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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<\ {E< eHK Aadr qr6firBrs <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<'E.?) [Rupali Bank Off- (Cash)-2018J
8.2
D.4
c.3
oSolution: @)
(2a+l)-(a+1) = (4a-1) - (2a+l) (rlr<g' {<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 <ctim qktE
q'H"f qGN qsftrt
is ?
etT[Bt
Ans: 2
E{ q+) , Q.xQ.+) q<rs, 8xt-)
<iitt
rtrI{f
EeXq
s, c q<!. 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 <I< qr< ?)
"K
[Rupali Bank Off_ (Cash)_20 t SJ
A. Saturday B. Monday
C. Tuesday
(qtgT
eq-<lr
r
D. Friday
oSolution: (A)
qrq :q fr-{ \e@-{k qrE qT"K
5cET,
J{Eq, Q.svr,
q6{ I slqfE scETfr{Er< a4-{lr<-?r
b\
egvr, 8evq, covr, ccET q<( gag,T fr{e tsG r{
"f6rfr-{\TeX\,1fr<6
rffit
ffirsr{frr{3r<IK{Hrs
q
frmwnr< ) \ffifi? efismqst{<qs
T-{m eTa <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<K I {s_fl\ \9A
c q< eftwo \9s q<\ 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$T 6q.q*frfi} qtra-x{fr-wqfrssr..T
r ersrE.Iwrcrft<r
mfr-qq qenBT q,Fp-t{rr r vR E-s-*, B
6'
Which of the following angle can be constructed with the
help of a ruler and a pair of
compasses? (frrua c+.6 6spfr eTE rt-q e< qF n{rr< qfsm q$_{$_$
w<?) [Rupali Bank Off
(Cash)-20tBJ
A.
35o
B.
4oo
c.37.5.
OSolution: (C)
qR-T {rEr eteHFrqdqk't{.<tm<E
rffil{qs csl.t qs-rT{ q-ll'dqT <if{qla $-fl6o qt r fte- a{
rsdr
D .47.5"
r
..m<
cRRl.
wFT sil_6o Erdr
@
q-f,Ecr{t bnrs
q<q <rFTK fi(T rrtrEriFtt{ ert
"r<
ft.r tr.6rs}} wDpr o{fs.(; qo, 6-qETl.-T
{<-q $fiT Bq< y@ vr+T-{k'kr qst <lm(frrs
EE wEI"r qs-{ o-<rq esF qrmf"f Eks qr< r q<oR
qrmFf
qlRl
voGft
TsEtreBT om at=.+ ireE. +r-< qcGR ror.t qo"r
r qsr-F
ryoR-uIF
rr<srEf csFrm'<kl. <lr
qr(orm srr<
qffi
v*f1.6>r<
."8
fi(
# {r{
r
EC$ Eq-s
qeFf{ q-$tft o \e qc G0n-or<rq
900
750
{K
qr{s rcq.c frQ coFt cl-st {s-{ I qvtF
slrcl fr EEq TgT CSt6t E6{ st q$.{ s<T WK
e&-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< eB <tq {qr@cr a,b e<i c < ut=re
(Cash1-2018J
A.a*b <
c
B. a-b
<c
C.
fr,ui;Ftr
a*!: s
Solution bv Khairul
n"ir',, Bank
"s"t^
D.afb > c
off_
1;
li Banko
Solution: @)
EEwpTf qfihm
qafrmv$lrilq+FrB. Fqqs
8.
a-b < c q8s
I qefsetr<tqtc-qr'rm66rsTyfuqq
Whichline is paralleltoy= x-2? (firs<C+FIEy-x-2 q{qflE(f{2 ) [Rupali
ceFF
cqfiqr<
r
Bank Off-
(Cash)-20tBJ
A.
y:2x*1
B.2y:2x-6
C.2y:x*7
D.
y:
3x*1
OSolution: @)
y:x'2
Since
y: mx+c
:
Here slope 1 (x qrrrqrf c{cry- I ioRvn slope <luFr s I )
qfi ffi{cs qr{ q'f'rrffi :rKr coFr
El{ I ET I sBrt wlwfiEr
qffi{
<s
qq'rrrdT q$'ceI6F'
2x:2y
.'.
y-x*3
I
So,Here slope:
qrf{
EF.
qr{
(<{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 >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$1g
elzfr efq-sqeFE\srEt{ q.Gl
4x3+ 3x2-4x + ko is (<fr x- 1, 4x3+
TE ? ) [Rupali Bank off- (C as h) - 2 0 I 8J
c. -3
D.3
1) is a factor
off
D.2,110
OSolution: (A)
If the H.C.F of two numbers is I then they said to be Co-Prime numbers.
{.qT.e ) qTER6EuEq-{rs ofrqrryqfifus <f Co- Prime
Aro qqs I €<< \e qT 'f.cLe I qtB-s( A.
Bank
Solution by Khairul Alam- 3
Bflfq
3*-4x+ k TIftF{
1
lRupali Bank- (Cash) - 20181
oSolution: (C)
,{6{il1{: csl"rilFi\nqiilFKEq'mo'{c{ c{:Ft: *- 1 qffiEB{qsioFqrEx-l
EI & q-I.f ilFrEr<'6qfi6nfr641
:0 <t x: 1 T{Rm
wrlq
f(x) :4x3+312-4*aL
.'.(1)
:
4(l)3+3(1;2-4.t+k :+
:0
((+rqqxNow, k*3
.'. k: -3 (Ans)
1
4+3-4+k
k+3
ffift6$qeftqsqtx:=I T{lFflT e6rTtr{l{q1.a[<gt
o €T{rrl;t<-{
I)
12. There are 5 red and 3 black balls in a bag. Probability of drawing a black ball is (e+E
<ln'{ c'fi ETm e<( eF $tffi] <6T qlrq r o{l+ cqcF ?n-<s11T q+E <-q fr6E g,r +m qerk wlT{I $s?)
[Rupali Bank Off- (Cash)-2018]
a.l
c.
8.1
-
o. 1
4
8
OSolution: (c)
Total
balls: 5*3 :
8 and black
ball:
So, probability of getting black ball
3
is:
J
(ficu mF +n q<( S,f6{ m <s frcu qr< Ef{
8
13. The total surface area of a hemisphere of radius r
s-'c?)
is (eoB q(
6efl-a6q qqE
{$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<1 ap6.m B"f<-<
ffie
qfrfl &'rf< qr{
f -r-n--:**- Ih----r
-\ i
I
crE thsq <EFDlflIrEr qk<r6kt csqll5Ei
qfi cttl-q-f <t Sphere ffiq.{$E1f<-+*utr"ttt-i<qFK(GRt (sqTcl = 4fir2
ERr{TB{sBks.qFlrIl{frrr c+tD Gp-q6{E-t.{sDf ffi{$oqr{ r .o=Fr cqt {ffi{<mr{f q(r.f{
6E4p-a q< 1t-<c+< {U sT ffi 6q-qrm{ qdo qdls 4nr2 + 2 : 2nf fu s-.fq & ,itBwB-< ifOrqf q(-f
qf6qs frru-{ qrE6I q<: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<t 6qq'TEI \r< 2xf+ nrz :3nf
I
14. Theroots of theequationgx2 - bx+81=Cwillbeequal, if thevalueof b is (be<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$):2Q10I
ax2+bx+c:0
and b2 - Aac :0 ( ,eDf qq qn6 <sx6 {o r)
or b2: 4ac
or, b2:4x9x81 (ax2+bx+c :0 {Elqtfrs a:9
€R\
c:81)
or,b:./[*9r31 4x9x8l
b : *( 2x3x9): * 54
O
Alternative solution:
9x2-bx+81
<6frpo (a+b)2 verfl (a-b)2 et Wq GEr6o
,{fi,
Er<
r
vrgq qfro<qfr<
{Esi"{ crFr qr<
I
9x2-bx+81
+(3x)2-bx+92
+ (3x)2-2.3x.9 +92 +54 (qrcK bx qcraoraetcu 2ab <t{ro
qc<)
(3x-9)2+54
=
qRIr
qi 54 {fr + qt frr-q -54 rqrl q$ sl-q(E (a+b)z lro{ rTfcat fr-ffi TIr{
1
qw<(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 & 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
>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:<_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 $<t <ttr-s q% qk* tlttfro DqRro aoo Bmr *ur6
*tfi;6q ,+flErf g?{r TRrE <qr cm EI Er{
ooDrfiqr<? ) [Rupati Bank off-
4.542
8.536
icash)-2LtsJ
c.512
D.524
oSolution: @)
etqrr c% dqrs qfr'rr q{ +T r rr.c% {taks qr+
r 6n+ r% qry <FcR-s
qT'kIn'lCE Goo e{ 5orr.C%
€T )orr.C7o = Asg ( EIT)
=
mHR
frrq<
TrT
(
oo.a%
)
GT Grt ) n8+ ltn <q i.ffi c*as
'4srFr
fu
firDT
GK
cftu
q,u \ertfi-s
fimq cfi T{r
1u TE*,
r)
I
1frqryq:rFfi*
500 (s {FrsL< r <k)
interest of interest
17.5 (vp6E-s1p;
,S< 3.5yo
17.5 (v1q6s n5;
0.6125
lotal interest
L
Amount
/.5+17.5+.6125=35.61 or 36
s36
I
19. log*a 7 -2,thex=? [Rupali
A. -
1
Bank
Off
(Cash)_2LtSJ
s. 1
2
c.2
2
D.t7-
osolution: (C)
l.
log*i:
') I
-2 or,*":
'
ot,x2:)-2
...x:2
;
20' rt 5o/o is gained by selling an article for BDT 350
than selling it for BDT 340, the cost of
the article is (qrFqr e8o Elp56
Erorsna+<rq c.z qrsqs rq<rfr{G.{Tqrrs0
"fffirrco
/BD
House Buildins Fc- (so)-2|rzJ s.
IBDBL - (so )--2017] & fRupari Bank off_ (cdih)_201s]
A.BDT
B.BDT
c.so.i
D. BDT 1s0
180
1s0
iSolution:( C)
zod
'
Selling price difference :350-340:10 tk. And % difference
5olo
of cost =10tk, or, ryoof
cost:*,n
5
so 100% of cost
Solution by Khairul
is:5zo
-
10x100
AlamJ
5
-200
-""'tk
[Rupali Bank Off- (Cash)-2018J
B.0
A.1
oSolution:(A)
x: yu Or, 1=2ub
Alternativeway,
22.
D.Infinity
c.0.5
z\ Or, x : xtu lsince z: x" ) Or, xubt :;l Or, abc :
y:zb or, y:*bc or, y:yub'or,abc:l (qafl\c{rsl$f {r<tEtsT))
(Since
y-
1
xis 30% greater than y, what percent of y is x? (<frx qrr|"ty qr
lf
4.70
8.77
oSolution: (D)
y:
c.120
celc<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<\<tcregqqyqstqr<vfroS"frs6^4.1-*u*foq-aa-s6eqs
€{lr{ y: 100 then x : 130
,{fi, rls?Fil qK c{{T I<r*,
130 x
ff
1
0o 130%o (qr1<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<RTffi<etlo,6{ )e \e c rXft<g{ffir-) TBDBL(SO
)
-20171
&
[Rupali Bank Off- (Cash)-2018J
A.13
B"17
D.t2
A
c.11
OSolution: (D)
ftffi'flrfrT{Tqffi
qftg.ce.d=qr\+yGi <u<cnenB
fr-gffi \{e9q )e \e qr a ECE qT yqT <R q{.Bt )e .e( wf{
qrrctft ft-WsT<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<( FFflT <6ltq <lrq-{ \tr{"llu s:8 I c
<qTqtr'f vkq-{<rrc-{q.{'tlsG:ofr4 r <6qrrrqtRrcs<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{ &6nc< wg qfl{f{
s frrr s't{ s-fl Tr{ qr{ c(qrr frF Ec<,
\T'rrirffi rFterElrsQ s frffivtui{-68
1
I
fu otqrmfi cerrs c <qr<tqftrq
ftm W n-gf {tT \}{Tlq. rro {it-6fl
(v s c <s qtRrE{ <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<tEeT))
22. lf x is 30% greater than y, what percent of y is x? (<fr x qr rf{ y qr
eo% ffi qs \oT{ffi
(Since
y-
1
cclc<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<1<trogq4lqtfqrEvfroS"frs6^4.1-.u*ftrrr<n-spqT
€{lG{
100 then x 130
130x100
,{fi,
{{ Tilkr
= l30Yo (qr trr<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<Rilffi<qo,6{ )e \e c rXft<g{ffir-} TBDBL(SO
)
-201U
&
[Rupali Bank Off- (Cash)-2018J
A.13
B.17
D.t2
A
c.11
OSolution: (D)
Tqffi
ftefr'flTrrT{
q&yrcTd = qd + Vff qcsqcqqTE
fr-gffi \{eyq )e \e qir a qcm \dT yqT <Iq q{.Bt )e
qrr$tft fuWsT<IEsrEtfrq-flls )Q.:(: )e R{
(( wf{ q5q
I
B
I
C
24. The present age of Habib and Shikha are in the ratio of 6 z 4. Five years ago their ages
were in the ratio of 5 : 3. How old is Habib now? (qtk{ q<( ftflT <6ltq <rrq-< \tr{"llu s:8 I c
<qKqlr'f Elm-TT{-rffiq-{'tlsG:ofr4 r <6qtrrqtRrcs<rpis-s?) [Rupali Bankoff (cash)-2018J
4.24
8.30
c.36
D.42
oSolution: @)
Let,
present age of Habib and Shikha is 6x and 4x
ATQ,
6x-5
_=_
4x-5
5
3
>20x-25: l8x-15 =2x: -!5+25: 10 m...x:5
Habib :6 x 5:30 years old now. Ans: 30
olntqnlqqHf{'
x FI {6{, qq-rf{ &6nc< wg c:rt{f{
s frcl s'trt s-fl {r{ .qT{ r\$t frp qc<,
q'Flrffi rFlerElrs Q s frrr vtul {-(E
r
r
fu
prtxqrtfr cetr$ c <qr<mftrq a
ftm W n-<t {lT \e{Tlq eo $nE
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Rupali Bank Math Solution by Khairul Alam).pdf (PDF, 3.02 MB)
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