ganit prabhutwa examination-2018 date: 09.12 ... - rao …...rao iit academy / ganit prabhutwa...
TRANSCRIPT
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1 1
N.B. For Q. No. 2 to 5 proper procedure and explanation is necessary.
Q.1 Choose the correct alternative answer in each of the following. [10 M]
1. 50.1 ......
(A) 0.1 (B) 1 (C) 0.001 (D) 0.00001
Sol: (D)
55 1 5 10.1 10 10 0.00001100000
Topic:Integers, Decimals & Fractions / Sub-topic:Decimals/ L-Easy / Ganit Prabhutwa Examination
2. Find the hypotenuse of a right angled triangle having sides 20 and 21
(A) 29 (B) 28 (C) 41 (D) 25
Sol: (A)2 2 2c a b
2 2 220 21c
400 441
C
a=20
b=21
841
2 841c
841 29c
Topic:Geometry / Sub-topic:Triangles / L-Easy / Ganit Prabhutwa Examination
3. Find the value of 2 2a b if 12a b and 10ab (A) 124 (B) 104 (C) 164 (D) 144
Sol: (A)
12a b ; 10ab
JEE | MEDICAL-UG | BOARDS | KVPY | NTSE | OLYMPIADS
GANIT PRABHUTWA EXAMINATION-2018Time: 3 hrs.
Date: 09.12.2018 Std. VIII Max.Marks : 100
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
2 2
2 2 2 2a b a b ab
2 2 212 2 10a b
2 2144 20 a b
2 2 124a b
Topic:Algebra / Sub-topic:_/ L-Easy / Ganit Prabhutwa Examination
4. Which member of the set 2,3,5,7,9,11,13 is not a prime number ?
(A) 2 (B) 11 (C) 9 (D) 5
Sol: (C)
9 is not a prime number.
9 3 3
Topic:Number System / Sub-topic:Prime Numbers / L-Easy / Ganit Prabhutwa Examination
5. Which of the following is the product of 8,937 and 125 ?
(A) 93700 (B) 937000 (C) 7496500 (D) 4685000
Sol: (B)
The given three numbers are 8; 937; 125
8 937 125
937 125 8
937 1000
937000Topic:Integers, Decimals & Fractions / Sub-topic: Integers/ L-Easy / Ganit Prabhutwa Examination
6. Find : :x y z if 2 3 4x y z
(A) 6 : 4 : 3 (B) 2 :3: 4 (C) 4: 3:8 (D) 3: 2 :3Sol: (A)
2 3 4x y z k
2kx ; 3
ky ; 4kz
: : : :2 3 4k k kx y z
1 1 1: :2 3 4
6 : 4 : 3
Topic: Ratios and Proportions / Sub-topic:Proportions / L-Easy / Ganit Prabhutwa Examination
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
3 3
7. Find the difference between the simple interest and the compound interest on Rs. 1600 at the rate 5 p.c.p.a.for 2 years.
(A) Rs. 160 (B) Rs. 80 (C) Rs. 4 (D) Rs. 5
Sol: (C)
S.I. 1600 2 5 160
100 100PTR
. . 1100
trC I P P
251600 1 1600100
4411600 1400
411600 164400
. . . . 164 160C I S I
Rs. 4
Topic:Simple Interest and Compound Interest/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
8. Find the middle term (geometric mean) of 0.25 and 400.
(A) 10 (B) 1 (C) 100 (D) 0.1
Sol: (A)2b ac , ,a b c geometric progression
2 400 0.25b
2 4 25b
4 25b
100 10b
Topic:Sequence and Series/ Sub-topic: Geometric Progressions/ L-Easy / Ganit Prabhutwa Examina-tion
9. Mohanlal got a profit 14
th
of the cost price when he sold an article for Rs. 400. Find the profit percent.
(A) 40 (B) 10 (C) 25 (D) 20
Sol: (C)
Let cost price be x
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
4 4
profit 4x
Selling price 400
Profit percentage P ro fi t 1 0 0
.C P
/ 4 100xx
25%
Topic:Profit and Loss/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
10. Whole numbers m,n are such that 121nm . Find the value of 11 nm
(A) 1024 (B) 10000 (C) 1 (D) 1000
Sol: (D)2121 11 121nm
11, 2m n
1 2 1 31 11 1 10 1000nm
Topic:Number System / Sub-topic:Exponents / L-Medium / Ganit Prabhutwa Examination
(B) Write only answer of each of the following subquestions. [10 M]
1. The sides of a rectangle are 24 cm and 18 cm. Find the perimeter of the square drawn on its diagonal.
Sol. In :BCD
2 2 2BD BC CD
2 224 18
A B
CDE
F
24 cm
18 cm
576 324
2 900BD cm
30 , perimeter 4 30 120BD cm cm
Topic:Mensuration/ Sub-topic:Rectangles_/ L-Medium / Ganit Prabhutwa Examination
2. Find the values of x and a, from the information given in the adjoining figure.
105o65o
Sol. 180ACP ACB
105 180a
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
5 5
180 105o oa
75a
Also, ABC ACB x {external angle of a triangle}
A x
aB C P
105o
65o
65o a x
65 75o ox
140x
140 , 75ox a
Topic:Lines and Angles / Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
3. Rakhi completes a task in 10 days, while Rama takes 5 days to finish the same task. If they work
together, in how many days will they finish the task ?
Sol. Rakhi completes a task in 10 days.
In one day, Rakhi completes 1
10 of the task.
Similarly, in one day, Rama completes 15 of the task.
If Rakhi and Rama completes the task in ‘x’ days working together.
In one day, they will do 1x of the task.
1 1 110 5 x
1 1 210x
10 days3
x
They will finish the task in 103 or 3.33 days.
Topic:Time and Work / Sub-topic:_/ L-Easy / Ganit Prabhutwa Examination
4. If 183 = 5832, then find the value of 23 5.832 5 .
Sol. 318 5832
32 3 2 13 5.832 5 5832 10 5 18 10 25 45
Topic:Integers, Decimals & Fractions / Sub-topic:Decimals_/ L-Easy / Ganit Prabhutwa Examination
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
6 6
5. The bisectors of and B C of ABC meet at incentre I. 54m A , find the measure of BIC .
Sol.
A
B C
I
In , 180ABC A B C
54 180B C
126B C ...(i)
In , 180BIC IBC ICB BIC ...(ii)
1But 2
IBC B ...(iii) { the angles are bisected}
1and 2
ICB C ...(iv)
from (ii), (iii), (iv)
1 1 1802 2
B C BIC
1 1802
B C BIC
1 126 1802
O BIC
180 63BIC
117BIC
Topic:Geometry / Sub-topic:Triangles/ L-Medium / Ganit Prabhutwa Examination
Q.2 Solve the following : [15 M]
1. PQRS is a rhombus : 40m MQR . Find the measures of ; , ,QSR PQR QPS .
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
7 7
Sol. Given : 40oMQR
2PQR MQR { QM is angle bisector of PQR }
40°
2 40 80o o
180oQRS PQR
180 80o oQRS
100oQRS
In :QRS
180oQRS QSR SQR
100 40 180o o oQSR { SQR MQR }
40oQSR
Also, QPS QRS
100oQPS
40 , 80 and 100o o oQSR PQR QPS
Topic:Quadrilaterals and Polygons/ Sub-topic:Quadrilaterals/ L-Medium / Ganit Prabhutwa Examina-tion
2. Exactly at what time between 2 and 3 will the hour hand overlap the minute hand ?
Sol. At 2 o’ clock, hour hand will be at 2 and minute hand will be at 12.
In one hour, hour hand covers 360 3012
oo per hour..
In one minute, hour hand cover 030 1
60 min 2
o
per minute.
Also, in one minute, minute hand covers 360 6 per minute60
oo
12 12
3
4567
8910
11
Let they meet after x minutes :
16 602
ox x
6 602
oxx
11 602
ox
120 minutes11
x
They will after 12011 or 10.909 minutes or
10 minutes 10 60 seconds11
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
8 8
10 minutes + 55 seconds They will overlap at 2 hours 10 minutes and 55 seconds
Topic:Geometry/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
3. Find the average of the first 20 consecutive odd numbers.
Sol. First 20 consecutive odd numbers are 1, 3, 5, ----
Sum 2 12n a n d
20 2 1 20 1 22
10 2 19 2
10 2 38
10 40 400
400Average= 2020
Topic:Sequence and Series / Sub-topic:Arithmetic Progression/ L-Easy / Ganit Prabhutwa Examination
4. By simple interest, a certain amount triples in 12 years at a certain rate of interest.Find the rate of interest.
Sol. Let rate of interest be R
12
3100
P RP P
{ T = 12 years}
123 1100
R
12 2100
R
2 10012
R
50 % 16.67% p.a.3
R
Topic:Simple Interest and Compound Interest/ Sub-topic:Simple Interest_/ L-Medium / Ganit PrabhutwaExamination
5. Construct a rectangle having diagonal 6.0 cm and the measure of an angle between the diagonals 120°.
Sol.
A D
B C0
3cm 3cm
3cm 3cm
Clearly CD = 3 cmOD = 3 cm
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
9 9
i) With he help of ruler draw a line segment AC of length 6 cm and mark its mid point O on it.
A O C3 3ii) With the help of compass draw an arc of radius 3 cm from O and from C on one side of line segment
AC to get point D.
A O C3 3iii) Similarly draw an arc from O and from A on other side of line segment AC to get point B.
Join ABCD
A O C3 3
Topic:Constructions / Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
Q.3 Solve the following subquestions. [20 M]
1. The points A, B, C, D, E, F lie on a circle. Find m BAF m FED m DCB .
Sol.
A
B
C D
E
F
Join F and C
Now, FEDC is a cyclic quadrilateral
also, FABC is a cyclic quadrilateral
Now, 0180 .......FED FCD i (opposite angles of a cyclic quadrilateral)
also 0180 .......BAF FCB ii (opposite angles of a cyclic quadrilateral)
Now adding (i) and (ii)0 0180 180FED FCD BAF FCB
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1010
0360
0360BAF FED DCB DCB FCB FCD
Topic:Quadrilaterals and Polygons/ Sub-topic:Polygons/ L-Medium / Ganit Prabhutwa Examination2. GCD of two numbers is 23 and their product is 19044. Find all possible pairs of such numbers.
Sol. Let the numbers be x, y
GCD of , 23x y
19044xy
19044 828
23LCM
of , 23GCD x y , 828 23 36LCM 2 2of , 23 2LCM x y
Numbers can be 2 223,828 , 23 2 , 23 3
23,828 and 92,207
Topic:Number System/ Sub-topic:HCF and LCM_/ L-Difficult / Ganit Prabhutwa Examination
3) Simplify 2
2
12 277 18
x xx x
Sol. 2
2
3 912 277 18
x xx xx x
9x 2x
3 .2
xx
x + 2 - 5 5or 1x + 2 2x
Topic:Algebra/ Sub-topic:Quadratic equation/ L-Easy / Ganit Prabhutwa Examination
4) Solve :1 2 1 7 12
6 3 4 6x x x
Sol.1 2 1 7 2 6 1
6 3 4 6x x x
1 8 3 21 136 12 6
x x x
2 2 29 3 26x x
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1111
27 27x
1x
Topic:Algebra/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
5) In the adjoining figure, line || line m. From the information given in the figure find the measure of .ABC
Sol.
A
BD C
0110ABC
Topic:Lines and Angles/ Sub-topic:_/ L-Easy / Ganit Prabhutwa ExaminationQ.4) Solve the following subquestions. [20 M]
1. Divide 4 24 by 2 2 .x x x Find quotient and remainder. Write answer as
dividend = divisor × quotient + remainderSol.
2 2 2x x
2 2 2x x 4 4x 4 3 22 2x x x ( )
( )
3 22 2 4x x 3 22 4 4xx x
( )
22 4 4x x 22 4 4x x
0
2Quotient 2 2x x
Remainder = 0
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1212
4 2 24 2 2 2 2 0x x x x x
Topic:Algebra/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination2. The speed of a boat in still water is 25 km/hr. The time required for the boat to travel 120 km against the
stream is 32 times the time required to travel the same distance along the same stream. Find the speed of the
stream.
Sol. Let speed of stream /x km hr
Speed against stream 25 /x km hr
Speed along stream 25 /x km hr
distanceTime =speed
Time against stream 32
(Time along stream)
120 3 12025 2 25x x
2 25 3 25x x
5 25x 5 /x km hr
Topic:Time, Speed and Distance/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
3. Solve : 2 326 0.63
xo
Sol. 2 326 0.63
xo
2 32 613 10
x
2 35 33 5
x
1 3 225 5
3 3
x
13 22
x
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1313
13 22
x
56
x
Topic:Algebra/ Sub-topic:Exponents_/ L-Easy / Ganit Prabhutwa Examination4. If a polygon has 90 diagonals, then find the number of sides of the polygon.
Sol. Number of diagonals 3
2n n
2 3 902
n n
2 3 180n n 2 3 180 0n n
12 15 0n n
12 Rejectedn
15n
Topic:Geometry/ Sub-topic:Polygons/ L-Medium / Ganit Prabhutwa ExaminationQ.5) Solve the following subquestions. [25 M]
1. Factorise : 2 28 8 5 14x x x x
Sol. 2 28 8 5 14x x x x
2Let 8x x y
5 14y y
2 5 14y y
2 7y y
2 28 2 8 7x x x x ( 2 8x x y )
2 8 2 1 7x x x x
Consider : 2 8 2x x
2 4Roots2
b b aca
8 64 82
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1414
8 722
8 6 22
4 3 2
4 3 2 4 3 2 1 7x x x x
Topic:Algebra/ Sub-topic:Factorisation_/ L-Medium / Ganit Prabhutwa Examination
2. Find 33
1 3if 3 4x xx x
Sol.33 4xx
1 43
xx
On cubing,
31 6427
xx
33
1 1 1 64327
x x xx x x
33
1 4 643 13 27
xx
33
1 64 427
xx
33
1 17227
xx
Topic:Algebra/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination
3. In the adjoining figure, 90 , , , , , 12, 15.oQPS QPR PSR PR QS PS y RS x PR PQ
then - (i) Prove QPS is similar to QRP
(ii) Find the values of , .x y
P
Q R S
15 12
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1515
Sol. In &QPS QRP
90oQPS QRP
same anglesPQS RQP
Thus andQPS QRP are similar by A A test
P
Q R S
15 12
QP QS PSQR QP RP
Also in PQR
2 2 2PQ QR PR
2 2 215 12QR
9QR
159 15 12
QS PS
5 93 15 12
x y
16 and 20x y
Topic:Geometry/ Sub-topic:Triangles/ L-Medium / Ganit Prabhutwa Examination
4. In the adjoining figure ABC and PQR are congruent. All small triangles are congruent, each side ofsmall triangle is 4 find the area of the figure.
P
Q R
A B
C
4
4
4 4 4
4
44
Sol.
4 44 4
44
4 4
44 4
4
4 4
44
4A B
RQ
C
P
Area of the figure = Area of PQR (equilateral with side length = 12)
+ 3 (area of smaller equilateral triangles with side length = 4)
RAO IIT ACADEMY / GANIT PRABHUTWA EXAMINATION-2018 / STD - VIII / QP + SOLUTIONS
1616
2 23 312 3 44 4
36 3 12 3 48 3 sq.units
Topic:Geometry/ Sub-topic:Triangles and Polygons_/ L-Medium / Ganit Prabhutwa Examination5. Some kg of tea at the rate of Rs. 320 per kg is mixed with 5 kg of tea at the rate of Rs. 280 per kg. Now
the rate of the mixture so formed is Rs. 300 per kg. How much tea of the rate of Rs. 320 per kg was taken?Sol. Let the amount of tea of Rs. 320 per kg taken be x kg.
Mixture contains x kg. of Rs. 320 per kg tea. + 5 kg. of Rs. 280 per kg tea.
Rate of mixture 320 5 280
3005
xx
320 280 5 300 5x x
32 140 30 150x x
2 10x
5 .x kg
Topic:Mixtures/ Sub-topic:_/ L-Medium / Ganit Prabhutwa Examination