JAC Class 11 Model Question Paper Maths

झारखंड बोर्ड

मॉडल पेपर

Class 11

(Class 11th)
(Mathematics)
1. Write the Roster form of the set A = {x : x is letter of word BETTER)

^TJ^f A = {x : x is BETTER ^T^ ^> ^ft 3T^^^t ^T TFJ^ fi}

(A) A = {B, E, T, R} (B) A = {B, E, T, E, R}
(C) A = {B, E, T, T, E, R} (D) A = {B, T, R}

2- If A = {0,1,2,3,4} and B ^ {1,2,3} Then find
^ft A = {0,1,2,3,4} ^B = {1,2,3} ?fl(4n^)

(A) {0,1,2} (B) {1,2,3} (C) {1,2,3,4} (D) {0,1}

3 Ifj^^^^) (A\JBf=t?
(A) A1 n ^1 (B) A1 u ^1 (C) (^ u ^) (D) (^ n
4. If ^y and B are two sets such that n(A) ^? 32, n(B) ^ 28 and n(^u^)= 50, then find

= 32, n(B) = 28 ?TT (^u^) = 50 eft i

(A) 10 (B) 20 (C) 28 (D) 8
Find x andy, if (s + 2,4) = (2,2x + y)

I (A) (3,-2) (B)(-2,3) (C)(0,2) (D)(0,4)
6.If A * {2,3}, B = {4,5} and C ^ {5,6} then find Ax (BnC)

i^^'A = {2, 3}, B = {4, 5}^^ C = {5,6}^ft Ax (BnC) TRT

(A) {(2,5),(3,5)} (B) {(4,5), (5,4)} (C) {(2,5),(5,6)} (D) {(3,5),(6,3)}

7.If/(^) = jc2+4,thenfind/(2)

(A) 4 (B) 8 (C)2 (D) -2
- Find the domain of f(x) = Vjc-T .

9. The angles of triangle are in the ratio 1:3:5. Find the greatest angle.

^^^t ^^rjvJT c^ cFt^ 1:3:5 cf> ^T^TI^^ ^ t eft ^ft ^T chT TTFT W\

(A) 90 (B)60 (C)20 (D) 100

107
If tan 9 = — and 9 lie in 3rd quadrant. Then find the value of sin 9 - cos 9.
24
^^^ tan<9 =—3f^^ 0,3rdT^^^t cf
24
(A)—177244
(B)-- (C)— (D)-^-
V ^ 25252525
11.^ cos20 -sin20
Find the value ofr— _
cos 20+sin 20

cos 20 + sin 20

(A)tan25 (B) tan45 (C)tan20 (D)tan35
12. _. ' l-cos20
Find —
sin 29
rv^1-COS20

sin 29
(A) cot<9 (B) cot29 (C) cot- (D) tan<9

* •^• Find the principal solution of the equation tan jc = V3 . If x lie in 1st quadrant.

II 1 MK n o I

(A)- (B)- V
v J 62 (C)- (D)-
} 3 V4
14. Find the general solution of the equation tan jc + cot x = 2.

tan jc + cot x = 2

,^^I l-c I v — M^T _1_ ___11 IV 1/iTT -^—fill V — MTT ^_ ^^
4 J34 . ^2

15.
Evaluate:
l + /2+i3

(A)l+z (B) l-i (C) -z-1 (D)2
16. Find multiplicative inverse of 3 + 2/

3 + 2z cm Hull^H4) nf^lci^^ W^T
(A) 3 - 4/ (B) 3 + 2z (C) —-— (D) ^- + —
v )\ )v ^13 13 v M3 13
Find the modulus of -1 -1

(A) 2 (B)-2 (C) 3 (D)6
18. Find jc and;; if (3jc-2^(2+/)2 = 10(1 + i)
x 3jfk v ^1 BFT ^TTcT c^lRii^ "^rf^ (3jc-2/y)(2+/)2 = 10(1 + z)
•*N^^\^X^
(A)jc =—,y = - (B) x =—,^ = i (C) x = -,y ^ — (P)x = — ,y = -

15 515 35515 3
• Find all the roots of equation x2 +1 = 0.

(A)2z,-2z (B)3z,-3z (C) z, -z (D) 1+z, 1-z

20. Solve 3x +5 < x- 7, if x is an integer.
^^^ 3x +5 < x- 7, ^^^ jc ^p\i ^ife t !
(A){-4,-3,-2} (B){-9,-8,-7} (C){2,3,4. } (D) {3, 4, 6, 7}

•21. _. , .^ 1 1 x
Find x, if —+— = -—.
[8 [9 [10
+ =JL
xfld
! 15 12 ^o
(A) 100 (B) 10 (C) 20 (D) 8
22. ifn =12.(/i),findw.
4
^p =12.(p).

(A) 6 |(B)8 (C)10 (D)-2
23. Find the number of permutation of the letter of the word "ROSE"

"ROSE^ ^ie! s^Wlt

(A) 24 (B) 42 (C) 12 (D) 36
24. If = n^ , find ^r^.
r'=r , eft ^TR
C8 C22
(A) 10 (B)45 (C)35 (D) 53
25 What is the numberof term in the expansion of 11 + 5v2x J ?

(A) 5 (B)7 (C)6 (D)10
Find the co-efficient of x10 in the expansion of (x - 2x2)

(A) -9. (18C3) (B) -8. (18c, ) (C) -27. (18^(0) -8.
12
27.
Find the middle term in the expansion of x—^ .
2x

12
x
2x

(A) 16
231
(B)
220
v ' 16
(Of
28. Find the 10th term of a sequence whose 7th and 12th term are 34 and 64 respectively.

3Fpf^ cJTT 7cff ^F^ cT^TT 12^T ^ ff^^ 34 #^ 64 t eft vF^^ ^TJpI^ ^T 10cff

(A) 42 (B) 52 (C) 63 (D) 36
29. Find the sum of the sereis 99 + 95 + 91+ to 20 term

M 99 + 95 + 91 +c^ 20

clef) cf^ ffd

(A) 1220 (B) 120 (Q220 (D) 360

30. Ifx + 2, 3x and 4x+lare in AP, then find x.

x + 2, 3x rT^TT 4x + 1 W^Z ^t^ft^ftjc^

(A)x^4 (B)x = 2 (C)x^14 (D)x = 3

31. Find ^heGM of 3 and 27.
3 ^fcf 27 c^T 'J^fkN W^ ^^c^T^ I

(A) 9 (B) 7 (C) 6 (D) 2
Find the 12th term of a G.P. whose 8th term is 192 and common ratio is 2.
32.

cfTT 12cJT ^ W c^^^^r^, (vJr^i 8cff ^ 192 ^T^TT ^f ^Tj^RT 2 1

(A) 3(28) (B) 3(27) (C) 3(2)10 (D) 247
iiow many terms of the sereis 1 + 2 + 22 + 23 +must be taken to make 511.
33.

+ 2[f22+23+..."^ ^^^ ^t cf^^ fe^TT vjf^ ^ ^^FT il^l^ei 511

(A) 10 (B) 8 (C) 9 (D) 7
34. Find the slope of the line joining (3, -2) and (7, -2).

(3, -2) craj (7, -2) e^t ft^IFf cficff ^S\ e^^ ^lef

(A) 0 (B) 1 (C) 3 (D) 1
Find the equation of line which make intercept -3 and 2 on the x and y axis

respectively.
vjft x 3TST cT^TT y 3^^f >^^ sF^^ ~3 3jf^^ 2

-3 27 3 22-341()l (C)()
36.
Find the length of the perpendicular from the point (2, -3) to the line 4x + 3_y + 16 = 0.

ft^ (2, -3) ^ W^\ ^T 4x + 3^ + 16 = 0 ^R #^ ^ e^ ^f eRT^ ^^cFTef I

(A) 3 (B) 0 (C) 4 (D) 5
37. Find the equation of the circle whose radius is 4 and centre is (0, 1).
^^T ^xT cjTT ^i^jcr^u| P^i^^k^ ^^R^^^ f^^T 4 ^ c^ (0, 1) 11
•,••••
(A)x2+^=16 (B) x2+(y-l)2=16 (C) (x-1)2 +/ =16 (D) x2 + (y + l)2 =16.

38.
Find the centre of the circle whose diameter is the line joining the points (5, -3) and

(3J).
^JT c|tT cRT ^S f^^^ ^TT; fR^ cq^^ c^ ^ (5, -3) ^TSR (3,1) 11

(A) (4,-1) (B) (2,-1) (C) (4,-3) (D) (1,-2)

39. Find the focus of the parabola jc2 = 16y

x2 =

(A) (0,2) (B)(0,4) (C)(2,0) (D) (4,0)
40. Vjc v
Find the eccentricity of the ellipse — + — = 1,
^169 144

169 144

fA) ^ (B) -I (C) I (D) i
14 13
41 • Find the length of latus rectum of the ellipse 2^2 + 3y2 = 6

2jc2 +3^ = 6 ^

| (B)|(C)J
42.

jc-O jc

(B) i (C) - (D) i
v ' 34 ^ 2

43.Limit si
Evaluate —^
jc -^ 0 sin Ix

()| ()
44. iff(x) = sin jc, find f{0).

= sin jc, eft f(0) cf>T

(A) 2 (B) 1 (C) 0 (D) 1

45- it-2 s- , dy
If y = cos jc, find -^-.
i
co s2 x eft —
dx

(A)Sin4jc (B) Sin3x (C)-Sin2jc (D) Sin2x.
46. If a leap year is selected at random, what is the change that it will contain 53

Sundays?
cftq cp^ l|Kt^^A|| T^^\ vjTTcTT t, eft 53 ^^^R ^ ^t OT ^rTfcRT I?

(A) | (B) | (C) I (D) I

47' If P(A) = -, P(B) = - and P(A n B) = -. Then find
834

(A)— (B)ii
v 1224

482= ^- ,find
If

,^

7397
(A)^- (B) - (C) - (D) ^
1111119
49.The mean of 4, 7, 2, 8, 6 and a is 7. Find the value of a.

^ 4, 7, 2, 8, 6 ^^ a cf>T W[ 7 t ^t a cf)T

(A) 1 (B) 6 (C) 15 (D) 7
50.If P : It is cold.
^ : It is raning, find p v q.

^ ^t ^t t,
(A) It is cold and It is raining

^t Ft ^\ 1
(B) It is cold or It is raining.

FF t ^ c^^^ Ft ^ 11
(C)It is cold and It is not raining.

FF t 3f^^ cp^^ ^! Ft ^i\ 11
(D)It is not cold and It is raining.

FF F^f t #^ e^^ Ft ^t 11

ANSWER SHEET OF SET -
1 A 26 D
2 B 27 A
3 A 28 B
4 A 29 A
5 D 30 D
6 A 31 A
7 B 32 C
8 A 33 C
9 D 34 A
10 A 35 A
11 A 3^ A
12 D 37 B
13 C 38 A
14 A 39 B
15 B 40 B
16 C 41 D
17 A 42 D
18 A 43 D
19 C 44 D
20 B 45 C
21 A 46 B
22 A 47 B
23 A 48 C
24 B 49 C
25 D 50 B