JAC Class 12 Model Question Paper 2025 BMT

2025

MODEL
PAPERS
JAC BOARD JHARKHAND
EXAM ACADEMIC
COUNCIL MODEL
PREPARATION QUESTION
PAPER 2025

JHARKHAND ACADEMIC COUNCIL

ं ान एवं प्रक्षशिण पररषद् ,रााँची
झारखण्ड शैक्षिक अनुसध
Jharkhand Council of Educational Research and Training, Ranchi

MODEL QUESTION PAPER

Session: 2024-25 ( - )

Class – 12 F. M. – 80 Time – 3 Hours
Subject – BMT

INSTRUCTIONS / निर्दे श :
1. Examinee are required to answer in their own words as far as practicable.
ijh{kkFkhZ ;FkklaHko vius 'kCnksa esa gh mÙkj nsAa
2. This question papers have four sections: A, B, C and D. Total number of
questions are 52.
bl iz’ui= esa pkj [k.M & A, B, C ,oa D gSaA dqy iz'uksa dh la[;k gSA
3. There are 30 Multiple Choice Questions in the Section A. Four options are given
for each question, choose one of the correct options.
A esa dqy 30 cgqfodYih; ç'u gSa A izR;sd iz'u ds pkj fodYi fn, x, gSa]
buesa ls ,d lgh fodYi dk p;u dhft,A
4. Section B – Question numbers 31 – 38 are very short answer type. Answer
any six of these questions. Each question carries 2 marks.
B esa iz'u la[;k gSaA buesa ls fdUgh Ng
iz'uksa ds mÙkj nhft,A izR;sd iz'u dk eku vad fu/kkZfjr gSA
5. Section C – Question numbers 39 – 46 are short answer type. Answer any six
of these questions. Each question carries 3 marks.
C esa iz' u la[;k gSa A buesa ls fdUgh Ng iz' uksa
ds mÙkj nhft,A izR;sd iz'u dk eku vad fu/kkZfjr gSA
6. Section D – Question numbers 47 – 52 are long answer type. Answer any four
of these questions. Each question carries 5 marks.
D esa iz'u la[;k gSaA buesa ls fdUgh pkj

iz'uksa ds mÙkj nhft,A izR;sd iz'u dk eku vad fu/kkZfjr gSA

Page 1 of 7

Section-A - (𝟏 × 𝟑𝟎 = 𝟑𝟎)
1. Which is the 27th term of the sequence 5, 14, 23, ………….?
vuqdez 5] 14] 23]---------------- dk 27okW in fuEukafdr esa dkSu gS \
(a) 239 (b) 100 (c) 101 (d) 900
2. In an A.P. first term is 1 and last term is 11. If the sum of n terms is 36, the value of
n will be :
,d lkekarj Js<h es igyk in 1 gS vkSj vfUre in 11 gS A ;fn n inksa dk ;ksx 36 gks rks n dk eku
gksxk %
(a) 10 (b) 7 (c) 6 (d) 5
3. The third term in G.P. is 4. The product of first 5 term is :
,d xq.kksŸkj Js<h esa rhljk ib 4 gSA blds izFke 5 inksa dk xq.kuQy gS &
(a) 256 (b) 2,048 (c) 512 (d) 1,024
4. If 15pr = 2,730 then the value of r will be :
;fn 15pr = 2,730 gks rks r dk eku gksxk &
(a) 3 (b) 4 (c) 5 (d) 6
5. If n c12 = n c8 then n is equal to :
;fn n c12 = n c8 rc n cjkcj gS %
(a) 20 (b) 12 (c) 6 (d) 30
6. How many different word of 2 letters can be formed out of the letter of the word
CAT ?
CAT “kCn ds v{kjksa ls 2&2 v{kjksa ds fdrus “kCn cu ldrs gSa \
(a) 8 (b) 6 (c) 3 (d) 2
7. If n P3 =60 then the value of n is :
;fn n P3 =60 ] rks n dk eku gS&
(a) 3 (b) 5 (c) 9 (d) 20

X2 X
8. The value of 5x 5
(a)0 (b) 1 (c) 5 (d) 25
9. In a row matrix, the no. of row is :
iafDr vkO;wg esa iafDr;ksa dh la[;k gksrh gS )-

(a) 1 (b) 2 (c) 3 (d) None of these (buesa ls dksbZ ugha)

3 1 4 7
10. If A = [ ],B=[ ], then A + B :
7 6 5 2

Page 2 of 7

3 1 4 7
;fn A = [ ], B =[ ], rks A + B : -
7 6 5 2

12 7 7 8 −1 −6 3 7
(a) [ ] (b) [ ] (c) [ ] (d) [ ]
35 12 12 8 −2 4 5 6

11. (If A= {a, b, c, d}, B= {b, d, e, f} then the value of A ∩ B will be) : If uniVersel set
x = {1.2.3…20}
यदि A= {a, b, c, d.}, B= {b, d, e, f,} rks A ∩ B
(a) {a, b, c, d, e.f) (b) {b, d} (c) {d, e,f} (d) {c, d, e}
12. If A= {p, q, r, s}, B= {q, s, t}, C = {m, q, n},then the value of C – (A∩ B)
यदि A = {p,q,r, s}, B= {q, s, t,}, C = {m, q, n}, rks C-(A∩B) dk eku gksxk

(a) {m, n} (b) {p, q} (c) (r, s} (d) {p, r}
13. The differential coefficient of 3x4 w.r.t. x will be:
x ds lkis{k 3x4 dk vodyu xq.kkad gksxk %
(a) 16x (b) 16x2 (c) 12x2 (d) 4x3
𝑑𝑦
14. If y = 2 log 𝑥 then is equal to:
𝑑𝑥
𝑑𝑦
;fn y = 2 log 𝑥 rks cjkcj gS%
𝑑𝑥
(a) X (b) 2 (c) 0 (d) 2/x
15. ∫(2𝑥 + 3)5 𝑑𝑥 = ?
(2𝑥+3)6
(a) +C
6
(2𝑥+3)4
(b) +C
8
(2𝑥+3)6
(c) +C
12

(d) N0ne of these (buesa ls dksbZ ugha)
16. The best measure to central tendency is A.M is it true ?
dseUnzh; izof` r dk loksÙZ ke eki lekUrj ek/; gSA D;k ;g lR; gS \
(a) yes (b) No
17. Mean of 5, 8, 11, 16, 15 is:
5] 8] 11] 16] 15 dk ek/; gS%
(a) 10 (b) 11 (c) 12 (d) 13

18. Median of 80, 100, 90, 170, 60, 50, 40.
80, 100, 90, 170, 60, 50, 40 dk ekf/;dk gS &
(a) 80 (b) 170 (c) 90 (d) 60

Page 3 of 7

19. Median is:
ekf/;dk gS%
(a) Most frequent value, lcls vf/kd ckj vkus okyk eku
(b) Least frequent value, lcls de ckj vkus okyk eku
(c) Center of gravity, x:Ro dsUnz
(d) Middle most value, chp dk eku
20. Mode is:
cgqyd gS%
(a) Most frequent value, lcls vf/kd ckj vkus okyk eku
(b) Least frequent value, lcls de ckj vkus okyk eku
(c) Middle most value, chp dk eku
(d) Representing majority out of total frequency, dqy ckjEckj es lokZf/kd dk fu:fir djus
okyk
21. Which of the following is true?
fuEukafdr esa dkSu&lk lR; gS\
(a) Mean= 3 Median – 2 Mode, ek/; =3 ekf/;dk & 2 cgqyd
(b) Median = 3 Mode – 2 Mean, ekf/;dk = 3 cgqyd & 2 ek/;
(c) Mode = 3 Median – 2 mean, cgqyd = 3 ekf/;dk & 2 ek/;
(d) Mode = Mean + Median , cgqyd = ek/; $ ekf/;dk
22. Which of the following relationship is correct?
fuEu es ls dkSu&ls lacU/k lgh gS\
(a) A.M. = √𝐺. 𝑀 × 𝐻. 𝑀. (b) H.M. = √𝐴. 𝑀.× 𝐺. 𝑀 (c) G.M. = √𝐺. 𝑀.× 𝐻. 𝑀.
𝐴.𝑀+𝐻.𝑀.
(d ) G.M. =
2

23. The geometric mean of two number 8 and 18 shall be:
nks vadks 8 vkSj 18 dk xq.kksÙkj ek/; gksxk%
(a) 12 (b) 13 (c) 15 (d) 11.09
24. Least square method is used for calculating trend:
U;wure oxZ jhfr dk iz;ksx miufr Kkr djus ds fy, fd;k tkrk gS%
(a) True, lgh (b) false, xyr (c) Both (d) None of these
25. The most important factor causing seasonal variations are:
ekSleh forj.kksa dks mRiUu djus okys lcls egRoiw.kZ dkjd gS%
(a) growth of population, tula[;k c`f)

(b) change in fashion QS” ku esa ifjorZu
(c) weather and social customs ekSle vkSj lkekfrd jhfrfjokt
(d) technological improvement rduhfd lq/kkj

Page 4 of 7

26. The probability of drawing a red ball from a bag containing 4 red and 5 white balls
is:
4 yky rFkk 5 lQsn xsnksa okys ,d FkSys esa ls ,d yky xsan fudkyus dh izkf;drk gS%
(a) 4/5 (b)3/5 (c) 1/5 (d) 4/9

27. The probability of 53 Sundays in randomly chosen leap year is:
,d ;kn`PN;k pqus x, vf/k&o’kZ esa 53 jfookj gksus izkf;drk gS%
(a) 3/7 (b) 1/7 (c) 2/3 (d) 2/7
28. In a single throw of two dice the probability of getting a total greater than 8 is:
nks ik¡ls ,d ckj Qsd
a us ij 8 ls vf/kd ;ksx izkIr gksus dh izkf;drk gS%
(a) 8/36 (b) 12/36 (c) 5/8 (d) 4/16
29. At the time of interpolation continuous series is not cumulated under:
vkUrjx.ku djrs le; lrr~ Js.kh dks ---- lap;h ugha cuk;k tkrk gS%
(a) Binomial expansion method f}in foLrkj jhfr esa
(b) Netwon’s method U;wVu jhfr esa
(c) Lagrange’s method ySaxjst jhfr esa
(d) All the above mi;qDZ r lHkh esa
30. Binomial expansion method is based on:
f}in foLrkj jhfr vk/kkfjr gS%
(a) Multiplication theorem xq.ku izes; ij
(b) Additive theorem ;ksx izes; ij
(c) Binomial theorem f}in izes; ij
(d) None of these buesa ls dksbZ ugha

Section-B - (𝟐 × 𝟔 = 𝟏𝟐)

31. यदि n C4 = 5 x n P3 तो n का मान ज्ञात करें ।

If n C4 = 5 x n P3, find n.
32. मान दनकादिये (Evaluate)
5 10 8
4 3 2
7 9 8
33. समाकिन करें (Integrate)

ʃ 25𝑑𝑥− 𝑥2 (x<5)

34. 52 पत्ोों वािे ताश की एक गड्डी से एक रानी के खीोंचे जाने की प्रदयकता क्या है ?
What is the probability of drawing a Queen in a draw from a pack of 52 cards?
Page 5 of 7

35. एक छात्र द्वारा अोंग्रेजी, गदित एवों अर्थ शास्त्र में प्राप्ाों क क्रमशः 75, 92 तर्ा 49 है तो उसका औसत प्राप्ाों क
दनकािें ।
The marks obtained by a student in English, Mathematics and Economics are
75, 92, and 49. Find its Average score.
2 13
36. यदि (If) A = [ ] तो 𝐴𝐼 ज्ञात करें । (then find 𝐴𝐼 ).
4 −32
37. यदि (If) A = { 3,5,7,9} , B = { 6,8,10} तो (then find) A U B ज्ञात करें ।
38. If 𝐴 and 𝐵 are two events such that 𝑃(𝐴) = 1/4, 𝑃(𝐵) = 1/2 and 𝑃(𝐴 ∩ 𝐵) =
1/8, then find 𝑃(not 𝐴 and not 𝐵).
1 1
;fn 𝐴 vkSj 𝐵 nks ,slh ?kVuk,¡ gS fd 𝑃(𝐴) = , 𝑃(𝐵) = vkSj 𝑃(𝐴 ∩ 𝐵) =
4 2
1/8 rks 𝑃( 𝐴-ugha vkSj 𝐵-ugha) Kkr dhft,A

Section-C - (𝟑 × 𝟔 = 𝟏𝟖)

39. यदि दकसी समान्तर श्रे िी का 8 वॉ और 25 वॉ पि क्रमशः 15 और 49 है तो पहिा पि और पिान्तर ज्ञात कीदजए।
If 8th and 25th term of an A.P are 15 and 49 respectively then find its first term and
common difference.
2 6
40. मैदरि क्स [ ]का व्युत्क्रम ज्ञात करें ।
3 5
2 6
Find the inverse of Matrix [ ].
3 5
41. 520 व्यक्तियोों के समूह में 360 केवि दहन्दी तर्ा 130 केवि अोंग्रजी बोि सकते हैं । दकतने व्यक्ति दहन्दी और अोंग्रजी िोनोों
बोि सकते हैं ?
In a group of 520 persons, 360 can speak only Hindi and 130 only English. How many
persons can speak both Hindi and English?
42. x के सापेक्ष अवकिन कीदजए (Differentiate with respect to x).
(𝑥 − 3)(𝑥 + 2)
𝑥
43. मान दनकािें (Evaluate).

ʃ 𝑒 𝑛 (𝑛−1)
𝑥2
dx
44. एक व्यक्ति 4 में से 3 दनशानें सही िगाता है और िू सरा व्यक्ति 3 में से 2 दनशानें सही िगाता है । यदि िोनोों ही व्यक्ति एक

सार् प्रयत्न करें तो िक्ष्य के भे ि प्रदयकता ज्ञात कीदजए।
A person is known to hit the target in 3 out of 4 shots, whereas another person is
known to hit 2 out of 3 shots. Find the probability of the target being hit at all when
they both try.
Page 6 of 7

45. यदि िो सों ख्याओों का समान्तर माध्य 10 है और उनका गुिोत्र माध्य 8 है तो उनका हरात्मक माध्य ज्ञात कीदजए।
If Arithmetic mean and Geometric mean of two numbers are 10 and 8 respectively,
find its Harmonic mean.
46. 8 और 11 और का गुणोत्तर माध्य निकालें ।
Find the G. P. of 8 and 11.

Section-D - (𝟓 × 𝟒 = 𝟐𝟎)

47. दनम्न आँ कड़ोों से माक्तध्य का ज्ञात कीदजएः
Calculate median from the following data:
प्राप्ाोंक (Marks) : 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45

छात्रोों की सोंख्या 6 5 18 10 5 4 2 2
(Number of students)

48. काि श्रे िी क्या है ? काि श्रे िी दवश्लेषि का महत्व की व्याख्या करें ।
What is a time series? Explain the importance of Time Series Analysis.
49. दनम्न तादिका में तत्काि जीवन की वादषथकी 100 रू0 चुकाने के दिए दिखाया गया है ः
The following table shows the value of an immediate life annuity for Rs. 100 paid:
उम्र वषों में 40 50 60 70
(Age in years)
वादषथ की (Annuity) 6.2 7.2 9.1 12.0

42 वषथ की आयु के दिए वादषथ की ज्ञात कीदजए।
Interpolate the annuity for the age of 42.
50. समाकिन करें (Integrate)
(i). ∫ log 𝑥 𝑑𝑥 (ii). ʃ x √𝑥 − 1 dx
51. 5+55+555+…………………….. n पिोों तक का योगफि ज्ञात करें ।
Find the Sum to the n terms
5+55+555+…………………….. n
𝑥2 +1
52. Find the differential coefficient of function .
𝑥2

Page 7 of 7
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