JAC Class 12 Model Question Paper 2025 Maths

2025

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

JHARKHAND ACADEMIC COUNCIL

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

MODEL QUESTION PAPER

Session: 2024-25 ( - )

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

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 paper has 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 gSA 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; iz’u gSaA 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 9

Section-A - (𝟏 × 𝟑𝟎 = 𝟑𝟎)
1. A relation 𝑅 on set {1, 2, 3} is given by 𝑅 = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then
the relation 𝑅 is
(a) reflexive (b) symmetric
(c) transitive (d) symmetric and transitive
,d laca/k 𝑅 leqPp; {1, 2, 3} ij 𝑅 = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)} }kjk ifjHkkf"kr
gS] rks laca/k 𝑅 gS
(a) LorqY; (b) Lkefer
(c) LkaØked (d) Lkefer vkSj LkaØked
2. Let 𝑓: 𝑅 → 𝑅 be defined as 𝑓(𝑥 ) = 3𝑥. Choose the correct answer.
(a) 𝑓 is one-one onto (b) 𝑓 is many-one onto
(c) 𝑓 is one-one but not onto (d) 𝑓 is neither one-one nor onto
Ekku fyft, fd 𝑓(𝑥) = 3𝑥 )kjk ifjHkkf"kr Qyu 𝑓: 𝑅 → 𝑅 gSA lgh mÙkj pqfu,
(a) 𝑓 ,dSdh vkPNknd gS (b) 𝑓 cgq,d vkPNknd gS
(c) 𝑓 ,dSdh gS fdarq vkPNknd ugha gS (d) 𝑓 u rks ,dSdh gS vkSj u vkPNknd gSA
3. If 𝑓(𝑥) = 𝑥 2 + 𝑥 + 7 then 𝑓𝑜𝑓(0) is
(a) 7 (b) 63 (c) 49 (d) 21
;fn 𝑓(𝑥) = 𝑥 2 + 𝑥 + 7 rks 𝑓𝑜𝑓(0) =
(a) 7 (b) 63 (c) 49 (d) 21

4. Principal value of tan−1 (−1) is
(a) 𝜋/4 (b) −𝜋/4 (c) 3𝜋/4 (d) −3𝜋/4
tan−1 (−1) dk eq[; eku gS
(a) 𝜋/4 (b) −𝜋/4 (c) 3𝜋/4 (d) −3𝜋/4
2𝑥 + 𝑦 4𝑥 7 5𝑦 − 7
5. If [ ]= [ ], then the value of 𝑥, 𝑦 are respectively
5𝑥 − 7 4𝑥 𝑦 𝑥+6
2𝑥 + 𝑦 4𝑥 7 5𝑦 − 7
;fn [ ]= [
𝑦 𝑥+6
] rks 𝑥, 𝑦 ds eku Øe’k% gS
5𝑥 − 7 4𝑥
(a) 3, 1 (b) 2, 3 (c) 2, 4 (d) 3, 3
6. If 𝐴 be any square matrix, then (𝐴 + 𝐴′) is
(a) identity matrix (b) symmetric matrix

(c) skew-symmetric matrix (d) none of these
;fn 𝐴 dksbZ oxZ vkO;wg gS] rks (𝐴 + 𝐴′) gS
(a) rRled vkO;wg (b) lefer vkO;wg
(c) fo"ke lefer vkO;wg (d) buesa ls dksbZ ugha
Page 2 of 9

7. If 𝐴 = [ −1 2 3 ], then order of matrix 𝐴 is
(a) 1 × 3 (b) 3 × 1 (c) 1 × 1 (d) none of these
;fn 𝐴 = [ −1 2 3 ], rks vkO;wg 𝐴 dh dksfV gS
(a) 1 × 3 (b) 3 × 1 (c) 1 × 1 (d) buesa ls dksbZ ugha
1 2
8. If 𝐴 = [ ], then |2𝐴| is equal to
4 2
;fn 𝐴 = [ 1 2 ] rks |2𝐴| dk eku gS
4 2
(a) 2|𝐴| (b) |𝐴| (c) 4|𝐴| (d) 8|𝐴|
9. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
3 × 3 dksfV ds ,sls vkO;wgksa dh dqy fdruh la[;k gksxh ftudh izR;sd izfof"V 0 ;k 1 gS?
(a) 27 (b) 18 (c) 81 (d) 512

2 3 𝑥 3
10. If | |=| |, then 𝑥 is
4 5 2𝑥 5
(a) 2 (b) -2 (c)0 (d) none of these

;fn |2 3| = | 𝑥 3
| , rks 𝑥 gS
4 5 2𝑥 5
(a) 2 (b) -2 (c)0 (d) buesa ls dksbZ ugha
𝑑𝑦
11. If 𝑦 = log(log𝑥 ) , 𝑥 > 1 then is
𝑑𝑥
𝑑𝑦
;fn 𝑦 = log(log𝑥 ) , 𝑥 > 1 rks gS
𝑑𝑥
1 𝑥 1 −1
(a) (b) (c) (d)
log𝑥 log𝑥 𝑥 log𝑥 𝑥 log𝑥

𝑑𝑦
12. If (;fn) √𝑥 + √𝑦 = √𝑎 , then (rks) =?
𝑑𝑥
√𝑥 1 √𝑦 √𝑦
(a) − (b) − (c) − (d) 0
√𝑦 2 √𝑥 √𝑥
𝑑 2𝑦
13. If (;fn) 𝑦 = 5cos𝑥 − 3sin𝑥, then (rks) =
𝑑𝑥2
(a) 0 (b) 𝑦 (c) −𝑦 (d) 𝑥

14. The rate of change of the area of a circle with respect to its radius 𝑟 at 𝑟 = 5cm is

o`r dh {ks=Qy esa ifjorZu dh nj blds f=T;k ds lkis{k D;k gksxh tc f=T;k 5 cm gks\
(a) 10𝜋 cm2 /cm (b) 20𝜋 cm2 /cm
22
(c) cm2 /cm (d) 110𝜋 cm2 /cm
7
Page 3 of 9

𝑑𝑥
15. ∫ 𝑥 is equal to ¼cjkcj gS½
𝑒 +𝑒 −𝑥

(a) tan−1 (𝑒𝑥 ) + 𝑐 (b) tan−1(𝑒 −𝑥 ) + 𝑐
(c) log(𝑒 𝑥 − 𝑒−𝑥 ) + 𝑐 (d) log (𝑒 𝑥 + 𝑒 −𝑥 ) + 𝑐

sec 2 𝑥
16. ∫ 𝑑𝑥 is equal to ¼cjkcj gS½
cosec 2 𝑥

(a) tan 𝑥 + 𝑥 + 𝑐 (b) 𝑥 − tan 𝑥 + 𝑐
(c) tan 𝑥 − 𝑥 + 𝑐 (d) tan 𝑥 + 𝑐
𝜋/2
17. ∫−𝜋/2 sin7 𝑥 𝑑𝑥 is equal to ¼cjkcj gS½

(a) 𝜋/2 (b) −𝜋/2 (c) 𝜋 (d) 0
1 1
18. ∫0 1+𝑥2 𝑑𝑥 =

(a) 𝜋/2 (b) 𝜋/3 (c) 𝜋/4 (d) 𝜋/6

𝑑2 𝑦 𝑑𝑦 2
19. Sum of the order and degree of the differential equation 2
= √1 + ( ) is
𝑑𝑥 𝑑𝑥

𝑑2 𝑦 𝑑𝑦 2
vody lehdj.k 𝑑𝑥2 = √1 + (𝑑𝑥 ) dh dksfV rFkk ?kkr dk ;ksxQy gS
(a) 1 (b) 2 (c) 3 (d) 4

20. What is the integrating factor of the differential equation
𝑑𝑦
+ 𝑦 sec 𝑥 = tan 𝑥?
𝑑𝑥
𝑑𝑦
vody lehdj.k + 𝑦 sec 𝑥 = tan 𝑥 dk lekdyu xq.kkad D;k gS\
𝑑𝑥

(a) sec 𝑥 + tan 𝑥 (b) log (sec 𝑥 + tan 𝑥 )
(c) 𝑒sec 𝑥 (d) sec 𝑥

21. If the vectors 𝑎𝑖̂ + 3𝑗̂ − 2𝑘̂ and 3𝑖̂ − 4𝑗̂ + 𝑏𝑘̂ are collinear, then (𝑎, 𝑏) =
;fn lfn’k 𝑎𝑖̂ + 3𝑗̂ − 2𝑘̂ rFkk 3𝑖̂ − 4𝑗̂ + 𝑏𝑘̂ lajs[k gSa] rks (𝑎, 𝑏) =
9 8 9 8 9 8 9 8
(a) ( , ) (b) ( − , ) (c) ( , − ) (d) ( − , − )
4 3 4 3 4 3 4 3

22. The value of 𝑖̂ ∙ (𝑗̂ × 𝑘̂) + 𝑗̂ ∙ (𝑖̂ × 𝑘̂) + 𝑘̂ ∙ (𝑖̂ × 𝑗̂) is
𝑖̂ ∙ (𝑗̂ × 𝑘̂) + 𝑗̂ ∙ (𝑖̂ × 𝑘̂) + 𝑘̂ ∙ (𝑖̂ × 𝑗̂) dk eku gS
(a) 0 (b) −1 (c) 1 (d) 3
Page 4 of 9

23. ⃗⃗⃗ = 5 𝑖̂ + 𝑗̂ − 3 𝑘̂ and ⃗⃗⃗
If 𝑎 𝑏 = 3 𝑖̂ − 4 𝑗̂ + 7 𝑘̂, the 𝑎 ⃗⃗⃗ ∙ ⃗⃗⃗
𝑏 is
;fn 𝑎 ⃗⃗⃗ = 5 𝑖̂ + 𝑗̂ − 3 𝑘̂ vkSj 𝑏
⃗⃗⃗ = 3 𝑖̂ − 4 𝑗̂ + 7 𝑘̂, rks 𝑎 ⃗⃗⃗ gksxk
⃗⃗⃗ ∙ 𝑏
(a) 15 (b) -15 (c) 10 (d) -10

24. ⃗⃗⃗ | ≠ 0, | ⃗⃗⃗
If | 𝑎 𝑏 | ≠ 0 and 𝑎⃗⃗⃗ × ⃗⃗⃗
𝑏 = ⃗⃗⃗
0 , then
;fn | 𝑎 ⃗⃗⃗ | ≠ 0, | ⃗⃗⃗
𝑏 | ≠ 0 vkSj 𝑎⃗⃗⃗ × ⃗⃗⃗
𝑏 = ⃗⃗⃗ 0 gks] rks
(a) 𝑎 ⃗⃗⃗
⃗⃗⃗ = 𝑏 (b) 𝑎 ⃗⃗⃗
⃗⃗⃗ ⊥ 𝑏 (c) 𝑎 ⃗⃗⃗
⃗⃗⃗ ∥ 𝑏 (d) 𝑎 ⃗⃗⃗ = 𝑎
⃗⃗⃗ ∙ 𝑏 ⃗⃗⃗
⃗⃗⃗ × 𝑏

25. The direction cosines of the vector 𝑖̂ + 2 𝑗̂ + 2 𝑘̂ are
Lkfn’k 𝑖̂ + 2 𝑗̂ + 2 𝑘̂ dk fnd~&dkslkbu gksxk
1 2 2 1 2 2 1 2 2
(a) 1, 2, 2 (b) , , (c) , , (d) , ,
9 9 9 √3 √3 √3 3 3 3

26. The vector equation of 𝑥-axis is
𝑥-v{k dk lfn’k lehdj.k gS
(a) ⃗⃗𝑟 = 𝑖̂ (b) 𝑟⃗⃗ = 𝑗̂ + 𝑘̂ (c) 𝑟⃗⃗ = 𝜆𝑖̂ (d) 𝑟⃗⃗ = 𝜆𝑗̂
𝑥−5 𝑦−2 𝑧+4
27. If the cartesian equation of a line 𝑙 is = =
3 2 −8 , then the vector
equation of that line 𝑙 is
𝑥−5 𝑦−2 𝑧+4
;fn ,d js[kk 𝑙 dk dkrhZ; lehdj.k = = gS] rks mlh js[kk 𝑙 dk
3 2 −8
lfn’k lehdj.k gksxk
(a) ⃗⃗𝑟 = (5 𝑖̂ + 2 𝑗̂ + 4 𝑘̂) + 𝜆(3 𝑖̂ + 2 𝑗̂ − 8 𝑘̂)
(b) ⃗⃗𝑟 = (3 𝑖̂ + 2 𝑗̂ − 8 𝑘̂) + 𝜆(5 𝑖̂ + 2 𝑗̂ − 4 𝑘̂)
(c) ⃗⃗𝑟 = (5 𝑖̂ + 2 𝑗̂ − 4𝑘̂) + 𝜆(3 𝑖̂ + 2 𝑗̂ − 8𝑘̂)
(d) ⃗⃗𝑟 = (5 𝑖̂ + 2 𝑗̂ − 4𝑘̂) + (3 𝑖̂ + 2 𝑗̂ − 8𝑘̂)
𝑥−1 𝑦−1 𝑧−6 𝑥−1 𝑦−2 𝑧−3
28. If lines = = and = = are perpendicular,
3𝑘 2 1 1 2𝑘 −7
then the value of 𝑘 is
𝑥−1 𝑦−1 𝑧−6 𝑥−1 𝑦−2 𝑧−3
;fn js[kk,¡ = = rFkk = = ijLij yEcor gSa]
3𝑘 2 1 1 2𝑘 −7
rks 𝑘 dk eku gS

(a) -1 (b) 1 (c) 0 (d) 7
29. If 𝑃(𝐴̅ ) = 0.2, 𝑃(𝐵) = 0.5 and 𝑃(𝐵/𝐴) = 0.4, then 𝑃(𝐴/𝐵) = ________
;fn 𝑃(𝐴̅ ) = 0.2, 𝑃(𝐵) = 0.5 rFkk (𝐵/𝐴) = 0.4] rks 𝑃(𝐴/𝐵) = ________
Page 5 of 9

(a) 0.32 (b) 0.64 (c) 0.16 (d) 0.25

30. If 𝐴 and 𝐵 are independent events, then which is not true
;fn 𝐴 vkSj 𝐵 nks Lora= ?kVuk,¡ gSa, rks dkSu lR; ugha gS
(a) 𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴)𝑃(𝐵) (b) 𝑃(𝐴 ∩ 𝐵̅) = 𝑃(𝐴)𝑃(𝐵̅)
(c) 𝑃(𝐴 ∪ 𝐵) = 1 − 𝑃(𝐴̅)𝑃(𝐵̅) (d) 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

Section-B - (𝟐 × 𝟔 = 𝟏𝟐)

31. Let 𝑓: 𝑹 → 𝑹 be given by 𝑓(𝑥 ) = 𝑥 2 − 5𝑥 + 4, then find the value of 𝑓𝑜𝑓(1).
;fn 𝑓: 𝑹 → 𝑹, 𝑓(𝑥 ) = 𝑥 2 − 5𝑥 + 4 }kjk ÁnŸk gS] rks 𝑓𝑜𝑓(1) dk eku Kkr dhft,A
32. Write all one-one functions from set 𝐴 = {1, 2, 3} to itself.
leqPp; 𝐴 = {1, 2, 3} ls Lo;a rd lHkh ,dSdh Qyu dks fy[ksAa
2 3 17
33. Prove that (fl} dhft, fd): tan−1 + sin−1 = tan−1
3 5 6
34. Find minor and cofactor of elements 6 in the following determinant
fuEufyf[kr lkjf.kd esa vo;o 6 dk milkjf.kd vkSj lg[k.M Kkr dhft,
1 2 2
∆= |4 5 6|
7 8 9
𝑑𝑦
35. If 𝑥 = 𝑎(𝜃 − sin 𝜃 ), 𝑦 = 𝑎(1 − cos 𝜃 ), then find .
𝑑𝑥
𝑑𝑦
;fn 𝑥 = 𝑎(𝜃 − sin 𝜃 ), 𝑦 = 𝑎(1 − cos 𝜃 ), rks Kkr djsAa
𝑑𝑥
𝑑𝑥
36. Evaluate (Kkr djsa): ∫
√1 − cos 𝑥
37. Find the integrating factor of the following differential equation
fuEufyf[kr vody lehdj.k dk lekdyu xq.kd Kkr dhft,
𝑑𝑦
𝑥 + 2𝑦 = 𝑥 2 (𝑥 ≠ 0)
𝑑𝑥
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).
;fn 𝐴 vkSj 𝐵 nks ,slh ?kVuk,¡ gS fd 𝑃(𝐴) = 1/4, 𝑃(𝐵) = 1/2 vkSj 𝑃 (𝐴 ∩ 𝐵) = 1/8
rks 𝑃( 𝐴-ugha vkSj 𝐵-ugha) Kkr dhft,A
Page 6 of 9

Section-C - (𝟑 × 𝟔 = 𝟏𝟖)
𝑥
𝑖𝑓 𝑥 ≠ 0
39. Prove that the function 𝑓(𝑥 ) = { 𝑥|
| is not continuous at point 𝑥 = 0.
−1 𝑖𝑓 𝑥 = 0
𝑥
𝑖𝑓 𝑥 ≠ 0
fl} djsa fd Qyu 𝑓 (𝑥 ) = { |𝑥| fcUnq 𝑥 = 0 ij larr ugh gSA
−1 𝑖𝑓 𝑥 = 0

40. If area of triangle is 35 sq units with vertices (2, −6), (5, 4) and (𝑘, 4), then find
value of 𝑘.

;fn 'kh"kZ (2, −6), (5, 4) vkSj (𝑘, 4) okys f=Hkqt dk {ks=Qy 35 oXkZ bdkbZ gS rks 𝑘 dk
eku Kkr djsAa
41. Find the interval in which the function 𝑓(𝑥 ) = 2𝑥3 − 3𝑥 2 − 36𝑥 + 7 is
(a) increasing, (b) decreasing.

varjky Kkr dhft, ftuesa Qyu 𝑓(𝑥 ) = 2𝑥 3 − 3𝑥 2 − 36𝑥 + 7
(a) o/kZeku (b) gzkleku gSA
𝑑𝑦
42. Find if 𝑦 = 𝑥 sin 𝑥 + (sin 𝑥 )cos 𝑥
𝑑𝑥
𝑑𝑦
Kkr dhft, ;fn 𝑦 = 𝑥 sin 𝑥 + (sin 𝑥 )cos 𝑥
𝑑𝑥
𝑥+2
43. Evaluate (eku fudkysa): ∫ 𝑑𝑥
√𝑥 2 + 2𝑥 + 3
4
√𝑥
44. Evaluate (eku fudkysa): ∫ 𝑑𝑥
0 √4 − 𝑥 + √𝑥

⃗⃗⃗ = 3 𝑖̂ + 𝑗̂ + 4 𝑘̂ and ⃗⃗⃗
45. If 𝑎 𝑏 = 3 𝑖̂ − 𝑗̂ + 5 𝑘̂, then find

⃗⃗⃗ = 3 𝑖̂ + 𝑗̂ + 4 𝑘̂ rFkk ⃗⃗⃗
;fn 𝑎 𝑏 = 3 𝑖̂ − 𝑗̂ + 5 𝑘̂, rks Kkr dhft,
(i) |𝑎 ⃗⃗⃗ |
⃗⃗⃗ | + |𝑏 ⃗⃗⃗ × ⃗⃗⃗
(ii) 𝑎 𝑏 ⃗⃗⃗ ∙ ⃗⃗⃗
(iii) 𝑎 𝑏
46. If the vertices 𝐴, 𝐵, 𝐶 of a triangle 𝐴𝐵𝐶 have position vectors
(1, 2, 3), (−1, 0, 0) and (0, 1, 2) respectively, then find ∠𝐴𝐵𝐶.

;fn fdlh f=Hkqt 𝐴𝐵𝐶 ds 'kh"kZ 𝐴, 𝐵, 𝐶 Øe'k% (1, 2, 3), (−1, 0, 0) rFkk (0, 1, 2) gSa
rks ∠𝐴𝐵𝐶 Kkr dhft,A

Page 7 of 9

Section-D - (𝟓 × 𝟒 = 𝟐𝟎)

47. Solve the following system of equations by matrix method
fuEufyf[kr lehdj.k fudk; dks vkC;wg fof/k ls gy djsa
5𝑥 + 3𝑦 + 𝑧 = 16
2𝑥 + 𝑦 + 3𝑧 = 19
𝑥 + 2𝑦 + 4𝑧 = 25
48. Find the maximum and minimum value of 𝑥 3 − 3𝑥 + 3

𝑥 3 − 3𝑥 + 3 dk egÙke rFkk U;wure eku Kkr djsAa
49. Find the shortest distance between the following pair of lines
fuEufyf[kr js[kk&;qXeksa ds chp dh U;wure nwjh Kkr djsa
⃗⃗𝑟 = (𝑖̂ + 2 𝑗̂ + 𝑘̂) + 𝜇(𝑖̂ − 𝑗̂ + 𝑘̂) and 𝑟⃗⃗ = (2 𝑖̂ − 𝑗̂ − 𝑘̂) + 𝜆(2 𝑖̂ + 𝑗̂ + 2 𝑘̂)

50. A card from a pack of 52 cards is lost. From the remaining cards of the pack,
two cards are drawn and are found to be both diamonds. What is the
probability of the lost card being a diamond?
52 rk’ksa dh xÏh ls ,d iÙkk [kks tkrk gSA 'ks"k iÙkksa esa ls nks iÙks fudkys tkrs gSa tks
bZV ds iÙks gSaA [kks x, iÙks ds bZV gksus dh izkf;drk D;k gS?

51. Solve the following L.P.P. by graphical method:
Minimize 𝑧 = 20𝑥 + 10𝑦
Subject to 𝑥 + 2𝑦 ≤ 40
3𝑥 + 𝑦 ≥ 30
4𝑥 + 3𝑦 ≥ 60 and 𝑥, 𝑦 ≥ 0.

fuEufyf[kr jSf[kd izksxzkeu leL;k dks vkys[kh; fof/k ls gy djsa :
U;wurehdj.k djsa 𝑧 = 20𝑥 + 10𝑦
tcfd 𝑥 + 2𝑦 ≤ 40
3𝑥 + 𝑦 ≥ 30
4𝑥 + 3𝑦 ≥ 60 and 𝑥, 𝑦 ≥ 0.

52. Using integration find the area of the region bounded by the parabola 𝑦 2 = 16𝑥
and the line 𝑥 = 4.
lekdyu dk iz;ksx dj ijoy; 𝑦 2 = 16𝑥 rFkk ljy js[kk 𝑥 = 4 ls f?kjs {ks= dk

{ks=Qy Kkr djsAa

Page 8 of 9

Answer – Key

Q.N. 1 2 3 4 5 6 7 8 9 10
Key A a b b b b a c d a
Q.N. 11 12 13 14 15 16 17 18 19 20
Key c c c a a c d c d a
Q.N. 21 22 23 24 25 26 27 28 29 30
Key b c d c d c c b b d

Page 9 of 9
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