COMPULSORY MATHS
Model Set 1
Time: 3.00 hours
Full Marks: 100
Pass
Marks: 32
;d'x …sÚ (Group ‘A’) [9×(2+2)=36]
1.
a. dfg
lgsfNg'xf];\ (Evaluate):
b. ;/n ug{'xf];\ (Simplify):
2. a. xn ug{'xf];\ (Solve) :
b. olb Pp6f wgfTds ;ª\Vofsf] ju{af6 7
36fpFbf kl/0ffd 9
x'G5 eg] pQm ;ª\Vof
kQf nufpg'xf];\ .
If
7 is subtracted from the square of a positive number, the result is 9. Find the
number.
3. a. olb =
400+20a, =18+2a
/ lbOPsf] >]0fLsf] dWos @) eP a
sf] dfg lgsfNg'xf]; .
If = 400+20a ,=18+2a, and the mean of the given series is 20, find
the value of a.
b.
;Fu} lbOPsf ;l~rt jf/Djf/tf jsjf6 dlWosf / dlWsfsf]
ju{
kQf
nufpg'xf];\ .
Find the median class and value of median from the adjoining
cumulative frequency curve.
4. a. /fd/L lkml6Psf] 52 kQL
ePsf] tf;sf] u8\8Laf6 Pp6f kQL
lgsflnPsf]
5 eg] pQm klQ /fgL cyjf sfnf] /ªsf] PSsf
kg{] ;DefJotf kQf nufpg'xf];\ .
A card is drawn from a
wellshuffled deck of 52 cards. Find the probability of getting such card is
queen or a black ace.
b. Pp6f l;SsfnfO{ b'O{k6s ;Dd pkmfbf{ aGg] ;DefJotfnfO{
j[Iflrqdf k:t't ug{'xf];\ .
A
coin is tossed two times and represents the probabilities in a tree diagram.
5. a. lqe'h
ABC df AB=8 ;]=ld= BC= 12 ;]=ld= / ÐABC=60° eP ;f] lqe'hsf] If]qkmn kQf nufpg'xf];\ .
In ∆ABC,
AB=8cm, BC= 12 cm and ÐABC=60°.
Find the
area of the triangle.
b. lbOPsf] lrq lqe'hfsf/ cfwf/ ePsf]
Pp6f 7f]; lkHd xf] . olb AB= 3;]=ld= BC=5;]=ld= / CF= 12;]=ld= eP pQm lkHdsf] cfotg kQf nufpg'xf];\ .
The adjoining diagram is a triangular
based solid prism. If AB= 3cm, BC=5cm and CF= 12cm find the volume of the
prism.
6. a . Pp6f a]ngfsf] cw{Jof; /
prfOsf] of]ukmn 12 ;]=ld /
cfwf/sf] kl/lw 416
;]=ld= eP pQm
a]ngfsf] k"/f ;txsf] If]qkmn lgsfNg'xf];\ .
If the sum of radius and height of cylinder is
12 cm and circumference of base is 416
cm find the total surface area of that cylinder.
b. ;Fu} lbOPsf] lrq Pp6f 7f];
uf]nfsf] xf] . olb cfwf/sf] Jof;  AB)= 28 ;]=ld= eP pQm uf]nfsf] cfotg
lgsfNg'xf];\ .
The diagram given
alongside is of a solid sphere. If AB= 28 cm, Find the volume of the sphere.
7. a. Pp6f j:t'sf] jf:tljs d"Nodf15%
a9fO{ clª\st d"No ?= 2760 sfod ul/of] . ;f] j:t'sf] jf:tljs
d"No kQf nufpg'xf];\ .
The
marked price of an article was fixed to Rs. 2760 by increasing 15% in its
actual price. Find its actual price.
b. ?= 5000 sf] kltjif{ 10%
jflif{s rqmLo Aofhb/n] 2
jif{df x'g] rlqmo
ld>wg kQf nufpg'xf];\ .
Find
the compound amount on Rs. 5000 in 2 years at 10% per annum.
8. a. lbOPsf] lrqdf, WXYZ Pp6f
;dfgfGt/ rt'e{'h 5 . olb WX nfO laGb'
V ;Dd
a9fpFbf ag]sf] ∆ZYV
sf] If]qkmn 15cm^{2}
eP ∆WXT
sf] If]qkmn kQf nufpg'xf];\ .
If the given figure,
WXYZ is a parallelogram . WX is extended up
to U and ∆ZYU is formed. If Area of ∆ZYU is 15cm^{2}, find the area of ∆WXT.
b. lbOPsf] lrqdf PR^QS 5 . olb ÐPQS=46° eP ÐQSR kQf nufpg'xf];\ . In
the given figure, PR^QS.
If ÐPQS=46°,
find ÐQSR.
9. a. lbOPsf] lrqdf laGb'x? A,
D, C / B cw{j[Qdf 5g\ . olb ÐDAC=30°
/ ÐABC=
70° eP ÐACD kQf nufpg'xf];\ .
In
the given figure, points A, D, C and B are on semicircle. If ÐDAC=30°
and ÐABC= 70°, find ÐACD.
b.
lbOPsf] lrqdf PT n] laGb' A df j[QnfO{ :kz{ u/]sf] 5 . olbÐBAT=60° / ÐBAC=50°
eP ÐABC kQf nufpg'xf];\ .
In the given figure, PT touches a circle at a point A. If ÐBAT=60°
and ÐBAC=50°,
find ÐABC.
;d'x …vÚ (Group ‘B’) [16×4=36]
10 Pp6f ljBfyL{x¿sf] ;d"xdf ul/Psf] ;j{]If0fdf 70%
ljBfyL{x¿n] j}1flgsx¿sf ;DaGwdf , 65%
n] v]nf8Lx?sf ;DaGwdf / 430 hgfn] b'j}sf af/]df cWoog u/]sf]
kfOof] . olb 8% n] s'g} sf] af/]df
klg cWoog u/]sf] kfOPg eg] M
In
a survey of the group of students, it was found that 70% of students studied about scientists, 65% about players and 430
studied about both scientists and players. If 8% did not study about scientists
and players, then,
i)
dflysf]
tYofªsnfO{ e]glrqdf k:t't ug{'xf];\ .
Represent the above information in a Venndiagram.
ii)
;j{]If0fdf
efu lnPs]f hDdf ljBfyL{;ª\Vof kQf nufpg'xf];\ .
Find the total number of students who took
part in the survey.
11. dxQd
;dfkjt{s lgsfNg'xf];\ . (Find
the H.C.F of):
and
12. xn ug{'xf];\ . (Solve) : 5^{x1}
+ 5^{x} = 1
13. ;/n ug{'xf];\ . (Simplify):
14. b'O{ cÍsf] s'g} Pp6f ;ª\Vof, Tof] ;ª\Vofsf] cª\sx¿sf]
of]usf] rf/ u'0ff 5 . olb Tof] ;ª\Vofsf] cª\sx¿sf] :yfg abn]/ aGg] ;ª\Vof / 9 sf] of]ukmn] pQm ;ª\Vofsf] b'O{
u'0ff x'G5 eg], ;f] ;ª\Vof kQf nufpg'xf];\ .
A
two digit number is four times the sum of its digits. If the sum of the number
formed by reversing its digits and 9 is two times the original number, find the
original number.
15. olb tn lbOPs]f cfFs8fsf] dWos 68 eP x sf] dfg kQf
nufpg'xf];\ .
If the mean
of the following data is 68, find the value of x.
Marks obtained kfKtfÍ_

4050

5060

6070

7080

8090

90100

No.of students ljBfyL{sf] ;+Vof_

17

22

28

26

x

12

16. Pp6f gbLsf] lsgf/df ePsf] 40 ld6/ cUnf] ¿vsf] 6'Kkf]df pQm
gbLsf] csf{] lsgf/af6 cjnf]sg ubf{ pGgtf+z sf]0f 30° kfOof] eg] ;f] gbLsf] rf}8fO kQf nufpg'xf];\ .
The angle of elevation of the top of a
tree, 40m high situated at the bank of a river when observed from the opposite
bank of the river is found to be 30°, find the breadth of the river.
17. lbOPsf] 7f]; a:t' j]ngf / cw{uf]nf ldn]/ ag]sf] 5 . h;sf]
cfwf/sf] Jof; 14;]=ld= / k"/f nDafO 21;]=ld= 5 eg] ;f] 7f]; a:t'sf]
k"/f ;txsf] If]qkmn kQf nufpg'xf];\ .
The given solid object
is made up of a cylinder and a hemisphere whose diameter of the base is 14cm
and total length is 21 cm. Find the total surface area of the solid object.
18. tn lbOPsf
ju{ cfwf/ ePsf] lk/fld8sf] k"/f ;txsf]
If]qkmn
lgsfNg'xf];\ .
Find the total surface
area of the following
square based pyramid.
19. A / B n] Pp6f sfd sdz M 12 / 16 lbgdf ug{ ;S5g\ . A / B b'j}hgf ldn]/ 4 lbg sfd u/]kl5 B n] ;f] sfd 5f]8\5 eg] afFsL sfd
ug{ A nfO{ slt lbg nfUnf < kQf
nufpg'xf];\ .
A and B can do a piece of work in 12 and
16 days respectively. A and B work together for 4 days and B leaves the work,
find how long will A take to complete the remaining work.
20. Pp6f Sofd/f 25% 5'6 lbP/ 10% d"No clej[l4 s/ nufO{ a]lrof]
. olb 5'6 /sd ?=
750 eP pQm Sofd/fsf]
d"Nodf d"No clej[l4 s/ /sd slt lyof] kQf nufpg'xf];\ .
A camera was sold after
allowing 25% discount on the marked price and then levying 10% value added tax
(VAT). If the discounted amount was Rs.750, how much value added tax (VAT) was
levied on the price of the camera?
21. Pp6f ufpFsf] hg;ª\Vof kTo]s jif{ 5 kltztn] a9\b} hfG5 . olb b'O{
jif{sf] cGTodf 1025 hgf a;fOF ;/]/ cGoq hfFbf ;f]
ufpFsf] hg;ª\Vof 10,000 eof] eg] ;'?df ;f] ufpFsf]
hg;ª\Vof slt lyof] <
The
population of a village increases every year by 5%. If 1025 people leave the
village at the end of two years and the population of the village is 10,000,
find the population of the village in the beginning.
22. Pp6} cfwf/ QR / pxL ;dfgfGt/ /]vfx? QR / PS sf] jLrdf ag]sf lqe'hx¿ PQR / SQR sf] If]qkmn a/fa/ x'G5g egL
kdfl0ft ug'{xf];\ .
Prove that the triangles
PQR and SQR standing on same base QR and between same parallel lines QR and PS
are equal in area.
23. ;Fu}sf] lrqdf PT j[Qsf] Jof; xf] / O s]GblaGb' xf] olb
rfk SR= rfk RT eP PS//OR.x'G5 egL l;4 ug'{xf];\ .
In alongside diagram, PT
is the diameter and O is centre of circle. If
arc SR=arc RT, prove that PS//OR.
24. Pp6f j[Qsf] pxL rfkdf cfwfl/t kl/lwsf]0fx¿ a/fa/ x'G5g\ egL
kof]u4f/f l;4 ug'{xf];\ . slDtdf 3;]=ld= cw{Jof; ePsf b'O{ cf]6f j[Qx¿ cfjZos 5g\._ Verify experimentally
that the angles at the circumference standing on the same arc of a circle are equal.(Two circles of radii at
least 3 cm are necessary.)
25. rt'e'{h ABCD
sf] /rgf ug'{xf];\ h;df AB=5.8
;]=ld, BC=6.2;]=ld , CD=5.1;]=ld , DA=4.8;]=ld
/ ÐBAD=60° 5g\ .;fy} pQm rt'e'{h;Fu If]qkmn
a/fa/ x'g] lqe'hsf] /rgf ug'{xf];\ .
Construct a
quadrilateral ABCD in which AB=5.8cm, BC=6.2cm , CD=5.1cm , DA=4.8cm and ÐBAD=60°.also construct a
triangle equal in area to the quadrilateral ABCD.