TBJEE 2023 Question Paper - Mathematics

FOR TBJEE EXAM PREPARATION

TBJEE 2023
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

TBJEE 2023 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

om
FrtSffl7?PlllM

. c
. c e mTBJEE 2023 Question Paper Mathematics

m las
se ag
DO NOT OPEN THE SEAL UNTIL YOU ARE ASKED TO DO SO ·

2023
Question Paper Series
m
om
p
. co
. c e m
em l as
l as MATHEMATICS. JM
ag
ag
' Time : 45 Minutes · Maximum Marks : 120

Total Marks : 120 (4 x 30)
m
Answer all questions
m .co
e
s Each Multiple Choice Question (MCQ)
l a
This· Q.uestion Paper consists of 16 pages.
g (C) and (D). Identify the correct option and
is provided with four options (A), a
(B),
dm-ken/fill the corresponding circle (A)/(B)/(C)/(D) with Blue/Black Ballpoint Pen
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~~~"1Jilut'!>l6fG~~~I MCQ-1.€1~ ~.~~(A),a (B), (C) 1.€1-l:~ (D)
l
g la Of\Sm 1
agf.f~ ~'itm
1.€1-l:~ OMR Answer Sheet-I.€!~
a (A)/(B)/(C)/(D) <l:t Ballpoint Pen~~~ I

1.€1-l:~~Waf~~l~~~I

m .
.co s e m
s em l a

la
For more Question Papers, Sample Papers, Notes & Syllabus visit
ag
Page 1 of 15

1. Let, T be the set of all triangles in a plane. Then the relation
R = {(T1, T2 ): T1, T2 e T and T is congruent to T2 } on Tis
1

(A) reflexive and symmetric but not transitive

(B) reflexive and transitive but not symmetric

(C) symmetric and transitive but not reflexive

(D) equivalence

I <R', R = {(T1, T2 ): 1i, T2 e T ~<1~ 7i, T2 ~} T~ dl<Jtb ~,
T ~<fiffl >l~\!>Cdl~ fJl~C<sf~ I R

(A) ffitR~'6 ~<1~ Dl\'.G<.15 ffl ~l~f6'6 effl

(8) fflcJ15~'6 ~<l~ ~l~f6'6 m ~Cil\'.G<.15 effl
(C) ~Cil\'.G<.15 ~<l~ ~l~f6'6 fflcJl5~'6 effl

(D) ~1~C'6Cdl&I

2. The number of binruy operations on the set A= {l, 2, 3, 4} is

(A) 2 4

(B) 216

(C) 4 2

(D) 416

(A) 2 4

(B) 216

(C) 4 2

. (D) 416

8-JM-Series P 2

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 15

m . c
c. o s e mTBJEE 2023 Question Paper Mathematics

s em g l a
a
3. Let, f be any function defined on R such that lf(a)- f(b) l~l(a - bf I,
Va, b e R . If JlO) = 1, then

(A) f (x) > 0, 'v x e R

(B) f (x) can take any value in R

(C) f (x) = 0, 'v x e R
m
m .co
(D) f(x)<O, \JxeR
m .co s e m
s e ~~ii'6IC~ ~~Sit;§~ lf(a)- f(b) l~l(a-b) I, Va, be Rg l a
a a
2
"'
I llNa
l
fl~ f IOIC"liJMilt
g = 1 ~,
.flO)
R

(A) f (x) > 0, V x E R

(B). f (x)-~~ 1l'f.f c.qC41Ciil

(C) f (x) = 0, V x e R

m
(0) f (x) < 0, Vx E R

m .co
4. Let, a,
s e
be the roots of the equation x 2 + x + 1 = 0 . The equation whose roots
are a19, 137 i~
g la
a
(A) x2 + X + 1 = 0

(B) x 2 - x - 1 = 0
2 .
(C) x -x+l = 0

(D) x 2 +x-1 = 0 m
c o m m .co
. s e
em
2 . .

s
81 ~cR, a,~~ x +x+l=0 >1~4~Cernrfij~1 ~>lsft4~C'BI~
g l a a 19 '6131, Q'®~

la a
ag
2
(A) x + x + 1 0

(B) x 2 - x - 1 = O

(C) x2 - x +1 = 0
2
(0) x + x - 1 = 0
8-JM-Series P

om .
3 [ P.T.O.
.c e m
em l as

las
For more Question Papers, Sample Papers, Notes & Syllabus visit ag
Page 3 of 15

I

5. If z = x-iy and z 1l 3 =a+ib, then(:+ t);(a 2 2
+b ) is equal to

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

(A) 1 (B) -1
(C) 2 (D) ·-2

6. The sum of integers froi:n 1 to 100 that are divisible by 2 or 5 is
(A) 3050 (B) 2850
(C) 3600 (D) 3250

(A) 3050 (B) 2850
(C) 3600 (D) 3250

· 7. . The values of A for which the system of equations
(31. - 8)x + 3y + 3z - · 0
3x+ (31.-8)y +3z = 0
3x+ 3y + (31.-8)z = 0
has a non-trivial solutiot?,, are
(A) 2/3, 17 /3 (B) 2/3, 11/3
(C) 8/3, 2/3 (D) 8/3, 11/3

(31.-8)x+ 3y + 3z = 0
3x + (3).. - 8)y + 3z = 0
3x+ 3y + (3A-8)z = 0
(A) 2/3, 17 /3 (B) 2/3, 11 /3
(C) 8/3, 2/3 . (D) 8/3, 11/3

8-JM-Series P 4

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 15

om . co
c m

m . s e
s e g l a
p .b C
a
8. If a-:;: p, b -:t q, c -:tr and a q c = 0, then the value of--.L.+_q_+-'-is ·
p-a q-b r-:c
a b r
(A) 2 . (B) 4

(D) -5
m
.co
(C) -2
m
m .co . p b
s e m
la
C

s e
l:rl zjir a-:i:p, b-:tq, c:t.r 1.£1<:T~ a q
p q r
C =0~, ~--+--+---1.£1~~~
g
l a · p-a q-b r-c
a
ag
a b r

(A) 2 (B) 4

(C) -2 (D) -5

m
m .co
s e
g la
. (A) 3n_ 1/2
a
(B) 3n + 1/2

(C) (3n + 1)/2

(D) (1 - 3n)/2

m
m .co
m .co s e m
s e g l a
g l a a
a (A) 3n_ 1/2

(B) 3n + 1/2

(C) (3n + 1)/2

(D) (1 - 3n)/2

· [P.T.O.
m
8-JM- Series P
.
5

.co s e m
s em l a

glaFor more Question Papers, Sample Papers, Notes & Syllabus visit ag
Page 5 of 15

...... . nffls ?:I
~SZ-:XTs5i AT

10. x 2 + y 2 + 2(2k + 3)x- 2ky +.(2k + 3)2 + k 2 - r 2 = 0 represents the family of
circles with centres on the line
(A) X - 2y - 3 = 0

(B) X + 2y - 3 = 0

(C) x + 2y + 3 = 0 ·

(D) x-2y + 3 = 0

:> o I x 2 + y 2 + 2(2k + 3)x - 2ky + (2k + 3)2 + k 2 - r 2 = 0
QT >t~<i!C~~ ts~ '¢14~,
(A) x - 2y - 3 = 0

(B) x + 2y - 3 = 0

(C) x+2y+3=0

(D) x-2y + 3 = 0

x2 y2 · 2
11. If the curves - +- = 1 and + lL = l intersect each other at right angle,
P q a b
then
(A) a+b=p+q

(B) a-b = p-q
r (C) ap = bq
(D) p +a=q+b

x2 y2 x2 2
:> :> 1 zjit - + -q =1 ~'4'~ - + JL =l 41ii>C~"'ftfit >t~C<ISIC'i
p a b ·,

(A) a +b = p+q

(B) a .:... b = p - q

(C) ap = bq

(D) p +a = q+b

8-JM- Series P 6

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 15

om . co

. c e m
m a s
se 12. The equation of the . ellipse whose focii (±5, 0) and
ag lone of its directrix is
Sx = 36, is
x2 y2
(A) -+-=1
6 11
x2 Y2
(C) -+-=1 (D) None of these
36 11

m
om . co
. c e m
e m l as
as
x2 y2
l ag
36 g
(C) -+-=1
a 11

13. The general solution of the equation 4 sin 4 x + cos 4 x = 1 is

(A) mt or mt± ½, a. = cos- (
1
!)
m
(B) n½ or mt±a., a.=cos-' 1 (~)
m .co
s e
1 l
a
(C) (2n + 1)% or mt± a., a.= cos- g(~)
a
(D) None of the above
[n e N]

)~I 4sin 4 x+cos 4 x = 1 >,~c:p-AC'R:I ~~'f

m
.co
1
m
(A) mt or mt±½, a.=cos- (~)

.co
m (B) n ½ or n1t ± a., a.= cos- 1 ( ~) s e m
s e g la
g la a
a
(C) (2n + 1)% or n1t ± a., a.= cos- 1 (~)

(D) ~9fm . C41~1t\ ;rn

[n EN]

8-JM-Series P [P.T.O.
om .
7

.c e m
em l as
s ag

glaFor more Question Papers, Sample Papers, Notes & Syllabus
J' visit Page 7 of 15

21 · 27 . cos(cx.- J3) is
14. If sin a+ sinJ3 = -- and cos a+ cosJ3 = -- then the value of 2
65 65'
(A) -3 / ./130

(B) 3/./130

(C) 6/65
(D) -6/65

[where 7t < a - J3 < 31t)

27 cos(cx.- J3)
,
., 81
•
<-11'T sma + smJ3
.
= - 21 cos a+ cosJ3 = - ~,
2
-·· '"'.,
65 65

(A) ~3 / ./130

(B) 3 / ./130

(C) 6/65

(D) -6/65

[~ 7t < a-J3 < 31t]

15. In a triangle ABC, if 2 cos A + cos B + 2 cos C = + ..!!_ , then the triangle is
· a b c bcca

(A) right-angled triangle
(B) equilateral triangle
(C) isosceles triangle
(D) None of the above

) <l I ABC Q)~Cl$i~ zjif 2 cos A + cos B + 2 cos C = + !!_ fJ!~tstf&
· a b c bcca'

(A) ~qt~

(B)~~

(C)

(D) C<tSl-ilu\-ffl .
8-JM-Series P 8

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 15

om . co
s e m .c
ag l as e
16. If the plane x-2y + 3z = 4 is rotated through a right angle ,about the line of
mTBJEE 2023 Question Paper Mathematics

l
. intersection of the plane 2x + 3y-4z = 5, then the equation of the plane in
its new position is

(A) x-22y-3z = 67

(B} 22x+Sy-4z = 67
m
m .co
.co m
(C} 22x-5y +4z = 67

s e
em
(D) None of the above
s g la
g la a
)~I a + 3z = 4 >t~l.!Siilft 2x + 3y ·- 4z = 5 >t~\!ScftBI
x-2y >t~ii'IC~~ >tlCPfC'Jli 90°
~, >t~\!Siiliw ~<l"'C--1~ ~'f

(A) x-22y-3z = 67

. (B) 22x + Sy - 4z =· 67

(C) 22x-5y + 4z = 67
m
.co
em
(D) {S~ C<l51--lf&~effl

la s
ag
17. The distance of the point .(4, -5, 3) from the straight line x- 5 = Y 2 + =z - 6
. 3 · -4 5
is

../157 (B) .J157 ..
(A) unit · unit
3 5
.J457 . .
m
.co
.J457
(C) unit
m
(D) . unit

.co
5 3
e m
e)C\Im (4, -5, 3) r·'i-:i_ l as
las x-5 y+2 z-6~-
- - = = >t<Jlii'IC~~
ag
ag 3

(A) 3 ·\!l<tS<I$ (B)
./157
5

C)
( 5 \!I~ (D) 3

8-JM-Series P 9 . (P.T.O.
m .
.co s e m
s em l a

la ..
f
For more Question Papers, Sample Papers, Notes & Syllabus visit ag
Page 9 of 15

. .·
. . .

ia. Let, d, p, y be three vectors such that ~+ 1+ y = 0 and I~ I= ; I f3 I= ,
7 4

. . .
Yl=5.Then cx•f3+f3•y+y•cx is
(A) 35 (B) 140
• I

(C) -45 (D) -140

. . .
CX• f3+ f3· y+ Y•.cx-1.Sl~ 1(j.f
I •

' (A) 35 (B) 140
'
(¢) -45 (D) -140 • • j t

-·
' .-
19. iri(9)=9 and /;(9)=4, then •-~ Jl[x)-
' Tx-3
3 -~
• ·

. (A) ~ . (B) 3
(C) O· (D) 4

3
)291 /~9) = 9 di~, /;(9) = 4. ~, fun ffixj-
./x-3
=
·
.
(A) 9 (B) 3

(C) 0 (D) 4

20. Which of
in R? the
. .
following functions has a finite
. .
number of points of discon
. ..
tinuity
·.·. .

(A) tanx c. · , , ! (B) x[x] . ji -~' ._, _);_~'. ,_\._

(C) Ix -I (D) sin(nx) ,- .. •.
X -· . t • ·- -

· {l.x) represents the greatest integer less than or equal to.x, {S x)} .. . : ·

~ol f.ttffif ~C91'1jkp~fimll'OO '51C911JMS!ml "l~~ '51>1~'-' R OfC6 ~?
, . I . I
.' f,
)
, ' . .

(A) ~x (B) x[x)

(C) @ .. (D) sin(nx)
X

{[x]. 1$J~ (.<fT<llt1r x-~~ ~ -~, (S x)} . , - - . ,,·. · 1
;

10
8-JM-Beries P

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 15

se
m . c
g l as e ~- 7

a
21. Which of the following functions satisfies the all three conditions of Rolle's
· theorem?
(A) /(x) = I x - 21, x e [O, 4]
. 1
(B) g(x) = 2 ,x e [-1,1]
X

m
m .co
(C) h(x) = cos x, x E [0, 21t].

.co
. '

e m
(D) k(x) = I sinx I ,x E [O,21t]
em l as
las ag
ag
(A) f(x)=lx-21,xe[O,4]
1
(B) g(x) = 2 ,x E [-1,1]
X .

· (C) h(x) = cosx,x E [O,21t]

(D) k(x) = I sinx I ,x E [O,21t] .
m
m .co
22. f0 loge(!+ cos 0) d0 =?
1t

s e
g la
(A)
-7t
2 loge2 a
7t
· (B) · loge 2
2
(C) -1tloge 2

(D) 1tloge 2

m
m .co
1t

.co
J0 loge(l+cos0)
m
d0 =?

s e
s em (A) 2 loge2 -7t

g l a
g la a
a . (B)
2
loge 2
7t

(C) -1tloge 2

(D) 1tloge 2

8-JM-Series P 11 [P.T:o.
m .
.co e m
em
For more Question Papers, Sample Papers, Notes & Syllabus visit
las
Page 11 of 15

23. f e 2 x(2cos x-sinx) dx =? ·
(A) e 2 x sinx + c

(B) -e 2 x sinx+c
(C) -e 2 x cosx+c
(D) e 2 x cosx+c

f e 2 x(2cos _x-sinx) dx =? ' . (

(A) e 2 x sinx+c

(B) -e 2 x si~x+c
(C) -e 2 x cos :X + c

(D) e 2 x cosx+c -- • . I •r

,
1
24. Solution of the differential equation (1 + y 2 ) dx = (tan- y-x) dy js ,1
1 -1
(A) x=tan- y+l-ce-tan Y

1 . tan-1
(B) x=tan- y-l+ce- Y

1

(C) ·x = tan- y +l+cetan.:. Y
1

. . -1
1
(D) x=tan- y-l+cetan Y I

. . . -1
(A) x=tan- 1 y+l-ce-tan Y_

-1
. ·(B) x=tan- 1 y-l+ce-tan Y

tan-1
(C) x=tan- 1 y+l+ce Y

. -1
(D) x::,;tan- 1 y-l+cetan Y

12 .
8-JM-Series P

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 15
J L i,

om . co
.c e mTBJEE 2023 Question Paper Mathematics

e m l as
s g
a the maximum volume of
25. If slant height of a right circular cone is 3 cm, then
the cone is

(A) cm 3

(B} cm 3

m
3
m .co
.co
(C) (2 +-/3)1t cm
e m
e m las
l as
(D) (2--/3)1t cm3
ag
ag
(A) cm 3

(B) cm 3

m
(C) cm 3
m .co
s e
(D) cm 3
g la
a
26. The area bounded by the parabola y = x 2 -1, tangent to it at (2, 3) and y-axis ·
is

4
(A) sq. unit (B) sq. unit
3
m
m
c. o 3
8 . .
.co
em
(C) sq. unit (D) 1 sq. unit

e m s
lay-~
l as 2
y = x -1 '5!f~, (2, 3) '5!f~
ag ~~l<lF.ti
ag '51'~ C~J!~iil

2 .
4
(A) 3 ~'if~~ (B) 3 ~'if~~
8
(C) 3 ~'if~~ (D) 1 ~'if~~

· 8-JM-Series P 13 [P.T.O.
m .
.co s e m
s em l a

la For more Question Papers, Sample Papers, Notes & Syllabus visit ag
Page 13 of 15
j

es~:mc::r:mz

· . h •· t where the curve
27. The normal to the curve y(x - 2)(x - 3) = x + 6 at t e po1n , ·
intersects the y-axis, passes through the point

(A) (- ,- ~)

(B) (~,-~)

(C) (~' !)
(D) (~' ~)

~C\I y(x-2)(x-3) = x+6 y-~ <1JF!t~ '-!ll~at°'lt~

(A) (-! _!)
2' 2

(B) (! _!)
2' 3

(C) (~·~)
(D) (~·~)
28. The mean of five observations is 4 and their variance is 5·2. If three of these
observations are 1, 2 and 6, then other two are
(A) 2 and 9 (B) 3 and 8

(C) 4 and 7 (D) 5 and 6

~b'I "14C<l'JtiC'r:fmean ~'<I'~ variance~~~ 4 ~'<I'~ 5·2 I~ "14C<l'Jti'-l~~ 3~
~'t -1, 2 ~'<I'~- 6 ~,~~~fit ~'t

(A) 2 ~'<I'~ 9 (B) 3 ~'<I'~ 8

(C) 4 ~'<I'~ 7 (D) 5 ~'<I'~ 6

8-JM - Series P 14

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 15

-em.co las e mTBJEE 2023 Question Paper Mathematics

l
s ag
29. The statement ~ (p v q) v {~ p" q) is equivalent to
(A) ~q
(B) ~p

(C) (pvq)

m
(D) (p" q)
m . co
c. o of the statement x)
(here ~x means negation
s e m
s em g l a
g la a
(A) ~q a

(B) ~p

(C) (p V q)

(D) (p" q)

*l m
.co
(~~, ~x-~~ i5f~ x-~~ ~Gftfl

e m
30.
as
Let, the two variables x and y satisfy the following conditions :
l
x+3y 3,g
a
x+ y 2,
X 0, y~ 0
Then minimum value of Z = 3x + Sy is
(A) 5 (B) 7

(C) 10 (D) 11
m
m .co
.co
'Oo I ~, x ~<f~ y biiBllfirt1i_'fu ~~far
e m
e m x+3y 3,
las
las x+ y 2,
ag
ag X 0, y 0

(A) 5 (B) 7 ·

(C) 10 (D) 11

8-JM-Series P 15 ( P.T.O.

m .
.co e m

se
m
For more Question Papers, Sample Papers, Notes & Syllabus visit las
Page 15 of 15