TBJEE 2022 Question Paper - Mathematics

FOR TBJEE EXAM PREPARATION

TBJEE 2022
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

TBJEE 2022 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

.
m .co s e m

se l a
ag
DO NOT OPEN THE SEAL UNTIL YOUARE
ASKED TO DO SO

2022
m
co
Question Paper Serles

. c om P
e m .
em l as
l as ag
ag MATHEMATICS JM

Time: 45 Minutes Maximum Marks : 120

m
Total Marks: 120 (4 x 30)
. c o
m
Answer all questions
e
a s
l pages. Each MultipleChoice Question(MCQ)
This QuestionPaper consistsofa16 g
is provided with four options (A), (B), (C) and (D). Identify the correct option and SEAL
darken/fillthe correspondingcircle (4)/(B)/(C)/(D)with Blue/BlackBallpointPen
on the OMR Answer Sheet.

For each question, 4 marks will be awarded for correct answer and for each
wrong answer 1 mark will be deducted.

m
m .co
.co s e m
s em g la
g la a
a (A)/(B)/(C)/(D) aT IAI Ballpoint Pen f S` AI

m
m .co s e m
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 1 of 16

1. The period of the function, f(x) =(sin3x+| cos 6x| is (x] denotes the greatest integer
less than or equal to x)

(B) 2%
(C) 2

(D) ½

SI (x]-*-4% AÁ6 AR Sx fx) =[sin3x] +| cos6x| cteÍtA ieA
(A) x

(B) 2%
(C) 2r

(D) %

2. Let, Sbe the set of all real numbers. Then the relation P= (x,y):*,ye S,1+ xy >0} on
S is

(A) reflexive and symmetric but not transitive

(B) reflexive and transitive but not symmetric

(C) symmetric and transitive but not reflexive

(D) reflexive, symmetric and transitive

QI AA FA, P={(x, y) : x,y eS, 1+ xy > 0} gt s RIA S TRE RA AIA t, P ft

JM-Series P

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 16

.
m .co s e m

l a
ag
3.Which of the following functions is not injective mapping?
(A) f)=|x+1|, xe-1, )

(B gx)= x+,x (0, o)
(C) h(x)=+4x-5,xe(0, o)

om . co
(D) k(x) =e,xe[0,o)
. c e m
e m l as
as
l=|x+1|, ag
ag
(A) f(x) xe-1 )
B gx)=x+,xe(0, )
(C) h(x) =+4x-5, xe (0, o)
(D) k(x) =e,xe[0, oo)

m
.co
n 1

4. If S, =) and then equals to
r-0 C, f=0
TC,
e m
Sn
(A) n-1
l as
(B)
2n-1 ag
2

-1

(D)

m
m .co
.co
n
1
Sn
e m
s
r=o C,
e m la
las (A) n-1
ag
2n-1
(B) 2

n
(C) a

(D)

om
JM-Series P 3
[P.T.O.
. c s e
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 3 of 16

(i-a)00
5. The value of + , where i=/-1, is
J3-i)
(A) 1
(B) -i
(C) i

(D) -1
\l00 100
(i-W3 +
(V3 +i)
(i+8
J3-i)
(A) 1

(B) -i
(C) i
(D) -1

Progression, then
6. lf a,, ag, ag,..., a, are in Geometric

log a, log a,+1 log a,2
log an+3 loga,+4 loga,+5
|log a,+6 log an7 log an+8

(A) O (B) 1

(C) 2 (D) -2

|loga, log a,+1 log a,+2|
log an+3 log ans4 log an5=
log an+6 log a,+7 log an+8

(A) O (B) 1

(C) 2 (D) -2

4
JM-Series P

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 16

.
m .co s e m

l a
7. pe q' is logically equivalentto
ag
(A) (p’q) ’ (g’ p) (B) (p’ q)v(g’ p)
(C) (p+ q)a (q’ p) (D) (PAq)’ (gap)

(A) (p’q)’ (g’ p) (B) (p’ q)v(g’ p)
() (p’q)a(g’ p)
om
(D) (Paq)’ (qa p)
. co
. c e m
em
8. Feasible region (shaded) for a LPP
l as
l as
Maximize Z=5x+7y
ag
a
s.t.g x20,y >0
is shown in the following figure :

B (3,4)
c(0,2)

m
o(0, 0)1 c. oA(7, Þ)
e m
Then
l as
(A) maximum value is 43 at (3, 4)ag (B) maximum value is 35 at (7, 0)
(C) maximum value is 46 at (5, 2) (D) no maximum value exists
bl Maximize Z=5x+7y
s.t. x0, y 20
a LPP-gg sOD (shaded) AC fbUA SS:

m
m .co
.co
B(3,4)
e m
e m C(0, 2)7
las
las ag
o (0, 0)1 A(7, 0)

(A) 43 A SAAA, (3, 4) 5 (B) 35 A bAH AA, (7, 0) gS
(C) 46 A SAN AR, (5, 2) S
JM-Series P
[P.T.0.
m
.co s e
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 5 of 16

9. Acard from a pack of 52 cards is lost. From the remainingcards of the pack, two cards
are drawn and both are found to be clubs. Then the probability of the lost card being
club is

(A) 11/50 (B) 26/425

(C) 22/425 (D) 13/50

(A) 11/50 (B) 26/425

(C) 22/425 (D) 13/50

10, If the function f defined by

sin(a +1] + 2 sin x x<0
X

flx) = X=0
1+ bx-1 X>0

is continuous at x=0, then the values of a and bare

(A) a = 4, b=1 (B) a=-4, b=-1

(C) a =1,b=4 (D) a= -1, b= 4

sin(a +1)x+ 2sin x
X

f(x)= 2 x=0

V1+ bx -1

(A) a =4, b=1 (B) a=-4, b=-1

(C) a= l,b=4 (D) a=-1, b= 4
JM-Series P 6

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 16

.
m .co s e m

l a
ag
11, If the functionflx)=-6ax +5x satisfis the conditions of Lagrange's Mean Value
Theorem for the interval [1, 2] and tangent to the curve y= f(x) at x =7/4 is parallel
to the chord that joins the points of intersectionof the curve with the ordinates x =1
and x = 2. Then the value of a is
(A) 356 (B) 348

om
(D) 6
. co
331 S(x).c=*-6ar+5x
L,2] fR8IG m ft Lagrange'sMean Value Theorem-4xbsfr se m
fG A qRseX=7/4 ys y= fix) nfeft x=1, x=2 GaibE (ordinates) gRgla
gal a
a
(A) 36 (B) 348
(C) h6 D) 6

12. f fx) =|cosx-sinx|, then f'(%) =
m
(A) -1)
m .co
s e
) l a
ag
(B)

(C) -M5+1)

(D) a-1)
m
2I f(x) =| cos x- sin x| , SA fY) =
m
c. o(A) m.co
m s e
s e g la
la (B) a
(C)

(D)
JM--Series P 7 [P.T.0.
m
.co s e
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 7 of 16

13. Area of the region bounded between y=2-|2-x| and y=xi is
|x|
4+3 In 3 4-3 In3
(A) 2 (B) 2

3
(C) +In3 (D) ;+n3
2

3

4+3 In3 4-3 In3
(A) 2 (B) 2

3
(C)+n3 (D) +In3
2
2

2x- 2y = 3
14. The point on the curve s =xlog x at which the normal is parallel to the line
is

(A) (0, 0) (B) (e, e)

(C) (e, 2e') (D) (e,2e)

(A) (0, 0) (B) (e, e)

(C) (e,2e) (D) (e,2e)

15. If three positive real numbers a, b, c are in Arithmetic Progression and abc = 4. then
the minimum possible value of b is
(A) 23/2 (B) 22/3

(C) 2'/3 (D) 25/2

(A) 23/2 (B) 22/3

(C) 2/3 (D) 25/2

JM-Series P 8

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 16

.
.co s e m

em l a
ag
16. Solution of the differential equation 1-**)-
dx
xy=* is
(A) y1--x1-x =cosx+c

(B) i-x +x1-=c
(C 2yvi-+i- = sin x+c
m . co
c. o
(D) None of the above
s e m
s em g l a
g la a
a dx

(A) y1--x1-x= cosx+e

(B w1-+x1-=c
(C 2y1-t+x1- =sin'x+c
m
m .co
s e
l a
ag less than or equal to x, then {x-2|+[x} dx =
3

17. If[] denotes the greatestinteger function 1

(A) 7

(B) 5

(C) 4

m
.co
(D) 3
m
m .co s e m
s e g la
gla (A) 7
a
(B) 5

(C) 4

(D) 3
JM-Series P (P.T.O.
m
m .co s e m
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 9 of 16

18.

(B dog xf dog x' -1-log (log x + logx-1+
(C)

(D) None of the above

(B)

(C)

y--3
19. If the angle between the line 1 2 and the plane x+2y +3z = 4 is

cosN4). then the value of is
(A) 26 (B) %
(D) %
Xy-l_ 2-3
HAA0 QTR x+ 2y+3z= 4 AOAK AK Acos%A

(A) % (B) 3%
(D) %
JM-Series P 10

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 16

.
m .co s e m

g l a
a
20. The image of the point (4,-2,3) in the plane 2x-3y+z=7 is

(A)

(B)

m . c
.co s e m
s em l a
g la ag
(D)
a
Qol (4,-2,3) fa 2x-3y +z=7 9A afoa 2

(A)

(8 16 11)
B) 777 m
m .co
8 16 11
s e
l a
ag

21. Let, a. b. be three unit vectors such that dx(Bxe)=2 and B, are non-parallel
vectors. Then the angles which á makes with b and c are respectively
m
m(A) ½%
c. o () %%
(B ½%
m.co
m (D) %.% s e
s e g la
la 2
a

(A) 2s (B) %%

(C) %s (D) %%
JM-Series P 11 [P.T.O.
m
.co s e
s em
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl a
Page 11 of 16

22. lf a *B, but o? =5a-3 and B² = 5B-3,then the equation having a/B and B/a as its
roots is

(A) 3x +19x+3=0
(B) 3x-19x-3 =0

(C) 3x-19x +3 =0

(D) x-5x+3 =0

(A) 3x +19x+3 = 0

(B) 3x2-19x-3 = 0

(C) 3*-19x+3 =0
(D) -5x +3 =0

1 -1 1 |4 2 21
23. Let, 1 -3| and 10B =-5 If B is inverse of matrix A, then x is
|1 1 1 12 3
(A) -2

(B) 1

(C) 5

(D) 2

1 -1 1] 4 2 21
1 -3 R 1OB =-5
1 1 1 1 -2 3|
(A) -2

(B) 1

(C) 5

(D) 2
JM-Series P 12

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 16

.
m .co s e m

l a
ag
a a? 1+a
24. |b b 1+b|=0 and vectors (L, a, a), 1. b, b), (1,c,c) are non-coplanar,then the

value of abc is

(A) 0
co
(B) 2

om .
(C) -1
. c
(D) 1
e m
e m l as
as a a1+a
ag
Q81 41 |b gbl 1+b =0 g (1, a, a), (1, b, b), (1, c, c) qA
a g at 3, UR

abc-4

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

m
co isin9ho)x(cos t%o+ isin ho)
25. (cosHo+ isin %o)x(cos 2%0 +isin2%o)x (cos ho+
.
m
e 0
(A) 1
l as (B).

(C) -1
ag (D) 2
2e1 (cos o+isin o)x(cos2o+isin2%o) x(cos %0 +isin o)x(cos A%0+isin4%0) -
(A) 1 (B) 0

(C) -1 (D) 2

26. The equation cos x(sin x- cos x)= has real solutions, when A is a real number. Then
m
m
c. o(A) 0SAs(V2+1)/2 .co
m
(B) 0s.s2-V3
s em
s e g la
la (C (42-1)/2sAs(/2+1)/2 a
D) -(/2+1)/2shs(/2-1)/2
Q9 -4R I cOs x(sin x- cos x) = ATa

(4) 0sAsV2+1)/2 (B) 0ss2-V3

) (2-1)/2sAs(u2+i)/2 D) -(/2+1)/2sAs(/2-1)/2
om
JM-Series P 13 [P.T.O.

. c s e
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 13 of 16

27. ln a triangle ABC, ZC= 900 r and R are the in-radius and circum-radius of the
triangle ABC respectively, then 2(r+ R) is equal to
(A) b+a

(B) a+c

(C) c+b
(D) a+b+c

91 ABC tag zc=90°, r qEII0IÉ 4 R RUÉ 2(r + R) =
(A) b+a

(B) a+c

(C) c+b
(D) a+b+c

1 1 1
28. Ifa straight line +-1 moves in such a way that where cis a constant,
a b a -+
then the locus of the foot of the perpendicularfrom the origin to the given line is

(A) x²+y =c?

(B) ²+2y =c?

(C) x+2xy:y= c?

(D) -y =

(A) +y? =c?

(B) *+2y² =c?

(C) x+23xy =c?

(D) -y² =c?
JM-Series P 14

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 16

.
.co s e m

em l a
ag
29. The dstance of the point (1, 2) from the straightline with slope 5and passing through
the point of intersectionof the lines x+ 2s=5 and
x-3y =7 1S
(A) 15 units

units

om . co
units
. c e m
em l as
(D) l50asunits ag
ag
2l x+2y =5 4R x-3s =7 AAA0AGIA QrfTanAi gR 5 841O1 RM ASIOA (1, 2) fi

(A) 15 q*

m
m .co
s e
l a
ag

30. If for all pe(-1,1),the line 2px +yi-p =1 touches a fixed elipse, then eccentricity
of the ellipse is
m
.co
(B) 2/3/7
m (A) V3/2
c. o (C) 1//2 s em
em (D) V3/5
la
s g
gla 19o| -1,1) fRatA p-4% AA AIAT 2px +y1-p =1
a
Afo qft fA togss sf

(A) V3/2 (B) 2/3/7

(C) //2 (D) 3/5
15 |P.T.0.
om
JM-Series P

. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 15 of 16

SPACE FOR ROUGH WORK

AL

JM-Series P 16 FF22900x3

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 16