JAC Class 12 Model Question Paper 2026 Business Mathematics

2026

MODEL
PAPERS
JAC BOARD JHARKHAND
EXAM ACADEMIC
COUNCIL MODEL
PREPARATION QUESTION
PAPER 2026



JHARKHAND ACADEMIC COUNCIL

Jharkhand Council of Educational Research and Training, Ranchi
झारखण्ड शैक्षिक अनुसंधान एवं प्रक्षशिण पररषद् ,रााँची
MODEL QUESTION PAPER
मॉडल प्रश्न पत्र
Session: 2025-26 (सत्र: 2025-26)
Class – 12 Subject – Business Mathematics F. M. – 80 Time – 3 Hours
(वगग -12) (क्षवषय- व्यावसाक्षयक गक्षणत) (पण
ू ाां क-80) (समय-3 घंटा)

Instructions / नर्नर्देश :
1. Examinees are required to answer in their own words as far as practicable. The
booklet contains 10 printed pages.
परीक्षार्थी यर्थासंभव अपर्ने शब्र्दों में ही उत्तर र्दें। पुनतिका में 10 मुद्रिि पृष्ठ है ।
2. This question paper has four sections: A, B, C, and D. The total number of
questions is 52.
इस प्रश्न पत्र में चार खण्ड - A, B, C, एवं D है। कु ल प्रश्नों की संख्या 52 है।
3. There are 30 multiple-choice questions in Section A. Four options are given for
each question, choose one of the correct options. Each question carries 1 marks.
खण्ड A में कु ल 30 बहुनवकल्पीय प्रश्न हैं। प्रत्येक प्रश्न के चार नवकल्प द्रर्दए गए हैं, इर्नमें से एक
सही नवकल्प का चयर्न कीनजए। प्रत्येक प्रश्न का मार्न 1 अंक नर्नर्धााररि है।
4. Section B – Question numbers 31 – 38 are very short answer type. Answer any
six of these questions. Each question carries 2 marks.
खण्ड B में प्रश्न संख्या 31 - 38 अनि लघु उत्तरीय प्रश्न हैं। इर्नमें से द्रकन्ही छह प्रश्नों के उत्तर
र्दीनजए। प्रत्येक प्रश्न का मार्न 2 अंक नर्नर्धााररि है।

5. Section C – Question numbers 39 – 46 are short answer type. Answer any six
of these questions. Each question carries 3 marks.
खण्ड C में प्रश्न संख्या 39 - 46 लघु उत्तरीय प्रश्न हैं। इर्नमें से द्रकन्ही छह प्रश्नों के उत्तर
र्दीनजए। प्रत्येक प्रश्न का मार्न 3 अंक नर्नर्धााररि है।
6. Section D – Question numbers 47 – 52 are long answer type. Answer any four
of these questions. Each question carries 5 marks.
खण्ड D में प्रश्न संख्या 47 - 52 र्दीघा उत्तरीय प्रश्न हैं। इर्नमें से द्रकन्ही चार प्रश्नों के उत्तर
र्दीनजए। प्रत्येक प्रश्न का मार्न 5 अंक नर्नर्धााररि है।

Section-A (खण्ड - A) (𝟏 × 𝟑𝟎 𝟑𝟎)
1. lekUrj Js.kh 20, 25, 30, ……..100 esa fdrus in gS\
How many terms are there in A.P. 20, 25, 30, …..100?
(A) (B)
(C) (D)
2. ;fn 5, K,11 AP esa gksa rks K dk eku Kkr dhft,A
Find the value of K, if 5, K, 11 are in A.P.
(A) (B)
(C) (D)
3. 4 vkSj 9 dk xq.kksÙkj ek/; Kkr dhft,A
Find the geometric mean of 4 and 9.
(A) (B)
(C) (D)
4. vuqØe 4, 12, 36, ……. ds ik¡pok in fudkysaA
Find the fifth term of the sequence 4, 12, 36, ……. .
(A) (B)
(C) (D)

5. rFkk 4 ds chp gjkRed ek/; fudkysaA

Find the harmonic mean between and 4.

(A) (B)

(C) (D) buesa ls dksbZ ugha (none of these)

6. gjkRed ek/; dSls fudkyk tkrk gS\
How to find harmonic mean ?

(A) (B) √

(C) (D)

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 2

10
7. C6 dk eku fudkysaA
Find the value of 10C6 .
(A) 210 (B)
(C) (D)
8. ‘SUNDAY’ ‘kCn ls ,d ckj esa nks v{kjksa dks ysdj dsoy fdrus ‘kCn cuk;s tk ldrs gS\
How many words can be formed with the letters of the word ‘SUNDAY’ taken two
at the time?
(A) 50 (B)
(C) (D)

9. | |= ?

(A) 1 (B)
(C) (D)
10. lkjf.kd dk #i dSlk gksrk gS\
(A) oxkZdkj (B) f=Hkqdkj
(C) vk;rkdkj (D) buesa ls dksbZ ugha
How is the shape of determinates?
(A) Square shape (B) Triangular
(C) Rectangular (D) none of these
11. og eSfVªDl ftlesa iafDr;ksa vkSj LREHkksa dh la[;k cjkcj gks] og eSfVªDl D;k dgykrk gSA
(A) {kSfrt eSfVªDl (B) iafDr eSfVªDl
(C) LrEHk eSfVªDl (D) oxZ eSfVªDl
Matricx with equal number of row and column is called
(A) Horizontal Matricx (B) Row Matricx
(C) Column Matricx ) (D) Square Matricx

12. ;fn * +=* + gks] rks x, y rFkk z dk eku Kkr dhft,A

* +=* +,then find the value of x,y and z.

(A) x = 5, y = 1, z = 2 (B) x = 2, y = 1, z = 5
(C) x = 5, y = 2, z = 1 (D) x = 1, y = 5, z = 2
JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 3

13. lerqY; leqPp; dk mnkgj.k gSA
Example of Equivalent sets is …..
(A) * + * + (B) * + * +
(C) * + * + (D) lHkh (All)

14. ;fn A = * + rks fuEufyf[kr esa dkSu A dk mi leqPp; gSA
If A = * + then which one is not sub-set of A.
(A) * + (B) * +
(C) * + (D)
15. fjDr LFkkuksa dks Hkjsa (Fill in the blanks)
(xn) = ………

(A) n xn +1 (B) n xn
(C) xn -1 (D) n xn -1
16. fjDr LFkkuksa dks Hkjsa (Fill in the blanks)
(2x) = ………

(A) 2x-1 (B) x 2x-1
(C) 2x (D) 2x -1

17. ∫ = ………

(A) sin-1 x + c (B) tan-1 x + c
1
(C) ( )+c (D) x+c

18. ∫ = ………

(A) +c (B)

(C) (D) None of these
19. lekUrj ek/; dh x.kuk ds fy, oxZ&varjky gksus pkfg,A
(A) viothZ (B) vleku
(C) leku (D) lHkh lEHko gSA
For the calculation of arithmetic mean the class intervals should be:
(A) Exclusive (B) Unequal
(C) Equal (D) All are possible
JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 4

20. Js.kh ds O;fDrxr voyksduksa ds fopyuksa dk ;ksx ‘kwU; gksrk gS %
(A) cgqyd ls (B) ekf/;dk ls
(C) lekUrj ek/; ls (D) buesa dksbZ ugha
The sum of derivations of individual observation of a series is zero from:
(A) Mode (B) Median
(C) Mean (D) None of these

21. Ekkf/;dk dh x.kuk ds fy, Js.kh dks O;ofLFkr fd;k tkrk gS %
(A) vkjksgh Øe esa (B) vojksgh Øe esa
(C) fdlh Hkh Øe esa (D) buesa dksbZ ugha
Series are arranged for calculation of median in :
(A) Ascending Order (B) Descending Order
(C) Any Order (D) None of These
22. bu vk¡dM+ksa dh ekf/;dk gksxh %
Median of following figures:
25, 40, 35, 38, 32, 30, 37
(A) 30 (B) 38
(C) 35 (D) 32
23. ;fn forj.k lefer gks rks fuEufyf[kr esa ls dkSu&lk dFku lgh gS \
If the distribution is symmetrical, which of the following statement is true?
(A) Mean = Median = Mode (B) Mean < Median < Mode
(C) Mean > Median > Mode (D) Mean < Median > Mode
24. 60, 70, 10, 35, 45, 30, 30, 20, 20, 30 dk cgqyd gS %
Mode of 60, 70, 10, 35, 45, 30, 30, 20, 20, 30 is:
(A) 30 (B) 70
(C) 60 (D) 10
25. 4 rFkk 64 dk xq.kksÙkj ek/; fudkysaA
Find G.M. of numbers 4 and 64.
(A) 16 (B) 10
(C) 12 (D) 9

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 5

26. 2 vkSj -6 dk xq.kksÙkj ek/; --------- gSA
The geometric mean of the observation 2 and -6 is ……. .
(A) 36 (B) -36
(C) 0 (D) dksbZ ugha (None of these)

27. vkSlr pky fuEufyf[kr ls Kkr fd;k tk ldrk gSA
(A) lekarj ek/; (B) xq.kksÙkj ek/;
(C) gjkRed ek/; (D) buesa ls dksbZ ughaA
The average speed can be calculated by:
(A) Arithmetic mean (B) Geometric mean
(C) Harmonic mean (D) None of these

28. miufr n’kkZrk gS nh?kZdkyhu izo`fÙk ds
(A) dsoy c<+us dh (B) dsoy ?kVus dh
(C) c<+us vFkok ?kVus dh (D) buesa ls dksbZ ughaA
Trend analyse refers to long-term tendency to:
(A) Increasing only (B) Decrease only
(C) Eigher increase or decrease (D) None of these

29. ,d ikls dks Qsadus ij fo”k; la[;k vkus dh izkf;drk D;k gksxhA
What will be the probability of getting odd numbers if a dice is thrown.

(A) (B) 2

(C) (D)

30. vkUrjx.ku rFkk ckáx.ku dh jhfr;k gSA
(A) fcUnqjs[kh; jhfr (B) chtxf.krh; jhfr;k¡
(C) nksuks A vkSj B (D) buesa ls dksbZ ughaA
Methods of interpolation and extrapolation are:
(A) Graphical method (B) Algebraic method
(C) Both A & B (D) None of these

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 6

Section-B (खण्ड – B) (𝟐 × 𝟔 𝟏𝟐)
31. ‘Vice-chancellor’ ‘kCn ds lHkh v{kjksa dks ysdj fdrus ‘kCn cuk;s tk ldrs gSa\

How many words can be formed with all the letters of the word vice-chancellor?

32. eku fudkfy, (Find the value of)

33. Evaluate ∫ dx

34. If P(B) = 0.5 and P(A ) then find P( ).

;fn P(B) = 0.5 vkSj P(A ) , rks P( ) Kkr dhft,A

35. ;fn cgqyd 15 rFkk ekf/;dk 12 gks] rks lekUrj ek/; fudkfy,A

If the mode is 15 and median is 12, then find arithmetic mean.

36. ;fn A = * +,B= * + rks A-B dk eku gksxkA

If A = * +,B= * + then find the value of A-B.

37. ;fn A = * + B=* + C=* + rks C - (A ) fudkfy,A

If A = * + B=* + C=* + find C - (A ).

38. 52 iÙkksa dh ,d xM~Mh esa ls ;n`PN;k fcuk izfrLFkkfir fd, x, nks iÙks fudkys x,A nksuks iÙkks
ds dkys jax dk gksus dh izkf;drk Kkr dhft,A
Two cards are drawn at random and without replacement from a pack of 52 playing
cards. Finds the probability that both the cards are black.

39. ;fn a, b, c H.P esa gksa rks b dk eku Kkr dhft,A
If a, b, c are in H.P. then find the value of b.

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 7

Section-C (खण्ड – C) (𝟑 × 𝟔 𝟏𝟖)

40. ;fn X = * + vkSj Y = * + rks X+Y dk eku Kkr dhft,A

If X = * + and Y = * + then find the value of X+Y.

41. 5000 tula[;k okys ,d uxj essa 2800 O;fDr fgUnqLrku i<+rs gS] 2300 O;fDr izHkkr i<+rs gS
rFkk 400 O;fDr nksuksa i<+rs gS fdrus O;fDr dksbZ lk Hkh v[kckj ugh i<+rs gSA
In a town of population 5000, 2800 persons read Hindustan, 2300 read Prabhat and
400 read both. How many do not read any newspaper?

42. If y = sin√ , find

43. Evaluate ∫ ( ) dx

44. ,d ifjokj esa nks cPps gSaA ;fn ;g Kkr gks fd cPpksa esa ls de ls de ,d cPpk yM+dk gS]
rks nksuks cPpksa ds yM+ds gksus dh D;k izkFkfedrk gS\
A family has two children. What is the probability that both the children are boys
given that at least one of them is a boy.

45. If the sum of three numbers in G.P. is 28 and their product is 512, find the G.P.
;fn xq.kksÙkj Js<+h esa rhu la[;kvksa dk ;ksx 28 gS vkSj xq.kuQy 512 gS] rks xq.kksÙkj Js<+h Kkr
djsaA

46. fuEukafdr la[;kvksa ds gjkRed ek/; fudkfy,-
Find the harmonic mean of the following.

1] ] ]

Section-D (खण्ड – D) (𝟓 × 𝟒 𝟐𝟎)

47. Calculate median:
Mid-value 15 25 35 45 55 65
Frequency 5 12 23 35 18 9

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 8

ekf/;dk Kkr djsa%
e/; ewY; 15 25 35 45 55 65
vko`fÙk 5 12 23 35 18 9

48. U;wure oxZ fof/k ls ewY;ksa dk miufr Kkr dhft,A
(find the trend values by the method of least squares)

o”kZ (Year) 1994 1995 1996 1997 1998 1999 2000
mRiknu 000Vu (Production 000 tons) 77 88 94 85 91 98 90

49. Find trend by least square method:

Year 2010 2011 2012 2013 2014
Value 34 50 67 75 85
U;wre oxZ fof/k ls miufr Kkr djsa%
o"kZ 2010 2011 2012 2013 2014
ewY; 34 50 67 75 85

50. lekdy djsa ( Integrate)

i. ∫

ii. ∫

51. fuEufyf[kr G.P. dk ;ksx Kkr dhft,A
Find the sum of the given series.
2 + 6 + 18 + ……….+ 4,374.

52. Find of .

*******************

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 9

Answer keys:-

01 A 11 D 21 C
02 D 12 A 22 C
03 A 13 D 23 A
04 A 14 A 24 A
05 A 15 D 25 A
06 A 16 C 26 D
07 A 17 B 27 C
08 B 18 C 28 C
09 A 19 C 29 A
10 A 20 C 30 C

JCERT, Ranchi Class-12_Model Question Paper Session: 2025 -26 Subject- Maths Page 10

Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions