# Rupali Bank Math Solution by Khairul Alam) .pdf

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lRupali Bank- (Cash) - 20181

1. If sinA + sin2A :

1,

then the value of the expression cos'A + cosaA is

(Cash)-20tBJ

A.r

e.l2

c.2

-

[Rupali Bank off-

D.3

OSolution: (A)
sinA + sin2A: I

sinA: 1-sin2A
sinA: costA

or,
or,

2,

cos'A: sinA or, cosoA: sin2A

A pole 6 m high casts a shadow

or, cos4A

: 1 - cos2A So, cos2A + cosaA:1

ZJl mlong on the ground, then the Sunrs elevation

(qrB .ift-{ Emsr \e fr. e&lt;\ {E&lt; eHK Aadr qr6firBrs &lt;q TT{ E{B

r+t"t

(Cash)-2018J

4.600

B.450

c.300

tan: ffo
Yfr
AB

BC.
of

tanO

6=

:

=

2^13

or, tanO : tpn60o
.'. e-ooolans;

3.

If a + lr 2a + l,
{l-?rkr etq'e[E[ a

A.l

[Rupati Bank off-

D.90.

*i

oSolution: (A)

qMtqlfr,

ssl)

3 ..6..6 E
4z J:
IJ

effi=2rE

-:{/1 tan60o: .16
[Since
]

l

4a -

* 1, 2a*

are in Arithmetic Progression, then the value of 'a' is (,qsB qrET
l,4a- | qrr a qir {lT&lt;'E.?) [Rupali Bank Off- (Cash)-2018J

8.2

D.4

c.3

oSolution: @)

(2a+l)-(a+1) = (4a-1) - (2a+l) (rlr&lt;g' {&lt;tE,q-+Eqqu{ qrrrqQr{ lffi{o'mrrr{wtr

o4Za*l-a-l
ot,

:

4a-l-2*l

a:2a-2 :.a:2

oelrll.t:

a = 2 &lt;ctim qktE

q'H"f qGN qsftrt

is ?

etT[Bt

Ans: 2

E{ q+) , Q.xQ.+) q&lt;rs, 8xt-)
&lt;iitt

rtrI{f

EeXq

s, c q&lt;!. r ( {mT vrfiFr

I

Solution by Khairul Alam-

I

q

s6{)

r)

4:

Suppose today is Friday. What day of the weekwill
it be 65 days from now?
qlq ccks sc fr{ fr &lt;I&lt; qr&lt; ?)
"K
[Rupali Bank Off_ (Cash)_20 t SJ
A. Saturday B. Monday
C. Tuesday

(qtgT

eq-&lt;lr

r

D. Friday

oSolution: (A)

qrq :q fr-{ \e@-{k qrE qT"K
5cET,
J{Eq, Q.svr,
q6{ I slqfE scETfr{Er&lt; a4-{lr&lt;-?r

b\

egvr, 8evq, covr, ccET q&lt;( gag,T fr{e tsG r{

"f6rfr-{\TeX\,1fr&lt;6

rffit

ffirsr{frr{3r&lt;IK{Hrs

q

frmwnr&lt; ) \ffifi? efismqst{&lt;qs

T-{m eTa &lt;k Er{ r eqtm \9c qT
60 q5q {fr-{IT

c{'ftt

*
5.

r

r

qtrf

rqax\ q e( qfiEcs-{ctcet )
s{ fr_{.e tsq&lt;K I {s_fl\ \9A

c q&lt; eftwo \9s q&lt;\ se+) = gs

ffi

,r{g: flsm now = q{-{ cr-mq{q qq'"rq
{.Icuq6

A median of a triangle divides it into two (fr-grwr{\$T[fr-EsTFqeTy{fr-sqft-ss
Bank Off (Cash) _2 0 I SJ
A .congruent triangles
B. triangles of

.Tdm...)[Rupali

equal area
D. right triangles

C. isosceles triangles

OSolution: (B)
.u cst{fr-s-qr q\$\$fr-Esr 6q*Bmq\$T 6q.q*frfi} qtra-x{fr-wqfrssr..T
r ersrE.Iwrcrft&lt;r
mfr-qq qenBT q,Fp-t{rr r vR E-s-*, B

6'

Which of the following angle can be constructed with the
help of a ruler and a pair of
compasses? (frrua c+.6 6spfr eTE rt-q e&lt; qF n{rr&lt; qfsm q\$_{\$_\$
w&lt;?) [Rupali Bank Off
(Cash)-20tBJ
A.

35o

B.

4oo

c.37.5.

OSolution: (C)
qR-T {rEr eteHFrqdqk't{.&lt;tm&lt;E
rffil{qs csl.t qs-rT{ q-ll'dqT &lt;if{qla \$-fl6o qt r fte- a{
rsdr

D .47.5"

r

..m&lt;

cRRl.

wFT sil_6o Erdr
@
q-f,Ecr{t bnrs
q&lt;q &lt;rFTK fi(T rrtrEriFtt{ ert
"r&lt;
ft.r tr.6rs}} wDpr o{fs.(; qo, 6-qETl.-T
{&lt;-q \$fiT Bq&lt; y@ vr+T-{k'kr qst &lt;lm(frrs
EE wEI"r qs-{ o-&lt;rq esF qrmf"f Eks qr&lt; r q&lt;oR
qrmFf
qlRl
voGft
TsEtreBT om at=.+ ireE. +r-&lt; qcGR ror.t qo"r
r qsr-F
ryoR-uIF
rr&lt;srEf csFrm'&lt;kl. &lt;lr
qr(orm srr&lt;

qffi

v*f1.6&gt;r&lt;

."8

fi(

# {r{

r

EC\$ Eq-s

qeFf{ q-\$tft o \e qc G0n-or&lt;rq

900

750

{K

qr{s rcq.c frQ coFt cl-st {s-{ I qvtF
slrcl fr EEq TgT CSt6t E6{ st q\$.{ s&lt;T WK
e&amp;-T

7

c\$fcf

Ef\rTlT c.a c{.Ff
I

' If a, b and c are the lengths of the three sides of a triangle, then which of the following is
true? tsfr e\$F ft-w&lt; eB &lt;tq {qr@cr a,b e&lt;i c &lt; ut=re
(Cash1-2018J

A.a*b &lt;

c

B. a-b

&lt;c

C.

fr,ui;Ftr

a*!: s

Solution bv Khairul

n"ir',, Bank
"s"t^
D.afb &gt; c

off_

1;

li Banko

Solution: @)

EEwpTf qfihm

qafrmv\$lrilq+FrB. Fqqs

8.

a-b &lt; c q8s

I qefsetr&lt;tqtc-qr'rm66rsTyfuqq

Whichline is paralleltoy= x-2? (firs&lt;C+FIEy-x-2 q{qflE(f{2 ) [Rupali

ceFF

cqfiqr&lt;

r

Bank Off-

(Cash)-20tBJ

A.

y:2x*1

B.2y:2x-6

C.2y:x*7

D.

y:

3x*1

OSolution: @)

y:x'2
Since

y: mx+c

:

Here slope 1 (x qrrrqrf c{cry- I ioRvn slope &lt;luFr s I )
qfi ffi{cs qr{ q'f'rrffi :rKr coFr
El{ I ET I sBrt wlwfiEr

qffi{

&lt;s

qq'rrrdT q\$'ceI6F'

2x:2y

.'.

y-x*3

I

So,Here slope:

qrf{

EF.

qr{

(&lt;{tf+rx q-{{q5t 1 )

The area of a triangle with sides 3 cm, 5 cm and 6 cm
a-grqT (EI€{s-s?)-[Rupati Bank off (cash)-201s]

A.2Ji

Q

-6

=x=y- 3 :+y-3:x

9.

qrE EFr 6H

cm'

B

.4

JA

C

cm2

is

(s trT.fr, am.fr. s s ffi.fr. a1qftfi?

.2^lA

D.2^li

cm2

cm2

OSolution: (C)
q(qR'qNr,

s:

3*?*6
2

=7

- J1.q2J &gt;z iacrfi (Ans)
10. The pair of co-prime numbers is (frrE{ csFq\$ftsrirq - cfrfrsq\$BT?) [Rupali
(Cash)-2018J

4.2,3

8.2,4

c.2,6

11. The value of k, if (xq\$6 UEfiq-o Es \5RrE

A.

1

k

er rr{
8.2

c\flT6{

r

of

q{s Ifrqtrx\$1g

elzfr efq-sqeFE\srEt{ q.Gl

4x3+ 3x2-4x + ko is (&lt;fr x- 1, 4x3+
TE ? ) [Rupali Bank off- (C as h) - 2 0 I 8J
c. -3
D.3

1) is a factor

off

D.2,110

OSolution: (A)
If the H.C.F of two numbers is I then they said to be Co-Prime numbers.
{.qT.e ) qTER6EuEq-{rs ofrqrryqfifus &lt;f Co- Prime
Aro qqs I €&lt;&lt; \e qT 'f.cLe I qtB-s( A.

Bank

Solution by Khairul Alam- 3

Bflfq

3*-4x+ k TIftF{

1

lRupali Bank- (Cash) - 20181

oSolution: (C)
,{6{il1{: csl"rilFi\nqiilFKEq'mo'{c{ c{:Ft: *- 1 qffiEB{qsioFqrEx-l
EI &amp; q-I.f ilFrEr&lt;'6qfi6nfr641

:0 &lt;t x: 1 T{Rm

wrlq

f(x) :4x3+312-4*aL

.'.(1)

:

4(l)3+3(1;2-4.t+k :+

:0

((+rqqxNow, k*3
.'. k: -3 (Ans)

1

4+3-4+k

k+3

ffift6\$qeftqsqtx:=I T{lFflT e6rTtr{l{q1.a[&lt;gt

o €T{rrl;t&lt;-{

I)

12. There are 5 red and 3 black balls in a bag. Probability of drawing a black ball is (e+E
&lt;ln'{ c'fi ETm e&lt;( eF \$tffi] &lt;6T qlrq r o{l+ cqcF ?n-&lt;s11T q+E &lt;-q fr6E g,r +m qerk wlT{I \$s?)
[Rupali Bank Off- (Cash)-2018]

a.l

c.

8.1

-

o. 1
4

8

OSolution: (c)
Total

balls: 5*3 :

8 and black

ball:

So, probability of getting black ball

3

is:

J

(ficu mF +n q&lt;( S,f6{ m &lt;s frcu qr&lt; Ef{

8

13. The total surface area of a hemisphere of radius r
s-'c?)

is (eoB q(

6efl-a6q qqE

{\$Ifi

t)

Erfft csqrFq

-IRzpali Bank Off- (Cash)-20151

A .4nf

B.nf

D.3nf

C.2nf

rSolution: (D)

total surfac e area of sphere is :4x{
but hemisphere surface is half of sphere surface :2nf
* surface area of a cfucle:
So total surface area of hemisphere is 2nf + nr'2 :3nf

xl

q@t

fi6&lt;1 ap6.m B"f&lt;-&lt;

ffie

qfrfl &amp;'rf&lt; qr{

f -r-n--:**- Ih----r

-\ i

I

crE thsq &lt;EFDlflIrEr qk&lt;r6kt csqll5Ei
qfi cttl-q-f &lt;t Sphere ffiq.{\$E1f&lt;-+*utr"ttt-i&lt;qFK(GRt (sqTcl = 4fir2
ERr{TB{sBks.qFlrIl{frrr c+tD Gp-q6{E-t.{sDf ffi{\$oqr{ r .o=Fr cqt {ffi{&lt;mr{f q(r.f{
6E4p-a q&lt; 1t-&lt;c+&lt; {U sT ffi 6q-qrm{ qdo qdls 4nr2 + 2 : 2nf fu s-.fq &amp; ,itBwB-&lt; ifOrqf q(-f
qf6qs frru-{ qrE6I q&lt;:E p ?oft EC{ {lR csEmal qK
qK ff u-ry-6.-isphere :{I
Tre-{ 6scI{FFl3t r-e, nr,
q(pffqr€qnq\e-rq&lt;t 6qq'TEI \r&lt; 2xf+ nrz :3nf
I

14. Theroots of theequationgx2 - bx+81=Cwillbeequal, if thevalueof b is (be&lt;rt-+nu
qcE 9x2 -

A.+9

bx + 81 : C Jtffi{T{ssmFqc{?) [Rupali Bank Off- (Cash)-2018]

oSolution: (D)

9x2-bx+81=C

B.r18

c.*27

D.+54

.-

nli:{ea\$):2Q10I
ax2+bx+c:0
and b2 - Aac :0 ( ,eDf qq qn6 &lt;sx6 {o r)
or b2: 4ac
or, b2:4x9x81 (ax2+bx+c :0 {Elqtfrs a:9

€R\

c:81)

or,b:./[*9r31 4x9x8l
b : *( 2x3x9): * 54
O

Alternative solution:
9x2-bx+81
&lt;6frpo (a+b)2 verfl (a-b)2 et Wq GEr6o

,{fi,

Er&lt;

r

vrgq qfro&lt;qfr&lt;

{Esi"{ crFr qr&lt;

I

9x2-bx+81
+(3x)2-bx+92
+ (3x)2-2.3x.9 +92 +54 (qrcK bx qcraoraetcu 2ab &lt;t{ro

qc&lt;)

(3x-9)2+54

=
qRIr

qi 54 {fr + qt frr-q -54 rqrl q\$ sl-q(E (a+b)z lro{ rTfcat fr-ffi TIr{

1

qw&lt;(E-c{: + 54
15.

If secO + tanO = x, then tan0 is? [Rupali Bank Off- (Cash)-2TtBJ
A.

o

x2 +1

B.

Solution: (D)

,'-1
x2x

a.

x2 +1

D.

*'-1
2x

:

We know that, sec20 - tan20 1
(secO + tan0 ) (secO - tan0): I
x(sec0- tan0): I
or.(secO- tan0)

: 1 - - - - - t,i
x

again,secO + tan0

:

x - - - - - (ii)

by (ii)-(i)
|
*2-l
2tan0:x-l
or,2tan0: ^ -'
xxZx

...tan0:

u2-1
^ -I

16. Considerthat*-1_I = -41**y=25 andy *w = 15. Then the average of w, x,y
IBKB - (cash ) -201u &amp; IBDBL - (so ) -201u [Rupali Bank off- (cash)-201s]
D.6

A.3

8.4

c.5

OSolution: (D)

w*x*x*yty*w:-4+25+15

=

36

+2(w+x+y) :36
w+x+y-36+2:18 So, average of w,x,518+3

&gt;2w+2x+2y =

:6

Ans:

Solution by Khairul Alam-

5

is-

-

'ttf rcz

brflr frq.s +ur q*.flifrr

qM fi rs qqq

[Rupali Bank Off- (Cash)-2LtSJ

A.300

8.280

q" Xr *
c32O

Rq?)z

fnoai _-fsOI

_2 0 1

Ua

D314

oSolution: (C)

g5yo:272

so,r%

:*
85 :.rc[%_

272:&lt;_100

85

=320 Ans:

18' TIC 500 is deposited in a savings account which pays
Tyoannual interest compounded
semi-annually' To the nearest Taka, how much
is in tne account at the end of the year?
('F \$&lt;t &lt;ttr-s q% qk* tlttfro DqRro aoo Bmr *ur6
*tfi;6q ,+flErf g?{r TRrE &lt;qr cm EI Er{
ooDrfiqr&lt;? ) [Rupati Bank off-

4.542

8.536

icash)-2LtsJ

c.512

D.524

oSolution: @)

etqrr c% dqrs qfr'rr q{ +T r rr.c% {taks qr+
r 6n+ r% qry &lt;FcR-s
qT'kIn'lCE Goo e{ 5orr.C%
€T )orr.C7o = Asg ( EIT)
=
mHR
frrq&lt;
TrT
(
oo.a%
)
GT Grt ) n8+ ltn &lt;q i.ffi c*as
'4srFr

fu

firDT

GK

cftu

q,u \ertfi-s

fimq cfi T{r

1u TE*,

r)

I

1frqryq:rFfi*
500 (s {FrsL&lt; r &lt;k)

interest of interest

17.5 (vp6E-s1p;

,S&lt; 3.5yo

17.5 (v1q6s n5;

0.6125

lotal interest
L

Amount

/.5+17.5+.6125=35.61 or 36

s36

I

19. log*a 7 -2,thex=? [Rupali

A. -

1

Bank

Off

(Cash)_2LtSJ

s. 1

2

c.2

2

D.t7-

osolution: (C)
l.

log*i:

') I
-2 or,*":

'
ot,x2:)-2
...x:2

;

20' rt 5o/o is gained by selling an article for BDT 350
than selling it for BDT 340, the cost of
the article is (qrFqr e8o Elp56
Erorsna+&lt;rq c.z qrsqs rq&lt;rfr{G.{Tqrrs0
"fffirrco
/BD
House Buildins Fc- (so)-2|rzJ s.
IBDBL - (so )--2017] &amp; fRupari Bank off_ (cdih)_201s]
A.BDT
B.BDT
c.so.i
D. BDT 1s0

180

1s0

iSolution:( C)

zod

'

Selling price difference :350-340:10 tk. And % difference
5olo

of cost =10tk, or, ryoof

cost:*,n
5

so 100% of cost

Solution by Khairul

is:5zo

-

10x100

AlamJ

5

-200
-""'tk

[Rupali Bank Off- (Cash)-2018J

B.0

A.1

oSolution:(A)
x: yu Or, 1=2ub
Alternativeway,
22.

D.Infinity

c.0.5

z\ Or, x : xtu lsince z: x" ) Or, xubt :;l Or, abc :
y:zb or, y:*bc or, y:yub'or,abc:l (qafl\c{rsl\$f {r&lt;tEtsT))

(Since

y-

1

xis 30% greater than y, what percent of y is x? (&lt;frx qrr|"ty qr

lf

4.70

8.77

oSolution: (D)

y:

c.120

celc&lt;Fer%

ffiqg\oF6

D.130

x:

if,
100 then
100+30: 130
then, x is 130% of y

o{qE[.rTI!-{:
TlTql'cqlEqTf

mlqrrrtrofirufr+cs'q6{ e&lt;\&lt;tcregqqyqstqr&lt;vfroS"frs6^4.1-*u*foq-aa-s6eqs

€{lr{ y: 100 then x : 130
,{fi, rls?Fil qK c{{T I&lt;r*,

130 x

ff

1

0o 130%o (qr1&lt;l c'HE 6sl.I
6sl.IftR{tfrrqt
frE {t frntt 5oo%
rrr
=

fitq]3r

r)

23. The lengths of two sides of a right angle triangle are 13cm and 5cm respectively. The
length of the third side is (eoB GprqrEB&lt;RTffi&lt;etlo,6{ )e \e c rXft&lt;g{ffir-) TBDBL(SO

)

-20171

&amp;

[Rupali Bank Off- (Cash)-2018J

A.13

B"17

D.t2
A

c.11

OSolution: (D)

ftffi'flrfrT{Tqffi

qftg.ce.d=qr\+yGi &lt;u&lt;cnenB
fr-gffi \{e9q )e \e qr a ECE qT yqT &lt;R q{.Bt )e .e( wf{
qrrctft ft-WsT&lt;IEsrEtfrq-{,fls )Q.:(: )e {T
I

q5q

I

B

C

24. The present age of Habib and Shikha are in the ratio of 6 z 4. Five years ago their ages
were in the ratio of 5 : 3. How old is Habib now? (qtk{ q&lt;( FFflT &lt;6ltq &lt;lrq-{ \tr{"llu s:8 I c
&lt;qTqtr'f vkq-{&lt;rrc-{q.{'tlsG:ofr4 r &lt;6qrrrqtRrcs&lt;rpis-\9'?) [Rupali Bankoff (Cash)-2018J
4.24
B.30
c.36
D.42

oSolution: @)
Let,
present age of Habib and Shikha is 6x and 4x

ATQ,

6x-5 _ 5

4x-5

3

-25: l8x-15
=2x: -15+25: l0 m...x:5
Habib:6 x 5 :30 years old now. Ans: 30
=+ 20x

oXntqnlqqHf{,
x TI {6{, qcFf{ &amp;6nc&lt; wg qfl{f{
s frrr s't{ s-fl Tr{ qr{ c(qrr frF Ec&lt;,
\T'rrirffi rFterElrsQ s frffivtui{-68
1

I

fu otqrmfi cerrs c &lt;qr&lt;tqftrq
ftm W n-gf {tT \}{Tlq. rro {it-6fl
(v s c &lt;s qtRrE{ &lt;T6T{ w{'frr-v)
I

a.

1

[Rupali Bank Off- (Cash)-2018J

B.0

A.1

oSolution:(A)
x: yu Or, rzub
Alternativeway,

D.Infinity

c.0.5

z\ Or, x : xtu lsince F x" ) Or, xub' :;l Or, abc :
y:zb or, y:*bc or, y:yuh or,abc:1 (qafl\Rrsf{il{r&lt;tEeT))
22. lf x is 30% greater than y, what percent of y is x? (&lt;fr x qr rf{ y qr
eo% ffi qs \oT{ffi
(Since

y-

1

cclc&lt;F

y qT'tqffitsuxqr{?) [Rupali BankOff (Cash)-2015J
4.70
8.77
c.120

oSolution: (D)

il y:

D.130

x:

100 then
100+30: 130
then, x is 130% of y

odqEllrSF!-{:
TlTql-cclEqqTertq*vtrofirufr+cs'E6{ e&lt;1&lt;trogq4lqtfqrEvfroS"frs6^4.1-.u*ftrrr&lt;n-spqT
€{lG{
100 then x 130
130x100
,{fi,
{{ Tilkr
= l30Yo (qr trr&lt;t c'H 6sFI ftR qt fireft rso% :Frl 16r r)

:
y:
rlE?FilqKc *,

ff

23. The lengths of two sides of a right angle triangle are 13cm and 5cm respectively. The
length of the third side is (e+E fryrsmqF&lt;Rilffi&lt;qo,6{ )e \e c rXft&lt;g{ffir-} TBDBL(SO

)

-201U

&amp;

[Rupali Bank Off- (Cash)-2018J

A.13

B.17

D.t2
A

c.11

OSolution: (D)

Tqffi

ftefr'flTrrT{
q&amp;yrcTd = qd + Vff qcsqcqqTE
fr-gffi \{eyq )e \e qir a qcm \dT yqT &lt;Iq q{.Bt )e
qrr\$tft fuWsT&lt;IEsrEtfrq-flls )Q.:(: )e R{

(( wf{ q5q

I

B

I

C

24. The present age of Habib and Shikha are in the ratio of 6 z 4. Five years ago their ages
were in the ratio of 5 : 3. How old is Habib now? (qtk{ q&lt;( ftflT &lt;6ltq &lt;rrq-&lt; \tr{"llu s:8 I c
&lt;qKqlr'f Elm-TT{-rffiq-{'tlsG:ofr4 r &lt;6qtrrqtRrcs&lt;rpis-s?) [Rupali Bankoff (cash)-2018J
4.24
8.30
c.36
D.42

oSolution: @)
Let,
present age of Habib and Shikha is 6x and 4x

ATQ,

6x-5
_=_
4x-5

5
3

&gt;20x-25: l8x-15 =2x: -!5+25: 10 m...x:5
Habib :6 x 5:30 years old now. Ans: 30

olntqnlqqHf{'
x FI {6{, qq-rf{ &amp;6nc&lt; wg c:rt{f{
s frcl s'trt s-fl {r{ .qT{ r\\$t frp qc&lt;,
q'Flrffi rFlerElrs Q s frrr vtul {-(E
r

r

fu

prtxqrtfr cetr\$ c &lt;qr&lt;mftrq a
ftm W n-&lt;t {lT \e{Tlq eo \$nE
(v s a &lt;s qtRrE{ &lt;T6T{ w{'frr-v)
I

r

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