Algebraic Expressions 123

AssiGNMENT 5.7
1 Multiple Choice Questions (MCQ) Choose the correct option.
() If 10less than a number is - 10, then the
number, is
(a) 3 (b) 2 (c) 0 (d) 1
(ii) The sum of two numbers is 30, If one number is four times the other, then the
smaller number is
(a) 5 (6) 6 (e) 7 (d) 8
(iii) Arectangle is 3 times as long as it is wide. If its perimeter is 56 metres, then
its length is
(a) 21 m (6) 22 m (c) 21.2 m (d) 22,2 m
9. 10added to thrice a whole number gives 46. Find the
number.
8. Find anumber such that when it is doubled and 11 added to it, the result is 27.
4, Two numbers differ by 5. If their sum is 19, then find the two numbers.
5. Find two consecutive numbers such that the greater number added to 3 times of
the smaller number makes a total of 53.
6. Find the three consecutive numbers whose sum is 183.
7. Finda number such that when it is added to two-thirds of itself, the result is 70.
8. 4times acertain number is as much less than 60 as 7times the number is greater
than 61. Find the number.
9. The difference between three-fourths and three-fifths of a number is 15. Determine
the number.
10. The perimeter of a rectangle is 30 metres. If its length exceeds its breadth by
3 metre, then find its length.
11. The length of a rectangle is twice the breadth. If its perimeter is 60 m, then find its
length.
12. The sides of a triangle are given by x, 2x + 2 and 3x -2. If its perimeter is 30 cm,
then find the smallest side of the triangle.
13. Find the breadth of a rectangle with length 15 metres and area 165 sq. metres.
14. The angles of a triangle are x, x + 15° and 2x 15°. Find the smallest angle of the
triangle.
[Hint : Since, the sum of three angles of a triangle is always 180°,
x+ (x + 15) + (2x- 15°) = 180°]
15. Sudha is twice as old as her brother. Three years ago, Sudha's age was three
times of her brother's age. Find the age of Sudh.
l6. Savita has 27 in the form of fifty paise and twenty-five paise coins. She has
twice as many twenty-five paise coins as she has fifty paise coins. How many coins
of each kind does she have ?
17. Rakesh thought of a number, tripled it and added 15 to it, the result was 60. Find
the number.
18. Divide the share 100 between A andB such that twice of A's share is less than
3 times of B's share by 200.
19. Sudha is twice as old as Garima. 10years ago, Sudha was three times as old as
Garima. Find Sudha's present age.
124 Excellence in Mathematics--VIlI

CHAPTER-END EXERCISES
Section A

(MCQ)
L MULTIPLE CHOICE QUESTIONS
question, there are four Options, out of which one is correct. Choose the correct or
For each
polynomial ?
1. Which of the following expresions is a 2x2-x+ 1 (d) 2x
1
+--4
(a) 3r+ 2vx-1 (b) 3ry2-2xy + 5x3
(c)

2. The factorisation of x -y is
y') (d) (x - yx + y\x
(a) -y (6) (x-y Xx -y') (c) (r -y Xx +yX*'+
3. If(2r-5\x + 3) = 2r +r+a, then the
value ofa is
(a) 15 (6) -2 (c) - 15 (d) 2
y) is
4. Ifx = 3 and y = 2, then the value of (* -ylr + xy + (d) 25
(a) 31 (6) 19 (c) 1
5. The factorisation of p + qr +pq +pr is
(a) (p + rp + qr) (6) (p + rlg + r) (c) (p + glg + r)r +p) (d) (p + qp + r)
6. The product of (* + 3) and (2x - 1) is
(a) 242+ 5x-3 (b) 2x2-5x +3 (c) 2x2 46x3 (d) 2r + 2r +3
7. 4-*-y'-2cy is equal to
(a) (2-x +y(2 + * - y) (6)(2 + x+ y\2 -*- y)
(c) (2 +x-y)(2 +*+y) (d) (2-x +y)2 -x- y)
8. (x -y -z² is equal to
(a) (x-y - z)(x +y +a) (6)(*- y+ zx -y - z)
(c) (x +y -z)*-y +2) (d)(x + y + z\x + y + z)
9. (* +y + 2(x +y) + 1 is equivalent to
(a) (x + y-1)(* +y+ 1) (6) (x-y+ 1\x +y+ 1)
(c) (-y- 1x +y + 1) (d)(x + y+ 1\x +y+ 1)
10. The number of terms in a binomial is
(a) 1 (6) 2 (c) 3 (d) 4

II. TRUE /FALSE

1. (x-a)' =x 2ax + a? 2. V3rx V3r =3r
3. (3r² yX- 4ry') = - 12r3y3 4. a : a' =q
5. l6x- 81ly' =(4r² +9y'N2r + 3y X2r -3y) 6. (m + n) = (m +nm -n)
7. (p +r = (p +rp + r) 8. (99)2 = (100 + 12-100 1
1
9. (101= (100 + l 10.
-1+1 4
 Aigebraic Expressions 125
FILLIN THE BLANKS
IIL
expression having more than 3 terms is called a
1. An
The greatest common factor of 4r'y and 2ry is
3r")
3. 2+" x (-
(8n3 + 2m) + 2m =
4.
5. When remainder is zero, the divisor is afactor of the
6. The product of 31 and- 5xy' =
7. If(2x- 5Xx + 3) = 2x? +X + a, then a =
8. r-y' =( )(x-y).
9. 3x2y + 42 - 2ry) = 6xy + 12x2 +
10. The product of two monomials is obtained by the application of the laws of
and

v. MATCH THE COLUMNS

1. Column A Column B

(a) The value of (20 -(65)8 + (45)° = (p) 9894

(b) 97 x 102 = (g) - 175500
(c) If a' + b² = 84 and a -b =8, (r) 25
then the value of ab =
(d) If c' = a'+ b2, where a =7 and b = 24, (s) 10
then the value of c=
2. Column A ColumnB

(a) (82)2-(18)² = (p) 63.91

(6) 197 >x 203 = (g) 6400
(c) (8.63)-(1.37)² = (r) 39991
(d) 8.3 x 7.7 = (s) 72.6

Section B

I SHORT AND LONG ANSWER TYPE QUESTIONS

1. Multiply - 5ab by 3ab and verify your answer taking a= l and b =-2.
1 1
2. If x + = 5, find the values of (i) x+ (ii) x +

3. Evaluate 104 x 96. 4. Expand (3r 7y - z.

5. Factorise (3x + 2y )'. 6. Expand (2r-3y,

7. Evaluate 95 x 96. 8. Factorise 12r²-7x + 1.

9. Find the square of (3x 10. Find the value of 4r + - 12, when .x = 2.
4
 Excellence in Mathematics-VIlI
126
II.MENTAL MATHEMATICS
-5
coefficient of x in 4 ay is
1. Fillin the blanks : expression. (iü) The
(i) 2r + y is an - 5x =
(iv) 4r + 3y - 3r
(iii) 5x x 4y =

(v) rx 9ry x

each of the following as a special product :

Z. Express (ii) (99)- (11)
() (27)2-(21)
3. Find the product :
(ü) 7ab x (- abe)
(iiü) 2ry x 2r x (-3ry')
(i) 3r2 x 23
12
(iv) - 3 x
following :
4. Using formulae, find the value of the
(i) (36 + 2a)X3b + 2a)
2
HOT Higher Order Thinking Skills
(ü)
1. Find the error in the following statement
(iii) (a - 2)\a -2) 3(y +8) =3y+ 8
(iv) 2. Show that (a + by-(a- b)² = 4ab and
using this identity find the value of
(75) - (25°.
5. Evaluate the following using identities :
(i) (105)² (ü) 69 x 71 3. Use the identity (a+ b)² = a + 2ab+ b
(iii) (98)2 (iv) 37 x 43 to evaluate (41 +(40.

VALUE-BASED QUESTIONS
1. The amount of water flowing into a
tank
in an hour. When was the tank half full? doubles every minute. The tank is full
2. A domino is exactly the same size as
two squares of a standard 8 x 8
Can 32 dominoes be arranged to tile the chessboard.
3. The ages of a father chessboard with no gaps or overlaps
and son added up to 66. The
son's age. How old could they be ? father's age is the reverse o
148 Excelence in Mathematics
to 882 at 5% per
vears will 800 amount annum
EXXAMPLE 31: In how many
compounded annually ?
and r = 5% p.a.
SOLUTION: Here. P=800, A=882
Let number of years be n.
A-P1+
Since. 100
1
= 8001+
882 = 800 1+ 20)
10820
882441 1 441 21
= 1+ 0r
20 400 20

21 )2 21
or
(: 441 = (21 and 400 =(2n:
20 20
= 2.
Since the bases are same on both sides, hence n
annually.
Hence, in 2 years, T800 will be 882 at 5% p.a. compounded
amounts to
EXAMPLE 32: Determine the rate per cent per annun, if? 25, 000
726,010 in 6 months, interest being compounded quarterly.
[:: 6 months = 2 quarter
sOLUTION: Here, n=2
Now, A=P1+ where r is the rate per cent per quarter.
100
2
r
26010 = 25000 1+ 100
2 2 2
r 26010 2601 51 r 51
or 1+ Or 1+
100) 25000 2500 50) 100 V50
r 51 51 51-50 1
1+ Or -1=
100) 50 100 50 50 50
1
or r= x100 = 2%
50
Hence, the required rate is 2% p.a.

AssiGNMENT 6.5
1. Multiple Choice Questions (MCQ) Choose the correct option.
compounded
) The cornpound interest on 15625for 1 years at 8% per annum
2
half yearly is
(u) 1462 (b) 1951 (c) 2621 (d) 3689
(iç) The armount paid for 160000 at 10% per annum compounded semi-annualls
for 2 years is
(a) 232212 (b) 194481 (e) 766166 (d) 100421
 Ratio and Proportion 149

2. Find
the amount for each of the following when the interest is compounded annually :
(i) P= 1,200; r= 4% p.a. ; n = 2years
(ii) P= 2,000 ; r= 10% p.a., n=3 years
(iü) P= 25.000 ;r= 12%o p.a. ;n =3 years
1
(iv) P= 3.200;r=17,% p.a. ; n =2 years
2
ln) P= 2,500; r=9% p.a. ;n =2 years
ndthe compound interest when it is compounded annually:
) P= 625; r = 4% p.a. ; n = 2 years (iü) P= 8.000:r=5% p.a. :n=3 years
Gii) P= 16,000 ;r= 10% p.a. ; n =3 years (iv) P=3.200:r= 25h p.a. ;n =3 years
ARamesh deposited 1,250 in his saving bank account. Find thecompound interest
earned by him after 3 years, if the rate of interest is 5% per annum and interest 1s
payable annually.
6 Find the compound interest on 26,000 for 3 years at the rate of 10% per annum
compounded annually.
6. Find the amount and the compound interest on 750 lent at compound interest of
12% per annum for one year, if the interest is payable half-yearly.
7. Find the compound interest on 25,000 for one and half years at 8% p.a., when the
interest is compounded half yearly.
s. Compute the compound interest on 3,200 for l year at 8% per annum when
compounded half yearly.
9. Find the compound interest on 1,000 for 6months at 20% per annum, compounded quarterly.
10. Find the compound interest on 25,000 for 6 months at 8% p.a. when the interest
is compounded quarterly.
11. Find the compound interest on 2,000 for 1 years at 10% p.a., when the interest
is compounded half yearly.
12. What is the compound interest on 8,000 at 10% p.a. for 2 years if the interest is
calculated half yearly ?
13. Calculate the amount due in 2 years on 1000, if the rates of compound interest for
successive years are 10% and 5% respectively.
14. Find the principal, if the compound interest payable annually at 10% per annum for
3years is 1331.
15. In what time will 1.200 amount to 1,323 at 5% per annum when the interest is
payable annually?
J6. In what time will 64,000 amount to 88,360 at 17,% per annum, interest being
compounded yearly ?
17. Sangeeta invested 20,000 in the bank for 4 years and got back 29,282 after
4 years. What was the rate of interest per annum payable annually ?
18. Roshanara deposited a certain amount with a leasing company at the rate of interest
of 20% compounded annually. At the end of 3 years, he received back
21,600.Find the amount deposited.
19. Mr. Raghava has deposited 8,000 with a finance company for a period of 1 vear.
The company credits the interest quarterly. He received 9,724.05 after one Vear
Find therate of interest per cent per annum.
0. Rajesh borrowed 5,000 from a bank. He will have to pay 10,000 after 5 years.
Find the rate of interest, if the interest is payable half yearly. (Take 2 -L072)
 Ratio and Proportion 159
EXAMPLE 44: A contractor undertakes to con struct a road in 20 days and engages
12 workers. After 16 days, he finds that only 2
part of the work has
been done. How many more
finish the job in time ? workers should he now engage in order t0
SOLUTION:From the question, it is clear that 2
part of the work has been
completed by 12 workers in 16 days.
Remaining work =1-2 1
3
Remaining number of days =20- 16 =4
Thus, part of the work is to be finished in 4 days.
2
Number of workers required to complete part of work in 16 days = 12.
Number of workers required to complete 1work in 1 day
= 12 x X 16
2
1
Number of workers required to complete work in 1day
3 1
=12 X G*
x16X3 1
Number of workersrequired to complete work in 4 days
3 6x3x4x1x1 = 24
= 12°x 1x3x1
3 A1
= 24 12 = 12
Number of additional workers required12 more workers to complete the
engage
Hence, the contractor willhave to
work in time.

AssiGNMENT 6.8
correct option.
Multiple Choice Questions (MCQ) Choose the
1. kmh is
when converted into
m/sec (c) 172 km/h (d) 27 km/h
(i) The speed of 45 (6)162 km/h train to
(a) 152 km/h
moving at 45 km/h. The time taken by the
long is
(iü) Atrain of 150 m platform is seconds
crossa 500 m long (b) 12 seconds (c) 52 seconds (d) 40
to travel
(a) 40 minutes
36 kilometres. How long will he take
hours to travel
Z. A man takes 6
long will it
120 kilometres ?
pole with a speed of 72 km/h. How
450 m crosses a
3. A train of length long will
take to cross the pole ?
and Sumit can do it in 6 days. How
in 4 days together ?
a piece of workSumit
* Sanju can doboth Sanjuand work
they take, if
160 Excellence in Mathematics-VII

1
5. Ramita can complete part of a work in one day. How long will she take to
20
complete the work?
6. A can complete a work in 12 days and Bcan complete the same work in 8
What part of the work willthey alltogether complete in 1day ? days.
7. A and B together can do a piece of work in 6 days and A alone can do in 8 d
In how many days can B alone do it ?
8. Aand Btogether can do a piece of work in 6 days and B alone can do the son.
work in 9 days. In how many days can A alone complete the work ?
9. A and B together can do a piece of work in 10days. A alone can finish the work in
30 days. In how many days willB alone finish the work ?
10. A and B can do a piece of work in 8 days and B alone can do it in 12
days. In how
many days can A do it alone ?
11. A can complete a work in 6 days andB can complete it in 5 days. How long will
both together take to complete the work ?
12. A alone can do a piece of work in 12 days and Balone can do it in 15
days. Wht
part of the work will they do in 3 days ?
13. A alone can do a piece of work in 12 days and B
alone can do the same work in
15 days. A works alone for 4 days. In how many days will A
the remaining work ?
and B together finish
14. A alone can do a piece of work in 12 days and B
alone can do the same work in
15 days. They start working together. After 4 days, B
many days will A alone complete the remaining work? leaves the work. In how
15. Mukesh can do a work in 25 days and Rajesh can
together for 5 days and then Mukesh leaves the work.finish it in 20 days. They work
In how many days will Rajesh finish the
remaining work ?
16. X and Y together can do a piece of work in 10
days, Y
together in 12 days, while X and Z can do together in and Z can do the same work
15 days. How long each
take to do it separately ? will
17. A work is to be finished in 12 days by 20
workers. After 8 davs, it is found that only
part of the work has been done. How many more
2 workers should now be engageu
in order to finish the job in time ?
 Ratio and Proportion 161
CHAPTER-Section
END EXERCI
A
SES
MULTIPLECHOICE
QUESTIONS (MCQ)
question there are four
Options, out of which one is
An article is sold for 5000 which correct. Choose the correct one
(a) 20% gain was bought for 4000.
(6) 20% loss The gain or loss %1s
(c) 25% gain (d) 25% loss
2. A
wholesaler sells 25 shirts, but
rgin % of the retailer, if he sellscharges for 24 shirts from the
all the 25 shirts at the retailer. What is
(a)4% (6) 5%
marked price ?
(c) 3-%
6 (d) 49 %
6
1he S.P. and C.P. of an article differ by 200. If
the profit is 10%, then the S.P. is
(a) 2000 (6) 2200 (c) 2100 (d) 2400
Acompletes a work in 8 days. A and B working together complete the same work
4
in 4 days. How long would B alone take to complete the same work ?
5
(a) 10days (6) 12 days (c) 16 days (d) 15 days
2 4
5. If A : B =
3
and B:C= then A:Cis
(a) 3:4 (6) 2:9 (c) 8:27 (d) 1:2
6. If 2:x::x:8, then x=
(a) 3 (6) 4 (c) 8 (d) 2

7. The list price of an article sold for 190 after 5% discount is

(6) 200 (c) 205 (d) 210
(a) 195
the marked price and gives a discount of
8. If ashopkeeper adds 20% profit to write
10%. What is the actual gains in percentage ? (d) 12%
(c) 8%
(a) 10% (b) 2%
836, then the
If the marked price of an article is 950 and the sellig price is
9.
discount is (d) 14%
32 (c) 12%
33 (6) 12 209
(a) 13 %
on the
and allows a discount of 20%
209
goods 20% above C.P.
10. Ashopkeeper marks his loss per cent is
marked price. His gain or (6) 8% gain
(a) No loss or gain per cent (d) 4% gain
(c) 4% loss
L. TRUE / FALSE
1. Ratio has no units.
2, Two ratios 3:4 and 5: 6 are equal.
like a fraction.
3. Ratio can be simplified article is called the marked price.
4. The price written on an
are same.
The C.I. and S.I. for 2 years replaced by(- R)
6. In case of depreciation, Ris
162 Eeeltece n Atathemate Vill

7. The (L dter every yer, but the NI remains the aane

N, The pwrixd ater which interest in credited tor caloulated) ia called converaion peria
9. Iwo ration Aand 6 are equal
10. Hthe need of atran iweanen, the time taken to complete njourney inereases
thesame ratio

mFILLIN THE BLANKS

I. Cain or loss per vent in caleulated on
2. Discount in allowed on prico.
8. Net price in between MP. and diacount.
4. Speed x time
6. Ifx and yvary inversely, then xy in
6. The ratio in alwayN

7. The time taken to finish a work in proportional to the number of persons

working on it.
8. Ifspeed inereases, then time
9. If the number of biscuits inereases 3 times, then their value
increases
times,
10. Distance covered is proportional to the speed.
IV. MATCH THE COLUMNS
1. Column A
Column B
(a) (100 + gain%) xC.P.
100 (p) Gain%
SP.x100
(100 loss%) (q) C.P.

(SP. -C.P)×100
CP. (r) Loss %
C.P.- S.P)x 100
C.P. (s) S.P.
2,
Column A
ta) The price paid to buy ColumnB
tb) The price charged (p) Selling Price
(e) The printed price (q) Discount
( )Reduction in the M.P. (r) Cost price
(s) Marked Price
 165
TEST PAPER-2
Based on Chapters 46

1. MULTIPLE CHOICE QUESTIONS (MCQ)

For each question. there are four Options, out of which one is correct Choose the correct
one
20
() If +3 = 1, then x=
(a) - 10 (b) 10 (c) 5 (d) -5
(i) If eight times a number is 32, the number is
(a)-1 (6) - 4 (c) 1 (d) 4
(ui) The consecutive multiples of 5, whose sum is 105, are
(a) 45, 60 (6) 35, 70 (c) 50, 55 (d) 25, 80
(iv) The number consists of 2 digits whose sum is 6. If 18 is added to the number, the
digits changetheir places. The number is
(a) 24 (6) 15 (c) 42 (d) 23
(u) Given that 5x - 2(6 + *) = 15, the value of xis
(a) 3 (6) 6 (c) 9 (d) 12
(vi) Awholesaler sells 25 shirts but charges for 24 shirts from the retailer. What is the
gain %of theretailer, if he sells all the 25 shirts at themarked price ?
1
(a) 4
(a) 4% (6) 5% (c) 3A 6
(vi) An article was sold for 45 at a discount of 10%.It was priced at
(a) 55 (b) 50 (c) 60 (d) 49.50
(viii) The S.P. and C.P. of an article differ by 200. If the profit is 10%, then the S.P. is
(a) 2000 (6) 2200 (c) 2100 (d) 2400

(ix) x varies directly as y²., Given that x = 3 when y = 4, then value of xwhen y = 6 will be
4 27 9
(a) (6) (c) (d)
27 4
same work in 6
(x) 12 men complete a work in 8 days. How many men will finish the
days?
(a) 9 (6) 4 (c) 12 (d) 16
time will she take
(xi) Priyanka drives at 45 km/h and reaches Delhi in 5 hours. What km/h?
to complete the same journey, if she increases her speed by 5
1 1
(a) 4 hours (6) 44 hours (e) 4 hours 34 hours
(0.31) - (0.09)
(xiü)
0.31 + 0.09
(a) 0.4 (6) 0.22 (e) 0.02 (d) 0.32

2. TRUE IFALSE
LH.S. = R.H.S.
) An equation has two sides 4.
ii) Ifa number is divisible by 8, it must be divisible by
by 4.
(ii) The sum of two odd numbers is always divisible cquation.
(iv) A statement of equality which involves one or more variables is called an
2
( 5x+ is a polynomial.
166 Excollence in Mathematcs-Vl

(vi) 7 can be written as "70."

(vii) Sales tax is a direct tax.
(viii) The degree of the polynomial xy is 2.
(ix) Two quantities x and yare saidto vary directly, if is constant.
(x) In inverse variation, if one quantity increases, the other quantity also
3. FILL IN THE BLANKS
increasea
5x-7
(i) If = 2, then x =
3x
(ü) When the dividend and the divisor have opposite signs, the quotient has
sign.
(üi) The smallest number (greater than 1), by which 319 is divisible, is
(iv) The degree of any constant is
(v) Discount = M.P. -
(vi) Ifa and b are positive integers such that a² > b2, then a
(vü) Ifa divides b, then a³ divides
2
(viiü) The degree of the polynomial a- 469 +2ab5 is
(ix) When speed is double, the time is to cover the same distance.
(*) In direct variation, if x decreases then y and x ify increases
(zi) If the number of biscuits increases 3times, then their value increases
times.
(zii) 40 articles cost 180. The cost of 12 articles is
4. MATCH THE COLUMNS
(i) Column A Column B
(a) S.I. = (100- loss) x C.P.
(p)
100
(b) Amount = PxRx T
(q)
100
(c) S.P. = (r) loss x 100
C.P.

(d) Loss% =
100
(iü) Column A ColumnB
(a) The no. of terms in a trinomial is
(p) 1
(b) (-2x + x2 (q) 2
(c) Degree of 2x'-5x + 1is (r) 4
(d) A factor of every algebraic term is (s) 3
 167
TEST PAPER-3
Based on Chapters 16

Multiple Choice Questions (MCO) SECTION-A

or each question. there are four Options, out of which one is correct.
Choose the correct one :
1. Arational number can be expressed as a
has factors terminating decimal, if its denominator
(a) 2 or 3 (6) 3or 5 (c) 2 or 5 (d) 2 or 3 or 5

2. The approximate value of is

(a) 0.82 (6) 0.67 (c) 6.7 (d) 8.2
3. The cube of 1 - is
5
8 8 27 27
(a) 1 (6) 1+ (c) (d) -
125 125 125 125
4. Which of the following is true statement?
(a) Cubes of all integers are positive.
(6) Cubes of even natural numbers are odd.
(c) Cubes of odd natural numbers are even.
(d) Cube of a natural number ending in a single zero ends in three zeroes.
m -17
5. Given that = 2m -7, the value of mis
2
31 31
(a) (6) - (c) -3 (d) -1
3
6. The sum of three consecutive odd numbers is 69. The smallest of the three numbers is
(a) 21 (6) 23 (c) 25 (d) 19
7. A bicycle is sold for 880 at a loss of 20%. At what price should it be sold to gain 15%?
(a) 1265 (6) 1165 (c) 1065 (d) 965
a
8. Bacteriain a culture grow 15 per thousand in an hour. If the count of bacteria in
sample is 1000000, after 2 hours it will be
(6) 1080225 (c) 1030125 (d) 1030200
(a) 1030225
9. A father is 4 times as old as his son. 5years ago, he was 7
times as old as his son was.
The present age of the son is (d) 20 years
(a) 15 years (6) 10years (c) 12 years
10. Ifa:b=2:3 and b:c=6:8, the a:c= (c) 1:3 (d) 3: 4
(a) 1:2 (6) 3:8

SECTION-B
Very Short Answer Type Questions
divisible by each one of thenumbers 4. 8. 12.
I1. Find the least square number which is exactly
square metres, find its side.
12. If the area of a square field is 12100 share of Rita and half share
13. Diyide 500 between Rita and Seema such that one-third
of Seema are equal.
decreased by 20%. Find the net inerease
14. A number is frst increased by 20% and then
0ar decrease per cent.
 l68 Excellence in Mathematics--Vil

l5. Tap Aflls atank in 4 hours and tap Bfills the tank in 8 hours. How long would n
take to fill the tank, if both the taps are open simultaneosly ?
16. Twotrains of 50 m and 110m long are moving at 34 km and 30 km per bolyr
respectively in opposite directions. How long would it take them to pass each other
17. Factorise r - a.
18. Aand Bcan do a piece of workin 6days and 4 days respectively. Astarted the
worked at it for 2 davs and then was ioined by B. Find the total time taken to work,
complete the work.
SECTION-C
Short Answer Type Questions
11
19. Represent the on anumber line.
3
7
20. The speed ofa car is km per hour. Find the distance travelled by it in 2 hours
35
minutes.
2

21. In what time will &

64,000 amount to 88,360 at 17% per annum, interest being
compounded yearly ?
22. If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of the pile of
294 cardboards.
23. A father is 30 vears elder than his son, and one year ago, he was four times as old as
his son. Find their present ages.
7
24. What must be added to each of the numerator and the denominator of the fraction to
11
3
make it equal to 4

25. Two trains starting at the same time, having lengths 200meach are moving in same
direction. If speeds of the two trains are 30km/h and 35 km/h respectively, find when
they will cross each other ?
26. If 10 men can do a part of work in 18 days, how many would do it in 30 days ?
SECTION-D
Long Answer Type Questions
27. A man leaves half of his property to his wife, one-third to his son and the remaining
to his daughter. If the daughter's share is 15,000, how much money did the man
leave ? How much money did his wife get and what was his son's share ?
28. A swimmer goes downstream in a river and covers a distance in two hours. It covers
the same distance upstream in three hours. If the speed of the stream is 2 kh, find
the speed of the swimmer in still water.
1 1
29. Find 5 rational numbers between and
2
1-3*
30. Solve =(4x-1) - 4x
2

81. Prove that, if the difference between a 3-digit number in the formn of a0b (ie. d1git at
number
tens place is 0.) and the sum of its digits is divided by 99, we always get the
equal to a.
 182 Excellence in Mathematics--Vll

CHAPTER-ENDEXERCISES
Section A
I. MULTIPLE CHOICE QUESTIONS (MCQ)
For each question. there are for Options, out of which one is corect. Choose the
1. The diagonals of a parallelogram
(6) bisect each other.
correct one
(a) are equal.
(c) bisect each other at 90°. (d) bisect opposite angles.
2. The diagonals of rhombus
(a) are equal. (6) bisect each other.
(c) bisect each other at 90°, (d) None of these
3. ABCD is a quadrilateral. If AC and BD bisect each other, then ABCD must h.
(a) square (6) rectangle
(c) rhombus (d) parallelogram
4. Which of the following cannot be the angles of a quadrilateral ?
(a) 90°, 70°, 110°, 90° (6) 85°, 89°, 71°, 115°
(c) 89°, 75°, 80°, 85° (d) 101°, 91°, 79°, 89°
5. The lengths of the diagonals of a rhombus are &
cm and 6 cm. Its each side is
(a) 10 cm (6) 4 cm (c) 4.5 cm (d) 5 cm
6. In a parallelogram if one angle is 60, the
(a) 60°, 60°, 60° other angles are
(6) 60°, 90°, 90° (c) 60°, 120°, 120° (d) 45°,
7. If in the 135°, 120°
adjoining figure,
ADE and CBF are straight lines,
E

D55°
then x =
(a) 55° 650y
(6) 60°
(c) 65° (d) 50°
B
60y
8. The
(a) quadrilateral
square formed by joining the mid-points of the
(6) rectangle sides of a quadrilateral is a
9. If a (c) parallelogram (d) kite
(a)quadrilateral
kite ABCD is such that AB = AD and
BC = CD, then it is a
(6) parallelogram
10. One of the (c) square
the rhombusdiagonals of a rhombus is (d) rhombus
are equal to a side of the
(a) 60°, 80°,110°, 110
(6) 100°, 80°, 100°,
rhombus. The anges u
II. TRUE/FALSE
80° (c) 60°, 120°., 60°,
120 (d) 90°, 90 ,0
1. The
diagonals of a rectangle bisect each
2. If two
pairs of adjacent sides of a other at right angles.
3. Every
quadrilateral quadrilateral
is either a are eaqual, then it is arhombus.
4. All
5. rectangles parallelogram.trapezium parallelogram
are or a
or a Kite.
6.
Opposite sides of a
trapezium are parallel.
Opposite angles of a
parallelogram are equal.
 Understanding Shapes 183
7 If three angles of a quadrilateral are 90°, 50° and 90°, then the fourth angle is 80°.
8. The length of each diagonal of a quadrilateral is 9 cm and they
Then, the quadrilateral is a parallelogram. bisect each other.
9. Each diagonal of a square bisects the square into two
congruent triangles.
10, All the angles and sides of a rhombus are equal.
II. FILL IN THE BLANKS
1. The diagonals of a square each other at right angles.
2. The diagonals of a parallelogram ABCD intersect at 0. If Z BOC = 80° and
Z BDC = 60°, then OAB is

3. If two adjacent angles of a parallelogram are in the ratio 4 : 5, then the measures of
the angles are
4. Two line segments, each 9 cm long, bisect each other at right angles. Their end-points
are joined together. The shape formed is
5. The diagonals of a parallelogram are
6. If the adjacent sides of a parallelogram are 9 cm and 6 cm, its perimeter is
7. In a parallelogram, opposite angles are
8. In a rhombus, all sides are
9. A rectangle is a square, if its diagonals bisect each other at
10. A rhombus has pairs of parallel sides.

IV. MATCH THE COLUMNS

1. Column A Column B

p) Rhombus
(a) Unequal diagonals bisect each other.
(6) Equal diagonals bisect each other. (q) Square
(c) Unequal diagonals bisect each other (r) Parallelogram
at right angles.
(d) Equal diagonals bisect each (s) Rectangle
other at right angles.
Column A ColumnB
2. A
(a) ZA=ZCZB=ZD= 90°, (p) Parallelogram
AB = CD, BC = AD D

(q) Square
(6) AB | CD
D

BC, (r) Rectangle

(c) ZA=Z0,AB = CD, AD =BC
A B

ZB=2D, AB || CD, AD | D

A
(d) AB= BC = CD = DA, (s) Trapezium
2A=ZB=2C=ZD= 90° C
D
184 Excellence in Mathematics-VII

Section B

I. SHORT AND LONG ANSWER TYPE QUESTIONS

1. Three angles of a quadrilateral are 100°, 50° and 50° respectively. Find
the
of the
fourth angle.
2. The four angles of a quadrilateral are in the ratio 3:5:7:9. Find the
measure
quadrilateral. A
angles of the
3. In the adjoining figure, E is a point in the D
interior of ZAOB, such that EIOB and (E
EDIOA. IfZ AOB = 36°, what is the
measure of CED ? C

4. Twoadjacent angles of parallelogram are in the ratio 7 :2. Find the measure of .
the angles of parallelogram.
3
5. The long side of a parallelogram is 8 cm. If the shorter side is 4
of the longer side
find the perimeter of the parallelogram.
D
6. In the adjoining figure, ABCD is a parallelogram.
If ZDAB = 85° and Z DBC = 60°, then calculate: 85 60°
(i) ZDB (iü) ZABD A P

7. If one of the angles formed by diagonals and adjacent sides of rhombus is 20°, fnd all
four angles of rhombus.
8. Show that the four triangles as shown in the adjoining
figure, formed by diagonals and sides of a rhombus are congruent.
9. Prove that diagonals of a rhombus bisect D

each other at right angles as given in

the adjoining figure.
A B
10. If one of the diagonals of a rhombus is equal to one of its
sides, find the angles of
rhombus.
11. Two angles of a quadrilateral are 55° and 175° and the other
What is the measures of each equal angles ? two angles are equal
12. The angles of aquadrilateral are 2x + 3°, x + 7°, 3x- 5° and 2x +
measure of each angle of the quadrilateral. 11°. Find the
D
13. From the adjoining figure, calculate the
remaining angles of the parallelogram ABCD. 80
A
B
14. The point of intersection of the diagonals of a quadrilateral
the ratio 3 :4. Can it be a parallelogram ? Why or why divides one diagonal in
not ?
15. Two adjacent angles of a parallelogram are in the ratio 4 : 5.
the parallelogram. Find all the angles o
16. Prove that each diagonal of arhombus bisects the
angle through which it passes.
17. Prove that in a parallelogram :
(i) opposite sides are equal. (ii) opposite angles are equal.
(ii) each diagonal bisects the parallelogram.
18. Prove that diagonals of arhombus bisect each
other at right angles.
19. Prove that diagonals of a square are equal and bisect each other perpendicularly.
20. Prove that if a pair of opposite sides of a quadrilateral are equal and paralle, it is a
parallelogram.
 Understanding Shapes 185
IL. MENTAL MATHEMATICS
1. In the adjoining A
30°
figure, if AB || CD,
then x=
Fillin the blanks and encircle the words
35
in the grid given below :
D
1. Sum of the of a quadrilateral is
360°
A, C
2. In the adjoining 2. If the diagonals of a parallelogram
figure, ifAO || CD, bisect each other at right angles.
OB ||CE and then it is a
2AOB= 40°, 3. A figure made of two isosceles triangles
then ECD = on the opposite side of the common
base is a
3. In the parallelogram ABCD, D
4. The angies of a paralelogram are
AP and BP are bisectors of supplementary.
ZDAB andCBA 5. Ina quadrilateral ABCD, AB. BC. CD
and AD are its and AC is a
respectively. B
6. If an angle of a quadrilateral is greater
If ZDAB = 60°, find the than 180°, then it is a quadrilateral
measure of the APB.
7. If a point is neither on the quadrilateral
4. In the parallelogram ABCD, AC and BD nor in its exterior, then it is in its
8. The opposite of interior is
are its diagonals intersecting at 0. P is
L X
mid-point of DO and Q is mid-point of OB. D A ON

Prove that APCQ is a parallelogram. A WR A L N

Nolmo
D T D O L N
P
K K N M

G M A RE
A B
BC D Y T VR

M E WF
5. Find the measure of each angle of the
parallelogram, if two adjacent angles PC z K o

of a parallelogram are equal. E X T E O R

HOT Higher Order Thinking Skills

corners of a cube.
1. An ant and ablind spider are on opposite
one
from
The ant is stationary and the spider moves at random
is the expected
corner to another along the edges only. VWhat
number of turns before the spider reaches the ant ? Also, solve
icosahedron, and dodecahedron.
for a square, octahedron,

VALUE-BASED QUESTIONS
1. Three horses are standing in a triangular field,
which is exactly 100 yards on each
simultaneously all three set of unnin
side. Onehorse stands at each corner, and on his left, thus followiny a
Each horse runs after the horse in the adjacent cornerfield, all three horses arrivnw
curved course. which terminates in the middle of the far did thev un )
sane speed, how
there together. If the horses ran at the
the ratio of 4 : 5. Find all the
2. Two adiacent angles of a parallelogram are in
angles of the parallelogram.
 Representing 3D in 2D 193
CHAPTER-END EXERCISES
Section A

L.MULTIPLE CHOICE QUESTIONS (MCQ)

For each question, there are four Options, out of which one is correct. Choose the correct one :
1. Number of faces in a cylinder is
(a) 1 (6) 2 (c) 3 (d) 4
2. Number of vertices in a cone is
(a) 1 (6) 2 (c) 3 (d) 4
3. Allfaces of a tetrahedron are
(a) rectangles (6) squares
(c) equilateral triangles (d) isosceles triangles
4. The three-dimensional figure obtained by rotating a right triangle about one of its
legs is a
(a) cylinder (6) cone (c) sphere (d) cube
5. Which one of the following is a three-dimensional figure?
(a) circle (6) rectangle (c) triangle (d) sphere
6. The place where two faces of a solid meet is called
(a) vertex (6) edge (c) face (d) surface
7. If the numbers of vertices and faces in a solid are 3 and 4 respectively, then the
number of edges is
(a) 5 (b) 7 (c) 4 (d) 2
8. In the Fig. given at right, the number of vertices is
(a) 7 (6) 8 (c) 10 (d) 12
9. In the Fig. of Q. 8, the number of edges is
(a) 13 (6) 18 (c) 16 (d) 14
10. An octagonal prism has
(a) 24 edges (b) 8 faces (c) 30 vertices (d) 12 vertices

II. TRUE / FALSE

1. Sphere has one flat surface.
2. A eylinder has one curved face.
3. Rectangle and cube are both two-dimensional figures.
4. A cone has one flat surface.

5. isa net for acube.

6. A solid. whose base and top are identical polygons and side faces are rectangles,
is called prism.
7. A rectangular prism has 8 faces.
8. Polvhedrons are the solid figures with line segments as their edges.
194 Excellence in Mathematics-V

3. Cylinder is obtained by rotating a

rectangle about one of its sides.
10. Octahedron has 6 vertices.

IL FILL IN THE BLANKS

1. Euler's formula is, V + F -E=
2. A pentagonal prism has faces.
3. Each face of tetrahedron is triangle.
4. A die looks like a

D. 1-iron used in the construction of buildings is an example of pristn.

6. Apyramid with 8 edges has faces.
7. Apyramid has always number of edges.
8. Road roller is an example of.
9. A joker'scap is an example of a
10. An octahedron has faces.

IV. MATCH THE COLUMNS

1. Column A Column B

(a) Square prism p)

Notee
A
prism is a solid object wit
. identical ends
(b) Cone . flat faces
q)
and the same
cross section along its
length.
A pyramid is a
(c) Octahedron (r) polyhedron
formed by
connecting a
(d) Pyramid (s) polygons base and
a point.

2. Column A Column B

(a) Open net of a cylinder is p)

(b) Open net of a square pyramid is (q)

(c) Open net of is a triangular prism is (r)

(d) Open net of a tetrahedron is

 Representing 3D in 2D 195

Section B
1SHORT AND LONGANSWER TYPE QUESTIONS
1. Draw the net of the following:
3 cm
1.4cm
cm
4 3 cm

4 cm
4 cm

2. Draw the net of the following figure.

3. Draw the side view, front view, top view of the following.
Top

Side

Front

4. Find the number of cubes in the base layer

of 3D object given at right.

5. Draw top, side and front views of the following figure.

Top

Front
A

Side B

6. Verify Euler's formula in the following figure.

E

solid.
7. Verify Euler's formula for the following

faces do the
8. How many vertices, edges and
following figure have ?

following
9. Name the vertices, edges and faces of the
polyhedron.
G
 207
TEST PAPER-4
Based on Chapters 7-9

MULTIPLE CHOICE QUESTIONS(MCQ)

Fot each question there are four Optons. out of which one is Correct Choose the correct
One

G) We cannot construct aquadrilateral, when we are given

(a) four sides and one diagonal.
(6) one side and four angles.
(c) four sides and one angles.
(d) three sides and two diagonals.
ü) Which of the following cannot be the angles of aquadrilateral ?
(a) 90°, 70°, 110°, 90° (6) 85°,89°, 71°, 115°
(c) 89°, 75°, 80°, 85° (d) 101°, 91°, 79°, 89°
(iii) Two line segments, each of 9 cm long, bisect each other at right angles.
Their end-points are joined together. The shape formed is
(a) square (6) kite (c) trapezium (d) pentagon
(iv) The diagonals of a rhombus
(a) are equal. (6) bisect each other.
(c) bisect each other at 90°. (d) None of these.
they bisect each other.
(v) The length of each diagonal of a quadrilateral is 9 cm and
The quadrilateral is a
(c) square (d) rhombus
(a) parallelogram (6) rectangle
angles are
(vi) In a parallelogram, if one angle is 60°, the other 120°, 120° (d) 45°, 135°, 120°
(a) 60°, 60°,60° (6) 60°, 90°, 90° (c) 60°,
(viü) An octagonal prism has (c) 30 vertices (d) 12 vertices
(a) 24 edges (6) 8 faces
(vii) The following figure represents a
(a) cylinder (6) polyhedron
(c) polygon (d) hexagon

2. TRUEIFALSE
quadrilateral is 360°.
(i) The sum of all the angles of a the diagonals lie outside the
quadrilateral.
quadrilateral is convex, if one of
(ii) A
parallelogram are not equal.
iii) The diagonals of a
Every quadrilateral is either a trapezium or a parallelogram or a kite.
(iv)
trapezium are parallel.
(U) Opposite sides of a
(i) All rhombus are parallelograms.
called a quadrilateral.
Um) A polygon of 4sides is
both two-dimensional figures.
C)Rectangle and cube are
= 2.
ix) Euler's formula is V + F-E
rectangular pyramid is given by 4 + 4-6 2.
(x) The Euler's relationship in a
208 Excellence in Mathematics-VIll

3. FILL IN THEBLANKS

(i) Opposite angles of a parallelogram are

(ii) Two sides of a quadrilateral with common point are
sides. called
(iiü) A pair of opposites sides of a trapezium are
(iv) Atriangular pyramid is called a
(w) If all four sides of a parallelogram are ,it is a rhombus.
(v) The no. of edges in a pentagonal prism is
(vii) The no. of faces in a tetrahedron is
(vii) The no. of vertices in a rectangular pyramid is
(ix) The diagonals do not necessarily bisect interior
angles at the vertices in a
(r) The bisectors of any two adjacent angles of a
parallelogram intersect at
4. MATCH THE COLUMNS

(i) Column A
Column B
(a) Diagonals bisect each other.
(p) Square
(6) Diagonals bisect each other
at right angles. (q) Parallelogram
(c) Diagonals bisect each other at
(r) Rectangle
right angles and equal also.
(d) Diagonals are equal and bisect each other. (s)
Rhombus
(iü) Match the columns regarding Euler's relationship in
solids.
Column A
Column B
(a) 6 + 6-10 = 2
(p) Tetrahedron
(6) 8 + 6-12 = 2 (q) Triangular prism
(c) 4 +4-6= 2
(r) Pentagonal pyramid
(d) 6+5 9=2 (s) Cuboid