TBJEE 2024 Question Paper - Mathematics

FOR TBJEE EXAM PREPARATION

TBJEE 2024
Question Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

TBJEE 2024 Question Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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DO NOT OPEN THE SEAL UNTIL YOU

2024
Question Paper Serles
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Time : 45 Minutes Maximum Marks : 120

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Total Marks : 120- (4 x 30)

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· , Answer all questions
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This Que·stion Paper consists ofag 16l pages. Each Multiple Choice Question (MCQ)
is provided with four options · (A), (B), (C) and (D). ~dentify the correct option and
darken/ fill the corresponding circle (A)/(B) / (C) / (D) with Blue /Black Ballpoint Pen
on the OMR Answer Sheet.

For each questi<;m, 4 marks will be awarded for correct answer and for each
wrong answer 1 markwill be deducted. ·

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(A)/(B)/(C)/(D) ~<fl~ Ballpoint Pen~~~ I ,

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Page 1 of 12

1. Let, q,i(x) = esinx, q,2 (x) = ecl>i(xl, ...... , <l>n+i(x)= ecl>n(xl, rtn 1. Then for any ·fixed
d
n, dx {<l>n (x)} is

(A) <I>~ (x) · <l>n-l(x)
(B) <l>n (x) · <l>n-dx)...... · <!>i(x)cosx
(C) <l>n(x) · <l>n-1(x)....... · <1>1(x)sinx
(D) <l>n(X) · <Pn-dx)...... · <!>i(x)esinx

)I cR, n~l-~~ q,i(x)=esinx,q, 2 (x)=ecl>1(xl,...... ,<l>n+l(x)=ecl>n(x),
. d.
n-~~ dx {<l>n(x)}

(A) <l>n(X)· <l>n-dx)
(B) <l>n (x) · <l>n-dx)...... · q,1(x) cos x
(C) <l>n(x) · <l>n-dx)...... · q,1(x)sinx
(D) <l>n(x). <l>n·-1(x).·..... · <l>1(x)esinx
2. The value(s) of c e (1,2), where the conclusion of the Lagrange's M.V.T. is
satisfied for the function f (x) = x 2 + 3x + 2 in [ 1,2], is/ are
3 1
(A) - 2' 2
1 3
(~) 2' 2
1
(C) -~
2
3
(D) -
2

~I (1,2) c-~~ ~/~~far:r f(x)=x 2 +3~+2 -~ [1,2]
Lagrange's M.V.T.-~~ ~~lijC<fi ~, ~/~~'M
.3 1
(A) - 2' 2
1 3
(B) 2' 2
1
(C) """-
2
3
(D) -
2
11-JM- Series P · 2

24
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3. Let a
a.
. 7t
(1+ I sin XI )lsinxl --<x<O
' 6

f(x) = b , X= 0

(tan2x) m
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1t
e tan3x O<x<-
m
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6
e m
em of a and b are las
s
Then the values
l2a b· = -2 ag
g
a 3 3
(A) a=--,

. 2 l
(B) a = , b = e 3
3

m
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2 _i
(D) a = , b = e 3

em
3
"I~~ .
la s
(1+ 1
_
g
·sinx I)lsinxla ' :_ < x < 0
. _a_ .
1t
6

x=O

(tan2x)
e tan3x

m
m
c. o a b-~~ ~-8far m.co
m (A) a =- 2 , b = 2 s e
s e g l a
g l a 3 3 a
a 2 l
. (B) a=-,b=e 3
3
l 2
(C) a =e 3 , b = -
3
2 . _l
(D) a = - , b = e 3
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3
e m
s
P [P.T.O. ·
em
11-JM-Series 3

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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 12

4. If

f 3ex +se-x dx = Ax+Bln I 4e 2x -51 + C
4ex -se-x .
then
7
(A) A = -1, B = - , C = constant of integration
8 . .
7
(B) A = 1,. B = 8 , C = constant of integration
.

(C) A = -1~ B = ; , C = constant of integration
7 · 3 .· . · .
· (D) A=-, B = -, C = constant of integration
8 . 8
· s1

f3ex +Se=x d.x=A.x+Blnl4e2x -Sl+C
. 4ex -Sex ·.
.

7
(A) A = -1, B = - , C = >i~l<Piif
8
7 .
(B) A = 1, B = , C = >i~l<Piif
8
7 . . .
(C) A= -1, B = · , C = ""'">i~-1<1S=iif
8
7 3 ......,...,r= .
(D) A= B, B = B , C = >i~l<Piif

2
s. f I x 2 +x-2 ldx =?
0

11 11
(A) 3. (B) .. 3 .
1 1•
(C) -
3 (D) -- ....
3
2
a: 1 JI x 2 + x - 2 Idx =?
0

11 11
(A) 3 (B)
3
1 1
(C) - . (D) -~
. 3 3
·11-JM-Series P 4

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se 6. The differential equation of all circles of r_adius aagisla
d )3 (d2 )
(A) ( 1+ ix = a2 dx¾
2
(B) (1~(:rr=a2(~tr
(C) (1-:r (~tr =a
2
(D) (1+(:rr=a2(~tJ
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~, a <1Jl1tl~Ri
. c omi5l<i<156! 11~<15-i:!'f e m .
e 2 m l as
(A)
a (1+:r (~J
g as
l =a ag

dy 3 . 2(2]2
d y
(C) 1- dx =a dx2
( )

7
· 7. The r~ge of the function f(x) = -xpx_3 is
(A) {l, 2, 3, 4, 5, 6} ·
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(B) {1, 2, 3, 4}
(C) {1,2}
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(D) {1,2, 3}

~l-i:!lu as
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(\I . f(x) = 7- xpx - 3.
g l
(A) {1, 2, 3, 4, 5, 6} a (B) {l, 2, 3, 4}
(C) {1,2} (D) {1,2,3}

8. If f (x) and g(x) are two functions of x su_ch that f(x) + g(x) = e·x and
f(x)-g(x)= e-x,- then
(A) f (x) is ~dd function, g(x) is odd function
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(B) f(x) is even function, g(x) is even function
c. ·o(C) f (x) is even function, g(x) is odd function m .co
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s em (D) f(x) is odd function, g(x) is even function g l a
g la ae .x ~<l~ f(x)- g(x) =e-x
a 171 f(x) ~<l~ g(x), x-~~ f$ 151C'1'Jti<15 f(x) +·g(x) =
~,~ .
(A) f (x) 151C11-q~, g(x) '51C11-q<15
.(B) f (x) '51C11-q<15, g(x) 151C11'q<15

(C) f (x) '51C11-q<l5, g(x) 151C11-q<15

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(D) f (x) ~, g(x) '51C11-q<15.
11-JM-Series P
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9. The mapping f : R R such that f (x) = I x - 11 , x e R is
(A) one-one, onto · (B) many-one, onto .
(C) one-one, into (D) neither one-one nor onto
I f f6Jrcfiu f4:tffiC"'i' "I'~ :

f : R R ; f (x) = I x - 11, x e R
~Jf6Jr'®~
(A) ~<IS-1.fl'<IS,~~Gt (B) ~~'f . .

.
(C) ~<IS-~<IS, ~@:IIBJM . (D) ~~'f ~l_ 11:~ c.<t>l.:if&\;rn .
10. The area bounded by the curves y =loge x and y = (loge 2 .
x) 1s
(A) (3- e) sq. units (B) (e- 3) sq. units
(C) -~ (3- e) sq. units (D) (e - 3) sq. units
oI y = loge x y =(loge x) 2
-~ ~~l<liiji c.~Ji~a,i
(A) (3- e) ~,n (B) (e- 3) ~,n
1 1
(C) -(3-e) ~,n (D)' -(e-3) ~"11
,t .
2 . 2
11. For what value of n the curve (
X y . .
:J (tr= + 2 touches the s.tra(ght line
a+,;= 2 at the point (a, b)?
(A) n = 3 (B) Any value of n
(C) n = 2 (D) n ;= 4

))I n-,m'! ,nt,rn 1SfoU (: r (tr =
+ 2 : + t= 2 (a, b) [4")_Clb"'I"( 'l/131
.

(A) n = 3 (B) n-~~ c.~C<t>lc.~I ·
(C) n == 2 (D) n = 4
12. The function . f (x) = x 3 - 3x is
(A) increasing in (-oo,-l)u(l,oo) and decreasing in (-1,1)
(B) decreasing in (-oo,-1) u (1, 00 ) and increasing in (-1, 1)
(C) increasing in (O,oo) and decreasing in (-oo,O)
(D) decreasing in (O,oo) and increasing in (-oo,O)
.f(x)=x 3 -3x
(A) (-~,-l)u(l,oo) (-1,1) Jii~gl>i~l.:i
(B) (-oo,-l)u (l,oo) Jii~gj>i~l-i (-1,1)
(C) (O,oo) (-oo,O) Jii~gj>i~l-i
{D) (O,oo) -~ Jii~gl>i~l.:j (_:_oo,O)
11-JM-Series P 6

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13.
2
If A is the A.M: ofthe roots of the equation x -:- a + b = 0 and G is the G.M.
2ax
2
of the roots of the equation x 2 - 2bx + a = 0, (a > 0), then ·
(A) A> G (B) A= G
{C) A< G (D) None of these
1.£1~~ x ...., 2bx + a =0
2 2
)'01 x 2 - 2ax + b =0 >l~<l>~C'M ~tst~cJI~ ,:i~l'ilffi~ll~ A
m
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>i~<l>~C'm ~\sr~C~~ ~t'11<::Sffi~ G ~,
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{A) A> G . (B) A= G

s e
{C) A< G
s em .
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{D) C<l>l~it~ ;rn

l a and . 4 girls, a committee of 5 members is to be formed. In ahow
ag can this be done, if at least 2 girls are included?
14. Out of 6 boys
many ways
{A) 126 {B) 186
{C) 140 ~ri-2" {D) 156
)81 6 1.£1~~ 4 <1lfal<1>1~ 5 >l'f>i]M~ ~"<l>fu~ I ~<fill'~
2 ffl<fS1 <1>filfGCG 1.£1~ <tSfilfG~ "f~~ ~~far-~? ..
(A) 126 . {B) 186
. (C) ·140
o m {D) 156
. c
2
e
15. (666 ...... up to n digits) + (888 ...... upmto n digits) = ?
s
la {B) · 9 (10n - 1)2
{A)
9
4
(10n .~ 1)
ag 4

4 4
2
(C) -(10 n+l) (D) -(10 2 n -1)
. 9 9
)Q:I (666 ..·.... n "f~~ ~)2_ (888 ...... n "f~~ ~) =?
9 9
(A) (10n-1) (B) (10n_-1)2
m
4 4

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g la 16. Sum of the last 40 coefficients in the expansion of (1 +a x)7 , when expanded
a in ascending power of x is
(A) 279 . (B) 240
(C) 239 (D) 278
9 ·
)~I (1 + x)7 C<I> x-1.£1~ ~C>IC<l 401'6 >l~C'mf
(A) 2 79 (B) 240
(D) 2 78
m .
(C) 239

11-JM-Series P .co 7 [P.T.O.
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17. If~ m, n are the pth, qth and rth terms of a G .P. respectively and m, n > O, then
logl p l
logm q 1 =?
logn r 1
(A) -1 (B) 2
(C) 1 (D) 0
)~I l, m, n !f•>tft~Pt~ p-~, q -~ r-~ 'Pflf Z, m, n > 0~,
logl p l
logm q 1 =?
logn r 1
(A) -1 (B) 2
(C) 1 (D) 0
18. For what values of Aandµ, the following system of equations has ~que solution?
2x+3y+Sz = 9
7x+3y-2z = 8
2x+3y+Az=µ
(A) A :t= 5 , any value ofµ (B) A = 5, µ = 9
(C) A :;c 5, µ = 9 (D) A= 5, any value ofµ
)b'I ~'t P!Cl'GC~-iq ~?
2x + 3y + Sz = 9 -·
7x+3y-2z= 8
2x + 3y + AZ = µ
(A) A :t= 5 , µ-~~ <AC~IC--11 (B) A= 5, µ = 9
(C) ).. :;c 5, µ = 9
. . 1 . . . .
19. If O < e < 1t and cose +sine = - , then the value of tane is
. 2

'. .·.
(A)
4 · 3
(4+ (D) (1 +
. (C)
3 4

<TN O < e < 1t cose +sine = _!:_~,~ tane-~~
. 2 .
(A) (B)
4 3
(4 + (1
(C) - 3 (D) 4
· 1 1-JM...:._Series P 8

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20. In a triangle ABC, if angles A, Band Care in A.P., then a; c is equal to

A-C
(A) 2sin A-C · (B) 2cos ·
2 2
. A-C . A-C
(C) cos (D) sm
m
.co
2 2
m
o I ABC fJl~C<at'R A, B c. ·oC ·~ct~fir ·
tr~
a+c
s e m
m
-b- =?

as e g la
l A-C a
ag 2
. (A) 2sin A_;C
(B) 2cos _... .
2
A-C . A-C
(C) cos · . (D) sm
2 2

21 • Th eval ueo f tan -1 (sin2
--- .-1) 1s
.·
· cos2

m
7t 1t

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(A) 1-- · (B) 2 - .~
4

(C) 2--
7t
s em 1t

la
(D) --1
2 ' 4

.~:>I .t~ - 1(sincos2
.2 _..: 1)-~~ ag
. .
7t ' .7t
(A) 1-- · (B) --1
4 ' 2 ·.

7t 1t '
(C) 2-- (D) - .1 .
2 4
m
22.
m
The equation of the image of the line 2y - x = 1 obtained by the reflection on
.co
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. the line 4y 2x = 5 is
s e m
s em(A) 2y-x = 4 g l a
la (C) 2y + x = 4
(B) 2x-y = 4
g a
a (D) 2x + y = 4
2!)- x = .1 >Bl61C-R~lfO'R 4y- 2x = 5 '1M1Ci:I~ ~'PM tf~qa,jC-i'R ~ -tl~~C"-i:I >i~~-i:1"'1

(A) 2y-x = 4 (B) 2x-y = 4

(C) 2y+x = 4 (D) 2x+ y = 4

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11-JM-Series P 9 [P.T.O.

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For more Question Papers, Sample Papers, Notes & Syllabus visit
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Page 9 of 12

- TBJEE 2024 Question Paper Mathematics

23. The equation of the circle of radius 3 unit which touches the circles
x 2 + y 2 - 6 I x I = 0 is
2 2
(A) x + y = 0 or x 2 + y 2 =0

(B) x2 + y2 =0 or x 2 + y 2 =0
2 2 r;:; .
(C) x + y + 6v3y + 18 = 0 or x 2 + y 2 - + 18 = 0

(D) or
31.£1~-uP'it~P't'i -(A~ x 2 +y 2 -6lxl=0 )1~<15:i:Mm~ .

(A) x +y
2 2 =0 x 2 +y 2 =0
2
(B) x +y
2 =0 x.2 +y 2 =0

(C) x2 + y2 =O x2 + y2 =0

(D) x 2 + =O x2 + y2 =0

24. The angle between the lines joining the foci of an ellipse to one particular
extremity of the minor axis is 90°. The eccentricity of the ellip&e is
1 1
(A) (B)
8

(C) f __.Q...- (D) 1 ll5Uif ~~9tff >l:i:l61C:i:i-:ctl'liC~:i:l
~81 1!1"<15iu~"'11_C<e:i:l iil~..:iC~BI 1.£1~'tlll:!f<I":(OO">t
Q.1it't 90° _ 'ts"'11_<e~~~C~'!t\!>I . .
1 1
(A) · (B)
8

.1
0

(C) (D)

25. The direction ratios · of the normal to the plane passing through the points
. . . x-2 y+l z
(1, 2, -3), (-1, -2, 1) and parallel to the hne - 2 - -= .- 3 - is
4
(A) (-2, 0, -3) (B) (14, -8, -1)
(C) (2, 3, 4) (D) (1, -2, -3)
x-2 y+l z . ..,,-..=rn,r •
>l~\!>Cdl:i:l~~iii~
>l:i:ld\C:i:l~)f~l~ldl 1.£1<1', (1, 2, -3), (-1, -2, 1)
O

~(11 -. - - = - - =
2 3 4

(A) (-2, 0, -3) (B) (14, -8, -1) -
(C) (2, 3, 4) (D) (1,-2,-3)
10 .
11-JM-Series P
I ' ,

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26. The area of a parallelogram whose diagonals are a
given by ti +.V .and v+ w,
1\1\ 1\1\
where u = 2 i - 3 j + k , v = - i + k , w = 2 j - k is
(A) ./14 sq. unit (B) ffi. sq. unit
(C) !..fii sq. unit (D) !.. Jl4. sq. unit
2 . . 2 . ,'
m
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. I\ I\ I\ I\ I\ I\ I\
.>tl~~C<M'¥'"1'41~ u + V ~cf~ V + w,
s
u = 2 i...,. 3 j + k' V = -i + k, w = 2j -k
e m l a
l as
Ot J1 l~l!!l~C<l>'!il C'JtiJl~a!· .
ag
· (A) ·
a g
cf'>t (B) cf'>t ~<fS<fS

(C) !.. cf'>t (D) !.. J14. cf'>t
2 2
. .. x y-1 · z=+-l
27. The shortest distance between the hnes - = -- = -- and
3 2 -1
x+l y-3 z .-1 .
--=--=--is
1 -1 -1 ·
m
3
(B)m
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(A) unit
s e unit

g la 1
(C)
3
unit a (D) unit
· x · ;y :_ 1 . z +1 . x+'i . y - '3 · z - 1 . , ..
<\I =- - = - - = = >i'!ilii1C<J:1"4llf~~~ (shortest distance) .. I
3 2 1

3 3

m
(A).Ju,~~ - (B)

m .co
.co m
3 1

m
. (C).· F3· ~~ .· ... , . ,
s e . (P) .
2·ss.e If the probability for A.to fail in an examination is 0·2 and
g l a
la t~n the probability eit~er of A or B fails, is a that for Bis 0·3,
ag
(A) =:;; 0·4 (B) =:;; 0·25
· (C) =:;; 0·5 (D) =:;; 0·7 .·
~b'I '5l<f"<l>l4~'8~ >i&l,q--ll A-~~ 0·2 ~cf~ B-~~ 0·3 ~, ~, A '151'~ B-~~
151~14 ~-s~ >i&l,q--ll
(A) =:;; 0·4 (B) =:;; 0·25

m
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(C) =:;; 0·5 (D) =:;; 0·7
e m
11-JM-Series P
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---- ---~ - - ----.aH;al&....-s rmn:rcr :r aau:c &~ a ~-• -- -
TBJEE 2024 Question Paper Mathematics -
29. If the probability density function of a random variable is given by

~- {i 2x (1-
2
_ x) , for 0 :5 x :5 1
f( . .
0 , elsewhere

then mean and variance are respectively
. (A) 0·6, 0·4 (B) 0·4, 0·6
(C) 0·2, 0·6 (D) 0·6, 0·2

I 156\C-:P?l (random variable) >it!l<IJGI '51C1111i<l5

2
f(x) ={12x (1- x) , ~ - 0 :5 x :51
0 . '~

'5C<f_ 156\C<IS?l ~ean ~<f~. vari~ce
. (A) 0·6, 0·4 (B) 0·4, 0·6

(C) 0·2, 0·6 . (D) 0·6, 0·2

. 30. Let, the two variables x and y satisfy the following conditions :

x+ y :5 50
x+2y :5 80
2x+y 20
x,y 0

Then maximum value of Z = 4x + 3y is
(A) 120 (B) 170 .
. (C) 200 (D) 210

x+ y :5 50
x+2y $ 80
2x+ y 20
x , y .~ 0

Z= 4x+
(A) 120 (B) 170
(C) 200 (D) 210
11-JM-Series P 12

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