SSC CGL Tier 2 (9 March) Shift 2 Past Year Paper (2018) | SSC CGL (Hindi) Tier - 1 Mock Test Series PDF Download

 Page 1


 
mebÙegòeâ mveelekeâ mlejerÙe hegvehe&jer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  If the unit digit of 433 × 456 × 43N is (N + 2), 
then what is the value of N ?  
  Ùeefo 433 × 456 × 43N  keâe FkeâeF& Debkeâ (N + 2) nw, 
lees N keâe ceeve keäÙee nw? 
 (a) 1 (b) 8  
 (c) 3 (d) 6 
2.  If N = (12345)
2
 + 12345 + 12346, then what is 
the value of N ?  
  Ùeefo N = (12345)
2
 + 12345 + 12346, nw, lees N 
keâe ceeve keäÙee nw? 
 (a) 12346 (b) 12345 
 (c) 12344 (d) 12347 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nQ? 
  I. (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + 
(0.00003/0.0002) = 0.6
 
 
 II. (0.01) + (0.01)
2
 + (0.001)
2
 = 0.010101 
 (a) Only I/ kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
4.  What is the value of 1/(0.1)
2
 + 1/(0.01)
2
 + 
1/(0.5)
2
 + 1/(0.05)
2
 ?  
  1/(0.1)
2
 + 1/(0.01)
2
 + 1/(0.5)
2
 + 1/(0.05)
2 
keâe ceeve 
keäÙee nw? 
 (a) 10504 (b) 10404 
 (c) 10004 (d) 11400 
5.  Which of the following statement(s) is/are 
True?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
? ? ? ? ? ? ? ?
? ?? ?? ? ? ?
? ? ? ? ? ? ? ?
1 1 1 1
1 + 1 + 1 + ... 1 + > 497
2 3 4 998
 
  II. 
3 1 1 1 3 1
14 + 5 - 2 > 11 + 12 - 7
4 4 2 8 8 4
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
3 9 7
< <
110 308 225
 
  II. 
1 2 3 6
99 + 99 + 99 + ...99 = 279
7 7 7 7
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
7.  If ( )
1 1
f x = - ,
x x + 1
 then what is the value of 
f(1) + f(2) + f(3) + ..... f(10) ?  
  Ùeefo ( )
1 1
f x = - ,
x x + 1
nw, lees f(1) + f(2) + f(3) + ..... 
f(10) keâe ceeve keäÙee nw? 
 (a) 9/10  (b) 10/11 
 (c) 11/12 (d) 12/13 
8.  If N = 4
11
 + 4
12
 + 4
13
 + 4
14
 , then how many 
positive factors of N are there ?  
  Ùeefo N = 4
11
 + 4
12
 + 4
13
 + 4
14
 nw, lees N kesâ efkeâleves 
Oeveelcekeâ iegCeveKeC[ nQ? 
 (a) 92 (b) 48  
 (c) 50 (d) 51 
9.  If N = 9
9
, then N is divisible by how many 
positive perfect cubes ?  
  Ùeefo N = 9
9
 nw, lees N efkeâleves Oeveelcekeâ IeveeW mes efJeYeepÙe 
nw? 
 (a) 6 (b) 7  
 (c) 4 (d) 5 
10.  If N = 3
14
 + 3
13
 – 12, then what is the largest 
prime factor of N ?  
  Ùeefo N = 3
14
 + 3
13
 – 12, nw, lees N keâe meyemes yeÌ[e 
DeYeepÙe iegCeveKeC[ keäÙee nw? 
 (a) 11 (b) 79 
 (c) 13 (d) 73 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 121 + 12321 + 1234321 = 1233 
  II. 0.64 + 64 + 36 + 0.36 > 15 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hegvehe&jer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  If the unit digit of 433 × 456 × 43N is (N + 2), 
then what is the value of N ?  
  Ùeefo 433 × 456 × 43N  keâe FkeâeF& Debkeâ (N + 2) nw, 
lees N keâe ceeve keäÙee nw? 
 (a) 1 (b) 8  
 (c) 3 (d) 6 
2.  If N = (12345)
2
 + 12345 + 12346, then what is 
the value of N ?  
  Ùeefo N = (12345)
2
 + 12345 + 12346, nw, lees N 
keâe ceeve keäÙee nw? 
 (a) 12346 (b) 12345 
 (c) 12344 (d) 12347 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nQ? 
  I. (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + 
(0.00003/0.0002) = 0.6
 
 
 II. (0.01) + (0.01)
2
 + (0.001)
2
 = 0.010101 
 (a) Only I/ kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
4.  What is the value of 1/(0.1)
2
 + 1/(0.01)
2
 + 
1/(0.5)
2
 + 1/(0.05)
2
 ?  
  1/(0.1)
2
 + 1/(0.01)
2
 + 1/(0.5)
2
 + 1/(0.05)
2 
keâe ceeve 
keäÙee nw? 
 (a) 10504 (b) 10404 
 (c) 10004 (d) 11400 
5.  Which of the following statement(s) is/are 
True?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
? ? ? ? ? ? ? ?
? ?? ?? ? ? ?
? ? ? ? ? ? ? ?
1 1 1 1
1 + 1 + 1 + ... 1 + > 497
2 3 4 998
 
  II. 
3 1 1 1 3 1
14 + 5 - 2 > 11 + 12 - 7
4 4 2 8 8 4
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
3 9 7
< <
110 308 225
 
  II. 
1 2 3 6
99 + 99 + 99 + ...99 = 279
7 7 7 7
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
7.  If ( )
1 1
f x = - ,
x x + 1
 then what is the value of 
f(1) + f(2) + f(3) + ..... f(10) ?  
  Ùeefo ( )
1 1
f x = - ,
x x + 1
nw, lees f(1) + f(2) + f(3) + ..... 
f(10) keâe ceeve keäÙee nw? 
 (a) 9/10  (b) 10/11 
 (c) 11/12 (d) 12/13 
8.  If N = 4
11
 + 4
12
 + 4
13
 + 4
14
 , then how many 
positive factors of N are there ?  
  Ùeefo N = 4
11
 + 4
12
 + 4
13
 + 4
14
 nw, lees N kesâ efkeâleves 
Oeveelcekeâ iegCeveKeC[ nQ? 
 (a) 92 (b) 48  
 (c) 50 (d) 51 
9.  If N = 9
9
, then N is divisible by how many 
positive perfect cubes ?  
  Ùeefo N = 9
9
 nw, lees N efkeâleves Oeveelcekeâ IeveeW mes efJeYeepÙe 
nw? 
 (a) 6 (b) 7  
 (c) 4 (d) 5 
10.  If N = 3
14
 + 3
13
 – 12, then what is the largest 
prime factor of N ?  
  Ùeefo N = 3
14
 + 3
13
 – 12, nw, lees N keâe meyemes yeÌ[e 
DeYeepÙe iegCeveKeC[ keäÙee nw? 
 (a) 11 (b) 79 
 (c) 13 (d) 73 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 121 + 12321 + 1234321 = 1233 
  II. 0.64 + 64 + 36 + 0.36 > 15 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
 
12.  What is the value of  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
 
  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
keâe ceeve 
keäÙee nw? 
 (a) 2 (b) 4  
 (c) 8 (d) 6 
13.  The sum of two positive numbers is 14 and 
difference between their squares is 56. What is 
the sum of their squares ?  
  oes Oeveelcekeâ mebKÙeeDeeW keâe Ùeesie 14 nw leLee Gvekesâ Jeie& 
kesâ ceOÙe keâe Deblej 56 nw~ Gvekesâ Jeie& keâe Ùeesie keäÙee nw? 
 (a) 106 (b) 196 
 (c) 53 (d) 68 
14.  What is the value of 1006
2
 – 1007 × 1005 + 1008 
× 1004 – 1009 × 1003 ?  
  1006
2
 – 1007 × 1005 + 1008 × 1004 – 1009 × 
1003 keâe ceeve keäÙee nw ? 
 (a) 6  (b) 3  
 (c) 12 (d) 24 
15.  If a
2
 + b
2
 = 4b + 6a – 13, then what is the value 
of a + b ?  
  Ùeefo a
2
 + b
2
 = 4b + 6a – 13, nw, lees a + b keâe ceeve 
keäÙee nw? 
 (a) 3  (b) 2  
 (c) 5 (d) 10 
16.  x and y are positive integers. If x
4
 + y
4
 + x
2
y
2
 = 
481 and xy = 12, then what is the value of  
x
2
 – xy + y
2
 ? 
  x leLee y Skeâ Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo x
4
 + y
4
 + x
2
y
2
 
= 481 leLee xy = 12 nw, lees x
2
 – xy + y
2
 keâe ceeve keäÙee 
nw? 
 (a) 16  (b) 13  
 (c) 11 (d) 15 
17.  If A = 1 + 2
P
 and B = 1 + 2
–P
, then what is the 
value of B ?  
  Ùeefo A = 1 + 2
P
 leLee B = 1 + 2
–P
 nw, lees B keâe ceeve 
keäÙee nw? 
 (a) (A + 1)/(A–1) (b) (A+2)/(A+1) 
 (c) A/(A–1) (d) (A–2)/(A+1) 
18.  If a and b are roots of the equation 
ax
2
+bx+c=0, then which equation will have 
roots (ab + a + b) and (ab–a–b) ?  
  Ùeefo a leLee b meceerkeâjCe ax
2 
+ bx + c = 0 kesâ cetue nQ, 
lees efkeâme meceerkeâjCe kesâ cetue (ab + a + b) leLee  
(ab–a–b) neWies? 
 (a) a
2
x
2
 + 2acx + c
2
 + b
2
 = 0  
 (b) a
2
x
2
 – 2acx + c
2
 – b
2
 = 0 
 (c) a
2
x
2
 – 2acx + c
2
 + b
2
 = 0 
 (d) a
2
x
2
 + 2acx + c
2
 – b
2
 = 0 
19.  If 
( )( )
2 2
3
1- p 1- q =
2
then what is the value 
of 
2 2 2 2
2p + 2q + 2pq + 2p + 2q - 2pq ? 
  Ùeefo 
( )( )
2 2
3
1 - p 1- q =
2
 nw lees 
2 2
2p + 2q + 2pq 
2 2
+ 2p + 2q - 2pq keâe ceeve keäÙee nw? 
 (a) 2 
 (b) 2  
 (c) 1 
 (d) None of these/FveceW mes keâesF& veneR 
20.  If (a+b)
2
 – 2(a+b) = 80 and ab = 16, then what 
can be the value of 3a–19b ?  
  Ùeefo (a+b)
2
 – 2(a+b) = 80 leLee ab = 16, nQ, lees  
3a–19b keâe ceeve keäÙee nes mekeâlee nw? 
 (a) –16 (b) –14 
 (c) –18 (d) –20 
21.  If x
y+z
 = 1, y
z+x
 = 1024 and z
x+y
 = 729 (x, y and z 
are natural numbers), then what is the value of  
(z+1)
y+x+1
 ? 
  Ùeefo x
y+z
 = 1, y
z+x
 = 1024  leLee z
x+y
 = 729 (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees  (z+1)
y+x+1 
keâe ceeve keäÙee 
nw? 
 (a) 6561  (b) 10000 
 (c) 4096 (d) 14641 
22.  If x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 and x
3
 + y
3
 + z
3
=3, 
then what is the value of xyz ?  
  Ùeefo x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 leLee x
3
 + y
3
 + 
z
3
=3, nQ, lees xyz keâe ceeve keäÙee nw? 
 (a) 1/3 (b) 1/6 
 (c) 1/2 (d) 1/4 
23.  In triangle PQR, the internal bisector of ?Q 
and ?R meets at O. If ?QPR = 70
0
, then what 
is the value (in degrees) of ?QOR ?  
  ef$eYegpe PQR ceW, ?Q leLee ?R keâe Deebleefjkeâ 
efÉYeepekeâ O hej efceueles nQ~ Ùeefo ?QPR = 70
0
, nQ, lees 
?QOR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 45  (b) 125  
 (c) 115 (d) 110 
24.  PQR is a triangle such that PQ = PR. RS and 
QT are the median to the sides PQ and PR 
respectively. If the medians RS and QT 
intersect at right angle, then what is the value 
of (PQ/QR)
2
 ?  
  PQR Fme Øekeâej Skeâ ef$eYegpe nw efkeâ PQ = PR nw~ RS 
leLee QT ›eâceMe: YegpeeDeeW PQ leLee PR hej ceeefOÙekeâeSB 
nQ~ Ùeefo ceeefOÙekeâeSB RS leLee QR mecekeâesCe hej ØeefleÛÚso 
keâjleer nQ, lees (PQ/QR)
2
 keâe ceeve keäÙee nw? 
 (a) 3/2 (b) 5/2 
 (c) 2 
 (d) None of these/FveceW mes keâesF& veneR 
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hegvehe&jer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  If the unit digit of 433 × 456 × 43N is (N + 2), 
then what is the value of N ?  
  Ùeefo 433 × 456 × 43N  keâe FkeâeF& Debkeâ (N + 2) nw, 
lees N keâe ceeve keäÙee nw? 
 (a) 1 (b) 8  
 (c) 3 (d) 6 
2.  If N = (12345)
2
 + 12345 + 12346, then what is 
the value of N ?  
  Ùeefo N = (12345)
2
 + 12345 + 12346, nw, lees N 
keâe ceeve keäÙee nw? 
 (a) 12346 (b) 12345 
 (c) 12344 (d) 12347 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nQ? 
  I. (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + 
(0.00003/0.0002) = 0.6
 
 
 II. (0.01) + (0.01)
2
 + (0.001)
2
 = 0.010101 
 (a) Only I/ kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
4.  What is the value of 1/(0.1)
2
 + 1/(0.01)
2
 + 
1/(0.5)
2
 + 1/(0.05)
2
 ?  
  1/(0.1)
2
 + 1/(0.01)
2
 + 1/(0.5)
2
 + 1/(0.05)
2 
keâe ceeve 
keäÙee nw? 
 (a) 10504 (b) 10404 
 (c) 10004 (d) 11400 
5.  Which of the following statement(s) is/are 
True?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
? ? ? ? ? ? ? ?
? ?? ?? ? ? ?
? ? ? ? ? ? ? ?
1 1 1 1
1 + 1 + 1 + ... 1 + > 497
2 3 4 998
 
  II. 
3 1 1 1 3 1
14 + 5 - 2 > 11 + 12 - 7
4 4 2 8 8 4
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
3 9 7
< <
110 308 225
 
  II. 
1 2 3 6
99 + 99 + 99 + ...99 = 279
7 7 7 7
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
7.  If ( )
1 1
f x = - ,
x x + 1
 then what is the value of 
f(1) + f(2) + f(3) + ..... f(10) ?  
  Ùeefo ( )
1 1
f x = - ,
x x + 1
nw, lees f(1) + f(2) + f(3) + ..... 
f(10) keâe ceeve keäÙee nw? 
 (a) 9/10  (b) 10/11 
 (c) 11/12 (d) 12/13 
8.  If N = 4
11
 + 4
12
 + 4
13
 + 4
14
 , then how many 
positive factors of N are there ?  
  Ùeefo N = 4
11
 + 4
12
 + 4
13
 + 4
14
 nw, lees N kesâ efkeâleves 
Oeveelcekeâ iegCeveKeC[ nQ? 
 (a) 92 (b) 48  
 (c) 50 (d) 51 
9.  If N = 9
9
, then N is divisible by how many 
positive perfect cubes ?  
  Ùeefo N = 9
9
 nw, lees N efkeâleves Oeveelcekeâ IeveeW mes efJeYeepÙe 
nw? 
 (a) 6 (b) 7  
 (c) 4 (d) 5 
10.  If N = 3
14
 + 3
13
 – 12, then what is the largest 
prime factor of N ?  
  Ùeefo N = 3
14
 + 3
13
 – 12, nw, lees N keâe meyemes yeÌ[e 
DeYeepÙe iegCeveKeC[ keäÙee nw? 
 (a) 11 (b) 79 
 (c) 13 (d) 73 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 121 + 12321 + 1234321 = 1233 
  II. 0.64 + 64 + 36 + 0.36 > 15 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
 
12.  What is the value of  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
 
  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
keâe ceeve 
keäÙee nw? 
 (a) 2 (b) 4  
 (c) 8 (d) 6 
13.  The sum of two positive numbers is 14 and 
difference between their squares is 56. What is 
the sum of their squares ?  
  oes Oeveelcekeâ mebKÙeeDeeW keâe Ùeesie 14 nw leLee Gvekesâ Jeie& 
kesâ ceOÙe keâe Deblej 56 nw~ Gvekesâ Jeie& keâe Ùeesie keäÙee nw? 
 (a) 106 (b) 196 
 (c) 53 (d) 68 
14.  What is the value of 1006
2
 – 1007 × 1005 + 1008 
× 1004 – 1009 × 1003 ?  
  1006
2
 – 1007 × 1005 + 1008 × 1004 – 1009 × 
1003 keâe ceeve keäÙee nw ? 
 (a) 6  (b) 3  
 (c) 12 (d) 24 
15.  If a
2
 + b
2
 = 4b + 6a – 13, then what is the value 
of a + b ?  
  Ùeefo a
2
 + b
2
 = 4b + 6a – 13, nw, lees a + b keâe ceeve 
keäÙee nw? 
 (a) 3  (b) 2  
 (c) 5 (d) 10 
16.  x and y are positive integers. If x
4
 + y
4
 + x
2
y
2
 = 
481 and xy = 12, then what is the value of  
x
2
 – xy + y
2
 ? 
  x leLee y Skeâ Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo x
4
 + y
4
 + x
2
y
2
 
= 481 leLee xy = 12 nw, lees x
2
 – xy + y
2
 keâe ceeve keäÙee 
nw? 
 (a) 16  (b) 13  
 (c) 11 (d) 15 
17.  If A = 1 + 2
P
 and B = 1 + 2
–P
, then what is the 
value of B ?  
  Ùeefo A = 1 + 2
P
 leLee B = 1 + 2
–P
 nw, lees B keâe ceeve 
keäÙee nw? 
 (a) (A + 1)/(A–1) (b) (A+2)/(A+1) 
 (c) A/(A–1) (d) (A–2)/(A+1) 
18.  If a and b are roots of the equation 
ax
2
+bx+c=0, then which equation will have 
roots (ab + a + b) and (ab–a–b) ?  
  Ùeefo a leLee b meceerkeâjCe ax
2 
+ bx + c = 0 kesâ cetue nQ, 
lees efkeâme meceerkeâjCe kesâ cetue (ab + a + b) leLee  
(ab–a–b) neWies? 
 (a) a
2
x
2
 + 2acx + c
2
 + b
2
 = 0  
 (b) a
2
x
2
 – 2acx + c
2
 – b
2
 = 0 
 (c) a
2
x
2
 – 2acx + c
2
 + b
2
 = 0 
 (d) a
2
x
2
 + 2acx + c
2
 – b
2
 = 0 
19.  If 
( )( )
2 2
3
1- p 1- q =
2
then what is the value 
of 
2 2 2 2
2p + 2q + 2pq + 2p + 2q - 2pq ? 
  Ùeefo 
( )( )
2 2
3
1 - p 1- q =
2
 nw lees 
2 2
2p + 2q + 2pq 
2 2
+ 2p + 2q - 2pq keâe ceeve keäÙee nw? 
 (a) 2 
 (b) 2  
 (c) 1 
 (d) None of these/FveceW mes keâesF& veneR 
20.  If (a+b)
2
 – 2(a+b) = 80 and ab = 16, then what 
can be the value of 3a–19b ?  
  Ùeefo (a+b)
2
 – 2(a+b) = 80 leLee ab = 16, nQ, lees  
3a–19b keâe ceeve keäÙee nes mekeâlee nw? 
 (a) –16 (b) –14 
 (c) –18 (d) –20 
21.  If x
y+z
 = 1, y
z+x
 = 1024 and z
x+y
 = 729 (x, y and z 
are natural numbers), then what is the value of  
(z+1)
y+x+1
 ? 
  Ùeefo x
y+z
 = 1, y
z+x
 = 1024  leLee z
x+y
 = 729 (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees  (z+1)
y+x+1 
keâe ceeve keäÙee 
nw? 
 (a) 6561  (b) 10000 
 (c) 4096 (d) 14641 
22.  If x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 and x
3
 + y
3
 + z
3
=3, 
then what is the value of xyz ?  
  Ùeefo x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 leLee x
3
 + y
3
 + 
z
3
=3, nQ, lees xyz keâe ceeve keäÙee nw? 
 (a) 1/3 (b) 1/6 
 (c) 1/2 (d) 1/4 
23.  In triangle PQR, the internal bisector of ?Q 
and ?R meets at O. If ?QPR = 70
0
, then what 
is the value (in degrees) of ?QOR ?  
  ef$eYegpe PQR ceW, ?Q leLee ?R keâe Deebleefjkeâ 
efÉYeepekeâ O hej efceueles nQ~ Ùeefo ?QPR = 70
0
, nQ, lees 
?QOR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 45  (b) 125  
 (c) 115 (d) 110 
24.  PQR is a triangle such that PQ = PR. RS and 
QT are the median to the sides PQ and PR 
respectively. If the medians RS and QT 
intersect at right angle, then what is the value 
of (PQ/QR)
2
 ?  
  PQR Fme Øekeâej Skeâ ef$eYegpe nw efkeâ PQ = PR nw~ RS 
leLee QT ›eâceMe: YegpeeDeeW PQ leLee PR hej ceeefOÙekeâeSB 
nQ~ Ùeefo ceeefOÙekeâeSB RS leLee QR mecekeâesCe hej ØeefleÛÚso 
keâjleer nQ, lees (PQ/QR)
2
 keâe ceeve keäÙee nw? 
 (a) 3/2 (b) 5/2 
 (c) 2 
 (d) None of these/FveceW mes keâesF& veneR 
 
25.  PQR is a triangle. S and T are the midpoints of 
the sides PQ and PR respectively. Which of the 
following is TRUE ?  
  I. Triangle PST is similar to triangle PQR. 
  II. ST = 1/2 (QR) 
  III. ST is parallel to QR.  
  PQR Skeâ ef$eYegpe nw~ S leLee T ›eâceMe: YegpeeDeeW PQ 
leLee PR kesâ ceOÙe efyevog nw~ efvecveefueefKele ceW mes keâewve mee 
melÙe nw? 
  I.    ef$eYegpe PST, ef$eYegpe PQR kesâ meceeve nw~ 
  II.   ST = 1/2 (QR) 
  III. ST, QR kesâ meceeblej nw~ 
 (a) Only I and II/kesâJeue I leLee II 
  (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
26.  ABC is a triangle in which ?ABC = 90
0
. BD is 
perpendicular to AC. Which of the following is 
TRUE ?  
  ABC Skeâ ef$eYegpe nQ efpemeceW ?ABC = 90
0
 nw~ BD, 
AC hej uecye nw~ efvecveefueefKele ceW mes keâewve mee melÙe nw? 
  I.  Triangle BAD is similar to triangle CBD./ 
   ef$eYegpe BAD, ef$eYegpe CBD kesâ meceeve nw~ 
  II.  Triangle BAD is similar to triangle CAB./ 
   ef$eYegpe BAD, ef$eYegpe CAB kesâ meceeve nw~ 
  III. Triangle CBD is similar to triangle CAB./ 
   ef$eYegpe CBD, ef$eYegpe CAB kesâ meceeve nw~ 
 (a) Only I/kesâJeue I  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
27.  Two parallel chords are on the one side of the 
centre of a circle. The length of the two chords 
is 24 cm and 32 cm. If the distance between the 
two chords is 8 cm, then what is the area (in 
cm
2
) of the circle ?  
  oes meceeblej peerJeeSB Skeâ Je=òe kesâ kesâvõ keâer Skeâ Deesj nQ~ 
oesveeW peerJeeDeeW keâer uecyeeF& 24 mes.ceer. leLee 32 mes.ceer. nw~ 
Ùeefo oesveeW peerJeeDeeW kesâ ceOÙe 8 mes.ceer. keâer otjer nw, lees 
Je=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 724.14  (b) 832.86 
 (c) 924.12 (d) 988.32 
28.  Two circles of radius 4 cm and 6 cm touch each 
other internally. What is the length (in cm) of 
the longest chord of the outer circle, which is 
also a tangent to inner circle ?  
  4 mes.ceer. leLee 6 mes.ceer. ef$epÙee Jeeues oes Je=òe Skeâ otmejs 
keâes Deboj mes Útles nQ~ yee¢e Je=òe keâer meyemes uecyeer peerJee 
pees Deble:Je=òe keâer mheMe& jsKee Yeer nw, keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 12 2 (b) 8 2 
 (c) 6 2 (d) 4 2 
29.  In the given figure, PT is a common tangent to 
three circles at points, A, B and C respectively. 
The radius of the small, medium and large 
circles is 4 cm, 6 cm and 9 cm. O
1
, O
2
 and O
3
 
are the centre of the three circles. What is the 
value (in cm) of PC ?  
  oer ieF& Deeke=âefle ceW, PT leerve Je=òeeW hej leerve efyevogDeeW 
›eâceMe: A, B leLee C hej GYeÙeefve<" DevegmheMe& jsKee nw~ 
Úesšs, ceOÙe leLee meyemes yeÌ[s Je=òeeW keâer ef$epÙee 4 mes.ceer., 
6 mes.ceer. SJeb 9 mes.ceer. nw~ O
1
, O
2
 leLee O
3
 leerveeW Je=òeeW 
kesâ kesâvõ nQ~ PC keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 6 (b) 9 6 
 (c) 24 6 (d) 15 6 
30.  PQRS is a cyclic quadrilateral. PR and QS 
intersect at T. If ?SPR = 40
0
 and ?PQS = 80
0
, 
then what is the value (in degrees) of ?PSR ?  
  PQRS Skeâ Ûe›eâerÙe ÛelegYeg&pe nw~ PR leLee QS, T hej 
ØeefleÛÚso keâjles nQ~ Ùeefo ?SPR = 40
0
 leLee ?PQS = 
80
0 
nw, ?PSR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 60  (b) 40  
 (c) 80 (d) 100 
31.  In the given figure, ?PSR = 105
0
 and PQ is the 
diameter of the circle. What is the value (in 
degrees) of ?QPR ?  
  oer ieF& Deeke=âefle ceW, ?PSR = 105
0
 leLee PQ Je=òe keâe 
JÙeeme nw~ ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 75 (b) 15  
 (c) 30 (d) 45 
32.  There are two identical circles of radius 10 cm 
each. If the length of the direct common 
tangent is 26 cm, then what is the length (in 
cm) of the transverse common tangent ?  
  10 mes.ceer. ef$epÙee Jeeues oes mece™heer Je=òe nQ~ Ùeefo 
GYeÙeefve<" DevegmheMe& jsKee keâer uecyeeF& 26 mes.ceer. nw, lees 
GYeÙeefve<" efleÙe&keâ DevegmheMe& jsKee keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 2 69 (b) 4 23 
 (c) 4 46 (d) 3 46 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hegvehe&jer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  If the unit digit of 433 × 456 × 43N is (N + 2), 
then what is the value of N ?  
  Ùeefo 433 × 456 × 43N  keâe FkeâeF& Debkeâ (N + 2) nw, 
lees N keâe ceeve keäÙee nw? 
 (a) 1 (b) 8  
 (c) 3 (d) 6 
2.  If N = (12345)
2
 + 12345 + 12346, then what is 
the value of N ?  
  Ùeefo N = (12345)
2
 + 12345 + 12346, nw, lees N 
keâe ceeve keäÙee nw? 
 (a) 12346 (b) 12345 
 (c) 12344 (d) 12347 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nQ? 
  I. (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + 
(0.00003/0.0002) = 0.6
 
 
 II. (0.01) + (0.01)
2
 + (0.001)
2
 = 0.010101 
 (a) Only I/ kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
4.  What is the value of 1/(0.1)
2
 + 1/(0.01)
2
 + 
1/(0.5)
2
 + 1/(0.05)
2
 ?  
  1/(0.1)
2
 + 1/(0.01)
2
 + 1/(0.5)
2
 + 1/(0.05)
2 
keâe ceeve 
keäÙee nw? 
 (a) 10504 (b) 10404 
 (c) 10004 (d) 11400 
5.  Which of the following statement(s) is/are 
True?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
? ? ? ? ? ? ? ?
? ?? ?? ? ? ?
? ? ? ? ? ? ? ?
1 1 1 1
1 + 1 + 1 + ... 1 + > 497
2 3 4 998
 
  II. 
3 1 1 1 3 1
14 + 5 - 2 > 11 + 12 - 7
4 4 2 8 8 4
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
3 9 7
< <
110 308 225
 
  II. 
1 2 3 6
99 + 99 + 99 + ...99 = 279
7 7 7 7
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
7.  If ( )
1 1
f x = - ,
x x + 1
 then what is the value of 
f(1) + f(2) + f(3) + ..... f(10) ?  
  Ùeefo ( )
1 1
f x = - ,
x x + 1
nw, lees f(1) + f(2) + f(3) + ..... 
f(10) keâe ceeve keäÙee nw? 
 (a) 9/10  (b) 10/11 
 (c) 11/12 (d) 12/13 
8.  If N = 4
11
 + 4
12
 + 4
13
 + 4
14
 , then how many 
positive factors of N are there ?  
  Ùeefo N = 4
11
 + 4
12
 + 4
13
 + 4
14
 nw, lees N kesâ efkeâleves 
Oeveelcekeâ iegCeveKeC[ nQ? 
 (a) 92 (b) 48  
 (c) 50 (d) 51 
9.  If N = 9
9
, then N is divisible by how many 
positive perfect cubes ?  
  Ùeefo N = 9
9
 nw, lees N efkeâleves Oeveelcekeâ IeveeW mes efJeYeepÙe 
nw? 
 (a) 6 (b) 7  
 (c) 4 (d) 5 
10.  If N = 3
14
 + 3
13
 – 12, then what is the largest 
prime factor of N ?  
  Ùeefo N = 3
14
 + 3
13
 – 12, nw, lees N keâe meyemes yeÌ[e 
DeYeepÙe iegCeveKeC[ keäÙee nw? 
 (a) 11 (b) 79 
 (c) 13 (d) 73 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 121 + 12321 + 1234321 = 1233 
  II. 0.64 + 64 + 36 + 0.36 > 15 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
 
12.  What is the value of  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
 
  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
keâe ceeve 
keäÙee nw? 
 (a) 2 (b) 4  
 (c) 8 (d) 6 
13.  The sum of two positive numbers is 14 and 
difference between their squares is 56. What is 
the sum of their squares ?  
  oes Oeveelcekeâ mebKÙeeDeeW keâe Ùeesie 14 nw leLee Gvekesâ Jeie& 
kesâ ceOÙe keâe Deblej 56 nw~ Gvekesâ Jeie& keâe Ùeesie keäÙee nw? 
 (a) 106 (b) 196 
 (c) 53 (d) 68 
14.  What is the value of 1006
2
 – 1007 × 1005 + 1008 
× 1004 – 1009 × 1003 ?  
  1006
2
 – 1007 × 1005 + 1008 × 1004 – 1009 × 
1003 keâe ceeve keäÙee nw ? 
 (a) 6  (b) 3  
 (c) 12 (d) 24 
15.  If a
2
 + b
2
 = 4b + 6a – 13, then what is the value 
of a + b ?  
  Ùeefo a
2
 + b
2
 = 4b + 6a – 13, nw, lees a + b keâe ceeve 
keäÙee nw? 
 (a) 3  (b) 2  
 (c) 5 (d) 10 
16.  x and y are positive integers. If x
4
 + y
4
 + x
2
y
2
 = 
481 and xy = 12, then what is the value of  
x
2
 – xy + y
2
 ? 
  x leLee y Skeâ Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo x
4
 + y
4
 + x
2
y
2
 
= 481 leLee xy = 12 nw, lees x
2
 – xy + y
2
 keâe ceeve keäÙee 
nw? 
 (a) 16  (b) 13  
 (c) 11 (d) 15 
17.  If A = 1 + 2
P
 and B = 1 + 2
–P
, then what is the 
value of B ?  
  Ùeefo A = 1 + 2
P
 leLee B = 1 + 2
–P
 nw, lees B keâe ceeve 
keäÙee nw? 
 (a) (A + 1)/(A–1) (b) (A+2)/(A+1) 
 (c) A/(A–1) (d) (A–2)/(A+1) 
18.  If a and b are roots of the equation 
ax
2
+bx+c=0, then which equation will have 
roots (ab + a + b) and (ab–a–b) ?  
  Ùeefo a leLee b meceerkeâjCe ax
2 
+ bx + c = 0 kesâ cetue nQ, 
lees efkeâme meceerkeâjCe kesâ cetue (ab + a + b) leLee  
(ab–a–b) neWies? 
 (a) a
2
x
2
 + 2acx + c
2
 + b
2
 = 0  
 (b) a
2
x
2
 – 2acx + c
2
 – b
2
 = 0 
 (c) a
2
x
2
 – 2acx + c
2
 + b
2
 = 0 
 (d) a
2
x
2
 + 2acx + c
2
 – b
2
 = 0 
19.  If 
( )( )
2 2
3
1- p 1- q =
2
then what is the value 
of 
2 2 2 2
2p + 2q + 2pq + 2p + 2q - 2pq ? 
  Ùeefo 
( )( )
2 2
3
1 - p 1- q =
2
 nw lees 
2 2
2p + 2q + 2pq 
2 2
+ 2p + 2q - 2pq keâe ceeve keäÙee nw? 
 (a) 2 
 (b) 2  
 (c) 1 
 (d) None of these/FveceW mes keâesF& veneR 
20.  If (a+b)
2
 – 2(a+b) = 80 and ab = 16, then what 
can be the value of 3a–19b ?  
  Ùeefo (a+b)
2
 – 2(a+b) = 80 leLee ab = 16, nQ, lees  
3a–19b keâe ceeve keäÙee nes mekeâlee nw? 
 (a) –16 (b) –14 
 (c) –18 (d) –20 
21.  If x
y+z
 = 1, y
z+x
 = 1024 and z
x+y
 = 729 (x, y and z 
are natural numbers), then what is the value of  
(z+1)
y+x+1
 ? 
  Ùeefo x
y+z
 = 1, y
z+x
 = 1024  leLee z
x+y
 = 729 (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees  (z+1)
y+x+1 
keâe ceeve keäÙee 
nw? 
 (a) 6561  (b) 10000 
 (c) 4096 (d) 14641 
22.  If x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 and x
3
 + y
3
 + z
3
=3, 
then what is the value of xyz ?  
  Ùeefo x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 leLee x
3
 + y
3
 + 
z
3
=3, nQ, lees xyz keâe ceeve keäÙee nw? 
 (a) 1/3 (b) 1/6 
 (c) 1/2 (d) 1/4 
23.  In triangle PQR, the internal bisector of ?Q 
and ?R meets at O. If ?QPR = 70
0
, then what 
is the value (in degrees) of ?QOR ?  
  ef$eYegpe PQR ceW, ?Q leLee ?R keâe Deebleefjkeâ 
efÉYeepekeâ O hej efceueles nQ~ Ùeefo ?QPR = 70
0
, nQ, lees 
?QOR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 45  (b) 125  
 (c) 115 (d) 110 
24.  PQR is a triangle such that PQ = PR. RS and 
QT are the median to the sides PQ and PR 
respectively. If the medians RS and QT 
intersect at right angle, then what is the value 
of (PQ/QR)
2
 ?  
  PQR Fme Øekeâej Skeâ ef$eYegpe nw efkeâ PQ = PR nw~ RS 
leLee QT ›eâceMe: YegpeeDeeW PQ leLee PR hej ceeefOÙekeâeSB 
nQ~ Ùeefo ceeefOÙekeâeSB RS leLee QR mecekeâesCe hej ØeefleÛÚso 
keâjleer nQ, lees (PQ/QR)
2
 keâe ceeve keäÙee nw? 
 (a) 3/2 (b) 5/2 
 (c) 2 
 (d) None of these/FveceW mes keâesF& veneR 
 
25.  PQR is a triangle. S and T are the midpoints of 
the sides PQ and PR respectively. Which of the 
following is TRUE ?  
  I. Triangle PST is similar to triangle PQR. 
  II. ST = 1/2 (QR) 
  III. ST is parallel to QR.  
  PQR Skeâ ef$eYegpe nw~ S leLee T ›eâceMe: YegpeeDeeW PQ 
leLee PR kesâ ceOÙe efyevog nw~ efvecveefueefKele ceW mes keâewve mee 
melÙe nw? 
  I.    ef$eYegpe PST, ef$eYegpe PQR kesâ meceeve nw~ 
  II.   ST = 1/2 (QR) 
  III. ST, QR kesâ meceeblej nw~ 
 (a) Only I and II/kesâJeue I leLee II 
  (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
26.  ABC is a triangle in which ?ABC = 90
0
. BD is 
perpendicular to AC. Which of the following is 
TRUE ?  
  ABC Skeâ ef$eYegpe nQ efpemeceW ?ABC = 90
0
 nw~ BD, 
AC hej uecye nw~ efvecveefueefKele ceW mes keâewve mee melÙe nw? 
  I.  Triangle BAD is similar to triangle CBD./ 
   ef$eYegpe BAD, ef$eYegpe CBD kesâ meceeve nw~ 
  II.  Triangle BAD is similar to triangle CAB./ 
   ef$eYegpe BAD, ef$eYegpe CAB kesâ meceeve nw~ 
  III. Triangle CBD is similar to triangle CAB./ 
   ef$eYegpe CBD, ef$eYegpe CAB kesâ meceeve nw~ 
 (a) Only I/kesâJeue I  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
27.  Two parallel chords are on the one side of the 
centre of a circle. The length of the two chords 
is 24 cm and 32 cm. If the distance between the 
two chords is 8 cm, then what is the area (in 
cm
2
) of the circle ?  
  oes meceeblej peerJeeSB Skeâ Je=òe kesâ kesâvõ keâer Skeâ Deesj nQ~ 
oesveeW peerJeeDeeW keâer uecyeeF& 24 mes.ceer. leLee 32 mes.ceer. nw~ 
Ùeefo oesveeW peerJeeDeeW kesâ ceOÙe 8 mes.ceer. keâer otjer nw, lees 
Je=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 724.14  (b) 832.86 
 (c) 924.12 (d) 988.32 
28.  Two circles of radius 4 cm and 6 cm touch each 
other internally. What is the length (in cm) of 
the longest chord of the outer circle, which is 
also a tangent to inner circle ?  
  4 mes.ceer. leLee 6 mes.ceer. ef$epÙee Jeeues oes Je=òe Skeâ otmejs 
keâes Deboj mes Útles nQ~ yee¢e Je=òe keâer meyemes uecyeer peerJee 
pees Deble:Je=òe keâer mheMe& jsKee Yeer nw, keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 12 2 (b) 8 2 
 (c) 6 2 (d) 4 2 
29.  In the given figure, PT is a common tangent to 
three circles at points, A, B and C respectively. 
The radius of the small, medium and large 
circles is 4 cm, 6 cm and 9 cm. O
1
, O
2
 and O
3
 
are the centre of the three circles. What is the 
value (in cm) of PC ?  
  oer ieF& Deeke=âefle ceW, PT leerve Je=òeeW hej leerve efyevogDeeW 
›eâceMe: A, B leLee C hej GYeÙeefve<" DevegmheMe& jsKee nw~ 
Úesšs, ceOÙe leLee meyemes yeÌ[s Je=òeeW keâer ef$epÙee 4 mes.ceer., 
6 mes.ceer. SJeb 9 mes.ceer. nw~ O
1
, O
2
 leLee O
3
 leerveeW Je=òeeW 
kesâ kesâvõ nQ~ PC keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 6 (b) 9 6 
 (c) 24 6 (d) 15 6 
30.  PQRS is a cyclic quadrilateral. PR and QS 
intersect at T. If ?SPR = 40
0
 and ?PQS = 80
0
, 
then what is the value (in degrees) of ?PSR ?  
  PQRS Skeâ Ûe›eâerÙe ÛelegYeg&pe nw~ PR leLee QS, T hej 
ØeefleÛÚso keâjles nQ~ Ùeefo ?SPR = 40
0
 leLee ?PQS = 
80
0 
nw, ?PSR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 60  (b) 40  
 (c) 80 (d) 100 
31.  In the given figure, ?PSR = 105
0
 and PQ is the 
diameter of the circle. What is the value (in 
degrees) of ?QPR ?  
  oer ieF& Deeke=âefle ceW, ?PSR = 105
0
 leLee PQ Je=òe keâe 
JÙeeme nw~ ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 75 (b) 15  
 (c) 30 (d) 45 
32.  There are two identical circles of radius 10 cm 
each. If the length of the direct common 
tangent is 26 cm, then what is the length (in 
cm) of the transverse common tangent ?  
  10 mes.ceer. ef$epÙee Jeeues oes mece™heer Je=òe nQ~ Ùeefo 
GYeÙeefve<" DevegmheMe& jsKee keâer uecyeeF& 26 mes.ceer. nw, lees 
GYeÙeefve<" efleÙe&keâ DevegmheMe& jsKee keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 2 69 (b) 4 23 
 (c) 4 46 (d) 3 46 
 
33.  PQRS is a rectangle in which side of PQ = 24 
cm and QR = 16 cm. T is a point on RS. What 
is the area (in cm) of the triangle PTQ ?  
  PQRS Skeâ DeeÙele nw efpemekeâer Yegpee PQ = 24 mes.ceer. 
leLee QR = 16 mes.ceer. nw~ efyevog T, RS hej nw~ ef$eYegpe 
PTQ keâe #es$eHeâue (mes.ceer. ceW) keäÙee nw? 
 (a) 192  
 (b) 162 
 (c) 148 
 (d) Cannot be determined/%eele veneR efkeâÙee pee mekeâlee 
34.  In the given figure, ABCD and BEFG are 
squares of sides 8 cm and 6 cm respectively. 
What is the area (in cm
2
) of the shaded region?  
  oer ieF& Deeke=âefle ceW, ABCD leLee BEFG ›eâceMe: 8 
mes.ceer. leLee 6 mes.ceer. Yegpee Jeeues Jeie& nQ~ DeeÛÚeefole 
Yeeie keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 14  (b) 12  
 (c) 8 (d) 16 
35.  PQRS is a parallelogram and its area is 300 
cm
2
. Side PQ is extended to X such that PQ = 
QX. If XS intersects QR at Y, then what is the 
area (in cm
2
) of triangle SYR ?  
  PQRS Skeâ meceevlej ÛelegYeg&pe nw leLee Gmekeâe #es$eHeâue 
300 mes.ceer.
2
 nw~ Yegpee PQ keâes X lekeâ Fme lejn yeÌ{eÙee 
ieÙee efkeâ PQ = QX nw~ Ùeefo XS, QR keâes Y hej keâešlee 
nw, lees ef$eYegpe SYR keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 75  (b) 50  
 (c) 120 (d) 100 
36.  PQRST is a regular pentagon. If PR and QT 
intersects each other at X, then what is the 
value (in degrees) of ?TXR ?  
  PQRST Skeâ mece hebÛeYegpe nw~ Ùeefo PR leLee QT Skeâ 
otmejs keâes X hej ØeefleÛÚso keâjles nQ, lees ?TXR keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 (a) 98  (b) 90  
 (c) 72 (d) 108 
37.  In the given figure, ABCDEF is a regular 
hexagon whose side is 12 cm. What is the 
shaded area (in cm
2
) ?  
  oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešYegpe nw 
efpemekeâer Yegpee 12 mes.ceer. nw~ DeeÛÚeefole Yeeie keâe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 54 3 (b) 36 3 
 (c) 48 3 (d) 52 3 
38.  ABCD passes through the centres of the three 
circles as shown in the figure. AB = 2 cm and 
CD = 1. If the area of middle circle is the 
average of the areas of the other two circles, 
then what is the length (in cm) of BC ?  
  pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw, ABCD leerveeW 
Je=òeeW kesâ kesâvõeW mes iegpejleer nw~ AB = 2 mes.ceer. leLee CD 
= 1 mes.ceer. nQ~ Ùeefo ceOÙe Je=òe keâe #es$eHeâue, Mes<e oesveeW 
Je=òeeW kesâ #es$eHeâueeW keâe Deewmele nw, lees BC keâer uecyeeF& 
(mes.ceer. ceW) keäÙee nw? 
 
 (a) 
( )
6 1 -  (b) 
( )
6 1 + 
 (c) 
( )
6 3 - (d) 
( )
6 3 + 
39.  A = Area of the largest circle drawn inside a 
square of side 1 cm./1 mes.ceer. Yegpee Jeeues Jeie& ceW 
meyemes yeÌ[s Je=òe keâe #es$eHeâue~ 
  B = Sum of areas of 4 identical (largest 
possible) circles drawn inside a square of side 1 
cm./1 mes. ceer. Yegpee Jeeues Jeie& ceW 4 mece™he Je=òeeW 
(meyemes yeÌ[s mebYeJe) kesâ #es$eHeâue keâe Ùeesie~ 
  C = Sum of areas of 9 identical circle (largest 
possible) drawn inside a square of side 1 cm./1 
mes.ceer. Yegpee Jeeues Jeie& ceW 9 mece™he Je=òeeW (meyemes yeÌ[s 
mebYeJe) kesâ #es$eHeâueeW keâe Ùeesie~ 
  D = Sum of area of 16 identical circles (largest 
possible) drawn inside a square of side 1 cm./1 
mes.ceer. Yegpee Jeeues Jeie& ceW 16 mece™he Je=òeeW (meyemes yeÌ[s 
mebYeJe) kesâ #es$eHeâue keâe Ùeesie~ 
  Which of the following is TRUE about A, B, C 
and D ?  
  efvecveefueefKele ceW mes A, B, C leLee D kesâ yeejs ceW keâewve mee 
melÙe nw? 
 (a) A > B > C > D 
 (b) A < B < C < D 
 (c) A > B = C > D 
 (d) No option is correct/keâesF& efJekeâuhe mener veneR nw~ 
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hegvehe&jer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  If the unit digit of 433 × 456 × 43N is (N + 2), 
then what is the value of N ?  
  Ùeefo 433 × 456 × 43N  keâe FkeâeF& Debkeâ (N + 2) nw, 
lees N keâe ceeve keäÙee nw? 
 (a) 1 (b) 8  
 (c) 3 (d) 6 
2.  If N = (12345)
2
 + 12345 + 12346, then what is 
the value of N ?  
  Ùeefo N = (12345)
2
 + 12345 + 12346, nw, lees N 
keâe ceeve keäÙee nw? 
 (a) 12346 (b) 12345 
 (c) 12344 (d) 12347 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nQ? 
  I. (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + 
(0.00003/0.0002) = 0.6
 
 
 II. (0.01) + (0.01)
2
 + (0.001)
2
 = 0.010101 
 (a) Only I/ kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
4.  What is the value of 1/(0.1)
2
 + 1/(0.01)
2
 + 
1/(0.5)
2
 + 1/(0.05)
2
 ?  
  1/(0.1)
2
 + 1/(0.01)
2
 + 1/(0.5)
2
 + 1/(0.05)
2 
keâe ceeve 
keäÙee nw? 
 (a) 10504 (b) 10404 
 (c) 10004 (d) 11400 
5.  Which of the following statement(s) is/are 
True?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
? ? ? ? ? ? ? ?
? ?? ?? ? ? ?
? ? ? ? ? ? ? ?
1 1 1 1
1 + 1 + 1 + ... 1 + > 497
2 3 4 998
 
  II. 
3 1 1 1 3 1
14 + 5 - 2 > 11 + 12 - 7
4 4 2 8 8 4
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
6.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
3 9 7
< <
110 308 225
 
  II. 
1 2 3 6
99 + 99 + 99 + ...99 = 279
7 7 7 7
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
7.  If ( )
1 1
f x = - ,
x x + 1
 then what is the value of 
f(1) + f(2) + f(3) + ..... f(10) ?  
  Ùeefo ( )
1 1
f x = - ,
x x + 1
nw, lees f(1) + f(2) + f(3) + ..... 
f(10) keâe ceeve keäÙee nw? 
 (a) 9/10  (b) 10/11 
 (c) 11/12 (d) 12/13 
8.  If N = 4
11
 + 4
12
 + 4
13
 + 4
14
 , then how many 
positive factors of N are there ?  
  Ùeefo N = 4
11
 + 4
12
 + 4
13
 + 4
14
 nw, lees N kesâ efkeâleves 
Oeveelcekeâ iegCeveKeC[ nQ? 
 (a) 92 (b) 48  
 (c) 50 (d) 51 
9.  If N = 9
9
, then N is divisible by how many 
positive perfect cubes ?  
  Ùeefo N = 9
9
 nw, lees N efkeâleves Oeveelcekeâ IeveeW mes efJeYeepÙe 
nw? 
 (a) 6 (b) 7  
 (c) 4 (d) 5 
10.  If N = 3
14
 + 3
13
 – 12, then what is the largest 
prime factor of N ?  
  Ùeefo N = 3
14
 + 3
13
 – 12, nw, lees N keâe meyemes yeÌ[e 
DeYeepÙe iegCeveKeC[ keäÙee nw? 
 (a) 11 (b) 79 
 (c) 13 (d) 73 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 121 + 12321 + 1234321 = 1233 
  II. 0.64 + 64 + 36 + 0.36 > 15 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Neither I nor II/ve lees I ve ner II 
 (d) Both I and II/I leLee II oesveeW 
 
12.  What is the value of  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
 
  
( ) ( )
? ? ? ?
? ? ? ?
? ? ? ?
1 1
2 + 2 + + + 2 - 2
2 + 2 2 - 2
keâe ceeve 
keäÙee nw? 
 (a) 2 (b) 4  
 (c) 8 (d) 6 
13.  The sum of two positive numbers is 14 and 
difference between their squares is 56. What is 
the sum of their squares ?  
  oes Oeveelcekeâ mebKÙeeDeeW keâe Ùeesie 14 nw leLee Gvekesâ Jeie& 
kesâ ceOÙe keâe Deblej 56 nw~ Gvekesâ Jeie& keâe Ùeesie keäÙee nw? 
 (a) 106 (b) 196 
 (c) 53 (d) 68 
14.  What is the value of 1006
2
 – 1007 × 1005 + 1008 
× 1004 – 1009 × 1003 ?  
  1006
2
 – 1007 × 1005 + 1008 × 1004 – 1009 × 
1003 keâe ceeve keäÙee nw ? 
 (a) 6  (b) 3  
 (c) 12 (d) 24 
15.  If a
2
 + b
2
 = 4b + 6a – 13, then what is the value 
of a + b ?  
  Ùeefo a
2
 + b
2
 = 4b + 6a – 13, nw, lees a + b keâe ceeve 
keäÙee nw? 
 (a) 3  (b) 2  
 (c) 5 (d) 10 
16.  x and y are positive integers. If x
4
 + y
4
 + x
2
y
2
 = 
481 and xy = 12, then what is the value of  
x
2
 – xy + y
2
 ? 
  x leLee y Skeâ Oeveelcekeâ hetCeeËkeâ nw~ Ùeefo x
4
 + y
4
 + x
2
y
2
 
= 481 leLee xy = 12 nw, lees x
2
 – xy + y
2
 keâe ceeve keäÙee 
nw? 
 (a) 16  (b) 13  
 (c) 11 (d) 15 
17.  If A = 1 + 2
P
 and B = 1 + 2
–P
, then what is the 
value of B ?  
  Ùeefo A = 1 + 2
P
 leLee B = 1 + 2
–P
 nw, lees B keâe ceeve 
keäÙee nw? 
 (a) (A + 1)/(A–1) (b) (A+2)/(A+1) 
 (c) A/(A–1) (d) (A–2)/(A+1) 
18.  If a and b are roots of the equation 
ax
2
+bx+c=0, then which equation will have 
roots (ab + a + b) and (ab–a–b) ?  
  Ùeefo a leLee b meceerkeâjCe ax
2 
+ bx + c = 0 kesâ cetue nQ, 
lees efkeâme meceerkeâjCe kesâ cetue (ab + a + b) leLee  
(ab–a–b) neWies? 
 (a) a
2
x
2
 + 2acx + c
2
 + b
2
 = 0  
 (b) a
2
x
2
 – 2acx + c
2
 – b
2
 = 0 
 (c) a
2
x
2
 – 2acx + c
2
 + b
2
 = 0 
 (d) a
2
x
2
 + 2acx + c
2
 – b
2
 = 0 
19.  If 
( )( )
2 2
3
1- p 1- q =
2
then what is the value 
of 
2 2 2 2
2p + 2q + 2pq + 2p + 2q - 2pq ? 
  Ùeefo 
( )( )
2 2
3
1 - p 1- q =
2
 nw lees 
2 2
2p + 2q + 2pq 
2 2
+ 2p + 2q - 2pq keâe ceeve keäÙee nw? 
 (a) 2 
 (b) 2  
 (c) 1 
 (d) None of these/FveceW mes keâesF& veneR 
20.  If (a+b)
2
 – 2(a+b) = 80 and ab = 16, then what 
can be the value of 3a–19b ?  
  Ùeefo (a+b)
2
 – 2(a+b) = 80 leLee ab = 16, nQ, lees  
3a–19b keâe ceeve keäÙee nes mekeâlee nw? 
 (a) –16 (b) –14 
 (c) –18 (d) –20 
21.  If x
y+z
 = 1, y
z+x
 = 1024 and z
x+y
 = 729 (x, y and z 
are natural numbers), then what is the value of  
(z+1)
y+x+1
 ? 
  Ùeefo x
y+z
 = 1, y
z+x
 = 1024  leLee z
x+y
 = 729 (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees  (z+1)
y+x+1 
keâe ceeve keäÙee 
nw? 
 (a) 6561  (b) 10000 
 (c) 4096 (d) 14641 
22.  If x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 and x
3
 + y
3
 + z
3
=3, 
then what is the value of xyz ?  
  Ùeefo x+y+z = 1, x
2
 + y
2
 + z
2
 = 2 leLee x
3
 + y
3
 + 
z
3
=3, nQ, lees xyz keâe ceeve keäÙee nw? 
 (a) 1/3 (b) 1/6 
 (c) 1/2 (d) 1/4 
23.  In triangle PQR, the internal bisector of ?Q 
and ?R meets at O. If ?QPR = 70
0
, then what 
is the value (in degrees) of ?QOR ?  
  ef$eYegpe PQR ceW, ?Q leLee ?R keâe Deebleefjkeâ 
efÉYeepekeâ O hej efceueles nQ~ Ùeefo ?QPR = 70
0
, nQ, lees 
?QOR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 45  (b) 125  
 (c) 115 (d) 110 
24.  PQR is a triangle such that PQ = PR. RS and 
QT are the median to the sides PQ and PR 
respectively. If the medians RS and QT 
intersect at right angle, then what is the value 
of (PQ/QR)
2
 ?  
  PQR Fme Øekeâej Skeâ ef$eYegpe nw efkeâ PQ = PR nw~ RS 
leLee QT ›eâceMe: YegpeeDeeW PQ leLee PR hej ceeefOÙekeâeSB 
nQ~ Ùeefo ceeefOÙekeâeSB RS leLee QR mecekeâesCe hej ØeefleÛÚso 
keâjleer nQ, lees (PQ/QR)
2
 keâe ceeve keäÙee nw? 
 (a) 3/2 (b) 5/2 
 (c) 2 
 (d) None of these/FveceW mes keâesF& veneR 
 
25.  PQR is a triangle. S and T are the midpoints of 
the sides PQ and PR respectively. Which of the 
following is TRUE ?  
  I. Triangle PST is similar to triangle PQR. 
  II. ST = 1/2 (QR) 
  III. ST is parallel to QR.  
  PQR Skeâ ef$eYegpe nw~ S leLee T ›eâceMe: YegpeeDeeW PQ 
leLee PR kesâ ceOÙe efyevog nw~ efvecveefueefKele ceW mes keâewve mee 
melÙe nw? 
  I.    ef$eYegpe PST, ef$eYegpe PQR kesâ meceeve nw~ 
  II.   ST = 1/2 (QR) 
  III. ST, QR kesâ meceeblej nw~ 
 (a) Only I and II/kesâJeue I leLee II 
  (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
26.  ABC is a triangle in which ?ABC = 90
0
. BD is 
perpendicular to AC. Which of the following is 
TRUE ?  
  ABC Skeâ ef$eYegpe nQ efpemeceW ?ABC = 90
0
 nw~ BD, 
AC hej uecye nw~ efvecveefueefKele ceW mes keâewve mee melÙe nw? 
  I.  Triangle BAD is similar to triangle CBD./ 
   ef$eYegpe BAD, ef$eYegpe CBD kesâ meceeve nw~ 
  II.  Triangle BAD is similar to triangle CAB./ 
   ef$eYegpe BAD, ef$eYegpe CAB kesâ meceeve nw~ 
  III. Triangle CBD is similar to triangle CAB./ 
   ef$eYegpe CBD, ef$eYegpe CAB kesâ meceeve nw~ 
 (a) Only I/kesâJeue I  
 (b) Only II and III/kesâJeue II leLee III  
 (c) Only I and III/kesâJeue I leLee III 
 (d) All I, II and III/I, II leLee III meYeer 
27.  Two parallel chords are on the one side of the 
centre of a circle. The length of the two chords 
is 24 cm and 32 cm. If the distance between the 
two chords is 8 cm, then what is the area (in 
cm
2
) of the circle ?  
  oes meceeblej peerJeeSB Skeâ Je=òe kesâ kesâvõ keâer Skeâ Deesj nQ~ 
oesveeW peerJeeDeeW keâer uecyeeF& 24 mes.ceer. leLee 32 mes.ceer. nw~ 
Ùeefo oesveeW peerJeeDeeW kesâ ceOÙe 8 mes.ceer. keâer otjer nw, lees 
Je=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 724.14  (b) 832.86 
 (c) 924.12 (d) 988.32 
28.  Two circles of radius 4 cm and 6 cm touch each 
other internally. What is the length (in cm) of 
the longest chord of the outer circle, which is 
also a tangent to inner circle ?  
  4 mes.ceer. leLee 6 mes.ceer. ef$epÙee Jeeues oes Je=òe Skeâ otmejs 
keâes Deboj mes Útles nQ~ yee¢e Je=òe keâer meyemes uecyeer peerJee 
pees Deble:Je=òe keâer mheMe& jsKee Yeer nw, keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 12 2 (b) 8 2 
 (c) 6 2 (d) 4 2 
29.  In the given figure, PT is a common tangent to 
three circles at points, A, B and C respectively. 
The radius of the small, medium and large 
circles is 4 cm, 6 cm and 9 cm. O
1
, O
2
 and O
3
 
are the centre of the three circles. What is the 
value (in cm) of PC ?  
  oer ieF& Deeke=âefle ceW, PT leerve Je=òeeW hej leerve efyevogDeeW 
›eâceMe: A, B leLee C hej GYeÙeefve<" DevegmheMe& jsKee nw~ 
Úesšs, ceOÙe leLee meyemes yeÌ[s Je=òeeW keâer ef$epÙee 4 mes.ceer., 
6 mes.ceer. SJeb 9 mes.ceer. nw~ O
1
, O
2
 leLee O
3
 leerveeW Je=òeeW 
kesâ kesâvõ nQ~ PC keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 18 6 (b) 9 6 
 (c) 24 6 (d) 15 6 
30.  PQRS is a cyclic quadrilateral. PR and QS 
intersect at T. If ?SPR = 40
0
 and ?PQS = 80
0
, 
then what is the value (in degrees) of ?PSR ?  
  PQRS Skeâ Ûe›eâerÙe ÛelegYeg&pe nw~ PR leLee QS, T hej 
ØeefleÛÚso keâjles nQ~ Ùeefo ?SPR = 40
0
 leLee ?PQS = 
80
0 
nw, ?PSR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 60  (b) 40  
 (c) 80 (d) 100 
31.  In the given figure, ?PSR = 105
0
 and PQ is the 
diameter of the circle. What is the value (in 
degrees) of ?QPR ?  
  oer ieF& Deeke=âefle ceW, ?PSR = 105
0
 leLee PQ Je=òe keâe 
JÙeeme nw~ ?QPR keâe ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 75 (b) 15  
 (c) 30 (d) 45 
32.  There are two identical circles of radius 10 cm 
each. If the length of the direct common 
tangent is 26 cm, then what is the length (in 
cm) of the transverse common tangent ?  
  10 mes.ceer. ef$epÙee Jeeues oes mece™heer Je=òe nQ~ Ùeefo 
GYeÙeefve<" DevegmheMe& jsKee keâer uecyeeF& 26 mes.ceer. nw, lees 
GYeÙeefve<" efleÙe&keâ DevegmheMe& jsKee keâer uecyeeF& (mes.ceer. 
ceW) keäÙee nw? 
 (a) 2 69 (b) 4 23 
 (c) 4 46 (d) 3 46 
 
33.  PQRS is a rectangle in which side of PQ = 24 
cm and QR = 16 cm. T is a point on RS. What 
is the area (in cm) of the triangle PTQ ?  
  PQRS Skeâ DeeÙele nw efpemekeâer Yegpee PQ = 24 mes.ceer. 
leLee QR = 16 mes.ceer. nw~ efyevog T, RS hej nw~ ef$eYegpe 
PTQ keâe #es$eHeâue (mes.ceer. ceW) keäÙee nw? 
 (a) 192  
 (b) 162 
 (c) 148 
 (d) Cannot be determined/%eele veneR efkeâÙee pee mekeâlee 
34.  In the given figure, ABCD and BEFG are 
squares of sides 8 cm and 6 cm respectively. 
What is the area (in cm
2
) of the shaded region?  
  oer ieF& Deeke=âefle ceW, ABCD leLee BEFG ›eâceMe: 8 
mes.ceer. leLee 6 mes.ceer. Yegpee Jeeues Jeie& nQ~ DeeÛÚeefole 
Yeeie keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 14  (b) 12  
 (c) 8 (d) 16 
35.  PQRS is a parallelogram and its area is 300 
cm
2
. Side PQ is extended to X such that PQ = 
QX. If XS intersects QR at Y, then what is the 
area (in cm
2
) of triangle SYR ?  
  PQRS Skeâ meceevlej ÛelegYeg&pe nw leLee Gmekeâe #es$eHeâue 
300 mes.ceer.
2
 nw~ Yegpee PQ keâes X lekeâ Fme lejn yeÌ{eÙee 
ieÙee efkeâ PQ = QX nw~ Ùeefo XS, QR keâes Y hej keâešlee 
nw, lees ef$eYegpe SYR keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 75  (b) 50  
 (c) 120 (d) 100 
36.  PQRST is a regular pentagon. If PR and QT 
intersects each other at X, then what is the 
value (in degrees) of ?TXR ?  
  PQRST Skeâ mece hebÛeYegpe nw~ Ùeefo PR leLee QT Skeâ 
otmejs keâes X hej ØeefleÛÚso keâjles nQ, lees ?TXR keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 (a) 98  (b) 90  
 (c) 72 (d) 108 
37.  In the given figure, ABCDEF is a regular 
hexagon whose side is 12 cm. What is the 
shaded area (in cm
2
) ?  
  oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešYegpe nw 
efpemekeâer Yegpee 12 mes.ceer. nw~ DeeÛÚeefole Yeeie keâe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 54 3 (b) 36 3 
 (c) 48 3 (d) 52 3 
38.  ABCD passes through the centres of the three 
circles as shown in the figure. AB = 2 cm and 
CD = 1. If the area of middle circle is the 
average of the areas of the other two circles, 
then what is the length (in cm) of BC ?  
  pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw, ABCD leerveeW 
Je=òeeW kesâ kesâvõeW mes iegpejleer nw~ AB = 2 mes.ceer. leLee CD 
= 1 mes.ceer. nQ~ Ùeefo ceOÙe Je=òe keâe #es$eHeâue, Mes<e oesveeW 
Je=òeeW kesâ #es$eHeâueeW keâe Deewmele nw, lees BC keâer uecyeeF& 
(mes.ceer. ceW) keäÙee nw? 
 
 (a) 
( )
6 1 -  (b) 
( )
6 1 + 
 (c) 
( )
6 3 - (d) 
( )
6 3 + 
39.  A = Area of the largest circle drawn inside a 
square of side 1 cm./1 mes.ceer. Yegpee Jeeues Jeie& ceW 
meyemes yeÌ[s Je=òe keâe #es$eHeâue~ 
  B = Sum of areas of 4 identical (largest 
possible) circles drawn inside a square of side 1 
cm./1 mes. ceer. Yegpee Jeeues Jeie& ceW 4 mece™he Je=òeeW 
(meyemes yeÌ[s mebYeJe) kesâ #es$eHeâue keâe Ùeesie~ 
  C = Sum of areas of 9 identical circle (largest 
possible) drawn inside a square of side 1 cm./1 
mes.ceer. Yegpee Jeeues Jeie& ceW 9 mece™he Je=òeeW (meyemes yeÌ[s 
mebYeJe) kesâ #es$eHeâueeW keâe Ùeesie~ 
  D = Sum of area of 16 identical circles (largest 
possible) drawn inside a square of side 1 cm./1 
mes.ceer. Yegpee Jeeues Jeie& ceW 16 mece™he Je=òeeW (meyemes yeÌ[s 
mebYeJe) kesâ #es$eHeâue keâe Ùeesie~ 
  Which of the following is TRUE about A, B, C 
and D ?  
  efvecveefueefKele ceW mes A, B, C leLee D kesâ yeejs ceW keâewve mee 
melÙe nw? 
 (a) A > B > C > D 
 (b) A < B < C < D 
 (c) A > B = C > D 
 (d) No option is correct/keâesF& efJekeâuhe mener veneR nw~ 
 
40.  A prism has a square base whose side is 8 cm. 
The height of prism is 80 cm. The prism is cut 
into 10 identical parts by 9 cuts which are 
parallel to base of prism. What is the total 
surface area (in cm
2
) of all the 10 parts 
together ?  
  Skeâ efØepce keâe DeeOeej Jeie& nw efpemekeâer Yegpee 8 mes.ceer. nw~ 
efØepce keâer TBÛeeF& 80 mes.ceer. nw~ efØepce keâes DeeOeej kesâ 
meceeblej 9 keâšeJeeW mes 10 YeeieeW ceW keâeše ieÙee~ 10 
YeeieeW keâe kegâue efceueekeâj kegâue he=<"erÙe #es$eHeâue 
(mes.ceer.
2
) ceW keäÙee nw? 
 (a) 4260 (b) 2560 
 (c) 3840 (d) 3220 
41.  A cone of radius 90 cm and height 120 cm 
stands on its base. It is cut into 3 parts by 2 cuts 
parallel to its base such that the height of the 
three parts (from top to bottom) are into ratio 
of 1 : 2 : 3. What is the total surface area (in 
cm
2
) of the middle part ?  
  Skeâ 90 mes.ceer. ef$epÙee leLee TBÛeeF& 120 mes.ceer. TBÛeeF& 
Jeeuee Mebkegâ Deheves DeeOeej hej KeÌ[e nw~ Fmes DeeOeej kesâ 
meceeblej 2 keâšeJe mes 3 YeeieeW ceW Fme Øekeâej keâeše peelee 
nw efkeâ leerveeW YeeieeW keâer TBÛeeF& (Thej mes veerÛes keâer Deesj) 
keâe Devegheele 1:2:3 nQ~ ceOÙe Yeeie keâe kegâue he=<"erÙe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 14600 (b) 16500 
 (c) 17800 (d) 18500 
42.  The curved surface area of a cylinder is 594 
cm
2
 and its volume is 1336.5 cm
3
. What is the 
height (in cm) of the cylinder ?  
  Skeâ yesueve keâe Je›eâ he=<"erÙe #es$eHeâue 594 mes.ceer.
2
 nw leLee 
Gmekeâe DeeÙeleve 1336.5 mes.ceer.
3
 nw~ yesueve keâer TBÛeeF& 
(mes.ceer. ceW) keäÙee nw? 
 (a) 14 (b) 21  
 (c) 24.5 (d) 10.5 
43.  A hollow cylinder is made up of metal. The 
difference between outer and inner curved 
surface area of this cylinder is 352 cm
2
. Height 
of the cylinder is 28 cm. If the total surface 
area of this hollow cylinder is 2640 cm
2
, then 
what are the inner and outer radius (in cm) ?  
  Oeeleg keâe Skeâ KeesKeuee yesueve yeveeÙee ieÙee nw~ yesueve kesâ 
yee¢e leLee Deebleefjkeâ Je›eâ he=<"erÙe #es$eHeâue kesâ ceOÙe 352 
mes.ceer.
2
 keâe Deblej nw~ yesueve keâer TBÛeeF& 28 mes.ceer. nw~ Ùeefo 
Fme KeesKeues yesueve keâe kegâue he=<"erÙe #es$eHeâue 2640 
mes.ceer.
2
 nw, lees yesueve keâer Deebleefjkeâ leLee yee¢e ef$epÙee 
(mes.ceer. ceW) keäÙee nw? 
 (a) 4, 6 (b) 10, 12  
 (c) 8, 10 (d) 6, 8 
44.  A solid metal sphere has radius 14 cm. It is 
melted to form small cones of radius 1.75 cm 
and height 3.5 cm. How many small cones will 
be obtained from the sphere ?  
  Skeâ Oeeleg kesâ "esme ieesues keâer ef$epÙee 14 mes.ceer. nw~ Fmes 
efheIeueekeâj 1.75 mes.ceer. ef$epÙee leLee 3.5 mes.ceer. TBÛeeF& 
Jeeues MebkegâDeeW ceW yeveeÙee ieÙee~ ieesues mes efkeâleves Úesšs Mebkegâ 
yeveeS pee mekeâles nQ? 
 (a) 512  (b) 256 
 (c) 1024 (d) 2048 
45.  A metallic hemispherical bowl is made up of 
steel. The total steel used in making the bowl is 
342p cm
3
. The bowl can hold 144p cm
3
 water. 
What is the thickness (in cm) of bowl and the 
curved surface area (in cm
2
) of outer side ?  
  Fmheele mes Oeeleg keâe Skeâ DeOe&ieesueekeâej keâšesje yeveeÙee 
ieÙee nw~ keâšesjs keâes yeveeves ceW kegâue 342p mes.ceer.
3
 Fmheele 
keâe ØeÙeesie efkeâÙee ieÙee nw~ keâšesje ceW 144p mes.ceer.
3
 peue 
Dee mekeâlee nw~ keâšesjs keâer ceesšeF& (mes.ceer. ceW) leLee yeenjer 
melen keâe Je›eâ he=<"erÙe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 6, 162cm
2 
(b) 3, 162cm
2
 
 (c) 6,81cm
2
 (d) 3, 81cm
2
 
46.  There is a box of cuboid shape. The smallest 
side of the box is 20 cm and largest side is 40 
cm. Which of the following can be volume (in 
cm
3
) of the box ?  
  IeveeYe Deekeâej keâe Skeâ yekeämee nw~ yekeämes keâer meyemes 
Úesšer Yegpee 20 mes.ceer. leLee meyemes yeÌ[er Yegpee 40 
mes.ceer. nw~ efvecveefueefKele ceW mes yekeämes keâe DeeÙeleve 
(mes.ceer.
3
 ceW) keäÙee nes mekeâlee nw? 
 (a) 18000 (b) 12000 
 (c) 36000 (d) 42000 
47.  A pyramid has a square base, whose side is 8 
cm. If the height of pyramid is 16 cm, then 
what is the total surface area (in cm
2
) of the 
pyramid?  
  Skeâ efhejeefce[ keâe DeeOeej Jeie& nw efpemekeâer Yegpee 8 mesceer. 
nw~ Ùeefo efhejeefce[ keâer G@BâÛeeF& 16 mesceer. nw, lees efhejeefce[ 
keâe kegâue he=‰erÙe #es$eheâue (mesceer.
2
 ceW) keäÙee nw~? 
 (a) 
( )
64 17 1 + (b) 
( )
31 13 1 + 
 (c) 
( )
64 3 1 + (d) 
( )
32 5 1 + 
48.  What is the value of 
( )
( )
2 2
2 2
2 1 - sin ? cosec ?
- 1
cot ? 1 + tan ?
?   
  
( )
( )
2 2
2 2
2 1 - sin ? cosec ?
- 1
cot ? 1 + tan ?
 keâe ceeve keäÙee nw? 
 (a) sin
2
?  (b) sin2? 
 (c) cos
2
? (d) cos 2? 
49.  What is the value of 
2
2
cos2A + 2cos A - 2cos2AcosA
sin2A - 2sin Asin2A
 
  
2
2
cos2A + 2cos A - 2cos2AcosA
sin2A - 2sin Asin2A
keâe ceeve keäÙee nw?