half yearly on Rs. 16000 in 2 years at 10% p.a.[Ans: Rs. 88.1]22. Prove that the triangles standing on the same base and
between ame parallels are equal in area.
23. In the given figure, M and N are
the mid points of arc AB and arc
AC respectively. Prove that AE =
AF.
(ii) H t d t h d l th 25
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47 48
3cm
5cm
15cm
24. Verify experimentally that inscribed angles standing on the
same arc of a circle are equal. (Two circles of radii at least
3cm are necessary.)
25. Construct a quadrilateral ABCD in which AB = BC = 5cm,
CD = DA = 6 cm and BAD = 60. Also construct atriangle whose area is equal to the area of quad ABCD.
SET XI
National PABSON
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :a
2x. a
x 1 a
x
a3x
ax + 1 [Ans:
1
a]
(b) Evaluate:5
32a2b
1c
524a
3b
1c
6 [Ans:
2a
3c]
2. (a) Solve:
3
x
2
1 2 = 0 [Ans:
3](b) When a number increases by 25% it becomes 10. Find
the number.
[Ans: 80]
3. (a) Find the class of the upper quartile of the data.[Ans: 50 60]
Class 0-10 10-
20
20-
30
30-
40
40-50 50-60
No. of
workers
3 4 6 5 11 10
(b) Study the given ogive and answer the following
questions.
(i) How many students have secured distinctionmarks? [Ans: 10]
(ii) How many students have secured less than 25
marks?
[Ans:25]
10 20 3 0 40 50 60 70 80 90 1 00
10
O
20
30
40
5060
70
80
90
100
Marks 4. (a) From a well shuffled pack of cards, a card is drawn at
random. Find the probability of getting the card red or
ace. .
Ans: 7
13
(b) In a bag there are 3 green and 4 red identical balls. If
two balls are drawn at random one after another. Show
all the probabilities in a tree diagram and find the
probability of not getting both balls green without
replacement . [Ans:1
7
]
5. (a) In ABC, AB = 6cm, A = 100 and C = 20. Find
the side BC, if the area of ABC is 12 3 cm2[Ans: 8 cm]
(b) Find the total surface area of the
given triangular prism.
[Ans: 72cm2
]
6. (a) If the radius and height of a right circular cone are 3cmand 4cm respectively, find its total surface area.[Ans: 75.43 cm
2]
(b) The sum of the radius and height of a cylinder is 15cm.
If its base circumference is 44cm, find its volume[Ans: 1235 cm3]
7. (a) An article was sold for Rs. 1560 at the profit of 30%.Find the cost price. [Ans: Rs. 1200]
(b) In how many years will the population of a town be only 40 are fond of playing basketball only If 20 students
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49 50
B M C
DA
O
P
M N
110
Q
O
FE
C
B
A
D
14 cm6cm
12cm12cm
(b) In how many years will the population of a town be
209475 from 190000 at the growth rate of 5% per
annum? [Ans: 2 yrs]
8. (a) In the adjoining figure, ABCD
is a trapezium in which AD //
BC and AD =1
2BC. If the area
of ABCD is 120 cm2and height
(DM) = 5cm, find the area of
ADC. [Ans: 40 cm2]
(b) In the given circle, O is thecentre and ABC = 150. Findthe value of x. [Ans: 60]
9. (a) In the given circle O is the
centre and MNQP is a cyclic
quadrilateral. If MPQ = 110,
find QMN. [Ans: 20]
(b) In the given figure O is the
centre of the circle EBF is a
tangent where B is the point of
contact. If AB is a diameter and
DBF = 72, find the value of
BCD. [Ans: 108]
Group 'B' [16 4 = 64]
10. In a survey of 200 students, 70 are fond of playing cricket,
80 football and 100 basketball. Similarly 20 are fond of
playing cricket and football only, 30 cricket and basketball
only, 40 are fond of playing basketball only. If 20 students
are fond of playing football and basketball only, by drawing
a Venn-diagram. Find
(i) the number of students who play all games.
(ii) how many students don't play any game? [Ans: 10, 40]
11. Find the HCF and LCM of :a
2+ b
2 c
2 + 2ab, b
2+ c
2 a
2+ 2bc and c
2+ a
2b
2+ 2ca.
[Ans: HCF = a + b + c, LCM = (a + b + c) (a + b c)
(a + c b) (b + c a)]
12. Solve:5x 4
5x + 2 = 2 +
5x 3
2 [Ans: 5]
13. Simplify:
1
a 3
1
a 1+
1
a + 3
1
a + 1[Ans:
16a
(a2 9) (a2 1) ]
14. A number of two digits exceeds seven times the sum of the
digits by 6. If 45 subtracted from the number, the digits are
interchanged. Find the number. [Ans: 83]
15. Find the median from the given data. [Ans: 16.875]
Age 5 -10 10
15
15
20
20
25
25
30
30
35
No. ofstudents
6 7 8 4 5 2
16. A man of height 1.68 m observes a pillar of height 31.68m
and finds the angle of elevation of the top of the pillar to be
60. How far is the man from the base the pillar. [Ans: 17.32m]
17. Find the volume of the solid given alone side. [Ans 667.33 cm2]
7 cm
15 cm
18. Find the total surface area of the
given solid figure which is the
combination of prism and pyramid. [Ans: 672 cm2]
O
BA
C150x
19 A tap can fill 25% of a tank in 3 hours and another tap can SET XII
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51 52
A
B
C
D
F
P
Q
A
B C
D
40
80
43cm
26cm
19. A tap can fill 25% of a tank in 3 hours and another tap can
empty whole tank in 15 hours. If both the taps are opened at
the same time and the capacity of a tank is 1000 liter in
what time 100 liter water will be collected in the tank.[Ans: 6 hrs]
20. After allowing 7% discount on the marked price and
levying 11% VAT, an article is sold. If the amount of VATis Rs. 102.30, find the marked price of the article and the
discount amount.
[Ans: MP = Rs. 1000, Discount = Rs. 70]
21. The simple interest on certain sum of money in 3 years at
30% per annum will be Rs. 1188 less than the compound
interest. Find the sum.
[Ans: Rs. 4000]
22. Prove that a rectangle and the parallelogram standing on the
same base and between the same parallel lines are equal in
area.
23. In the given figure if BC{ = DC{ ,
prove that PQ // DB.
24. Verify experimentally that the length of two tangents to a
circle at the point of contact from an external point are
equal. (Two circles of radii more than 3cm are necessary)
25. Construct a triangle PQR in which PQ = 7cm, QR = 5.5cm
and PR = 6cm. Construct a parallelogram OMNQ equal in
area to the triangle PQR such that OQ = 8cm.
SET XII
J.S.T. Examination, 2065
Attempt all the questions.
Group "A" [9 (2 + 2) = 36]
1. (a) Evaluate:
356 24
7 5
426 2076 [Ans: 1]
(b) Simplify:
3128 +
454
3250
4
500 108
[Ans:1
21
3
]
2. (a) Solve: 3x 3
= 32 x
[Ans: 1,9]
(b) A number is such that it is as much greater than 21 as itis less than 37. Find the number. [Ans: 29]
3. (a) In a data X
= 10.4, fx = 1040 and N = 25P what is
the value of P?
[Ans: 4]
(b) From the given ogive in thefigure, find the first quartile.
[Ans: 8 .67]
4. (a) A dice is rolled once. Write the sample space and find
the probability that the outcome is either a prime
number or an even numbers. [Ans: S = {1,2,3,4,5,6};5
6)
(b) There are 5 black and 8 white balls of same shape andsize in a basket. If two balls are drawn randomly in
succession without replacement from the basket. Show
the probability of all possible outcomes in tree diagram.
Y
X4O 8 12 16 20
4
8
12
16
20
Marks obtained
9 (a) In the figure O is the centre of
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53 54
A
B
C
A'
B'
C'h
6cm
8cm
8 cm
140cm
O
CD
A 35
x
B
OC
AB
8 cm
5. (a) Find the area of the adjoining
parallelogram.[Ans: 968.18 cm2]
(b) What value of h in the prism
shown in the figure makes itstotal surface area 528 cm
2?[Ans: 20cm]
6. (a) Find the curved surface area
of the given cylinder.[Ans: 3520 cm2]
(b) A cone whose radius of base is 7cm has a volume of1232 cm
3, Find the height of the cone. [Ans: 24cm]
7. (a) If a shopkeeper sold a watch for Rs. 640 at a loss of
20% . Find the cost price of the watch. [Ans: 800]
(b) A motorcycle which was purchased at Rs. 90000 wassold for Rs. 81000 after one year. At what percent was
it depreciated?
[Ans: 10 %]
8. (a) In the given figure parm. BCDE
and AED stand on same base
and between the same parallel
lines. The area of AED is
32cm2. Find the area of BCD.[Ans: 32 cm
2]
(b) In the adjoining figure O is the
centre of circle. Find the value
of x. [Ans: 125]
9. (a) In the figure, O is the centre of
circle. If OBC = 60 and BC
//OE, then find the measure of
BAE. [Ans: 60]
(b) From the given information infigure, find the measure of AB.[Ans: 15 cm]
Group "B" [16 4 = 64]10. In a survey of a group of people, showed that: 60 liked tea,
45 liked coffee, 30 liked milk, 25 liked coffee as well as tea.
20 liked tea well as milk, 15 liked coffee as well as milk
and 10 liked all the three. How many people were asked this
question? Solve by drawing the Venn-diagram. [Ans: 85]
11. Find the LCM of :
3x
2
+ 12x + 12, x
2
ax + 2x 2a, x
2
3x 10[Ans: 3(x + 2)
2(x a) (x 5)]
12. If a + b + c = 0 prove that:
1
xb+ x
c+ 1
+1
xc+ x
a+ 1
+1
xa
+ xb
+ 1 = 1
13. Simplify:
1
1 + yx
+1
xy y
x
1
1 + y
2
x2
1
x
2
y2 y
2
x2
[Ans:x
2y
2
x
4
y
4]
14. The product of the present ages of two brothers is 160. 4
years ago. elder brother was twice as old as is younger
brother. Find their present ages. [Ans: 16 yrs, 10 yrs]
15. The following table shows the age of the workers of a
factory in a village. Find the third quartile. [Ans: 51.5]
Age 20 - 30 - 40 50 60
B C
D
A
E
O
C
E
A
60
B
30 40 50 60 70 23. In the figure, AB // ED, BF //DC
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55 56
O
A
P
A'
A B
C
DE
F
30 40 50 60 70
No. of
worker
5 9 10 6 4
16. A man 1.6m tall, observes the top of a pillar of the height
26.6m situate d in front of him and the angle of elevation to
be 30. How far is the man from the pillar? Find it. [Ans: 43.3 m]
17. The given figure is a solid made of
cone and an hemisphere in which
OA = OA' = 7cm. A'P = 25cm, find
the volume of the given solid
objects. [Ans: 1950.67 cm3]
18. Given figure is combined form of
pyramid and cubical prism. If the
area of the base of cubic prism is
144 cm2and height of the obtained
figure is 20cm. Find the total
surface area of the given figure.[Ans: 960 cm2]
19. A man undertakes to do a certain job in 32 days. He hires12 men for the job. At the end of 8 days only one fifth of
the work was completed. How many extra men must be
employed in order to complete the work in time. [Ans: 4]
20. When an article is sold at a discount of 10% of marked
price, a profit of Rs. 8 is earned by the seller. If the same
article was sold without allowing a discount a profit of Rs.20 is earned. What should be the cost price of the article.[Ans: Rs. 100]
21. Find the compound amount and compound interest on Rs.
600 at 5% p.a. for 11
2 years interest is payable half yearly. [Ans: 646.13, Rs. 46.13]
22. Prove that the opposite angles of cyclic quadrilateral are
supplementary.
23. In the figure, AB // ED, BF //DC
and BF = DC. Prove that AFE =1
2 quadrilateral BFDC.
24. Verify experimentally that the angle at the circumference isequal to half of the angle at the centre, both standing on the
same arc of a circle. (Two circles of radii not less then 3cm
are necessary.)
25. Construct a triangle ABC having AB = 7.1cm, BAC = 60
and AC = 5.7cm. Also construct a parallelogram having one
side 7.5cm and equal in area to the triangle ADC.
20 cm
SET XIII
the probability that he will solve at least two problems
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57 58
010
30
40
50
10X
Y
20
60
20 30 40 50 60 7 0 80Markes obtained
8 cm
20 cm
M N
RP
6 cm
SET XIII
Joint S.L.C. Send-up Examination 2065
(KUHS/RBS/SXG/SXT]
Answer all the questions
Group 'A' [9 (2 + 2) = 36]
1. (a) Simplify :3. 9
x + 1+ 9.3
2x 1
12. 32x
6.9x [Ans: 5]
(b) Evaluate :4
128 a3
42
1a
9 [Ans: 4a
3]
2. (a) Solve : x + x 20 = 10 [Ans: 36]
(b) 250 bananas were divided equally among a certain
number of students. If there were 25 more students,each would receive half banana less. Find the total
number of students. [Ans: 25]
3. (a) The arithmetic mean of 15 members is 12. When two
numbers are eliminated the mean becomes 11. If the
difference of the two eliminated numbers is 3, find the
numbers. [Ans: 20, 17]
(b) Find the median of the
data related to the figure
given alongside.
[Ans: 40]
4. (a) A boy can solve a problem accurately with a
probability of4
5
. If he is given three problems, what is
p y p
accurately? [Ans:48
125]
(b) A bag contains 15 red balls and 20 white balls. Two
balls are taken randomly one after the other without
replacement. Find the probability of getting the balls ofsame color showing all the possible outcomes in the
tree diagram. [Ans:59
119]
5. (a) In the given figure along side, if
the area of the kite is 48 cm2,
find the measure of PRQ. [Ans: 30]
(b) Find the volume of the given
triangular prism. [Ans: 346.4 cm3]
6. (a) The circumference of the base of the cylinder is 44cm
and the sum of its radius and height is 17cm. Find the
total surface area of the cylinder. [Ans: 748 cm2]
(b) If the total surface area of the hemisphere is 462 cm2,
find its volume. [Ans: 718.67 cm3]
7. (a) If the selling price of an article is less by1
4 of the cost
price, find the profit or loss percentage. [Ans: 25%]
(b) A computer, which is supposed to depreciate at the rate
of 5% per annum, was sold at Rs. 36100 after two
years. At what price was it bought? [Ans: Rs. 40,000]
8. (a) In the given figure, MNRP is a
trapezium in which MN // PR,
MNR = PRN = 90, NR =
8cm, PM = 10cm and MN =
6cm. Calculate the area of thetrapezium MNRP.
R
S
P
Q
OO8 cm
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22. Prove that the areas of the parallelogram on the same bas e
SET XIV
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61 62
E
C
BH
D
A
LK
and between the same parallel lines are equal.
23. ABCD is a cyclic quadrilateral. AB
and DC produced to meet at E, the
circle with center E and radius EC
cuts AB at H and HC, BC meet ADat K, L, respectively. Prove that CL
= KL.
24. Verify experimentally that the sum of the opposite angles of
a cyclic quadrilateral is 180. (Two circles of radii not less
than 3 cm are necessary)
25. Construct a triangle equal on area with the given
quadrilateral ABCD in which AB = 4cm, BC = 5cm, CD =
4.5cm, DA= 6cm, and diagonal AC = 7cm.
JOINT S.L.C. SEND-UP EXAMINATION-2065
Attempt all the questions.
Group A [ 10(2+2)=40]
1. a Simplify:
3.4x + 3
2.4x + 2
5.42 + x
3.4x + 1
[Ans:
40
17]
b. Evaluate:3
16x5
y7
52x
2y
4 [Ans: 2xy]
2. a. Solve : x + x2- 3 = 3 [Ans: 2]
b. Rs.60 was divided equally among a certain number of
boys. If there were 2 more boys, each would receive
Rs.1 less. Find the total number of boys and the total
amount of money.[Ans:Rs. 60, Rs.10]
3. a. The arithmetic mean of 25 numbers is 8. If the three
numbers, which are in the ratio of 2:3:4 are added, the
mean becomes 8.75, find those three number
[Ans: 10,15,20]
b. Find the median of the data related to the figure given
alongside.[Ans: 15]
0
10
30
40
50
5X
Y
20
60
10 15 20 25 30 35Age of people
4. a. The probability of a day to be fine is 2/5. What is the
probability of having only one day to be fine out of
three days ? [Ans: 54/125]
b. A bag contains 5 red balls and 4 white balls of same
size. Two balls are taken randomly one after otherwithout replacement . Find the probability of getting
the balls of different colors showing all the possible
i h di [A 5/9]
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63 64
R
S
P
Q
OO
8 cm
6 cm
10 cm
O
40
D
B
E
A
C
QAD
C
B
P
outcomes in the tree diagram . [Ans: 5/9]
5. a. In the given figure along side, if
QR=8cm,PR=12cm and
PRQ=30, find the area ofkite. [Ans: 48cm
2]
b. Find the surface area of the
given triangular prism.[Ans: 155cm2]
6. a. The circumference of the base of a cylinder is 88cmand the sum of its radius and height is 40 cm. Find the
volume of the cylinder
[Ans: 3520cm3]
b. If the total surface area of a hemisphere is 462 cm2, find
its curved surface area. [Ans: 308cm2]
7. a. If the cost price of an article is less by 1/4 of its selling
price, find the profit of loss percentage. [Ans: 33%]
b. The population of a town at the beginning of the
previous year was 10,000. If it is believed that the
population is growing at the rate of 4%,6% and 8% in
the respective years, what will be the population at the
end of the next year ? [Ans: 11906]
8. a. In the given figure, ABCD is a
trapezium in which AB//DC,
ABC = BCD = 900 , BC =8cm and AD = 10cm . If the
area of the trapezium is 72 cm2,
calculate the length of the AB.[Ans: 6cm]
b. In the given figure , If AE//CD,
CBA = 920
and EAR=200
.find the value of BCD.[Ans: 108
0]
9. a. In the given figure, AB is the
diameter and AB//CD. If
BEC= 400, find the value of
BCD. [Ans: 500
]
b. P and Q are centers of circleswhich touch at A. BC is a direct
common tangent. Find the
measure of
BAC.[Ans: 90]
Group - B [164=64]
10. In a group of students, 20 study accountancy, 21 studymathematics,18 study history, 7 study accountancy only, 10
study mathematics only, 6 study accountancy and
mathematics only, 3 study mathematics and history only .
(i) Represent the above information in the Venn diagram.
(ii) How many students study all the subjects ?
(iii) How many students are there altogether ? [Ans: 2, 41]
11. Find the H.C.F. of :
( a + c)( a - c ) + b ( 2a + b )( b + a ) ( b - a ) + c ( 2b + c )
and ( c + b ) ( c - b ) + a ( 2c + a ) [Ans: a + b
+c]
12. Solve : 5x-5
+ 54-x
= 11
5 [Ans: 4 and 5 ]
13. Simplify :1
x + 1+
2
x2+ 1
+4
x4+ 1
+8
x8 1
[Ans:1
x 1]
14. Tara said to Sabittre, '' I am half as old as you will be when
I will be as old as you are.'' If the sum of therir present ages
is 50, find their present ages. [Ans: 20 years,30 years]
A B
CD
R
E
AB
C
D
92 20
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PY
24
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67 68
20 cm
3.5 cm
W
X Y
Z
O
O
Q R
3525
DC
AB
32
70
E
P
QS
T
R
36
X4O 8 12 16 20
4
8
12
16
20
Marks24
4. a. A Card is drawn from a well shuffeled pack of 52
cards. Find the probability of not getting a black face
card . [Ans: 23/26]
b. A ball is drawn from a bag containing 4 black and 7
white balls randomly and not replaced, then another
ball is drawn, Draw the tree diagram to show the
probabilities.5. a. Find the area of Quadrilateral
ABCD. [Ans: 45 cm2]
b. Find the volume of given
triangular prism. [Ans: 480cm
3]
6. a. What is the total surface area of
given hemisphere .[Ans: 115.5cm2]
b. Find the area of the curved surface of a cone whoseslant height is 25 cm and height is 24 cm. [Ans: 550cm
2]
7. a. Find the profit percent when 6 pens are sold for the cost
price of 9 pens. [Ans: 50%]
b. A motorcycle of Rs. 1,00,000 is depreciated at 10% p.a.
find its value after one year . [Ans: 90000]
8. a. In given figure WZ// XY Provethat WOX=YOZ .
b. Find QPR From figure.
[Ans: 60]
9. a. In adjoining figure,
BDC=320, ABE= 70
0find
the measure of ACB.[Ans: 380]
b. In figure PTQ=360 and
PT=TQ then find the value of
STQ. [Ans: 72]
Group 'B'
Group - B ( 164=64)
10. Among 100 students of a school, 85 students like
Arithmetics, 65 like Geometry and 10 students did not like
both. Then, find .(i) How many like both ( Geometry and Arithmetic)
(ii) How many like Geometry only .
(iii) Show these information in Venn-diagram [Ans: 60, 5]
11. Find the LCM of :
2a3+ a
2+ a +2 and a
3- a
2+ a - 1 [Ans: a + 1]
12. Solve :
a 4
a 2 = a + 16 [Ans: 9]
75
115
35
BA
D C
8 cm
13. Simplify:1
a + x +
2a
a2
+ x2 +
4a3
a4
+ x4
8a7
a8
x8 [Ans:
1
x a]
23. In figure, O Is the center of circle,
AC is the chord If BT=TC Prove
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69 70
20 cm
5.6 cm
O
C
A
T
E
p ya + x a + x a + x a - x x a
14. The difference between the length and breadth of arectangular field is 4 m. If the area of the field is 96 m
2, find
its perimeter. [Ans: 40 m]
15. Calculate third quartile(Q3) from data : Ans: 16.43]Marks obtained 25 35 45 55 65 75
No. Of Student 5 6 8 10 7 4
16. The angle of elevation of a tower was observed to 450.
From a point on walking 100m away from the tower. it was
found to be 300. Find the height of the tower . [Ans: 136.6m]
17. Find the volume and total surface
area of given cylinder with
hemispherical ends. [Ans: 2707.11cm3, 1098.24cm
2]
18. Find the total surface area of square based pyramid whose
base is 6 cm and height is 4 cm . [Ans: 96cm2]
19. Madan Bahadur and Hari Bahadur can do a piece of work in20 days and 50 days respectively. They both started the
work together and Hari Bahadur left after 5 days. In how
many days will Madan Bahadur finish the remaining work? [Ans: 13 days]
20. The price of an article is marked at 25% above the costprice. If it is sold at a profit of Rs. 125 after allowing 15%
discount, what will be the selling price. [Ans: 132.80]
21. A certain sum of money amounts to Rs. 1323 in 2 years and
Rs. 1389.15 in 3 years. Find the compound rate of interest
and sum.
[Ans: R=5%, Rs.145.86]
22. Prove that the parallelograms standing on same base and
between the same parallels are equals in area.
AC is the chord. If BT=TC. Prove
that OAT=OBT.
24. Experimentally verify that sum of opposite angle of a cyclicquadrilateral are supplementary. (Two circles of radii not
less than 3 cm are necessary)
25. Construct a triangle ABC in which AB = 4.2 cm, BC = 5.4
cm and AC =5.8 cm Construct a parallelogram with an
angle 600and its area equal to triangle ABC.