SSC CGL Tier 2 (20 Feb) Past Year Paper (2018) | SSC CGL (Hindi) Tier - 1 Mock Test Series PDF Download

 Page 1


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 20-2-2018] [Time : 10 AM to 12 PM 
1.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 33
3
 > 3
33
 
  II. 333 > (3
3
)
3
 
 (a) Only I/kesâJeue I    
 (b) Only II/kesâJeue II 
 (c) Both I and II/ I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
2.  If P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2
 and Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, then what is the value of P–Q ?  
  Ùeefo P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2 
leLee Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, nQ, lees P–Q keâe ceeve keäÙee nw? 
 (a) 24645 (b) 26075 
 (c) 29317 (d) 31515 
3.  If A = (1/0.4) + (1/0.04) + (1/0.004) + ..... upto 8
th
 
terms, then what is the value of A ?  
  Ùeefo A = (1/0.4) + (1/0.04) + (1/0.004) + .....8
th
 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) 27272727.5 (b) 25252525.5 
 (c) 27777777.5 (d) 25555555.5 
4.  If M = 0.1 + (0.1)
2
 + (0.01)
2
 and N = 0.3 + (0.03)
2
 
+ (0.003)
2
, then what is the value of M + N?  
  Ùeefo M = 0.1 + (0.1)
2
 + (0.01)
2
 leLee N = 0.3 + 
(0.03)
2
 + (0.003)
2
 nQ, lees M + N keâe ceeve keäÙee nw? 
 (a) 0.411009 (b) 0.413131 
 (c) 0.313131 (d) 0.131313 
5.  If 
96 97
P = , Q =
95× 97 96× 98
and
1
R = ,
97
then 
which of the following is TRUE ?  
  Ùeefo 
96 97
P = , Q =
95× 97 96× 98
 leLee 
1
R =
97
 nQ, 
lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) P < Q < R (b) R < Q < P 
 (c) Q < P < R (d) R < P < Q 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
1 3 1 1 439
11 + 17 - 5 - 2 =
2 4 5 10 20
 
  II. 
9 11 12
> >
1078 1127 1219
 
  III. 
149 153 157
> >
151 155 159
 
 (a) Only I/keâsJeue I   
 (b) Only II/kesâJeue II   
 (c) Only III/kesâJeue III 
 (d) None is true/keâesF& melÙe veneR nw  
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
2 3 5
< <
3 5 2 5 4 3
 
  II. 
3 2 7
< <
2 5 3 3 4 5
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
8.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. The total number of positive factors of 72 is 
12./72 kesâ kegâue 12 Oeveelcekeâ iegCeveKeC[ nQ~ 
  II. The sum of first 20 odd numbers is 400./ØeLece 
20 efJe<ece mebKÙeeDeeW keâe Ùeesie 400 nw~ 
  III. Largest two digit prime number is 97./oes 
DebkeâeW keâer meyemes yeÌ[er DeYeepÙe mebKÙee 97 nw~ 
 (a) Only I and III/kesâJeue I leLee II  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All are true/meYeer melÙe nQ 
9.  If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N 
= (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then 
what is the value of M/N ?  
  Ùeefo M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) leLee 
N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), nQ, 
lees M/N keâe ceeve keäÙee nw? 
 (a) 207/560  (b) 339/1120 
 (c) 113/350 (d) 69/175 
10.  M is the largest 4 digit number, which when 
divided by 4, 5, 6 and 7 leaves remainder as 2, 
3, 4 and 5 respectively. What will be the 
remainder when M is divided by 9 ?  
  M, 4 DebkeâeW keâer meyemes yeÌ[er mebKÙee nw, efpemes 4, 5, 6 
leLee 7 mes efJeYeeefpele keâjves hej Mes<eHeâue ›eâceMe: 2,3,4 
leLee 5 Deelee nw~ peye M keâes 9 mes efJeYeeefpele efkeâÙee 
peeÙes, lees Mes<eHeâue keäÙee nesiee? 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 20-2-2018] [Time : 10 AM to 12 PM 
1.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 33
3
 > 3
33
 
  II. 333 > (3
3
)
3
 
 (a) Only I/kesâJeue I    
 (b) Only II/kesâJeue II 
 (c) Both I and II/ I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
2.  If P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2
 and Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, then what is the value of P–Q ?  
  Ùeefo P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2 
leLee Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, nQ, lees P–Q keâe ceeve keäÙee nw? 
 (a) 24645 (b) 26075 
 (c) 29317 (d) 31515 
3.  If A = (1/0.4) + (1/0.04) + (1/0.004) + ..... upto 8
th
 
terms, then what is the value of A ?  
  Ùeefo A = (1/0.4) + (1/0.04) + (1/0.004) + .....8
th
 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) 27272727.5 (b) 25252525.5 
 (c) 27777777.5 (d) 25555555.5 
4.  If M = 0.1 + (0.1)
2
 + (0.01)
2
 and N = 0.3 + (0.03)
2
 
+ (0.003)
2
, then what is the value of M + N?  
  Ùeefo M = 0.1 + (0.1)
2
 + (0.01)
2
 leLee N = 0.3 + 
(0.03)
2
 + (0.003)
2
 nQ, lees M + N keâe ceeve keäÙee nw? 
 (a) 0.411009 (b) 0.413131 
 (c) 0.313131 (d) 0.131313 
5.  If 
96 97
P = , Q =
95× 97 96× 98
and
1
R = ,
97
then 
which of the following is TRUE ?  
  Ùeefo 
96 97
P = , Q =
95× 97 96× 98
 leLee 
1
R =
97
 nQ, 
lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) P < Q < R (b) R < Q < P 
 (c) Q < P < R (d) R < P < Q 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
1 3 1 1 439
11 + 17 - 5 - 2 =
2 4 5 10 20
 
  II. 
9 11 12
> >
1078 1127 1219
 
  III. 
149 153 157
> >
151 155 159
 
 (a) Only I/keâsJeue I   
 (b) Only II/kesâJeue II   
 (c) Only III/kesâJeue III 
 (d) None is true/keâesF& melÙe veneR nw  
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
2 3 5
< <
3 5 2 5 4 3
 
  II. 
3 2 7
< <
2 5 3 3 4 5
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
8.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. The total number of positive factors of 72 is 
12./72 kesâ kegâue 12 Oeveelcekeâ iegCeveKeC[ nQ~ 
  II. The sum of first 20 odd numbers is 400./ØeLece 
20 efJe<ece mebKÙeeDeeW keâe Ùeesie 400 nw~ 
  III. Largest two digit prime number is 97./oes 
DebkeâeW keâer meyemes yeÌ[er DeYeepÙe mebKÙee 97 nw~ 
 (a) Only I and III/kesâJeue I leLee II  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All are true/meYeer melÙe nQ 
9.  If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N 
= (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then 
what is the value of M/N ?  
  Ùeefo M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) leLee 
N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), nQ, 
lees M/N keâe ceeve keäÙee nw? 
 (a) 207/560  (b) 339/1120 
 (c) 113/350 (d) 69/175 
10.  M is the largest 4 digit number, which when 
divided by 4, 5, 6 and 7 leaves remainder as 2, 
3, 4 and 5 respectively. What will be the 
remainder when M is divided by 9 ?  
  M, 4 DebkeâeW keâer meyemes yeÌ[er mebKÙee nw, efpemes 4, 5, 6 
leLee 7 mes efJeYeeefpele keâjves hej Mes<eHeâue ›eâceMe: 2,3,4 
leLee 5 Deelee nw~ peye M keâes 9 mes efJeYeeefpele efkeâÙee 
peeÙes, lees Mes<eHeâue keäÙee nesiee? 
 
 (a) 2 (b) 1  
 (c) 3 (d) 6 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 11 + 7 < 10 + 8 
  II. 17 + 11 < 15 + 13 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
12.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
4 3
12 > 16 > 24 
  II. 
3 6 4
25 > 32 > 48 
  III. 
6 3 4
9 > 15 > 24 
 (a) Only I and II/kesâJeue I leLee II  
 (b) Only I and III/kesâJeue I leLee III  
 (c) Only I/kesâJeue I 
 (d) All are true/meYeer melÙe nQ 
13.  If x + y + z = 22 and xy + yz + zx = 35, then 
what is the value of (x–y)
2
 + (y–z)
2
 + (z–x)
2
 ?  
  Ùeefo x + y + z = 22 leLee xy + yz + zx = 35 nQ, lees 
(x–y)
2
 + (y–z)
2
 + (z–x)
2
 keâe ceeve keäÙee nw? 
 (a) 793 (b) 681 
 (c) 758 (d) 715 
14.  If (x+y)/z = 2, then what is the value of [y/(y–z)] 
+ [x/(x–z)] ?  
  Ùeefo (x+y)/z = 2 nw, lees [y/(y–z)] + [x/(x–z)] keâe 
ceeve keäÙee nw? 
 (a) 0 (b) 1 
 (c) 2 (d) –1 
15.  If a and ß are the roots of equation x
2
–2x+4=0, 
then what is the equation whose roots are a
3
/ß
2
 
and ß
3
/a
2
 ?   
  Ùeefo a leLee ß meceerkeâjCe x
2
–2x+4=0 kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
3
/ß
2
 leLee ß
3
/a
2 
nQ? 
 (a) x
2
 – 4x + 8 = 0  
 (b) x
2
 – 32 x + 4 = 0 
 (c) x
2
 – 2x + 4 = 0 
 (d) x
2
 – 16x + 4 = 0 
16.  If one root of the equation Ax
2
 + Bx + C = 0 is 
two and a half times the others, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 + Bx + C = 0 keâe Skeâ cetue otmejs mes 
{eF& iegCee nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) 7B
2
 = 3 CA  (b) 7B
2
 = 4  CA 
 (c) 7B
2
 = 36 CA (d) 10B
2
 = 49 CA 
17.  If x
2
 – 12x + 33 = 0, then what is the value of  
(x–4)
2
 + [1/(x–4)
2
] ?  
  Ùeefo x
2
 – 12x + 33 = 0 nw, lees (x–4)
2
 + [1/(x–4)
2
] 
keâe ceeve keäÙee nw? 
 (a) 16 (b) 14  
 (c) 18 (d) 20 
18.  If a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1), then what is the 
value of a
4 
+ b
4
 ?  
  Ùeefo a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1) nw, lees a
4 
+ b
4
 keâe 
ceeve keäÙee nw? 
 (a) 2 (b) 16  
 (c) 32 (d) 64 
19.  If 
1 - a a
3 + 9 = 19 - 3
a 1 - a
then what is the 
value of a ? 
  Ùeefo 
1 - a a
3 + 9 = 19 - 3
a 1 - a
 nw, lees a keâe ceeve 
keäÙee nw? 
 (a) 3/10, 7/10  (b) 1/10, 9/10 
 (c) 2/5, 3/5 (d) 1/5, 4/5 
20.  If a + b = 10 and 
a b
- 13 = - - 11
b a
, then what 
is the value of 3ab + 4a
2
 + 5b
2
 ? 
  Ùeefo a + b = 10 leLee
a b
- 13 = - - 11
b a
 nQ, lees 3ab 
+ 4a
2
 + 5b
2
 keâe ceeve keäÙee nw? 
 (a) 450 (b) 300 
 (c) 600 (d) 750 
21.  If 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 23 
and 5x + 9y + 6z – 4 = 18, then what is the value 
of x + y + z – 34 ?  
  Ùeefo 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 
23 leLee 5x + 9y + 6z – 4 = 18 nQ, lees x + y + z – 34 
keâe ceeve keäÙee nw? 
 (a) –28 (b) –14 
 (c) –31 (d) –45 
22.  If ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
and 
( )
1
x + y + z + 2z = 9
7
, then what is the value of 
46x + 131y ?  
  Ùeefo ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
leLee 
( )
1
x + y + z + 2z = 9
7
nQ, lees 46x+131y keâe ceeve 
keäÙee nw? 
 (a) 414 (b) 364 
 (c) 384 (d) 464 
23.  In the given figure, in triangle STU, ST = 8cm, 
TU = 9 cm and SU = 12 cm. QU = 24 cm, SR 
=32 cm and PT = 27 cm. What is the ratio of 
the area of triangle PQU and area of triangle 
PTR?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe STU ceW, ST = 8 mes.ceer., 
TU = 9 mes.ceer. leLee SU = 12 mes.ceer. nQ~ QU = 24 
mes.ceer., SR = 32 mes.ceer. leLee PT = 27 mes.ceer. nQ~ ef$eYegpe 
PQU kesâ #es$eHeâue leLee ef$eYegpe PTR kesâ #es$eHeâue mes 
keäÙee Devegheele nw? 
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 20-2-2018] [Time : 10 AM to 12 PM 
1.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 33
3
 > 3
33
 
  II. 333 > (3
3
)
3
 
 (a) Only I/kesâJeue I    
 (b) Only II/kesâJeue II 
 (c) Both I and II/ I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
2.  If P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2
 and Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, then what is the value of P–Q ?  
  Ùeefo P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2 
leLee Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, nQ, lees P–Q keâe ceeve keäÙee nw? 
 (a) 24645 (b) 26075 
 (c) 29317 (d) 31515 
3.  If A = (1/0.4) + (1/0.04) + (1/0.004) + ..... upto 8
th
 
terms, then what is the value of A ?  
  Ùeefo A = (1/0.4) + (1/0.04) + (1/0.004) + .....8
th
 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) 27272727.5 (b) 25252525.5 
 (c) 27777777.5 (d) 25555555.5 
4.  If M = 0.1 + (0.1)
2
 + (0.01)
2
 and N = 0.3 + (0.03)
2
 
+ (0.003)
2
, then what is the value of M + N?  
  Ùeefo M = 0.1 + (0.1)
2
 + (0.01)
2
 leLee N = 0.3 + 
(0.03)
2
 + (0.003)
2
 nQ, lees M + N keâe ceeve keäÙee nw? 
 (a) 0.411009 (b) 0.413131 
 (c) 0.313131 (d) 0.131313 
5.  If 
96 97
P = , Q =
95× 97 96× 98
and
1
R = ,
97
then 
which of the following is TRUE ?  
  Ùeefo 
96 97
P = , Q =
95× 97 96× 98
 leLee 
1
R =
97
 nQ, 
lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) P < Q < R (b) R < Q < P 
 (c) Q < P < R (d) R < P < Q 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
1 3 1 1 439
11 + 17 - 5 - 2 =
2 4 5 10 20
 
  II. 
9 11 12
> >
1078 1127 1219
 
  III. 
149 153 157
> >
151 155 159
 
 (a) Only I/keâsJeue I   
 (b) Only II/kesâJeue II   
 (c) Only III/kesâJeue III 
 (d) None is true/keâesF& melÙe veneR nw  
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
2 3 5
< <
3 5 2 5 4 3
 
  II. 
3 2 7
< <
2 5 3 3 4 5
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
8.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. The total number of positive factors of 72 is 
12./72 kesâ kegâue 12 Oeveelcekeâ iegCeveKeC[ nQ~ 
  II. The sum of first 20 odd numbers is 400./ØeLece 
20 efJe<ece mebKÙeeDeeW keâe Ùeesie 400 nw~ 
  III. Largest two digit prime number is 97./oes 
DebkeâeW keâer meyemes yeÌ[er DeYeepÙe mebKÙee 97 nw~ 
 (a) Only I and III/kesâJeue I leLee II  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All are true/meYeer melÙe nQ 
9.  If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N 
= (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then 
what is the value of M/N ?  
  Ùeefo M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) leLee 
N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), nQ, 
lees M/N keâe ceeve keäÙee nw? 
 (a) 207/560  (b) 339/1120 
 (c) 113/350 (d) 69/175 
10.  M is the largest 4 digit number, which when 
divided by 4, 5, 6 and 7 leaves remainder as 2, 
3, 4 and 5 respectively. What will be the 
remainder when M is divided by 9 ?  
  M, 4 DebkeâeW keâer meyemes yeÌ[er mebKÙee nw, efpemes 4, 5, 6 
leLee 7 mes efJeYeeefpele keâjves hej Mes<eHeâue ›eâceMe: 2,3,4 
leLee 5 Deelee nw~ peye M keâes 9 mes efJeYeeefpele efkeâÙee 
peeÙes, lees Mes<eHeâue keäÙee nesiee? 
 
 (a) 2 (b) 1  
 (c) 3 (d) 6 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 11 + 7 < 10 + 8 
  II. 17 + 11 < 15 + 13 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
12.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
4 3
12 > 16 > 24 
  II. 
3 6 4
25 > 32 > 48 
  III. 
6 3 4
9 > 15 > 24 
 (a) Only I and II/kesâJeue I leLee II  
 (b) Only I and III/kesâJeue I leLee III  
 (c) Only I/kesâJeue I 
 (d) All are true/meYeer melÙe nQ 
13.  If x + y + z = 22 and xy + yz + zx = 35, then 
what is the value of (x–y)
2
 + (y–z)
2
 + (z–x)
2
 ?  
  Ùeefo x + y + z = 22 leLee xy + yz + zx = 35 nQ, lees 
(x–y)
2
 + (y–z)
2
 + (z–x)
2
 keâe ceeve keäÙee nw? 
 (a) 793 (b) 681 
 (c) 758 (d) 715 
14.  If (x+y)/z = 2, then what is the value of [y/(y–z)] 
+ [x/(x–z)] ?  
  Ùeefo (x+y)/z = 2 nw, lees [y/(y–z)] + [x/(x–z)] keâe 
ceeve keäÙee nw? 
 (a) 0 (b) 1 
 (c) 2 (d) –1 
15.  If a and ß are the roots of equation x
2
–2x+4=0, 
then what is the equation whose roots are a
3
/ß
2
 
and ß
3
/a
2
 ?   
  Ùeefo a leLee ß meceerkeâjCe x
2
–2x+4=0 kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
3
/ß
2
 leLee ß
3
/a
2 
nQ? 
 (a) x
2
 – 4x + 8 = 0  
 (b) x
2
 – 32 x + 4 = 0 
 (c) x
2
 – 2x + 4 = 0 
 (d) x
2
 – 16x + 4 = 0 
16.  If one root of the equation Ax
2
 + Bx + C = 0 is 
two and a half times the others, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 + Bx + C = 0 keâe Skeâ cetue otmejs mes 
{eF& iegCee nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) 7B
2
 = 3 CA  (b) 7B
2
 = 4  CA 
 (c) 7B
2
 = 36 CA (d) 10B
2
 = 49 CA 
17.  If x
2
 – 12x + 33 = 0, then what is the value of  
(x–4)
2
 + [1/(x–4)
2
] ?  
  Ùeefo x
2
 – 12x + 33 = 0 nw, lees (x–4)
2
 + [1/(x–4)
2
] 
keâe ceeve keäÙee nw? 
 (a) 16 (b) 14  
 (c) 18 (d) 20 
18.  If a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1), then what is the 
value of a
4 
+ b
4
 ?  
  Ùeefo a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1) nw, lees a
4 
+ b
4
 keâe 
ceeve keäÙee nw? 
 (a) 2 (b) 16  
 (c) 32 (d) 64 
19.  If 
1 - a a
3 + 9 = 19 - 3
a 1 - a
then what is the 
value of a ? 
  Ùeefo 
1 - a a
3 + 9 = 19 - 3
a 1 - a
 nw, lees a keâe ceeve 
keäÙee nw? 
 (a) 3/10, 7/10  (b) 1/10, 9/10 
 (c) 2/5, 3/5 (d) 1/5, 4/5 
20.  If a + b = 10 and 
a b
- 13 = - - 11
b a
, then what 
is the value of 3ab + 4a
2
 + 5b
2
 ? 
  Ùeefo a + b = 10 leLee
a b
- 13 = - - 11
b a
 nQ, lees 3ab 
+ 4a
2
 + 5b
2
 keâe ceeve keäÙee nw? 
 (a) 450 (b) 300 
 (c) 600 (d) 750 
21.  If 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 23 
and 5x + 9y + 6z – 4 = 18, then what is the value 
of x + y + z – 34 ?  
  Ùeefo 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 
23 leLee 5x + 9y + 6z – 4 = 18 nQ, lees x + y + z – 34 
keâe ceeve keäÙee nw? 
 (a) –28 (b) –14 
 (c) –31 (d) –45 
22.  If ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
and 
( )
1
x + y + z + 2z = 9
7
, then what is the value of 
46x + 131y ?  
  Ùeefo ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
leLee 
( )
1
x + y + z + 2z = 9
7
nQ, lees 46x+131y keâe ceeve 
keäÙee nw? 
 (a) 414 (b) 364 
 (c) 384 (d) 464 
23.  In the given figure, in triangle STU, ST = 8cm, 
TU = 9 cm and SU = 12 cm. QU = 24 cm, SR 
=32 cm and PT = 27 cm. What is the ratio of 
the area of triangle PQU and area of triangle 
PTR?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe STU ceW, ST = 8 mes.ceer., 
TU = 9 mes.ceer. leLee SU = 12 mes.ceer. nQ~ QU = 24 
mes.ceer., SR = 32 mes.ceer. leLee PT = 27 mes.ceer. nQ~ ef$eYegpe 
PQU kesâ #es$eHeâue leLee ef$eYegpe PTR kesâ #es$eHeâue mes 
keäÙee Devegheele nw? 
 
 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 5 : 2  
24.  In triangle XYZ, G is the centroid. If XY = 11 
cm, YZ = 14 cm and XZ = 7 cm, then what is 
the value (in cm) of GM ?  
  ef$eYegpe XYZ ceW, G kesâvõkeâ nw~ Ùeefo XY = 11 mes.ceer., 
YZ = 14 mes.ceer. leLee XZ = 7 mes.ceer. nQ, lees GM keâe 
ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 6 (b) 4  
 (c) 2 (d) 3 
25.  In the given figure, PQRS is a square inscribed 
in a circle of radius 4cm. PQ is produced till 
point Y. From Y a tangent is drawn to the 
circle at point R. What is the length (in cm) of 
SY ?  
  oer ieF& Deeke=âefle ceW, PQRS, 4 mes.ceer. ef$epÙee Jeeues 
Skeâ Je=òe ceW Debefkeâle Skeâ Jeie& nw~ PQ keâes efyevog Y 
lekeâ yeÌ{eÙee ieÙee nw~ Je=òe hej Y mes efyevog R hej Skeâ 
mheMe& jsKee KeeRÛeer ieÙeer nw~ SY keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw?  
 
 (a) 4 10 (b) 2 10 
 (c) 6 10 (d) 3 5 
26.  In a trapezium, one diagonal divides the other 
in the ratio 2 : 9. If the length of the larger of 
the two parallel sides is 45 cm, then what is the 
length (in cm) of the other parallel side ?  
  Skeâ meceuecye ceW, Skeâ efJekeâCe& otmejs efJekeâCe& keâes 2:9 kesâ 
Devegheele ceW efJeYeeefpele keâjlee nw~ Ùeefo oes meceeblej 
YegpeeDeeW ceW mes meyemes yeÌ[er Yegpee keâer uecyeeF& 45 mes.ceer. 
nQ, lees otmejer meceeblej Yegpee keâer uecyeeF& (mes.ceer. ceW) keäÙee 
nw? 
 (a) 10 (b) 5  
 (c) 18 (d) 14 
27.  In the given figure, CD and AB are diameters 
of circles and AB and CD are perpendicular to 
each other. LQ and SR are perpendiculars to 
AB and CD respectively. Radius of circle is 5 
cm, PB : PA = 2 : 3 and CN : ND = 2 : 3. What 
is the length (in cm) of SM ?  
  oer ieF& Deeke=âefle ceW, CD leLee AB Je=òe kesâ JÙeeme nQ leLee 
AB leLee CD Skeâ otmejs hej uecye nQ~ LQ leLee SR 
›eâceMe: AB leLee CD hej uecye nQ~ Je==òe keâer ef$epÙee 5 
mes.ceer. nQ, PB : PA =  2 : 3 leLee CN : ND = 2 : 3 nQ~ 
SM keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 
 (a) 
( )
5 3 3
? ?
-
? ?
 (b) 
( )
4 3 2
? ?
-
? ?
 
 (c) 
( )
2 5 1
? ?
-
? ?
 (d) 
( )
2 6 1
? ?
-
? ?
 
28.  In the given figure, PQRS is a square of side 20 
cm and SR is extended to point T. If the length 
of QT is 25 cm, then what is the distance (in 
cm) between the centres O
1
 and O
2
 of the two 
circles?  
  oer ieF& Deeke=âefle ceW, PQRS, 20 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw leLee SR keâes efyevog T lekeâ yeÌ{eÙee ieÙee nw~ Ùeefo 
QT keâer uecyeeF& 25 mes.ceer. nw, lees oesveeW Je=òeeW kesâ kesâvõ 
O
1
 leLee O
2 
kesâ ceOÙe keâer otjer (mes.ceer. ceW) keäÙee nw? 
 
 (a) 5 10 (b) 4 10 
 (c) 8 5 (d) 16 2 
29.  In the given figure, MNOP is a square of side 6 
cm. What is the value (in cm) of radius of 
circle?  
  oer ieF& Deeke=âefle ceW, MNOP, 6 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw~ Je=òe keâer ef$epÙee keâe ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 4.25 (b) 3.75 
 (c) 3.5 (d) 4.55 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 20-2-2018] [Time : 10 AM to 12 PM 
1.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 33
3
 > 3
33
 
  II. 333 > (3
3
)
3
 
 (a) Only I/kesâJeue I    
 (b) Only II/kesâJeue II 
 (c) Both I and II/ I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
2.  If P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2
 and Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, then what is the value of P–Q ?  
  Ùeefo P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2 
leLee Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, nQ, lees P–Q keâe ceeve keäÙee nw? 
 (a) 24645 (b) 26075 
 (c) 29317 (d) 31515 
3.  If A = (1/0.4) + (1/0.04) + (1/0.004) + ..... upto 8
th
 
terms, then what is the value of A ?  
  Ùeefo A = (1/0.4) + (1/0.04) + (1/0.004) + .....8
th
 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) 27272727.5 (b) 25252525.5 
 (c) 27777777.5 (d) 25555555.5 
4.  If M = 0.1 + (0.1)
2
 + (0.01)
2
 and N = 0.3 + (0.03)
2
 
+ (0.003)
2
, then what is the value of M + N?  
  Ùeefo M = 0.1 + (0.1)
2
 + (0.01)
2
 leLee N = 0.3 + 
(0.03)
2
 + (0.003)
2
 nQ, lees M + N keâe ceeve keäÙee nw? 
 (a) 0.411009 (b) 0.413131 
 (c) 0.313131 (d) 0.131313 
5.  If 
96 97
P = , Q =
95× 97 96× 98
and
1
R = ,
97
then 
which of the following is TRUE ?  
  Ùeefo 
96 97
P = , Q =
95× 97 96× 98
 leLee 
1
R =
97
 nQ, 
lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) P < Q < R (b) R < Q < P 
 (c) Q < P < R (d) R < P < Q 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
1 3 1 1 439
11 + 17 - 5 - 2 =
2 4 5 10 20
 
  II. 
9 11 12
> >
1078 1127 1219
 
  III. 
149 153 157
> >
151 155 159
 
 (a) Only I/keâsJeue I   
 (b) Only II/kesâJeue II   
 (c) Only III/kesâJeue III 
 (d) None is true/keâesF& melÙe veneR nw  
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
2 3 5
< <
3 5 2 5 4 3
 
  II. 
3 2 7
< <
2 5 3 3 4 5
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
8.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. The total number of positive factors of 72 is 
12./72 kesâ kegâue 12 Oeveelcekeâ iegCeveKeC[ nQ~ 
  II. The sum of first 20 odd numbers is 400./ØeLece 
20 efJe<ece mebKÙeeDeeW keâe Ùeesie 400 nw~ 
  III. Largest two digit prime number is 97./oes 
DebkeâeW keâer meyemes yeÌ[er DeYeepÙe mebKÙee 97 nw~ 
 (a) Only I and III/kesâJeue I leLee II  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All are true/meYeer melÙe nQ 
9.  If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N 
= (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then 
what is the value of M/N ?  
  Ùeefo M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) leLee 
N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), nQ, 
lees M/N keâe ceeve keäÙee nw? 
 (a) 207/560  (b) 339/1120 
 (c) 113/350 (d) 69/175 
10.  M is the largest 4 digit number, which when 
divided by 4, 5, 6 and 7 leaves remainder as 2, 
3, 4 and 5 respectively. What will be the 
remainder when M is divided by 9 ?  
  M, 4 DebkeâeW keâer meyemes yeÌ[er mebKÙee nw, efpemes 4, 5, 6 
leLee 7 mes efJeYeeefpele keâjves hej Mes<eHeâue ›eâceMe: 2,3,4 
leLee 5 Deelee nw~ peye M keâes 9 mes efJeYeeefpele efkeâÙee 
peeÙes, lees Mes<eHeâue keäÙee nesiee? 
 
 (a) 2 (b) 1  
 (c) 3 (d) 6 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 11 + 7 < 10 + 8 
  II. 17 + 11 < 15 + 13 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
12.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
4 3
12 > 16 > 24 
  II. 
3 6 4
25 > 32 > 48 
  III. 
6 3 4
9 > 15 > 24 
 (a) Only I and II/kesâJeue I leLee II  
 (b) Only I and III/kesâJeue I leLee III  
 (c) Only I/kesâJeue I 
 (d) All are true/meYeer melÙe nQ 
13.  If x + y + z = 22 and xy + yz + zx = 35, then 
what is the value of (x–y)
2
 + (y–z)
2
 + (z–x)
2
 ?  
  Ùeefo x + y + z = 22 leLee xy + yz + zx = 35 nQ, lees 
(x–y)
2
 + (y–z)
2
 + (z–x)
2
 keâe ceeve keäÙee nw? 
 (a) 793 (b) 681 
 (c) 758 (d) 715 
14.  If (x+y)/z = 2, then what is the value of [y/(y–z)] 
+ [x/(x–z)] ?  
  Ùeefo (x+y)/z = 2 nw, lees [y/(y–z)] + [x/(x–z)] keâe 
ceeve keäÙee nw? 
 (a) 0 (b) 1 
 (c) 2 (d) –1 
15.  If a and ß are the roots of equation x
2
–2x+4=0, 
then what is the equation whose roots are a
3
/ß
2
 
and ß
3
/a
2
 ?   
  Ùeefo a leLee ß meceerkeâjCe x
2
–2x+4=0 kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
3
/ß
2
 leLee ß
3
/a
2 
nQ? 
 (a) x
2
 – 4x + 8 = 0  
 (b) x
2
 – 32 x + 4 = 0 
 (c) x
2
 – 2x + 4 = 0 
 (d) x
2
 – 16x + 4 = 0 
16.  If one root of the equation Ax
2
 + Bx + C = 0 is 
two and a half times the others, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 + Bx + C = 0 keâe Skeâ cetue otmejs mes 
{eF& iegCee nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) 7B
2
 = 3 CA  (b) 7B
2
 = 4  CA 
 (c) 7B
2
 = 36 CA (d) 10B
2
 = 49 CA 
17.  If x
2
 – 12x + 33 = 0, then what is the value of  
(x–4)
2
 + [1/(x–4)
2
] ?  
  Ùeefo x
2
 – 12x + 33 = 0 nw, lees (x–4)
2
 + [1/(x–4)
2
] 
keâe ceeve keäÙee nw? 
 (a) 16 (b) 14  
 (c) 18 (d) 20 
18.  If a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1), then what is the 
value of a
4 
+ b
4
 ?  
  Ùeefo a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1) nw, lees a
4 
+ b
4
 keâe 
ceeve keäÙee nw? 
 (a) 2 (b) 16  
 (c) 32 (d) 64 
19.  If 
1 - a a
3 + 9 = 19 - 3
a 1 - a
then what is the 
value of a ? 
  Ùeefo 
1 - a a
3 + 9 = 19 - 3
a 1 - a
 nw, lees a keâe ceeve 
keäÙee nw? 
 (a) 3/10, 7/10  (b) 1/10, 9/10 
 (c) 2/5, 3/5 (d) 1/5, 4/5 
20.  If a + b = 10 and 
a b
- 13 = - - 11
b a
, then what 
is the value of 3ab + 4a
2
 + 5b
2
 ? 
  Ùeefo a + b = 10 leLee
a b
- 13 = - - 11
b a
 nQ, lees 3ab 
+ 4a
2
 + 5b
2
 keâe ceeve keäÙee nw? 
 (a) 450 (b) 300 
 (c) 600 (d) 750 
21.  If 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 23 
and 5x + 9y + 6z – 4 = 18, then what is the value 
of x + y + z – 34 ?  
  Ùeefo 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 
23 leLee 5x + 9y + 6z – 4 = 18 nQ, lees x + y + z – 34 
keâe ceeve keäÙee nw? 
 (a) –28 (b) –14 
 (c) –31 (d) –45 
22.  If ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
and 
( )
1
x + y + z + 2z = 9
7
, then what is the value of 
46x + 131y ?  
  Ùeefo ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
leLee 
( )
1
x + y + z + 2z = 9
7
nQ, lees 46x+131y keâe ceeve 
keäÙee nw? 
 (a) 414 (b) 364 
 (c) 384 (d) 464 
23.  In the given figure, in triangle STU, ST = 8cm, 
TU = 9 cm and SU = 12 cm. QU = 24 cm, SR 
=32 cm and PT = 27 cm. What is the ratio of 
the area of triangle PQU and area of triangle 
PTR?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe STU ceW, ST = 8 mes.ceer., 
TU = 9 mes.ceer. leLee SU = 12 mes.ceer. nQ~ QU = 24 
mes.ceer., SR = 32 mes.ceer. leLee PT = 27 mes.ceer. nQ~ ef$eYegpe 
PQU kesâ #es$eHeâue leLee ef$eYegpe PTR kesâ #es$eHeâue mes 
keäÙee Devegheele nw? 
 
 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 5 : 2  
24.  In triangle XYZ, G is the centroid. If XY = 11 
cm, YZ = 14 cm and XZ = 7 cm, then what is 
the value (in cm) of GM ?  
  ef$eYegpe XYZ ceW, G kesâvõkeâ nw~ Ùeefo XY = 11 mes.ceer., 
YZ = 14 mes.ceer. leLee XZ = 7 mes.ceer. nQ, lees GM keâe 
ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 6 (b) 4  
 (c) 2 (d) 3 
25.  In the given figure, PQRS is a square inscribed 
in a circle of radius 4cm. PQ is produced till 
point Y. From Y a tangent is drawn to the 
circle at point R. What is the length (in cm) of 
SY ?  
  oer ieF& Deeke=âefle ceW, PQRS, 4 mes.ceer. ef$epÙee Jeeues 
Skeâ Je=òe ceW Debefkeâle Skeâ Jeie& nw~ PQ keâes efyevog Y 
lekeâ yeÌ{eÙee ieÙee nw~ Je=òe hej Y mes efyevog R hej Skeâ 
mheMe& jsKee KeeRÛeer ieÙeer nw~ SY keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw?  
 
 (a) 4 10 (b) 2 10 
 (c) 6 10 (d) 3 5 
26.  In a trapezium, one diagonal divides the other 
in the ratio 2 : 9. If the length of the larger of 
the two parallel sides is 45 cm, then what is the 
length (in cm) of the other parallel side ?  
  Skeâ meceuecye ceW, Skeâ efJekeâCe& otmejs efJekeâCe& keâes 2:9 kesâ 
Devegheele ceW efJeYeeefpele keâjlee nw~ Ùeefo oes meceeblej 
YegpeeDeeW ceW mes meyemes yeÌ[er Yegpee keâer uecyeeF& 45 mes.ceer. 
nQ, lees otmejer meceeblej Yegpee keâer uecyeeF& (mes.ceer. ceW) keäÙee 
nw? 
 (a) 10 (b) 5  
 (c) 18 (d) 14 
27.  In the given figure, CD and AB are diameters 
of circles and AB and CD are perpendicular to 
each other. LQ and SR are perpendiculars to 
AB and CD respectively. Radius of circle is 5 
cm, PB : PA = 2 : 3 and CN : ND = 2 : 3. What 
is the length (in cm) of SM ?  
  oer ieF& Deeke=âefle ceW, CD leLee AB Je=òe kesâ JÙeeme nQ leLee 
AB leLee CD Skeâ otmejs hej uecye nQ~ LQ leLee SR 
›eâceMe: AB leLee CD hej uecye nQ~ Je==òe keâer ef$epÙee 5 
mes.ceer. nQ, PB : PA =  2 : 3 leLee CN : ND = 2 : 3 nQ~ 
SM keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 
 (a) 
( )
5 3 3
? ?
-
? ?
 (b) 
( )
4 3 2
? ?
-
? ?
 
 (c) 
( )
2 5 1
? ?
-
? ?
 (d) 
( )
2 6 1
? ?
-
? ?
 
28.  In the given figure, PQRS is a square of side 20 
cm and SR is extended to point T. If the length 
of QT is 25 cm, then what is the distance (in 
cm) between the centres O
1
 and O
2
 of the two 
circles?  
  oer ieF& Deeke=âefle ceW, PQRS, 20 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw leLee SR keâes efyevog T lekeâ yeÌ{eÙee ieÙee nw~ Ùeefo 
QT keâer uecyeeF& 25 mes.ceer. nw, lees oesveeW Je=òeeW kesâ kesâvõ 
O
1
 leLee O
2 
kesâ ceOÙe keâer otjer (mes.ceer. ceW) keäÙee nw? 
 
 (a) 5 10 (b) 4 10 
 (c) 8 5 (d) 16 2 
29.  In the given figure, MNOP is a square of side 6 
cm. What is the value (in cm) of radius of 
circle?  
  oer ieF& Deeke=âefle ceW, MNOP, 6 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw~ Je=òe keâer ef$epÙee keâe ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 4.25 (b) 3.75 
 (c) 3.5 (d) 4.55 
 
30.  In the given figure, triangle PQR is a right 
angled triangle at Q. If PQ = 35 cm and QS = 
28 cm, then what is the value (in cm) of SR ?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe PQR, Q hej Skeâ mecekeâesCe 
ef$eYegpe nQ~ Ùeefo PQ = 35 mes.ceer. leLee QS = 28 mes.ceer. 
nQ, lees SR keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 35.33 (b) 37.33 
 (c) 41.33 (d) 43.33 
31.  In the given figure, P is the centre of the circle. 
If QS = PR, then what is the ratio of ?RSP to 
the ?TPR ?  
  oer ieF& Deeke=âefle ceW, P Je=òe keâe kesâvõ nw~ Ùeefo QS = PR 
nes, lees ?RSP keâe  ?TPR mes keäÙee Devegheele nw? 
 
 (a) 1 : 4  (b) 2 : 5 
 (c) 1 : 3 (d) 2 : 7 
32.  The distance between the centres of two cicles 
is 61 cm and their radii are 35 cm and 24 cm. 
What is the length (in cm) of the direct 
common tangent to the circles ?  
  oes Je=òeeW kessâ kesâvõeW kesâ ceOÙe keâer otjer 61 mes.ceer. nw leLee 
Gvekeâer ef$epÙeeSB 35 mes.ceer. leLee 24 mes.ceer. nQ~ Je=òeeW keâer 
GYeÙeefve<" DevegmheMe& jsKee keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 60 (b) 54  
 (c) 48 (d) 72 
33.  In the given figure, PQRS is a quadrilateral. If 
QR = 18 cm and PS = 9 cm, then what is the 
area (in cm
2
) of quadrilateral PQRS ?  
  oer ieF& Deeke=âefle ceW, PQRS Skeâ ÛelegYeg&pe nw~ Ùeefo QR = 
18 mes.ceer. leLee PS = 9 mes.ceer. nQ, lees ÛelegYeg&pe PQRS 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 
( )
64 3 / 3  (b) 
( )
177 3 / 2 
 (c) 
( )
135 3 / 2 (d) 
( )
98 3 / 3 
34.  PQR is a triangle, whose area is 180 cm
2
. S is a 
point on side QR, such that PS is the angle 
bisector of ?QPR. If PQ : PR = 2 : 3, then what 
is the area ( in cm
2
) triangle PSR ?   
  PQR Skeâ ef$eYegpe nw, efpemekeâe #es$eHeâue 180 mes.ceer.
2
 nw~ 
S, Yegpee QR hej Skeâ efyevog Fme Øekeâej nw efkeâ PS, 
?QPR hej keâesCe efÉYeepekeâ nw~ Ùeefo PQ : PR = 2 : 3 
nw, lees ef$eYegpe PSR keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 90 (b) 108  
 (c) 144 (d) 72 
35.  In the given figure, ABCD is a square. EFGH is 
a square formed by joining mid points of sides 
of ABCD. LMNO is a square formed by joining 
mid points of sides of EFGH. A circle is 
inscribed inside LMNO. If area of circle is 38.5 
cm
2
, then what is the area (in cm
2
) of square 
ABCD ?   
  oer ieF& Deeke=âefle ceW, ABCD Skeâ Jeie& nw~ ABCD keâer 
YegpeeDeeW kesâ kesâvõ efyevogDeeW keâes peesÌ[keâj Skeâ Jeie& 
EFGH yeveeÙee ieÙee nw~ EFGH keâer YegpeeDeeW kesâ kesâvõ 
efyevogDeeW keâes peesÌ[keâj Skeâ Jeie& LMNO yeveeÙee ieÙee nw~ 
Skeâ Je=òe keâes Jeie& LMNO ceW Debefkeâle efkeâÙee ieÙee nw~ 
Ùeefo Je=òe keâe #es$eHeâue 38.5 mes.ceer.
2
 nw, lees Jeie& ABCD 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 98 (b) 196  
 (c) 122.5 (d) 171.5 
36.  ABCDEF is a regular hexagon of side 12 cm. 
What is the area (in cm
2
) of the triangle ECD ?  
  ABCDEF 12 mes.ceer. Yegpee Jeeuee Skeâ mece <ešdYegpe nw~ 
ef$eYegpe ECD keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 18 3 (b) 24 3 
 (c) 36 3 (d) 42 3 
37.  PQRS is a square whose side is 16 cm. What is 
the value of the side (in cm) of the largest 
octagon that can be cut from the given square ?  
  PQRS, 16 mes.ceer. Yegpee Jeeuee Skeâ Jeie& nw~ efoÙes ieÙes 
Jeie& mes keâešs pee mekeâves Jeeues meyemes yeÌ[s mece De<šYegpe 
keâer Yegpee keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 8 4 2 -  (b) 16 8 2 + 
 (c) 16 2 16 - (d) 16 8 2 - 
38.  In the given figure, PQRS is a rectangle and a 
semicircle with SR as diameter is drawn. A 
circle is drawn as shown in the figure. If QR = 
7 cm, then what is the radius (in cm) of the 
small circle ? 
  oer ieF& Deeke=âefle ceW, PQRS Skeâ DeeÙele nw leLee SR 
JÙeeme Jeeuee Skeâ DeOe&ieesuee yeveeÙee ieÙee nw~ pewmee efkeâ 
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 20-2-2018] [Time : 10 AM to 12 PM 
1.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 33
3
 > 3
33
 
  II. 333 > (3
3
)
3
 
 (a) Only I/kesâJeue I    
 (b) Only II/kesâJeue II 
 (c) Both I and II/ I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
2.  If P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2
 and Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, then what is the value of P–Q ?  
  Ùeefo P = 2
2
 + 6
2
 + 10
2
 + 14
2
 + .... 94
2 
leLee Q = 1
2
 + 
5
2
 + 9
2
 + .... 81
2
, nQ, lees P–Q keâe ceeve keäÙee nw? 
 (a) 24645 (b) 26075 
 (c) 29317 (d) 31515 
3.  If A = (1/0.4) + (1/0.04) + (1/0.004) + ..... upto 8
th
 
terms, then what is the value of A ?  
  Ùeefo A = (1/0.4) + (1/0.04) + (1/0.004) + .....8
th
 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) 27272727.5 (b) 25252525.5 
 (c) 27777777.5 (d) 25555555.5 
4.  If M = 0.1 + (0.1)
2
 + (0.01)
2
 and N = 0.3 + (0.03)
2
 
+ (0.003)
2
, then what is the value of M + N?  
  Ùeefo M = 0.1 + (0.1)
2
 + (0.01)
2
 leLee N = 0.3 + 
(0.03)
2
 + (0.003)
2
 nQ, lees M + N keâe ceeve keäÙee nw? 
 (a) 0.411009 (b) 0.413131 
 (c) 0.313131 (d) 0.131313 
5.  If 
96 97
P = , Q =
95× 97 96× 98
and
1
R = ,
97
then 
which of the following is TRUE ?  
  Ùeefo 
96 97
P = , Q =
95× 97 96× 98
 leLee 
1
R =
97
 nQ, 
lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) P < Q < R (b) R < Q < P 
 (c) Q < P < R (d) R < P < Q 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
1 3 1 1 439
11 + 17 - 5 - 2 =
2 4 5 10 20
 
  II. 
9 11 12
> >
1078 1127 1219
 
  III. 
149 153 157
> >
151 155 159
 
 (a) Only I/keâsJeue I   
 (b) Only II/kesâJeue II   
 (c) Only III/kesâJeue III 
 (d) None is true/keâesF& melÙe veneR nw  
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw? 
  I. 
2 3 5
< <
3 5 2 5 4 3
 
  II. 
3 2 7
< <
2 5 3 3 4 5
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
8.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. The total number of positive factors of 72 is 
12./72 kesâ kegâue 12 Oeveelcekeâ iegCeveKeC[ nQ~ 
  II. The sum of first 20 odd numbers is 400./ØeLece 
20 efJe<ece mebKÙeeDeeW keâe Ùeesie 400 nw~ 
  III. Largest two digit prime number is 97./oes 
DebkeâeW keâer meyemes yeÌ[er DeYeepÙe mebKÙee 97 nw~ 
 (a) Only I and III/kesâJeue I leLee II  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All are true/meYeer melÙe nQ 
9.  If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N 
= (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then 
what is the value of M/N ?  
  Ùeefo M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) leLee 
N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), nQ, 
lees M/N keâe ceeve keäÙee nw? 
 (a) 207/560  (b) 339/1120 
 (c) 113/350 (d) 69/175 
10.  M is the largest 4 digit number, which when 
divided by 4, 5, 6 and 7 leaves remainder as 2, 
3, 4 and 5 respectively. What will be the 
remainder when M is divided by 9 ?  
  M, 4 DebkeâeW keâer meyemes yeÌ[er mebKÙee nw, efpemes 4, 5, 6 
leLee 7 mes efJeYeeefpele keâjves hej Mes<eHeâue ›eâceMe: 2,3,4 
leLee 5 Deelee nw~ peye M keâes 9 mes efJeYeeefpele efkeâÙee 
peeÙes, lees Mes<eHeâue keäÙee nesiee? 
 
 (a) 2 (b) 1  
 (c) 3 (d) 6 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 11 + 7 < 10 + 8 
  II. 17 + 11 < 15 + 13 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
12.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
4 3
12 > 16 > 24 
  II. 
3 6 4
25 > 32 > 48 
  III. 
6 3 4
9 > 15 > 24 
 (a) Only I and II/kesâJeue I leLee II  
 (b) Only I and III/kesâJeue I leLee III  
 (c) Only I/kesâJeue I 
 (d) All are true/meYeer melÙe nQ 
13.  If x + y + z = 22 and xy + yz + zx = 35, then 
what is the value of (x–y)
2
 + (y–z)
2
 + (z–x)
2
 ?  
  Ùeefo x + y + z = 22 leLee xy + yz + zx = 35 nQ, lees 
(x–y)
2
 + (y–z)
2
 + (z–x)
2
 keâe ceeve keäÙee nw? 
 (a) 793 (b) 681 
 (c) 758 (d) 715 
14.  If (x+y)/z = 2, then what is the value of [y/(y–z)] 
+ [x/(x–z)] ?  
  Ùeefo (x+y)/z = 2 nw, lees [y/(y–z)] + [x/(x–z)] keâe 
ceeve keäÙee nw? 
 (a) 0 (b) 1 
 (c) 2 (d) –1 
15.  If a and ß are the roots of equation x
2
–2x+4=0, 
then what is the equation whose roots are a
3
/ß
2
 
and ß
3
/a
2
 ?   
  Ùeefo a leLee ß meceerkeâjCe x
2
–2x+4=0 kesâ cetue nQ, lees Jen 
meceerkeâjCe keäÙee nw efpemekesâ cetue a
3
/ß
2
 leLee ß
3
/a
2 
nQ? 
 (a) x
2
 – 4x + 8 = 0  
 (b) x
2
 – 32 x + 4 = 0 
 (c) x
2
 – 2x + 4 = 0 
 (d) x
2
 – 16x + 4 = 0 
16.  If one root of the equation Ax
2
 + Bx + C = 0 is 
two and a half times the others, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 + Bx + C = 0 keâe Skeâ cetue otmejs mes 
{eF& iegCee nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) 7B
2
 = 3 CA  (b) 7B
2
 = 4  CA 
 (c) 7B
2
 = 36 CA (d) 10B
2
 = 49 CA 
17.  If x
2
 – 12x + 33 = 0, then what is the value of  
(x–4)
2
 + [1/(x–4)
2
] ?  
  Ùeefo x
2
 – 12x + 33 = 0 nw, lees (x–4)
2
 + [1/(x–4)
2
] 
keâe ceeve keäÙee nw? 
 (a) 16 (b) 14  
 (c) 18 (d) 20 
18.  If a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1), then what is the 
value of a
4 
+ b
4
 ?  
  Ùeefo a
4
 + 1 = [a
2
/b
2
] (4b
2
 – b
4
 –1) nw, lees a
4 
+ b
4
 keâe 
ceeve keäÙee nw? 
 (a) 2 (b) 16  
 (c) 32 (d) 64 
19.  If 
1 - a a
3 + 9 = 19 - 3
a 1 - a
then what is the 
value of a ? 
  Ùeefo 
1 - a a
3 + 9 = 19 - 3
a 1 - a
 nw, lees a keâe ceeve 
keäÙee nw? 
 (a) 3/10, 7/10  (b) 1/10, 9/10 
 (c) 2/5, 3/5 (d) 1/5, 4/5 
20.  If a + b = 10 and 
a b
- 13 = - - 11
b a
, then what 
is the value of 3ab + 4a
2
 + 5b
2
 ? 
  Ùeefo a + b = 10 leLee
a b
- 13 = - - 11
b a
 nQ, lees 3ab 
+ 4a
2
 + 5b
2
 keâe ceeve keäÙee nw? 
 (a) 450 (b) 300 
 (c) 600 (d) 750 
21.  If 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 23 
and 5x + 9y + 6z – 4 = 18, then what is the value 
of x + y + z – 34 ?  
  Ùeefo 3x + 4y – 2z + 9 = 17,  7x + 2y + 11z + 8 = 
23 leLee 5x + 9y + 6z – 4 = 18 nQ, lees x + y + z – 34 
keâe ceeve keäÙee nw? 
 (a) –28 (b) –14 
 (c) –31 (d) –45 
22.  If ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
and 
( )
1
x + y + z + 2z = 9
7
, then what is the value of 
46x + 131y ?  
  Ùeefo ( )
2z 2
x + 3y - = 6, x + 2y + 3z = 33
4 3
leLee 
( )
1
x + y + z + 2z = 9
7
nQ, lees 46x+131y keâe ceeve 
keäÙee nw? 
 (a) 414 (b) 364 
 (c) 384 (d) 464 
23.  In the given figure, in triangle STU, ST = 8cm, 
TU = 9 cm and SU = 12 cm. QU = 24 cm, SR 
=32 cm and PT = 27 cm. What is the ratio of 
the area of triangle PQU and area of triangle 
PTR?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe STU ceW, ST = 8 mes.ceer., 
TU = 9 mes.ceer. leLee SU = 12 mes.ceer. nQ~ QU = 24 
mes.ceer., SR = 32 mes.ceer. leLee PT = 27 mes.ceer. nQ~ ef$eYegpe 
PQU kesâ #es$eHeâue leLee ef$eYegpe PTR kesâ #es$eHeâue mes 
keäÙee Devegheele nw? 
 
 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 5 : 2  
24.  In triangle XYZ, G is the centroid. If XY = 11 
cm, YZ = 14 cm and XZ = 7 cm, then what is 
the value (in cm) of GM ?  
  ef$eYegpe XYZ ceW, G kesâvõkeâ nw~ Ùeefo XY = 11 mes.ceer., 
YZ = 14 mes.ceer. leLee XZ = 7 mes.ceer. nQ, lees GM keâe 
ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 6 (b) 4  
 (c) 2 (d) 3 
25.  In the given figure, PQRS is a square inscribed 
in a circle of radius 4cm. PQ is produced till 
point Y. From Y a tangent is drawn to the 
circle at point R. What is the length (in cm) of 
SY ?  
  oer ieF& Deeke=âefle ceW, PQRS, 4 mes.ceer. ef$epÙee Jeeues 
Skeâ Je=òe ceW Debefkeâle Skeâ Jeie& nw~ PQ keâes efyevog Y 
lekeâ yeÌ{eÙee ieÙee nw~ Je=òe hej Y mes efyevog R hej Skeâ 
mheMe& jsKee KeeRÛeer ieÙeer nw~ SY keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw?  
 
 (a) 4 10 (b) 2 10 
 (c) 6 10 (d) 3 5 
26.  In a trapezium, one diagonal divides the other 
in the ratio 2 : 9. If the length of the larger of 
the two parallel sides is 45 cm, then what is the 
length (in cm) of the other parallel side ?  
  Skeâ meceuecye ceW, Skeâ efJekeâCe& otmejs efJekeâCe& keâes 2:9 kesâ 
Devegheele ceW efJeYeeefpele keâjlee nw~ Ùeefo oes meceeblej 
YegpeeDeeW ceW mes meyemes yeÌ[er Yegpee keâer uecyeeF& 45 mes.ceer. 
nQ, lees otmejer meceeblej Yegpee keâer uecyeeF& (mes.ceer. ceW) keäÙee 
nw? 
 (a) 10 (b) 5  
 (c) 18 (d) 14 
27.  In the given figure, CD and AB are diameters 
of circles and AB and CD are perpendicular to 
each other. LQ and SR are perpendiculars to 
AB and CD respectively. Radius of circle is 5 
cm, PB : PA = 2 : 3 and CN : ND = 2 : 3. What 
is the length (in cm) of SM ?  
  oer ieF& Deeke=âefle ceW, CD leLee AB Je=òe kesâ JÙeeme nQ leLee 
AB leLee CD Skeâ otmejs hej uecye nQ~ LQ leLee SR 
›eâceMe: AB leLee CD hej uecye nQ~ Je==òe keâer ef$epÙee 5 
mes.ceer. nQ, PB : PA =  2 : 3 leLee CN : ND = 2 : 3 nQ~ 
SM keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 
 (a) 
( )
5 3 3
? ?
-
? ?
 (b) 
( )
4 3 2
? ?
-
? ?
 
 (c) 
( )
2 5 1
? ?
-
? ?
 (d) 
( )
2 6 1
? ?
-
? ?
 
28.  In the given figure, PQRS is a square of side 20 
cm and SR is extended to point T. If the length 
of QT is 25 cm, then what is the distance (in 
cm) between the centres O
1
 and O
2
 of the two 
circles?  
  oer ieF& Deeke=âefle ceW, PQRS, 20 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw leLee SR keâes efyevog T lekeâ yeÌ{eÙee ieÙee nw~ Ùeefo 
QT keâer uecyeeF& 25 mes.ceer. nw, lees oesveeW Je=òeeW kesâ kesâvõ 
O
1
 leLee O
2 
kesâ ceOÙe keâer otjer (mes.ceer. ceW) keäÙee nw? 
 
 (a) 5 10 (b) 4 10 
 (c) 8 5 (d) 16 2 
29.  In the given figure, MNOP is a square of side 6 
cm. What is the value (in cm) of radius of 
circle?  
  oer ieF& Deeke=âefle ceW, MNOP, 6 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw~ Je=òe keâer ef$epÙee keâe ceeve (mes.ceer. ceW) keäÙee nw?  
 
 (a) 4.25 (b) 3.75 
 (c) 3.5 (d) 4.55 
 
30.  In the given figure, triangle PQR is a right 
angled triangle at Q. If PQ = 35 cm and QS = 
28 cm, then what is the value (in cm) of SR ?  
  oer ieF& Deeke=âefle ceW, ef$eYegpe PQR, Q hej Skeâ mecekeâesCe 
ef$eYegpe nQ~ Ùeefo PQ = 35 mes.ceer. leLee QS = 28 mes.ceer. 
nQ, lees SR keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 35.33 (b) 37.33 
 (c) 41.33 (d) 43.33 
31.  In the given figure, P is the centre of the circle. 
If QS = PR, then what is the ratio of ?RSP to 
the ?TPR ?  
  oer ieF& Deeke=âefle ceW, P Je=òe keâe kesâvõ nw~ Ùeefo QS = PR 
nes, lees ?RSP keâe  ?TPR mes keäÙee Devegheele nw? 
 
 (a) 1 : 4  (b) 2 : 5 
 (c) 1 : 3 (d) 2 : 7 
32.  The distance between the centres of two cicles 
is 61 cm and their radii are 35 cm and 24 cm. 
What is the length (in cm) of the direct 
common tangent to the circles ?  
  oes Je=òeeW kessâ kesâvõeW kesâ ceOÙe keâer otjer 61 mes.ceer. nw leLee 
Gvekeâer ef$epÙeeSB 35 mes.ceer. leLee 24 mes.ceer. nQ~ Je=òeeW keâer 
GYeÙeefve<" DevegmheMe& jsKee keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 60 (b) 54  
 (c) 48 (d) 72 
33.  In the given figure, PQRS is a quadrilateral. If 
QR = 18 cm and PS = 9 cm, then what is the 
area (in cm
2
) of quadrilateral PQRS ?  
  oer ieF& Deeke=âefle ceW, PQRS Skeâ ÛelegYeg&pe nw~ Ùeefo QR = 
18 mes.ceer. leLee PS = 9 mes.ceer. nQ, lees ÛelegYeg&pe PQRS 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 
( )
64 3 / 3  (b) 
( )
177 3 / 2 
 (c) 
( )
135 3 / 2 (d) 
( )
98 3 / 3 
34.  PQR is a triangle, whose area is 180 cm
2
. S is a 
point on side QR, such that PS is the angle 
bisector of ?QPR. If PQ : PR = 2 : 3, then what 
is the area ( in cm
2
) triangle PSR ?   
  PQR Skeâ ef$eYegpe nw, efpemekeâe #es$eHeâue 180 mes.ceer.
2
 nw~ 
S, Yegpee QR hej Skeâ efyevog Fme Øekeâej nw efkeâ PS, 
?QPR hej keâesCe efÉYeepekeâ nw~ Ùeefo PQ : PR = 2 : 3 
nw, lees ef$eYegpe PSR keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 90 (b) 108  
 (c) 144 (d) 72 
35.  In the given figure, ABCD is a square. EFGH is 
a square formed by joining mid points of sides 
of ABCD. LMNO is a square formed by joining 
mid points of sides of EFGH. A circle is 
inscribed inside LMNO. If area of circle is 38.5 
cm
2
, then what is the area (in cm
2
) of square 
ABCD ?   
  oer ieF& Deeke=âefle ceW, ABCD Skeâ Jeie& nw~ ABCD keâer 
YegpeeDeeW kesâ kesâvõ efyevogDeeW keâes peesÌ[keâj Skeâ Jeie& 
EFGH yeveeÙee ieÙee nw~ EFGH keâer YegpeeDeeW kesâ kesâvõ 
efyevogDeeW keâes peesÌ[keâj Skeâ Jeie& LMNO yeveeÙee ieÙee nw~ 
Skeâ Je=òe keâes Jeie& LMNO ceW Debefkeâle efkeâÙee ieÙee nw~ 
Ùeefo Je=òe keâe #es$eHeâue 38.5 mes.ceer.
2
 nw, lees Jeie& ABCD 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 98 (b) 196  
 (c) 122.5 (d) 171.5 
36.  ABCDEF is a regular hexagon of side 12 cm. 
What is the area (in cm
2
) of the triangle ECD ?  
  ABCDEF 12 mes.ceer. Yegpee Jeeuee Skeâ mece <ešdYegpe nw~ 
ef$eYegpe ECD keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 18 3 (b) 24 3 
 (c) 36 3 (d) 42 3 
37.  PQRS is a square whose side is 16 cm. What is 
the value of the side (in cm) of the largest 
octagon that can be cut from the given square ?  
  PQRS, 16 mes.ceer. Yegpee Jeeuee Skeâ Jeie& nw~ efoÙes ieÙes 
Jeie& mes keâešs pee mekeâves Jeeues meyemes yeÌ[s mece De<šYegpe 
keâer Yegpee keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 8 4 2 -  (b) 16 8 2 + 
 (c) 16 2 16 - (d) 16 8 2 - 
38.  In the given figure, PQRS is a rectangle and a 
semicircle with SR as diameter is drawn. A 
circle is drawn as shown in the figure. If QR = 
7 cm, then what is the radius (in cm) of the 
small circle ? 
  oer ieF& Deeke=âefle ceW, PQRS Skeâ DeeÙele nw leLee SR 
JÙeeme Jeeuee Skeâ DeOe&ieesuee yeveeÙee ieÙee nw~ pewmee efkeâ 
 
Deeke=âefle ceW oMee&Ùee ieÙee nw efkeâ Skeâ Je=òe yeveeÙee ieÙee nw~ 
Ùeefo QR = 7 mes.ceer. nw, lees Úesšs Je=òe keâer ef$epÙee (mes.ceer. 
ceW) keäÙee nw? 
 
 (a) 21 14 2 +  
 (b) 21 14 2 - 
 (c) Both 21 14 2 + and 21 14 2 - / 21 14 2 + 
leLee 21 14 2 - oesveeW 
 (d) None of these/FveceW mes keâesF& veneR 
39.  In the given figure, PQR is a quadrant whose 
radius is 7 cm. A circle is inscribed in the 
quadrant as shown in the figure. What is the 
area (in cm
2
) of the circle ?  
  oer ieF& Deeke=âefle ceW, PQR Skeâ Je=òe–KeC[ nw efpemekeâer 
ef$epÙee 7 mes.ceer. nw~ pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw 
efkeâ Je=òe–KeC[ ceW Skeâ Je=òe keâes Debefkeâle efkeâÙee ieÙee nw~ 
Je=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 385 221 2 -  (b) 308 154 2 - 
 (c) 154 77 2 - (d) 462 308 2 - 
40.  A prism has a regular hexagonal base with side 
6 cm. If the total surface area of prism is 
216 3 cm
2
, then what is the height (in cm) of 
prism ?  
  Skeâ efØe]pce keâe DeeOeej, Skeâ 6 mes.ceer. Yegpee Jeeuee 
mece<ešdYegpe nw~ Ùeefo efØe]pce keâe kegâue he=<"erÙe #es$eHeâue 
216 3 mes.ceer.
2
 nw, lees efØe]pce keâer uecyeeF& (mes.ceer. ceW) 
keäÙee nw? 
 (a) 3 3 (b) 6 3  
 (c) 6 (d) 3 
41.  The radius of base of solid cone is 9 cm and its 
height is 21 cm. It cut into 3 parts by two cuts, 
which are parallel to its base. The cuts are at 
height of 7 cm and 14 cm from the base 
respectively. What is the ratio of curved 
surface areas of top, middle and bottom parts 
respectively ?  
  Skeâ "esme Mebkegâ kesâ DeeOeej keâer ef$epÙee 9 mes.ceer. nw leLee 
Gmekeâer TBÛeeF& 21 mes.ceer. nw~ Fmes oes keâšeJe, pees DeeOeej 
kesâ meceeblej nw mes 3 YeeieeW ceW keâeše ieÙee~ keâšeJe DeeOeej 
mes ›eâceMe: 7 mes.ceer. leLee 14 mes.ceer. keâer TBÛeeF& hej nw~ 
›eâceMe: Thejer, ceOÙe leLee efveÛeues YeeieeW kesâ Je›eâ he=<"erÙe 
#es$eHeâue keâe Devegheele keäÙee nw? 
 (a) 1 : 4 : 8  (b) 1 : 3 : 5 
 (c) 1 : 3 : 9 (d) 1 : 6 : 12 
42.  A right circular cylinder has height as 18 cm 
and radius as 7 cm. The cylinder is cut in three 
equal parts (by 2 cuts parallel to base). What is 
the percentage increase in total surface area ?  
  Skeâ uecyeJele ieesueekeâej yesueve keâer uecyeeF& 18 mes.ceer. 
leLee ef$epÙee 7 mes.ceer. nw~ yesueve keâes leerve yejeyej YeeieeW ceW 
keâeše peelee nQ (DeeOeej kesâ meceeblej 2 keâšeJe Éeje)~ kegâue 
he=<"erÙe #es$eHeâue ceW efkeâleves ØeefleMele keâer Je=efæ ngF& nw? 
 (a) 62 (b) 56  
 (c) 48 (d) 52 
43.  The ratio of curved surface area and volume of 
a cylinder is 1 : 7. The ratio of total surface 
area and volume is 187 : 770. What is the 
respective ratio of its base radius and height ? 
  Skeâ yesueve kesâ Je›eâ he=<"erÙe #es$eHeâue leLee DeeÙeleve keâe 
Devegheele 1:7 nw~ kegâue he=<"erÙe #es$eHeâue leLee DeeÙeleve keâe 
Devegheele 187:770 nw~ Fmekesâ DeeOeej keâer ef$epÙee leLee 
TBÛeeF& ›eâceMe: Devegheele keäÙee nw? 
 (a) 5 : 8  (b) 4 : 9  
 (c) 3 : 7 (d) 7 : 10 
44.  The ratio of total surface area and volume of a 
sphere is 1 : 7. This sphere is melted to form 
small spheres of equal size. The radius of each 
small sphere is 1/6th the radius of the large 
sphere. What is the sum (in cm
2
) of curved 
surface areas of all small spheres ?  
  Skeâ ieesues kesâ kegâue he=<"erÙe #es$eHeâue leLee DeeÙeleve keâe 
Devegheele 1:7 nw~ Fme ieesues keâes efheIeueekeâj yejeyej ceehe 
kesâ Úesšs ieesues yeveeÙes peeles nQ~ ØelÙeskeâ Úesšs ieesues keâer 
ef$epÙee yeÌ[s ieesues keâer ef$epÙee keâer 1/6 nQ~ meYeer Úesšs 
ieesues kesâ Je›eâ he=<"erÙe #es$eHeâue keâe Ùeesie (mes.ceer.
2
 ceW) keäÙee 
nw? 
 (a) 31276 (b) 36194 
 (c) 25182 (d) 33264 
45.  A hemisphere is kept on top of a cube. Its front 
view is shown in the given figure. The total 
height of the figure is 21 cm. The ratio of 
curved surface area of hemisphere and total 
surface area of cube is 11 : 42. What is the total 
volume (in cm
3
) of figure ?  
  Skeâ DeOe&ieesuee Skeâ Ieve hej jKee ieÙee nw~ Fmekesâ meeceves 
keâe ÂMÙe Deeke=âefle ceW oMee&Ùee ieÙee nw~ Deeke=âefle keâer kegâue 
TBÛeeF& 21 mes.ceer. nw~ DeOe&ieesues kesâ Je›eâ he=<"erÙe #es$eHeâue 
leLee Ieve kesâ kegâue he=<"erÙe #es$eHeâue keâe Devegheele 11:42 
nw~ Deeke=âefle keâe kegâue DeeÙeleve (mes.ceer.
3
 ceW) keäÙee nw? 
 
 (a) 3318.33 (b) 3462.67 
 (c) 3154.67 (d) 3248.33 
46.  A solid cube has side 8 cm. It is cut along 
diagonals of top face to get 4 equal parts. What 
is the total surface area (in cm
2
) of each part ?