AUAT 2024 Question Paper B.Tech and BCA

Entrance Exam
2024

QUESTION
PAPER

Question Booklet No. Question Booklet Series : A
AUAT — 2024
B. Tech./BCA (U21)
( TEST BASED ON MCQ )

Full Marks : 100 Duration : 2 Hours

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Date of Examination : _______________________________________

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AUAT-2024 /89- A

PART—I
SECTION—A
MATHEMATICS
4. Let
 0 2b c 
  1 + sin2 u cos2 u 4sin 2u 
1. If the matrix a b −c  is orthogonal,
 
a −b c  D (u ) =  sin2 u 1 + cos2 u 4sin 2u 
then the values of a, b, c are  
 sin2 u cos2 u 1 + 4sin 2u 
 0 2b c 
™[ƒ a b −c  "=¢ìKà>ຠ³¸à[i¡öG ÒÚ, t¡àÒìº  π
The value of u  0 ≤ u ≤  , for which
a −b c   2
a, b, c -&¹ ³à> Òì¤ D (u ) is maximum, is

1 1 1 ‹¹à ™àA¡
[A] a = ± ,b = ± ,c = ±
2 6 3
1 + sin2 u cos2 u 4sin 2u 
1 1 1  
[B] a = ± ,b = ± ,c = ±
2 6 3 D (u ) =  sin2 u 1 + cos2 u 4sin 2u 
 
[C] a=±
1
,b = ±
1
,c = ±
1  sin2 u cos2 u 1 + 4sin 2u 
3 7 5
1 1 1  π
[D] a=± ,b = ± ,c = ± D (u ) -&¹ Τ¢à[‹A¡ ³àì>¹ \>¸ u  0 ≤ u ≤ 
3 6 2 2
2. Let x + y + z = 1 , 2x + y + 4z = λ and -&¹ ³à> Òì¤
4x + y + 10z = λ 2
be a system of π
[A]
2
equations. The value of λ for which π
the system has a solution is [B]
6
x + y + z = 1, 2x + y + 4z = λ &¤} π
[C]
4x + y + 10z = λ 2 Òº [t¡>[i¡ γãA¡¹o¡ú λ -&¹ 3
π
ë™ ³àì>¹ \>¸ γãA¡¹oγèìÒ¹ &A¡[i¡ γà‹à> "àìá, [D]
4
ëÎ[i¡ Òº
[A] λ = 0 [B] λ = 1
[C] λ = −1 [D] λ = 3 5. Let A and B be two matrices such that
3. Let A and Ac be the coefficient and the product AB is compatible. If
augmented matrices of a system of n rank (5A) = 3 and rank (3B ) = 5, then
equations containing n variables. The the rank of AB is at most
system of equations AX = B has many ‹¹à ™àA¡ A &¤} B ƒå’[i¡ ³¸à[i¡öG &¤} AB-&¹ P¡o>
solutions, if
䱤¡ú ™[ƒ rank (5A) = 3 &¤}
‹¹à ™àA¡ A &¤} Ac Òº n W¡ºA¡ γ[Þt¡ n Î}J¸A¡
rank (3B) = 5, t¡àÒìº AB-&¹ Τ¢à[‹A¡ ³àyà
γãA¡¹ìo¹ ÎÒK &¤} ¤[‹¢t¡ ³¸à[i¡öG¡ú AX = B
(rank) Òìt¡ šàì¹
γãA¡¹ìo¹ "ì>A¡ γà‹à> =àA¡ì¤, ™[ƒ
[A] 1
[A] rank( A ) ≠ rank(Ac )
[B] 3
[B] rank( A ) = rank( Ac ) = n
[C] 5
[C] rank( A ) = rank( Ac ) < n
[D] 15
[D] rank(A ) = n

AUAT-2024 /89- A 2

π π 8. The maximum value of
6. If θi ∈  ,  , where i = 1, 2, 3, 4, 5
6 3  π
3 cos θ + 5 sin  θ −  for any real value
 6
and z 4 cos θ1 + z 3 cos θ2 + z 2 cos θ3 + of θ is
z cos θ 4 + cos θ5 = 2 3 , then θ -&¹ ë™ìA¡àì>à ¤àÑz¤ ³àì>¹ \>¸
 π
3 cos θ + 5 sin  θ −  -&¹ Î줢àZW¡ ³à> Òº
™[ƒ θi ∈  ,  , ë™Jàì> i = 1, 2, 3, 4, 5
π π  6
6 3 [A] 19
&¤} z 4 cos θ1 + z 3 cos θ2 + z 2 cos θ3 +
z cos θ 4 + cos θ5 = 2 3 , t¡àÒìº 79
[B]
2
1
[A] z <
4 [C] 31
3
[B] z > [D] 34
4
3
[C] z < 9. If tan4 θ + cot 4 φ + 2 cot2 θ tan2 φ =
4
4 sin2 (θ + φ ) , where θ, φ ∈  0,  , then
1 π
[D] z >  2
4
the value of θ + φ is
7. If pth, qth and rth terms of a G.P. are the ™[ƒ tan4 θ + cot 4 φ + 2 cot2 θ tan2 φ =
positive numbers a, b, c, then the
4 sin2 (θ + φ ) ÒÚ, ë™Jàì> θ, φ ∈  0,  , t¡àÒìº
angle between the vectors π
 2
→ → → θ + φ -&¹ ³à> ÒÚ
log a 2 i + log b2 j + log c 2 k and
[A] 0
→ → →
(q − r ) i + (r − p ) j + ( p − q ) k is [B] 1
[C] π
™[ƒ &A¡[i¡ G.P. &¹ p t¡³, q t¡³ &¤} r t¡³
π
šƒP¡[º a, b, c (‹>àuA¡ Î}J¸à) ÒÚ, t¡àÒìº [D]
2
→ → →
log a 2 i + log b2 j + log c 2 k &¤} 10. Let z be a complex number such that
→ → → the imaginary part of z is non-zero
(q − r ) i + (r − p ) j + ( p − q ) k 뮡C¡ì¹¹ ³ì‹¸ 2
and a = z + z + 1 is real. Then a
ëA¡ào Òì¤ cannot take the value
π z &A¡[i¡ \[i¡º Î}J¸à ™àìt¡ z-&¹ A¡à¿[>A¡ "}Å[i¡
[A]
3
"-Åè>¸ &¤} a = z 2 + z + 1 ¤àÑz¤¡ú t¡àÒìº a-&¹
π ³à> Òìt¡ šàì¹ >à
[B]
2
[A] –1
 1  1
[C] sin−1   [B]
2 2 2
 a +b +c  3
1
[C]
 1  2
[D] sin−1 
 p 2 + q 2 + r 2  3
  [D]
4

AUAT-2024 /89- A 3 [ P.T.O.

11. Two points, A and B move along the
13. The chord 6y = 8k x + 2 of the
positive direction of the x-axis and
y-axis respectively. Their distances curve k y 2 + 1 = 4x subtends a right-
from the origin are denoted as OA and
angle at the origin, then the value of k
OB respectively and their sum is
is
constant k. The locus of the foot of the
perpendicular from the origin O to the
line segment AB is k y 2 + 1 = 4x ¤yû¡ì¹J๠\¸à
ƒå’[i¡ [¤@ƒå A &¤} B, ™=àyû¡ì³ x-"Û¡ &¤} y-"ìÛ¡¹ 6y = 8k x + 2 ³èº[¤@ƒå¹ δ¶ååìJ &A¡[i¡
‹>àuA¡ [ƒA¡ ¤¹à¤¹ W¡ìº¡ú ³èº[¤@ƒå ë=ìA¡ t¡à샹 ƒè¹â«, γìA¡ào Kk¡> A¡ì¹, t¡àÒìº k-&¹ ³à> Òì¤
™=àyû¡ì³ OA &¤} OB [ÒÎàì¤ [W¡[Òû¡t¡ &¤} t¡à샹
ë™àKó¡º &A¡[i¡ ‹ø¡ç ¤A¡ k¡ú ³èº[¤@ƒå O ë=ìA¡ ë¹Jà Jr¡
−9 ± 33
AB š™¢”z ºì´¬¹ šàƒìƒìŹ Îe¡à¹š= Òº [A]
8

[A] (x + y )(x 2 − y 2 ) = k xy
−9 ± 34
2 2 [B]
[B] (x − y )(x + y ) = k xy 8

[C] (x + y )(x 2 + y 2 ) = k xy
9 ± 33
[C]
8
[D] (x + y )(x 2 + y ) = k xy

9 ± 34
12. A straight line passes through the [D]
8
point P (−2, −3) and cuts the pair of
straight lines, given by the equation
x 2 + 3y 2 + 4xy − 8x − 6y − 9 = 0 , at 14. If the tangent at (1, 7) to the curve
points Q and R. If the product of the x2 = y − 6 touches the circle
distances from P to Q and P to R is 20,
then the equation of one of the lines is x 2 + y 2 + 6x + 2y + c = 0 , then the
value of c is
&A¡[i¡ ιºì¹Jà P (−2, −3) [¤@ƒå¹ ³‹¸
[ƒìÚ ™àÚ &¤} Q * R [¤@ƒåìt¡
™[ƒ x2 = y − 6 ¤yû¡ì¹J๠(1, 7) [¤@ƒåìt¡
2 2
x + 3y + 4xy − 8x − 6y − 9 = 0 γãA¡¹o
‡à¹à l¡ü;šÄ ιºì¹J๠ë\àØl¡àìA¡ ëA¡ìi¡ ëƒÚ¡ú P ë=ìA¡ њŢA¡[i¡ x 2 + y 2 + 6x + 2y + c = 0 ¤õv¡[i¡ìA¡
Q &¤} P ë=ìA¡ R š™¢”z ƒè¹ì⫹ P¡oó¡º Òº 20, њŢ A¡ì¹, t¡àÒìº c-&¹ ³à> Òì¤
t¡àÒìº ë¹JàP¡[º¹ &A¡[i¡¹ γãA¡¹o Òº
[A] ± 10
[A] 3x + y + 9 = 0
[B] ±10
[B] x + 2y + 8 = 0

[C] x +y +5 = 0 [C] ± 20

[D] 3x − y + 3 = 0 [D] 10
AUAT-2024 /89- A 4

15. Let the curve C be the mirror image of →
2
17. The vector c , directed along the
the parabola y = 4x with respect to
bisector of the angle between the
the line x + y + 4 = 0 . If A and B are → → → → → →
the points of intersection of C with the
vectors 7 i − 4 j − 4 k and −2 i − j + 2 k
line y = –5, then the distance between →
A and B is with c = 5 6 , is

→ → → →
‹¹à ™àA¡ C ¤yû¡ì¹Jà[i¡ x + y + 4 = 0 ιºì¹J๠c &³> &A¡[i¡ 뮡C¡¹ ™à 7 i − 4 j − 4 k &¤}
ÎàìšìÛ¡ y 2 = 4x "[‹¤õìv¡¹ [¤šøt¡ãš → → →
−2 i − j + 2 k 뮡C¡ì¹¹ ³‹¸¤t¢¡ã ëA¡àìo¹ [‡Jr¡A¡
šàŬ¢šø[t¡[¤´¬¡ú A &¤} B ™[ƒ y = –5 ë¹J๠Îàì= →
C-&¹ ëáƒ[¤@ƒå ÒÚ, t¡àÒìº A &¤} B-&¹ ³ì‹¸ ¤¹à¤¹ [>샢[Åt¡ &¤} c = 5 6 ,¡ c→ 뮡C¡¹[i¡ Òº
ƒè¹â« Òì¤
5 → → →
[A] 16 [A] (5 i + 5 j + 2 k )
3

[B] 8
5 → → →
[B] ( i −7 j + 2k )
[C] 20 3

[D] 4 5 → → →
[C] ( i +7 j + 2k )
3

16. Let P be a variable point on the ellipse
5 → → →
x2 y2 [D] ( i −7 j − 2k )
+ = 1 with foci A and B. The 3
a 2 b2
maximum value of the area of the
triangle PAB is
 1 1
18. If f  x −  = x 3 + , then the value
 x  x3
x2 y2
‹¹à ™àA¡ + = 1 l¡üš¤õìv¡¹ l¡üšì¹ &A¡[i¡ of f (−1) is
a2 b2
š[¹¤t¢¡>Å㺠[¤@ƒå Òº P¡ú A &¤} B Òº l¡üš¤õìv¡¹
>à[®¡‡Ú¡ú t¡àÒìº PAB [y®å¡ì\¹ ëÛ¡yó¡ìº¹ Î줢àZW¡  1 1
™[ƒ f x −  = x3 + ÒÚ, t¡àÒìº
³à> Òº  x  x3
f (−1) -&¹ ³à> Òì¤
[A] abe
[A] 1
1
[B] 2 abe
[B] –1

[C] 2abe [C] 2

[D] 4abe [D] –2

AUAT-2024 /89- A 5 [ P.T.O.

1 21. The solution of the equation
19. The straight line y = x + k will be a
2 x 2 − 5 x + 6 = 0 is
2 2
x y
normal of the hyperbola − = a2 .
9 2 x 2 − 5 x + 6 = 0 γãA¡¹ìo¹ γà‹à> Òº
Find the relation between k and a.
[A] 2≤x <4
1 [B]
&A¡[i¡ ιºì¹Jà y = x +k &A¡[i¡ "[‹¤õv¡ 2<x <4
2 [C] 2≤x ≤4
x 2 y2
− = a 2 -&¹ l¡üš¹ "[®¡º´¬¡ú k &¤} [D] 2 < x ≤ 4
9 2
a-&¹ ³ì‹¸ δšA¢¡ [>o¢Ú A¡¹¡ú
22. The line 2x + 3y − 1 = 0 cuts the circle

11 x 2 + y 2 = 4 at points P and Q. The
[A] a = k
4 equation of the circle, described on
PQ as diameter, is

[B] a = ±
11
k &A¡[i¡ ιºì¹Jà 2x + 3y − 1 = 0 , &A¡[i¡ ¤õv¡
4
x 2 + y 2 = 4 ëA¡ P * Q [¤@ƒåìt¡ ëრA¡ì¹ìá¡ú
ëÎÒü ¤õìv¡¹ γãA¡¹o, ™à¹ &A¡[i¡ ¤¸àÎ Òì¤ PQ, Òº
11 2
[C] k = ± a
4 [A] 13(x 2 + y 2 ) − 4x − 6y − 50 = 0

[B] 13(x 2 + y 2 ) − 4x − 6y + 50 = 0
11
[D] k = ± a
4 [C] 13(x 2 − y 2 ) − 4x − 6y − 50 = 0

[D] 13(x 2 − y 2 ) − 4x − 6y + 50 = 0

20. The roots of the equation
1

a a x 23. lim (1n + 2n + 3n + ... + 999n )n = ?
n →∞
2025 2025 2025 = 0 in x, are
[A] Infinite ("Îã³)
b x b
[B] 1
[C] Undefined ("Î}`¡àt¡)
a a x
[D] 999
x-&¹ ³ì‹¸ 2025 2025 2025 = 0
b x b 24. Find the solution of the following
equation :
γãA¡¹ìo¹ ¤ã\P¡[º Òº tan−1(x − 1) + tan−1 x + tan−1(x + 1) = tan−1 3x

[A] −a, −b [>ìW¡¹ γãA¡¹ìo¹ γà‹à> [>o¢Ú A¡¹ –
−1
tan (x − 1) + tan−1 x + tan−1(x + 1) = tan−1 3x
[B] −a , b [A] 0
[B] 1
[C] a, −b [C] –1
[D] None of the above
[D] a, b
(l¡üšì¹¹ ëA¡àì>à[i¡Òü >Ú)
AUAT-2024 /89- A 6

28. The maximum value of
25. If  x 2e x dx = k1x 2e x − k2xe x + k3e x + c ,
then 2 cos2 x 4sin 2x
™[ƒ 2
f (x ) = 2 1 + cos x 4sin 2x

 x 2e x dx = k1x 2e x − k2xe x + k3e x + c , 1 cos2 x 1 + 4sin 2x

t¡àÒìº is

[A] k1 = 1,k2 = 2,k3 = 2 2 cos2 x 4sin 2x
2
f (x ) = 2 1 + cos x 4sin 2x
[B] k1 = 1,k2 = −2,k3 = 2
1 cos2 x 1 + 4sin 2x
[C] k1 = 1,k2 = 2,k3 = −2
-&¹ Î줢àZW¡ ³à> Òì¤
[D] k1 = −1,k2 = 2,k3 = 2
[A] 2
[B] –2
26. Total number of solutions of the [C] –1
4 4
equation sin x + cos x = sin x cos x in [D] 1
[0,2π], is
29. If  f (x )dx = g (x ) + c , then  f −1(x )dx =?
4 4 [0,2π]
sin x + cos x = sin x cos x in
γãA¡¹ìo¹ ë³ài¡ γà‹à> Î}J¸à Òº ™[ƒ  f (x )dx = g (x ) + c ÒÚ, t¡ì¤
[A] 2  f −1(x )dx =?

[B] 4 [A] xf −1(x ) − g ( f −1(x )) + c
[C] 6
[B] f −1(x ) − g ( f −1(x )) + c
[D] 8
[C] xf −1(x ) − g ( f (x )) + c
→ →
27. If a , b
→
and c are three vectors [D] xf (x ) − g ( f −1(x )) + c
→ → → → → →
such that a × b = c , b × c = a and
→ → → 30. Evaluate
c × a = b , then
³à> [>o¢Ú A¡¹
→ → →
™[ƒ a , b * c ë™ìA¡àì>à [t¡>[i¡ 뮡C¡ì¹¹ \>¸ dx
→ → → → → → → → →  tan x + cot x + sec x + cosecx
a× b = c , b× c = a &¤} c×a = b
ÒÚ, t¡àÒìº −
1
(sin x + cos x + x ) + c
[A]
2
→ → →
[A] | a | = | b | = | c |
1
[B] (sin x + cos x + x ) + c
→ → → 2
[B] | a | ≠ | b | = | c |
1
→ → → [C] (sin x + cos x − x ) + c
[C] | a | = | b | ≠ | c | 2

→ → →
1
[D] | a | ≠ | b | ≠ | c | [D] − (sin x + cos x − x ) + c
2

AUAT-2024 /89- A 7 [ P.T.O.

31. If |z 2 − 3| = 3| z |, then the maximum 34. When f ( x ) = x − x , then the value of
value of |z| is 5 tan−1 f (x )
 1 + ( f (x ))
0 2
dx
™[ƒ |z 2 − 3| = 3| z | ÒÚ, t¡àÒìº |z|-&¹
Î줢àZW¡ ³à> Òì¤ is

3 + 21 ™J> f (x ) = x − x , t¡àÒìº
[A]
2 5 tan−1 f (x )
−3 + 21  1 + ( f (x ))
0 2
dx
[B]
2 -&¹ ³à> Òì¤
−3 − 21
[C] π
2 [A]
32
3 − 21
[D]
2 π2
[B]
32
x 2 y2 x 2 y2
32. If + = 1 and + =1 5π
169 25 a 2 b2 [C]
having same eccentricity, then a : b is 32

x 2 y2 x 2 y2 5 π2
+ = 1 * 2 + 2 = 1 -&¹ l¡ü;ìA¡@ƒøt¡à [D]
169 25 a b 32
&A¡Òü, t¡ì¤ a : b Òì¤
[A] 5 : 13 y 
35. If f (x 2 + y 2 ) = tan−1   + c be the
[B] 13 : 5 x 
[C] 169 : 15 solution of the differential equation
[D] 15 : 169
x 2 + y 2 (xdx + ydy ) =
33. Let C0 ,C1,C2 ,...,CN be the coefficients
a 2 − x 2 − y 2 (xdy − ydx )
in the expansion of (1 + x )N . Then the
then
N Ci
value of  is ™[ƒ y 
f (x 2 + y 2 ) = tan−1   + c , "¤A¡º
i =0
i +1 x 
‹¹à ™àA¡ C0 ,C1,C2,...,CN Òº (1 + x )N
γãA¡¹o x 2 + y 2 (xdx + ydy ) =
N Ci
[¤>¸àìι ÎÒK¡ú t¡ì¤  -&¹ ³à> Òì¤ a 2 − x 2 − y 2 (xdy − ydx )
i =0
i +1
2N − 1 -&¹ γà‹à> ÒÚ, t¡ì¤
[A]
N +1
[A] f (x ) = sin x
2N + 1
[B]
N +1 [B] f (x ) = sin−1 x
2N +1 − 1
[C] [C] f (x ) = sin x
N +1
2N +1 + 1
[D] [D] f (x ) = sin−1 x
N +1
AUAT-2024 /89- A 8

SECTION—B
PHYSICS
36. Three forces are acting on a body as 38. Assertion : A solid sphere and a
shown in the figure below. To have the hollow sphere when allowed to roll
resultant force only along the down on an inclined plane, the solid
Y-direction, the magnitude of the sphere reaches the bottom first.
minimum additional force needed is Reason : The moment of inertia of a
solid sphere is greater than that of a
[>ìW¡¹ [W¡ìy 뙳> ëƒJàì>à ÒìÚìá, [t¡>[i¡ ¤º &A¡[i¡ hollow sphere.
¤Ññ¹ l¡üš¹ A¡à\ A¡ì¹¡ú A¡à™¢A¡¹ã ¤à Î}Òt¡ ¤º Ç¡‹å³ày [A] Both Assertion and Reason are
Y-[ƒA¡ ¤¹à¤¹ ¹àJìt¡ Òìº, >è¸>t¡³ "[t¡[¹v¡û¡ ¤ìº¹ correct and Reason is the correct
explanation for Assertion
šøìÚà\> ÒÚ
[B] Both Assertion and Reason are
correct but Reason is not the
correct explanation for Assertion
[C] Assertion is correct but Reason is
incorrect
[D] Both Assertion and Reason are
incorrect

A¡=> – &A¡[i¡ A¡[k¡> ëKàºA¡ &¤} &A¡[i¡ óò¡àšà
ëKàºA¡ìA¡ ™J> &A¡[i¡ ëÒºàì>à γt¡ìº K[Øl¡ìÚ ë™ìt¡
ëƒ*Úà ÒÚ, A¡[k¡> ëKàºA¡[i¡ šø=ì³ [>ìW¡ ëš]áàÚ¡ú
A¡à¹o – A¡[k¡> ëKàºìA¡¹ \Øl¡t¡à °à³A¡ óò¡àšà ëKàºìA¡¹
[A] 5 N ëW¡ìÚ ë¤[Å¡ú
[A] A¡=> &¤} A¡à¹o l¡ü®¡ÚÒü Î[k¡A¡ &¤} A¡à¹o Òº
[B] 0·5 N
A¡=>-&¹ Î[k¡A¡ ¤¸àJ¸à
[C] 25 N [B] A¡=> &¤} A¡à¹o l¡ü®¡ÚÒü Î[k¡A¡ [A¡”ñ A¡à¹o
A¡=>-&¹ Î[k¡A¡ ¤¸àJ¸à >Ú
[D] 1·5 N
[C] A¡=> Î[k¡A¡ [A¡”ñ A¡à¹o ®å¡º
[D] A¡=> &¤} A¡à¹o l¡ü®¡ÚÒü ®å¡º
37. Which of the following is not
represented in correct unit? 39. A monatomic gas at pressure P1 and
volume V1 is compressed adiabatically
[>´•[º[Jt¡ ëA¡à>[i¡ Î[k¡A¡ &A¡ìA¡ šøA¡àÅ A¡¹à ÒÚ[>? to 1/8th of its original volume. What is
the final pressure of the gas?
[A] Stress (šãØl¡>)/strain ([¤Aõ¡[t¡) = N/m2 V1 "àÚt¡ì>¹ &A¡[i¡ &A¡š¹³àoåA¡ K¸àìι W¡àš P1,
¹ç¡‡ý¡t¡àšãÚ š[¹¤t¢¡ì> K¸àÎ[i¡ t¡à¹ ³èº "àÚt¡ì>¹
[B] Surface tension(šõË¡i¡à>) = N/m 1/8 "}ìÅ Î}Aå¡[W¡t¡ ÒÚ¡ú K¸àìι Wè¡Øl¡à”z W¡àš A¡t¡?
[A] 64P1
[C] Energy (Å[v¡û¡) = kg-m/sec [B] P1
[C] 32P1
[D] Pressure (W¡àš) = kgm–1/sec2 [D] 16P1

AUAT-2024 /89- A 9 [ P.T.O.

40. If the length of a simple pendulum is 43. If a long hollow copper pipe carries a
increased by 2%, then the time period direct current, then the magnetic field
™[ƒ &A¡[i¡ Îà‹à¹o ëƒàºìA¡¹ íƒQ¢¸ 2% ¤õ[‡ý¡ šàÚ, associated with the current will be
t¡àÒìº Î³ÚA¡àº ™[ƒ &A¡[i¡ ƒãQ¢ óò¡àšà t¡à³à¹ šàÒüš γt¡[lØ ¡;¡ šø¤àÒ ¤Ò>
[A] increases by 1% (1% ¤õ[‡ý¡ šàÚ) A¡ì¹, t¡àÒìº t¡[lØ ¡;šø¤àìÒ¹ \>¸ ëW¡ï´¬A¡ ëÛ¡y Òì¤
[B] decreases by 1% (1% ÒùàÎ šàÚ) [A] only outside of the pipe
[C] increases by 2% (2% ¤õ[‡ý¡ šàÚ)
Ç¡‹å³ày šàÒüìš¹ ¤àÒüì¹
[D] decreases by 2% (2% ÒùàÎ šàÚ)
[B] only inside of the pipe
41. A thin conducting ring of radius R is Ç¡‹å³ày šàÒüìš¹ [®¡t¡ì¹
given a charge +Q. The electric field at
[C] Neither inside nor outside of the
the centre O of the ring due to the
pipe
charge on the part AKB of the ring is E.
The electric field at the centre due to šàÒüìš¹ [®¡t¡ì¹* >à ¤àÒüì¹* >à
the charge on the part ACDB of the [D] Both inside and outside of the
ring is
pipe
R ¤¸àÎàì‹¢¹ &A¡[i¡ šàt¡ºà š[¹¤àÒã ¤ºÚìA¡ +Q
"à‹à> ëƒ*Úà ÒÚ¡ú ¤ºìÚ¹ AKB "}ìÅ "à‹àì>¹ šàÒüìš¹ [®¡t¡ì¹ &¤} ¤àÒüì¹ l¡ü®¡ÚÒü
A¡à¹ìo ¤ºìÚ¹ O ëA¡ì@ƒø í¤ƒå¸[t¡A¡ ëÛ¡y[i¡ Òº E¡ú
¤ºìÚ¹ ACDB "}ìÅ "à‹àì>¹ A¡à¹ìo ëA¡ì@ƒø 44. Two capacitors, one of capacity C and
í¤ƒå¸[t¡A¡ ëÛ¡y[i¡ Òì¤ the other of capacity C/2 are
connected to a V-volt battery, as
shown in the figure below. The work
done in charging fully both the
capacitors is
[>ìW¡¹ [W¡ìy ëƒJàì>à "àìá ƒå’[i¡ ‹à¹A¡, &A¡[i¡¹
‹à¹oÛ¡³t¡à C &¤} ">¸[i¡¹ ‹à¹oÛ¡³t¡à C/2, &A¡[i¡
V 뮡àìÂi¡¹ ¤¸ài¡à[¹¹ Îàì= Î}™åv¡û¡ "àìá¡ú l¡ü®¡Ú ‹à¹A¡ìA¡¡
šåì¹àšå[¹ W¡à\¢ A¡¹à¹ \>¸ Aõ¡t¡A¡à\ Òì¤
[A] E, along KO (E, KO ¤¹à¤¹)
[B] 3E, along OK (3E, OK ¤¹à¤¹)
[C] 3E, along KO (3E, KO ¤¹à¤¹)
[D] E, along OK (E, OK ¤¹à¤¹)

42. A magnetized iron wire of length l has
a magnetic moment M. It is then bent
into a semicircular arc. The new [A] CV 2
magnetic moment is
l íƒìQ¢¸¹ &A¡[i¡ ˜¡\å Wå¡´¬[A¡t¡ ëºàÒ๠t¡àì¹¹ ëW¡ï´¬A¡ 3
[B] CV 2
°à³A¡ M¡ú &[i¡ìA¡ ¤òà[A¡ìÚ &A¡[i¡ "‹¢¤õìv¡ š[¹ot¡ A¡¹à 4
Òìº, >tå¡> ëW¡ï´¬A¡ °à³A¡ Òì¤
1
[A] M [C] CV 2
2
[B] 2M / π
[C] M/l [D] None of the above
[D] M × l (l¡üšì¹¹ ëA¡àì>à[i¡Òü >Ú)

AUAT-2024 /89- A 10

45. From the graph between current (I ) 48. A body of mass 0·9 kg is in
and voltage (V ) shown below, identify equilibrium under the action of two
the portion corresponding to negative strings as shown in the figure below.
resistance. The relation between tension forces
T1 and T2 is (Take g = 10 m/s2)

0·9 ëA¡[\ ®¡ì¹¹ &A¡[i¡ ¤Ññ ƒå’[i¡ [Сö}-&¹ [yû¡ÚàÚ
®¡à¹Îà쳸¹ ³ì‹¸ ¹ìÚìá ™à [>ìW¡¹ [W¡ìy ëƒJàì>à
ÒìÚìá¡ú i¡à> ¤º T1 &¤} T2-&¹ ³ì‹¸ δšA¢¡ Òº
A (g = 10 m/s2)

A¡àì¹@i¡ (I ) &¤} 뮡àìÂi¡\ (V )-&¹ ³ì‹¸ ëºJ[W¡y[i¡
ë=ìA¡ ëÎÒü "}Å[i¡ [W¡[Òû¡t¡ A¡¹ ë™[i¡ ˜¡oàuA¡ ë¹à싹
">å¹¡ê š¡ú
[A] AB
[B] BC
[C] CD
0.9 kg
[D] DE

46. A body covers 16 m in 3rd second and [A] T1 = T2
24 m in 5th second in its motion
along x-direction. The initial velocity
[B] T1 = 0·5T2
of the body is
&A¡[i¡ ¤Ññ x-[ƒA¡ ¤¹à¤¹ t¡à¹ K[t¡šì= 3 Ú ëÎìA¡ì“¡ [C] T1 = 2T2
16 [³i¡à¹ &¤} 5 t¡³ ëÎìA¡ì“¡ 24 [³i¡à¹ "[t¡yû¡à”z
A¡ì¹¡ú ¤Ññ¹ šøà=[³A¡ ë¤K Òº [D] T1 = 3T2
[A] 3 ms–1
[B] 4 ms–1
49. Work done in increasing the size of a
[C] 5 ms–1
soap bubble from its diameter 8 cm to
[D] 6 ms–1 12 cm is nearly (surface tension of
soap solution is 0·03 Nm–1)
47. A solid sphere is rolling on a
frictionless plane surface about its
axis of symmetry. The ratio of its
&A¡[i¡ Îà¤à> ¤åƒ¤å샹 ¤¸àÎ 8 ëÎ[@i¡[³i¡à¹ ë=ìA¡
rotational energy to its total energy is 12 ëÎ[@i¡[³i¡à¹ ¤¸àÎ ¤àØl¡àì>๠\>¸ Aõ¡t¡A¡à왢¹ š[¹³ào
&A¡[i¡ A¡[k¡> ëKàºA¡ t¡à¹ šø[t¡Îà쳸¹ "ìÛ¡¹ A¡àáàA¡à[á Òº (Îà¤à> ‰¤ìo¹ šõìË¡¹ i¡à> Òº 0·03 Nm–1)
&A¡[i¡ QÈ¢oÒã> γt¡º šõìË¡ Qèo¢àÚ³à>¡ú &¹ Qèo¢> Å[v¡û¡¹
Îàì= &¹ ë³ài¡ Å[v¡û¡¹ ">åšàt¡ Òº [A] 0 ⋅ 48 π mJ

[A] 1 : 5
[B] 0 ⋅ 216 π mJ
[B] 2 : 7
[C] 2 ⋅ 16 π mJ
[C] 3 : 5

[D] 4 ⋅ 8 π mJ
[D] 5 : 7
AUAT-2024 /89- A 11 [ P.T.O.

50. One mole of an ideal monatomic gas 53. A thin convex-concave lens (µ = 1—5)
( γ = 5 / 3) is mixed with three moles of with the radii of curvature 15 cm and
diatomic gas ( γ = 7 /5) . The γ of the 20 cm. The focal length of the lens is

mixture is ( γ = C P / CV ) &A¡[i¡ šàt¡ºà l¡üv¡º-"¤t¡º ëºX (µ = 1—5) ™à¹
&A¡[i¡ "àƒÅ¢ &A¡ š¹³àoå K¸àìι ( γ = 5 / 3) &A¡ ¤yû¡t¡à¹ ¤¸àÎà‹¢ 15 cm &¤} 20 cm¡ú ëºìX¹
ëó¡àA¡àº íƒQ¢¸ Òº
ë³à캹 Îàì= [‡-š¹³àoå K¸àìι ( γ = 7 /5) [t¡>
[A] 45 cm
ë³àº [³[Åøt¡ A¡¹à Òº¡ú [³Åøo[i¡¹ γ Òº
[B] 60 cm
( γ = C P / CV )
[C] 30 cm
[A] 4/9
[D] 120 cm
[B] 13/9
[C] 3/2 54. The magnitude of current i indicated
[D] 22/15 in the circuit shown in the figure
below is
51. Electric field in space is given by
[>ìW¡¹ [W¡ìy ëƒJàì>à Îà[A¢¡ìi¡ [>샢[Åt¡ A¡àì¹@i¡ i-&¹
→ ^ ^ ^
E = 3 i + 8 j + 4 k . The electric flux ³àyà Òº
through a surface of area 30 units in
x-z plane is
&A¡[i¡ "e¡ìº í¤ƒå¸[t¡A¡ ëÛ¡y
→ ^ ^ ^
E = 3 i + 8 j + 4 k ¡ú ' "e¡ìº x-z γt¡ºšõìË¡
30 &A¡A¡ ëÛ¡yó¡ìº¹ ³‹¸ [ƒìÚ í¤ƒå¸[t¡A¡ óáàìG¹ ³à>
Òº
[A] 90 units
[B] 210 units
[C] 240 units
[D] 120 units [A] E/3R
[B] E/2R
52. A current of 1 A is flowing in the sides
of an equilateral triangle of side 3 cm [C] E/R
in anti-clockwise direction. The [D] zero
magnitude of the magnetic field at the
centroid of the triangle is 55. Which of the following transitions in
&A¡[i¡ γ¤à× [y®å¡ì\¹ ¤à× ¤¹à¤¹ Q[lØ ¡¹ A¡òài¡à¹ hydrogen atom emits photon of
[¤š¹ãt¡ [ƒìA¡ &A¡ "¸à[´šÚ๠šø¤àÒ ™àìZá¡ú γ¤à× highest frequency?
[y®å¡ì\¹ šø[t¡[i¡ ¤à×¹ íƒQ¢¸ ÒàÒüìl¡öàì\> š¹³àoå¹ [>ìW¡¹ ëA¡à>ô Ñ‚à>à”z¹ Î줢àZW¡
3 ëÎ[@i¡[³i¡à¹¡ú [y®å¡ì\¹ ëA¡ì@ƒø ëW¡ï´¬A¡ ëÛ¡ìy¹ ³àyà A¡´šàìS¡¹ ëó¡ài¡> [>K¢t¡ A¡ì¹?
Òº [A] n = 2 to n = 1
[A] 4 × 10–5 T [B] n = 3 to n = 2
[B] 6 × 10–5 T [C] n = 4 to n = 3
[C] 9 × 10–5 T [D] n = 2 to n = 4
[D] 10 × 10–5 T

AUAT-2024 /89- A 12

SECTION—C
CHEMISTRY
56. Which of the following electronic 60. The correct order of stability and bond
configurations is incorrect ? dissociation energies is
[>ìW¡¹ ëA¡à>ô ÒüìºA¡i¡ö[>A¡ A¡>[ó¡Kàì¹Å>[i¡ ®å¡º? [Ñ‚[t¡Åãºt¡à &¤} ¤“¡ [¤[ZáÄt¡à Å[v¡û¡¹ Î[k¡A¡ yû¡³[i¡ Òº
+
[A] Cr : [Ar] 3d5 4s1 [A] O2 > O2 > O2− > O2
2
−

[B] Mo : [Kr] 4d5 5s1 [B] +
O2 > O2− > O2 > O2 −
2
[C] W : [Xe] 4f14 5d5 6s1 O2 > O2 − + −
[C] 2 > O2 > O2
[D] Pt : [Xe] 4f14 5d9 6s1 − 2− +
[D] O2 > O2 > O2 > O2
57. Which sequence of the ionisation
energies is incorrect ? 61. Which reagent is used for the conversion
of 2-butyne to trans-2-butene?
"àÚ[>A¡¹o Å[v¡û¡¹ ëA¡à>ô yû¡³[i¡ ®å¡º?
2-[¤l¡üi¡àÒü> ë=ìA¡ i¡öàX-2-[¤l¡ü[i¡ì> ¹ê¡šà”zì¹¹ \>¸
[A] IE1(N) > IE1(O)
ëA¡à>ô [¤A¡à¹A¡ ¤¸¤Ò๠A¡¹à ÒÚ?
[B] IE2(N) < IE2(O)
[A] H2/Pd/C
[C] IE1(P) > IE1(S)
[B] H2/Pd/BaSO4
[D] IE2(Be) > IE2(B) [C] H2/Na/liquid NH3
58. 1·00 g of a non-electrolyte solute [D] None of the above
dissolved in 50 g of benzene lowered (l¡üšì¹¹ ëA¡àì>à[i¡Òü >Ú)
the freezing point of benzene by 0·40 K.
The freezing point depression constant 62. Which one is Homoleptic complex?
of benzene is 5·12 K kg mol–1. Find ëÒàì³à캚[i¡A¡ A¡³ìšÃG ëA¡à>[i¡?
the molar mass of the solute.
[A] [Ni(CO)4]
50 g ë¤[gì> 1·00 g >>-ÒüìºìC¡öàºàÒüi¡ ‰¤o [B] [CuCl2(CH3NH2)2]
‰¤ã®è¡t¡ Òìº ë¤[gì>¹ [Ò³àS¡ [¤@ƒåìA¡ 0·40 K A¡[³ìÚ [C] K3[Fe(CN)5NO]
ëƒÚ¡ú ë¤[gì>¹ [Ò³àS¡ [¤@ƒå¹ "¤>³> ‹ø¡ç ¤A¡ Òº [D] K2[Cr(CN)2O2(O2)NH3]
5·12 K kg mol–1¡ú ‰à¤ìA¡¹ ë³àºà¹ ®¡¹ ëJòàì\à¡ú
63. Calculate the spin only magnetic
[A] 512 g mol–1
moment of Mn centre in MnF6–3
[B] 380 g mol–1 complexes.
[C] 326 g mol–1 MnF6–3 A¡³ìšÃìG Mn ëA¡ì@ƒø¹ Ç¡‹å³ày [Ñš>
[D] 256 g mol–1 ëW¡ï´¬A¡ãÚ ë³àì³@i¡ Ko>à A¡¹¡ú
59. In a chemical reaction X → Y , it is [A] 2·9 BM
found that the rate of reaction doubles [B] 3·9 BM
when the concentration of X is [C] 4·9 BM
increased four times. The order of [D] 5·9 BM
reaction with respect to X is
64. Which of the following compounds
X → Y &A¡[i¡ ¹àÎàÚ[>A¡ [¤[yû¡ÚàÚ ëƒJà ™àÚ ë™
can be identified by Molisch’s test?
X-&¹ Q>â« W¡à¹P¡o ¤àØl¡ìº [¤[yû¡Ú๠Ò๠[‡P¡o ÒìÚ
[>ìW¡¹ ëA¡à>ô ë™ïK[i¡ Molisch-&¹ š¹ãۡ๠³à‹¸ì³
™àÚ¡ú X-&¹ ÎàìšìÛ¡ [¤[yû¡Ú๠yû¡³ Òº [W¡[Òû¡t¡ A¡¹à ™àÚ?
[A] 0 [A] Amines
[B] 1/2 [B] Nitro compounds
[C] 1 [C] Sugars
[D] 2 [D] Ketones

AUAT-2024 /89- A 13 [ P.T.O.

65. The final product(B) formed in the 67. The correct order of increasing
following reaction sequence is electronegativity of B, C, N, O and F is
B, C, N, O &¤} F-&¹ t¡[Øl¡;¡ ˜¡oàuA¡t¡à ¤õ[‡ý¡¹
[>ì´•àv¡û¡ [¤[yû¡ÚàÚ yû¡³à>åÎàì¹ K[k¡t¡ Wè¡Øl¡à”z [¤[yû¡Úà\àt¡
Î[k¡A¡ yû¡³ Òº
‰¤¸[i¡ (B) Òº
[A] B < C < N < O < F
[B] F < O < N < C < B
[C] C < N < O < F < B
[D] O < N < C < B < F

68. The process by which alum purifies
turbid water is

ë™ šø[yû¡Ú๠³à‹¸ì³ alum ëQàºà \ºìA¡ Ç¡‡ý¡ A¡ì¹,
[A] t¡à Òº
[A] absorption
[B] adsorption
[B]
[C] coagulation
[D] dispersion

69. For a Face-Centered Cubic (FCC) unit
cell, the total number of particles per
unit cell is
[C]
&A¡[i¡ Face-Centered Cubic (FCC) &A¡A¡
ëA¡àìȹ \>¸ šø[t¡ Òül¡ü[>i¡ ëA¡àìÈ ë³ài¡ A¡o๠Î}J¸à Òº
[A] 1
[B] 2
[D]
[C] 3
[D] 4

66. The molarity of NaOH in the solution 70. The order of equivalent conductance
prepared by dissolving its 4 g in enough at infinite dilution for LiCl, NaCl and
water to form 250 ml of the solution is KCl is

4 g NaOH ™ì=Ê¡ \ìº ‰¤ã®è¡t¡ A¡ì¹ 250 ml ‰¤o LiCl, NaCl &¤} KCl-&¹ \>¸ "Îã³ t¡¹ºãA¡¹ìo
ít¡[¹ A¡¹à Òº¡ú ‰¤ìo NaOH-&¹ ë³àºà[¹[i¡ Òº γt塺¸ š[¹¤à[Òt¡à¹ yû¡³ Òº
[A] 4 M [A] LiCl > NaCl > KCl

[B] 0·4 M [B] KCl > NaCl > LiCl

[C] 8 M [C] NaCl > KCl > LiCl
[D] LiCl > KCl > NaCl
[D] 0·8 M

AUAT-2024 /89- A 14

PART—II
( Islamic History and Culture, General English & General Knowledge )
71. What is Zakat in Islam? 76. When we start any work, what should
we say?
Òüκàì³ ™àA¡àt¡ A¡ã?
[A] Charity
"à³¹à ™J> ëA¡àì>à A¡à\ Ç¡¹ç¡ A¡[¹, t¡J> "à³à샹 A¡ã
¤ºà l¡ü[W¡;?
[B] Fasting
[A] Alhamdulillah
[C] Pilgrimage
[B] Allahu Akbar
[D] Prayer
[C] Masha Allah
72. What is the punishment for theft in [D] Bismillah
Islam?
77. Which day of the week is very special
Òüκàì³ Wå¡[¹¹ Åà[Ñz A¡ã? for the Muslims?
[A] Imprisonment Îœ¡àìÒ¹ ëA¡à>ô [ƒ>[i¡ ³åκ³à>샹 \>¸ Jå¤Òü [¤ìÅÈ
[B] Amputation of hands [ƒ>?
[C] Fine [A] Sunday
[D] Death [B] Monday
[C] Thursday
73. What do Muslims say when thanking
[D] Friday
someone?
A¡àl¡üìA¡ ‹>¸¤àƒ \à>àìº ³åκ³à>¹à A¡ã ¤ìº? 78. Who were the parents of Prophet
[A] Subhanallah Muhammad (SAW)?
[B] Alhamdulillah >¤ã ³åÒà´¶ƒ (Îà–)-&¹ [št¡à-³àt¡à A¡à¹à [áìº>?
[C] Jazak Allah Khair [A] Abdullah and Amina
[D] Allahu Akbar [B] Ali and Fatima
[C] Abu Bakr and Khadija
74. In which month was Prophet [D] None of them
Muhammad (SAW) born?
>¤ã ³åÒà´¶ƒ (Îà–) ëA¡à>ô ³àìÎ \@µKøÒo A¡ì¹>? 79. How many chapters does the Qur’an
have?
[A] Muharram
A塹"àì> A¡Ú[i¡ "‹¸àÚ "àìá?
[B] Rabi ul Awal
[A] 110
[C] Ramadan
[B] 112
[D] Shawal
[C] 113
75. What do angels say when they meet [D] 114
believers?
80. What is the Islamic ruling of
ëó¡ì¹Åt¡à¹à ™J> [¤Å¬àÎã샹 Îàì= ëƒJà A¡ì¹ t¡J> consuming pork?
A¡ã ¤ìº? ÅèA¡ì¹¹ ³à}Î Jà*Ú๠Òüκà³ã ×A塳 A¡ã?
[A] Peace be upon you [A] Permissible
[B] Welcome [B] Prohibited
[C] Good luck [C] Discouraged
[D] Masha Allah [D] None of the above

AUAT-2024 /89- A 15 [ P.T.O.

81. In Islam, the number of god(s) is 86. Prophet Muhammad (PBUH) migrated
to
Òüκàì³ l¡üšàìθ¹ Î}J¸à Òº
[A] only one
>¤ã ³åÒà´¶ƒ (Îà–) ë™ ÅÒì¹ [Ò\¹t¡ A¡ì¹[áìº>, t¡à
Òº
[B] two
[A] Makkah
[C] three
[B] Medina
[D] many
[C] Taif
82. The first Prophet, according to Islam is [D] Tabuk

Òüκೠ">å™àÚã šø=³ >¤ã¹ >à³ Òº
87. During fasting, one is allowed to
[A] Prophet Muhammad drink
[B] Prophet Abraham ë¹à™à "¤Ñ‚àÚ šà> A¡¹à ™àÚ
[C] Prophet Nuh [A] water only
[D] Prophet Adam [B] fruit juice only
[C] any liquid food
83. Prayer at the dawn is called
[D] nothing
뮡àì¹¹ šøà=¢>àìA¡ ¤ºà ÒÚ
[A] Zuhr 88. The obligatory charity in Islam is
[B] Maghrib Òüκàì³ "à¤Å¸A¡ ƒà>ìA¡ ¤ºà ÒÚ
[C] Fajr [A] Fitra
[D] Asr [B] Sadqa
[C] Zakat
84. The person who leads prayer at masjid
is called [D] Infaq

³Î[\ìƒ [™[> >à³à™ šØl¡à>, tò¡àìA¡ ¤ºà ÒÚ
89. The first Caliph was
[A] Shaikh
šø=³ J[ºó¡à Òìº>
[B] Caliph
[A] Hazrat Umar
[C] Imam
[B] Abu Bakr
[D] Mufti
[C] Hazrat Ali
85. Which country has the largest [D] Hazrat Uthman
population of muslims?
ëA¡à> ëƒìŠΤìW¡ìÚ ë¤[Å Î}J¸A¡ Òüκೠ‹³¢à¤º´¬ã 90. The word ‘madrasa’ means
³à>åÈ ¤àÎ A¡ì¹? ‘³à‰àÎà’ Å즹 "=¢ Òº
[A] India [A] place of worship
[B] Saudi Arabia [B] place of judiciary
[C] Egypt [C] educational institution
[D] Indonesia [D] All of the above

AUAT-2024 /89- A 16

91. Find out the correctly spelt word from 96. Dr. V. Kurien is famous in the field of
the given alternatives.
l¡– [®¡. Aå¡[¹ìÚ> ëA¡à>ô ëÛ¡ìy A¡àì\¹ \>¸ [¤J¸àt¡?
[A] Assassination
[A] Atomic Power
[B] Asassination [B] Dairy Development
[C] Assasination [C] Economic Reforms
[D] Assasinasion [D] Poultry Farms

97. Which organ in the human body is
92. Choose the word nearest in meaning
responsible for filtering blood and
to “FASTIDIOUS”.
producing urine?
[A] Difficult
³à>¤ìƒìÒ¹ ëA¡à>ô "U ¹v¡û¡ š[¹ìÅà‹> * šøÑ÷ठít¡[¹¹
[B] Different \>¸ ƒàÚã?
[C] Meticulous [A] Heart
[D] Dainty [B] Liver
[C] Kidneys
93. Choose the word farthest in meaning [D] Spleen
to “ENDORSE”.
[A] Accept 98. Fathometer is used to measure

[B] Oppose ó¡¸àì=à[³i¡à¹ A¡ã š[¹³àš A¡¹ìt¡ ¤¸¤Òê¡t¡ ÒÚ?
[C] Disagree [A] earthquakes
[B] rainfall
[D] Approve
[C] ocean depth

94. Fill in the blank with the correct [D] sound intensity
alternative.
He has an _____ good food. 99. Who is the founder of the modern
theory of evolution?
[A] appetite for
"à‹å[>A¡ [¤¤t¢¡> t¡ìw¹ šø[t¡Ë¡àt¡à ëA¡?
[B] appetite to
[A] Charles Darwin
[C] appetite with [B] Isaac Newton
[D] appetite on [C] Albert Einstein
[D] Marie Curie
95. The expression dead and buried is
used to mean 100. Which is the largest coffee producing
[A] there is bad news State of India?

[B] bad times are over
®¡à¹ìt¡¹ ¤õÒv¡³ A¡[ó¡ l¡ü;šàƒ>A¡à¹ã ¹à\¸ ëA¡à>[i¡?
[A] Kerala
[C] something that is not going to
happen again [B] Tamil Nadu

[D] something is less important than [C] Karnataka
before [D] Arunachal Pradesh

AUAT-2024 /89- A 17 [ P.T.O.

SPACE FOR ROUGH WORK

AUAT-2024 /89- A 18

SPACE FOR ROUGH WORK

AUAT-2024 /89- A 19 [ P.T.O.

SPACE FOR ROUGH WORK

AUAT-2024 /89- A 20 NNN24(119)—402×4

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