CBSE Class 12 Question Paper 2023 Applied Mathematics (Solved)

Qu e st i o n

P a p e r
2023

Series EF1GH SET~4

Q.P. Code 465
Roll No. narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$
_wI-n¥ð >na Adí` {bIo§ &
Candidates must write the Q.P. Code on
the title page of the answer-book.

ì`mdhm[aH$ J{UV
APPLIED MATHEMATICS
*
:3 : 80
Time allowed : 3 hours Maximum Marks : 80

NOTE :
(i) - 23
Please check that this question paper contains 23 printed pages.
(ii) - - -
-
Q.P. Code given on the right hand side of the question paper should be written on the title
page of the answer-book by the candidate.
(iii) - 38
Please check that this question paper contains 38 questions.
(iv) -

Please write down the serial number of the question in the answer-book before
attempting it.
(v) - 15 -
10.15 10.15 10.30 -
-
15 minute time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.
465 JJJJ Page 1 P.T.O.

:
:
(i) 38
(ii)
(iii) 1 18 19 20

(iv) 21 25 (VSA)

(v) 26 31 (SA)

(vi) 32 35 (LA)
(vii) 36 38

(viii) 2 2
2 3

(ix)

IÊS> H$
1

1. (22)12 H$m Am{Iar (BH$mB© H$m) A§H$ h¡ :

(a) 2 (b) 4
(c) 6 (d) 8

2. 315 H$mo 7 go ^mJ H$aZo na Ý`yZV_ G$UoÎma eof\$b h¡ :

(a) 1 (b) 5

(c) 6 (d) 7

465 JJJJ Page 2

General Instructions :
Read the following instructions very carefully and strictly follow them :
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) This question paper is divided into five Sections A, B, C, D and E.
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and
questions number 19 and 20 are Assertion-Reason based questions of 1 mark
each.
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type
questions, carrying 2 marks each.
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions,
carrying 3 marks each.
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions
carrying 5 marks each.
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying
4 marks each.
(viii) There is no overall choice. However, an internal choice has been provided in
2 questions in Section B, 2 questions in Section C, 2 questions in Section D and
3 questions in Section E.
(ix) Use of calculators is not allowed.

SECTION A

This section comprises multiple choice questions (MCQs) of 1 mark each.

1. The last (unit) digit of (22)12 is :

(a) 2 (b) 4
(c) 6 (d) 8

2. The least non-negative remainder, when 315 is divided by 7 is :

(a) 1 (b) 5

(c) 6 (d) 7

465 JJJJ Page 3 P.T.O.

1 0 5 10
3. `{X A VWm B h¡, Vmo AB h¡ :
2 1 10 5

5 10 0 5
(a) (b)
0 5 25 10

10 25 5 10
(c) (d)
5 0 0 25

x y x 2 8 5
4. `{X = h¡, Vmo x VWm y Ho$ _mZ h¢ :
y 16 1 3y 1

(a) x = 3, y = 5 (b) x = 5, y = 3

(c) x = 2, y = 7 (d) x = 7, y = 2

5. dh AZwnmV {Og_| EH$ XþH$mZXma Xmo àH$ma H$s Xmbm|, {OZHo$ _yë` H«$_e: < 85 à{V {H$J«m
VWm < 100 à{V {H$J«m h¢, H$mo {_bmH$a < 92 à{V {H$J«m H$m {_lU àmá H$aVm h¡, h¡ :
(a) 7:8 (b) 8:7

(c) 5:7 (d) 7:5

x 1
6. `{X g^r x Ho$ {bE, 0 h¡, Vmo :
x 1

(a) x [ 1, ) (b) x ( 1, )

(c) x ( , 1) (d) x ( , 1]

465 JJJJ Page 4

1 0 5 10
3. If A and B , then AB is :
2 1 10 5

5 10 0 5
(a) (b)
0 5 25 10

10 25 5 10
(c) (d)
5 0 0 25

x y x 2 8 5
4. If = , then the values of x and y are :
y 16 1 3y 1

(a) x = 3, y = 5 (b) x = 5, y = 3

(c) x = 2, y = 7 (d) x = 7, y = 2

5. The ratio in which a grocer mixes two varieties of pulses costing 85 per

kg and 100 per kg respectively so as to get a mixture worth 92 per

kg, is :

(a) 7:8 (b) 8:7

(c) 5:7 (d) 7:5

x 1
6. If 0, x , then :
x 1

(a) x [ 1, ) (b) x ( 1, )

(c) x ( , 1) (d) x ( , 1]

465 JJJJ Page 5 P.T.O.

7. A VWm B XmoZm| H$mo{Q> 3 Ho$ Eogo dJ© Amì`yh h¢ {OZHo$ {bE |A| = 1 VWm |B| = 3 h¡ &
|3AB| H$m _mZ h¡ ?
(a) 9 (b) 18
(c) 27 (d) 81

2 3 2
8. `{X x x x 3 0 h¡, Vmo x H$m _mZ h¡ :
4 9 1

(a) 1 (b) 0
(c) 1 (d) 3

9. {H$gr CËnmX H$s BH$mB`m| Ho$ CËnmXZ Ho$ {bE gr_m§V bmJV (MC) VWm _mÜ` bmJV
(AC) _| g§~§Y h¡ :

d ( AC) d ( AC)
(a) = x(MC AC) (b) = x(AC MC)
dx dx

d ( AC) 1 d ( AC) 1
(c) = (AC MC) (d) = (MC AC)
dx x dx x

10. 1 e x dx ~am~a h¡ :

(a) (x 2) e x + C (b) xe x + C

(c) xe x + C (d) (x + 1) e x + C

11. AdH$b g_rH$aU dx dy
0 H$m hb h¡ :
x y
1 1
(a) C (b) xy = C
x y
(c) log x log y = C (d) x+y=C

465 JJJJ Page 6

7. A and B are square matrices each of order 3 such that
A = 1 and B = 3. What is the value of 3AB ?

(a) 9 (b) 18

(c) 27 (d) 81

2 3 2
8. If x x x 3 0 , then the value of x is :
4 9 1

(a) 1 (b) 0

(c) 1 (d) 3

9. The relation between
units of a product is :
d ( AC) d ( AC)
(a) = x(MC AC) (b) = x(AC MC)
dx dx
d ( AC) 1 d ( AC) 1
(c) = (AC MC) (d) = (MC AC)
dx x dx x

10. 1 e x dx is equal to :

(a) (x 2) e x + C (b) xe x + C

(c) xe x + C (d) (x + 1) e x + C

dx dy
11. The solution of the differential equation 0 is :
x y

1 1
(a) C (b) xy = C
x y

(c) log x log y = C (d) x+y=C

465 JJJJ Page 7 P.T.O.

12. `{X X EH$ Eogm ßdmgm| Ma h¡ {H$ P(X = 1) = 2P(X = 2), Vmo P(X = 0) h¡ :
1
(a) e (b)
e

(c) 1 (d) e2

13. `{X |t| H$m n[aH${bV _mZ < tv ( ) h¡, V~ {ZamH$aUr` n[aH$ënZm :

(a) AñdrH$ma H$s OmVr h¡

(b) ñdrH$ma H$s OmVr h¡

(c) {ZYm©©[aV Zht H$s Om gH$Vr

(d) Z ñdrH$ma H$s OmVr h¡ Am¡a Z hr AñdrH$ma

14. Xmo ñdV§Ì Z_yZm| Ho$ _mÜ`m| Ho$ ~rM Ho$ A§Va H$s gmW©H$Vm H$s Om±M H$aZo Ho$ {bE ñdmV§Í`
H$mo{Q> (v) br OmVr h¡ :

(a) n1 n2 + 2 (b) n1 n2 2

(c) n1 + n2 2 (d) n 1 + n2 1

15. a¡{IH$ àd¥{Îm {Og g_rH$aU go {Zê${nV H$s OmVr h¡, dh h¡ :

(a) yc = a + bx (b) yc = a bx

(c) yc = na + b x (d) yc = na b x

465 JJJJ Page 8

12. If X is a Poisson variable such that P(X = 1) = 2P(X = 2), then P(X = 0)
is :

1
(a) e (b)
e

(c) 1 (d) e2

13. If the calculated value of t tv( ), then the null hypothesis is :

(a) rejected

(b) accepted

(c) cannot be determined

(d) neither accepted nor rejected

14. For testing the significance of difference between the means of two
independent samples, the degree of freedom (v) is taken as :

(a) n1 n2 + 2 (b) n1 n2 2

(c) n1 + n2 2 (d) n 1 + n2 1

15. The straight line trend is represented by the equation :

(a) yc = a + bx (b) yc = a bx

(c) yc = na + b x (d) yc = na b x

465 JJJJ Page 9 P.T.O.

16. < R H$s ñWm`r dm{f©H$s, Omo {H$ àË`oH$ ^wJVmZ Ad{Y Ho$ A§V _| AXm H$aZr hmoVr h¡, H$m
dV©_mZ _yë`, O~{H$ n¡gm à{V Ad{Y, i Ho$ bm`H$ h¡, h¡ :
R
(a) Ri (b) R
i
R
(c) (d) R Ri
i

17. dh à^mdr Xa Omo 10% dm{f©H$, à{V {V_mhr g§H${bV hmoZo dmbr A§{H$V Xa Ho$ Vwë` h¡,
h¡ :
(a) 10·25% (b) 10·38%

(c) 10·47% (d) 10·53%

18. x 0, y 0 Ûmam {ZYm©[aV joÌ pñWV h¡ :

(a) I MVwWmªe _| (b) II MVwWmªe _|

(c) III MVwWmªe _| (d) IV MVwWmªe _|

19 20 1
(A) (R)
(a), (b), (c) (d)

(a) A{^H$WZ (A) Am¡a VH©$ (R) XmoZm| ghr h¢ Am¡a VH©$ (R), A{^H$WZ (A) H$s ghr
ì¶m»¶m H$aVm h¡ &
(b) A{^H$WZ (A) Am¡a VH©$ (R) XmoZm| ghr h¢, naÝVw VH©$ (R), A{^H$WZ (A) H$s ghr
ì¶m»¶m H$aVm h¡ &
(c) A{^H$WZ (A) ghr h¡ VWm VH©$ (R) µJbV h¡ &
(d) A{^H$WZ (A) µJbV h¡ VWm VH©$ (R) ghr h¡ &

19. (A) : \$bZ f(x) = (x + 2) e x, A§Vamb ( 1, ) _| dY©_mZ h¡ &

(R) : EH$ \$bZ f(x) dY©_mZ h¡, `{X f (x) > 0 h¡ &
465 JJJJ Page 10

16. The present value of a perpetuity of < R payable at the end of each
payment period, when the money is worth i per period, is given by :
R
(a) Ri (b) R
i
R
(c) (d) R Ri
i

17. The effective rate which is equivalent to nominal rate of 10% p.a.
compounded quarterly is :

(a) 10·25% (b) 10·38%

(c) 10·47% (d) 10·53%

18. Region represented by x 0, y 0 lies in

(a) I quadrant (b) II quadrant

(c) III quadrant (d) IV quadrant

Questions number 19 and 20 are Assertion and Reason based questions carrying
1 mark each. Two statements are given, one labelled Assertion (A) and the other
labelled Reason (R). Select the correct answer from the codes (a), (b), (c) and (d)
as given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the
correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not
the correct explanation of the Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

19. Assertion (A) : The function f(x) = (x + 2) e x is increasing in the interval
( 1, ).

Reason (R) : A function f(x) is increasing, if f (x) > 0.

465 JJJJ Page 11 P.T.O.

20. (A) : nadb` y2 = 4ax Ho$ Hw$b H$mo {Zê${nV H$aZo dmbm AdH$b g_rH$aU
dy
x 2y = 0 h¡, O~{H$ EH$ àmMb h¡ &
dx

(R) : `{X {XE JE dH«$m| Ho$ Hw$b _| àmMb hmo§, Vmo Bgo n ~ma AdH${bV
{H$`m OmVm h¡ Vm{H$ àmMb H$mo bwá H$a nth H$mo{Q> H$m AdH$b
g_rH$aU àmá {H$`m Om gHo$ &
IÊS> I
(VSA) 2

21. (H$) Xmo nmBn A VWm B EH$ Q>¢H$ H$mo H«$_e: 24 {_ZQ> VWm 32 {_ZQ> _| ^a gH$Vr h¢ &
`{X XmoZm| nmBnm| H$mo EH$ gmW Imob {X`m OmE Vmo nmBn B H$mo {H$VZo g_` Ho$ ~mX
~ÝX H$a XoZm Mm{hE Vm{H$ Q>¢H$ 18 {_ZQ> _| ^a OmE ?
AWdm

(I) EH$- A 30 goH§$S> go B H$mo hamVm h¡ VWm B 15 goH§$S> go

C H$mo hamVm h¡ & `{X A, C H$mo 180 _r. go hamVm h¡, Vmo A Ûmam EH$ {H$bmo_rQ>a

x 3
22. x Ho$ {bE hb H$s{OE : 2.
x 2

23. (H$) {ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo H«¡$_a {Z`_ go hb H$s{OE :
2x y = 17, 3x + 5y = 6

AWdm
x 1 3 4
(I) x Ho$ dh nyUmªH$ _mZ kmV H$s{OE {OZHo$ {bE Amì`yh A = 5 x 2 2
4 1 x 6
Aì`wËH«$_Ur` h¡ &
465 JJJJ Page 12

20. Assertion (A) : The differential equation representing the family
of parabolas y2 = 4ax,
dy
x 2y = 0.
dx

Reason (R) : If the given family of curves has n parameters, then it is
to be differentiated n times to eliminate the parameter
and obtain the nth order differential equation.

SECTION B

This section comprises very short answer (VSA) type questions of 2 marks each.

21. (a) Two pipes A and B can fill a tank in 24 minutes and 32 minutes
respectively. If both the pipes are opened simultaneously,
after how much time should B be closed so that the tank is full in
18 minutes ?
OR

(b) In a one-kilometre race, A beats B by 30 seconds and B beats C by
15 seconds. If A beats C by 180 metres, then find the time taken by
A to run 1 kilometre.

x 3
22. Solve for x : 2.
x 2

23. (a)
2x y = 17, 3x + 5y = 6
OR

(b) Determine the integral value(s) of x for which the matrix A is
singular :
x 1 3 4
A= 5 x 2 2
4 1 x 6

465 JJJJ Page 13 P.T.O.

24. EH$ H$U dH«$$ 6y = x3 + 2 H$s {Xem _| Mb ahm h¡ & dH«$ na dh q~Xþ kmV H$s{OE {OZ
na y-{ZX©oem§H$ Ho$ n[adV©Z H$s Xa, x-{ZX©oem§H$ Ho$ n[adV©Z H$s Xa H$s 8 JwZr h¡ &

25. _mZm {H$ EH$ \ 2% Iam~ h¢ & àm{`H$Vm kmV H$s{OE
{H$ `mÑÀN>`m {bE JE 100 dñVwAm| Ho$ EH$ Z_yZo _| 3 Iam~ dñVwE± h¢ &
({X`m h¡ e 2 = 0.135)

IÊS> J
(SA) 3

26. (H$) {S>Å>mob go ^ar hþB© EH$ ~moVb br JB© VWm Bg_| go EH$-{VhmB© {S>Å>mob {ZH$mb H$a
CVZm hr nmZr S>mb H$a ~moVb H$mo {\$a go ^a {X`m & Eogm VrZ ~ma {H$`m J`m &
AÝV _| ~moVb _| {S>Å>mob H$s _mÌm go nmZr H$s _mÌm H$m AZwnmV kmV H$s{OE &
AWdm
(I) EH$ nmBn A EH$ Q>¢H$ H$mo 3 K§Q>o _| ^a gH$Vr h¡ & Bg Q>¢H$ Ho$ gmW Xmo {ZH$mgr
nmBn B VWm C bJo h¢ Omo {H$ Q>¢H$ H$mo H«$_e: 7 K§Q>o VWm 10 K§Q>o _| Imbr H$a
gH$Vo h¢ & `{X VrZm| nmBn EH$ gmW Imob {XE OmE±, Vmo Q>¢H$ H$mo ^aZo _| {H$VZm
g_` bJoJm ?

27. \$bZ f(x) = x3 6x2 + 9x 8 q~Xþ kmV
H$s{OE &

28. EH$ AZ{^ZV nmgo H$mo ~ma-~ma V~ VH$ CN>mbm J`m O~ VH$ {H$ Bg na Vrgar ~ma N>:
Zht Am OmVm & Bg nmgo H$mo N>R>r ~ma CN>mbZo na Vrgar ~ma N>: AmZo H$s àm{`H$Vm kmV
H$s{OE &

29. EH$ Mma-nm{h`m dmhZ H$s gmám{hH$ _mÜ` {~H«$s, 20 EO|{g`m| _| 50 BH$mB© à{V EO|gr
Wr 55 BH$mB© hmo
JB© O~{H$ _mZH$ {dMbZ 10 BH$mB© Wm & Om±M H$s{OE { m `h {dkmnZ àMma g\$b
Wm &
(à`moJ H$s{OE t0.005 = 1.729, 19 d.f. Ho$ {bE)
465 JJJJ Page 14

24. A particle moves along the curve 6y = x 3 + 2. Find the points on the curve
at which the ordinate is changing 8 times as fast as abscissa.

25. Suppose 2% of the items made by a factory are defective. Find the
probability that there are 3 defective items in a sample of 100 items
selected at random. (Given e 2 = 0·135)

SECTION C

This section comprises short answer (SA) type questions of 3 marks each.

26. (a) A bottle is full of dettol. One-third of its dettol is taken away and
an equal amount of water is poured into the bottle to fill it again.
This operation is repeated three times. Find the final ratio of dettol
to water in the bottle.

OR

(b) A pipe A can fill a tank in 3 hours. There are two outlet pipes B
and C from the tank which can empty it in 7 and 10 hours
respectively. It all the three pipes are opened simultaneously, how
long will it take to fill the tank ?

27. Find all the points of local maxima and local minima for the
function f(x) = x3 6x2 + 9x 8.

28. An unbiased die is thrown again and again until three sixes are obtained.
Find the probability of obtaining a third six in the sixth throw of the die.

29. The mean weekly sales of a four-wheeler were 50 units per agency in
20 agencies. After an advertising campaign, the mean weekly sales
increased to 55 units per agency with standard deviation of 10 units. Test
whether the advertising campaign was successful.
(Use t0·005 = 1·729 for 19 d.f.)

465 JJJJ Page 15 P.T.O.

30. (H$) EH$ g§n{Îm H$m _yë` < 4,50,000 h¡ O~{H$ BgH$s AZw_m{ZV Am`w 5 df© h¡ VWm
BgH$m Ad{eîQ> _yë` < 1,00,000 h¡ & a¡{IH$ Ad_yë`Z {d{Y Ûmam Bg g§n{Îm H$m
dm{f©H$ Ad_yë`Z kmV H$s{OE VWm EH$ dm{f©H$ Ad_yë`Z AZwgyMr ~ZmBE &

AWdm

(I) A_¥Vm Zo < 12,50,000 _yë` H$s EH$ H$ma IarXr, {OgHo$ {bE CgZo
< 3,00,000 VËH$mb AXm`Jr H$s VWm eof am{e H$mo 4 dfmªo _| g_mZ _m{gH$ {H$íVm|
_| 15% dm{f©H$ ã`mO H$s Xa na dm{ng H$aZm h¡ & kmV H$s{OE {H$ A_¥Vm H$mo
{H$VZr B©.E_.AmB©. (EMI) XoZr hmoJr & { {X`m h¡ (1·0125) 48 = 0·5508565)}

31. ì`damoYm|
x+y 24,

2x + y 32,

x 0, y 0 Ho$ A§VJ©V,

z = 300x + 190y H$m A{YH$V_rH$aU H$s{OE &

IÊS> K
(LA) 5

32. (H$) Amì`yh
1 1 2
A= 3 1 1
1 3 4

H$m ì`wËH«$_ (A 1) kmV H$s{OE, AV: Xem©BE {H$ AA 1 = I.

AWdm
465 JJJJ Page 16

30. (a) An asset costs < 4,50,000 with an estimated useful life of 5 years
and a scrap value of < 1,00,000. Using linear depreciation method,

find the annual depreciation of the asset and construct a yearly
depreciation schedule.

OR

(b) Amrita bought a car worth < 12,50,000 and makes a down
payment of < 3,00,000. The balance amount is to be paid in 4 years

by equal monthly instalments at an interest rate of 15% p.a. Find
the EMI that Amrita has to pay for the car.

{Given (1·0125) 48 = 0·5508565)}

31. Maximise z = 300x + 190y

subject to constraints :

x+y 24,

2x + y 32,
x 0, y 0.

SECTION D
This section comprises long answer (LA) type questions of 5 marks each.

32. (a) Find the inverse of the matrix :
1 1 2
A= 3 1 1
1 3 4

and hence show that AA 1 = I.

OR

465 JJJJ Page 17 P.T.O.

(I) Amì`yh {d{Y Ho$ à`moJ go {ZåZ a¡{IH$ g_rH$aU {ZH$m` H$m x, y, z Ho$ {bE hb
kmV H$s{OE :
x y+z=4

2x + y 3z = 0

x+y+z=2

33. (H$) g§»`m 15 H$mo Eogo Xmo ^mJm| _| ~m±Q>| {H$ nhbo ^mJ Ho$ dJ© VWm Xÿgao ^mJ Ho$ KZ H$m
JwUZ\$b A{YH$V_ hmo &
AWdm
(I) dH«$ y2 = 2x na dh q~Xþ kmV H$s{OE Omo {H$ q~Xþ (1, 4) go {ZH$Q>V_ hmo &

34. -aoIr` CnZ{V {\$Q> H$s{OE VWm

CnZ{V _mZ kmV H$s{OE :

df© : 2010 2012 2013 2014 2015 2016 2019

{~H«$s (bmI < _|) : 65 68 70 72 75 67 73

35. MH«$d¥{Õ dm{f©H$ d¥{Õ Xa (CAGR) H$mo n[a^m{fV H$s{OE VWm Bgo kmV H$aZo H$m gyÌ
Xr{OE & Bg gyÌ Ho$ à`moJ go {dH$mg Ho$ {Zdoe H$m CAGR kmV H$s{OE O~{H$ {X`m h¡
{H$ : {dH$mg Zo EH$ H$ånZr Ho$ ñQ>m°H$ _| 6 df© Ho$ {bE < 10,000 H$m {Zdoe {H$`m &
àË`oH$ df© Ho$ A§V _| CgHo$ {Zdoe H$m _mZ {ZåZ h¡ :

df© 1 df© 2 df© 3 df© 4 df© 5 df© 6

< 11,000 < 11,500 < 11,650 < 11,800 < 12,200 < 14,000

[(1·4)1/6 = 1·058 H$m à`moJ H$s{OE ]
465 JJJJ Page 18

(b) Using matrix method, solve the following system of equations for x,
y and z :
x y+z=4
2x + y 3z = 0
x+y+z=2

33. (a) Divide a number 15 into two parts such that the square of one part
multiplied with the cube of the other part is maximum.

OR

(b) Find a point on the curve y2 = 2x which is nearest to the point
(1, 4).

34. Fit a straight line trend by method of least squares to the following data
and find the trend values :

Year : 2010 2012 2013 2014 2015 2016 2019

Sales (in lakh <) : 65 68 70 72 75 67 73

35. Define Compound Annual Growth Rate (CAGR) and give the formula for

investment given below :

Vikas invested < 10,000 in a stock of a company for 6 years. The value of
his investment at the end of each year is given below :

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

< 11,000 < 11,500 < 11,650 < 11,800 < 12,200 < 14,000

[Use (1·4)1/6 = 1·058]

465 JJJJ Page 19 P.T.O.

IÊS> L>
3 4

àH$aU AÜ``Z 1

36. EH$ \ 6% ~ë~ Iam~ hmoVo h¢ &
Cn`w©º$ gyMZmAm| Ho$ AmYma na, {ZåZ àíZm| Ho$ CÎma Xr{OE :
(i) àm{`H$Vm kmV H$s{OE {H$ `mÑÀN>`m MwZo JE 100 ~ë~m| Ho$ EH$ Z_yZo _| H$moB© ^r
Iam~ ~ë~ Zht h¡ & [e 6 = 0·0024 br{OE ] 1
(ii) àm{`H$Vm kmV H$s{OE {H$ 100 ~ë~m| Ho$ Z_yZo _| _mÌ 2 Iam~ ~ë~ h¡§ & 1
(iii) (H$) àm{`H$Vm kmV H$s{OE {H$ 100 ~ë~m| Ho$ Z_yZo _| EH$ go A{YH$ Iam~
~ë~ Zht h¡ & 2
AWdm
(iii) (I) 100 ~ë~m| Ho$ Z_yZo _| Iam~ ~ë~ H$s àm{`H$Vm ~§Q>Z H$m _mÜ` VWm
àgaU kmV H$s{OE & 2

àH$aU AÜ``Z 2

37. EH$ \ _| Q>¡{Zg Ho$ a¡{H$Q> VWm {H«$Ho$Q> Ho$ ~¡Q> ~ZVo h¢ & EH$ Q>¡{Zg a¡{H$Q> ~ZmZo _|
1
1 K§Q>o _erZ H$m g_` VWm 3 K§Q>o H$m g_` {eënH$m[aVm _| bJVm h¡, O~{H$ EH$
2
{H«$Ho$Q> ~¡Q> ~ZmZo _| 3 K§Q>o _erZ H$m g_` VWm 1 K§Q>o H$m g_` {eënH$m[aVm _| bJVm h¡ &
EH$ {XZ _| \ 42 K§Q>o go A{YH$ Zht h¡ O~{H$ {eënH$m[aVm
H$m g_` 24 K§Q>o go A{YH$ Zht h¡ & EH$ a¡{H$Q> VWm EH$ ~¡Q> na bm^ H«$_e: < 20 VWm
< 10 h¡ &
Cn`w©º$ gyMZmAm| Ho$ AmYma na, {ZåZ àíZm| Ho$ CÎma Xr{OE :
(i) `{X \ x VWm y h¡, Vmo Hw$b
bm^ H$m ì`§OH$ {b{IE & 1
(ii) {eënH$m[aVm na bJo K§Q>m| H$s g§»`m go g§~§{YV ì`damoY {b{IE & 1
(iii) (H$) \ (< _|) A{O©V A{YH$V_ bm^ kmV H$s{OE & 2
AWdm
(iii) (I) A{YH$V_ bm^ Ho$ {bE {H$VZo ~¡Q> VWm a¡{H$Q>, H«$_e: ~ZmE OmZo Mm{hE ? 2

465 JJJJ Page 20

SECTION E
This section comprises 3 case study based questions of 4 marks each.
Case Study 1

36. A factory produces bulbs, of which 6% are defective bulbs in a large bulk
of bulbs.
Based on the above information, answer the following questions :
(i) Find the probability that in a sample of 100 bulbs selected at
random, none of the bulbs is defective. (Use : e 6 = 0·0024) 1
(ii) Find the probability that the sample of 100 bulbs has exactly two
defective bulbs. 1
(iii) (a) Find the probability that the sample of 100 bulbs will include
not more than one defective bulb. 2
OR
(iii) (b) Find the mean and the variance of the distribution of number
of defective bulbs in a sample of 100 bulbs. 2
Case Study 2

37. A factory manufactures tennis rackets and cricket bats. A tennis racket
1
takes 1 hours of machine time and 3 hours of craftsmanship in its
2
making; while a cricket bat takes 3 hours of machine time and 1 hour of
craftsmanship. In a day, the factory has availability of not more than
42 hours of machine time and 24 hours of craftsmanship. Profit on a
racket and on a bat are < 20 and < 10 respectively.
Based on the above information, answer the following questions :
(i) If x and y are the numbers of bats and rackets manufactured by the
factory, then write the expression of total profit. 1
(ii) Write the constraint that relates the number of craftsmanship
hours. 1
(iii) (a) Determine the maximum profit (in <) earned by the factory. 2
OR
(iii) (b) How many bats and rackets respectively, are to be
manufactured to earn maximum profit ? 2

465 JJJJ Page 21 P.T.O.

àH$aU AÜ``Z 3

38. df© 2010 _|, lr AJ«dmb Zo ñQ>oQ> ~¢H$ Am°\$ B§{S>`m go 20 df© Ho$ {bE, < 30,00,000 H$m
J¥h G$U 7·5% dm{f©H$ Xa na {b`m J`m O~{H$ ã`mO _m{gH$ g§`mo{OV hmoVm h¡ &
Cn`w©º$ gyMZmAm| Ho$ AmYma na, {ZåZ àíZm| Ho$ CÎma Xr{OE :

(i) B©.E_.AmB©. (EMI) kmV H$s{OE & 1

(ii) lr AJ«dmb Ûmam 150dt {H$íV _| AXm H$s JB© _ybYZ H$s am{e kmV H$s{OE & 1

(iii) (H$) lr AJ«dmb Ûmam Xr JB© Hw$b ã`mO H$s am{e kmV H$s{OE & 2

AWdm

(iii) (I) lr AJ«dmb Ûmam nyao J¥h G$U H$s AXm`Jr _| Hw$b {H$VZr am{e Xr JB© ? 2

[(1·00625)240 = 4·4608; (1·00625)91 = 1·7629 br{OE ]

465 JJJJ Page 22

Case Study 3

38. In the year 2010, Mr. Aggarwal took a home loan of < 30,00,000 from
State Bank of India at 7·5% p.a. compounded monthly for 20 years.
Based on the above information, answer the following questions :

(i) Determine the EMI. 1

(ii) Find the principal paid by Mr. Aggarwal in the 150th instalment. 1

(iii) (a) Find the total interest paid by Mr. Aggarwal. 2

OR

(iii) (b) How much was paid by Mr. Aggarwal to repay the entire
amount of home loan ? 2

[Use (1·00625)240 = 4·4608; (1·00625)91 = 1·7629]

465 JJJJ Page 23 P.T.O.