SSC CGL Tier 2 (9 March) Shift 1 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 : 9-03-2018, Shift-I  
1.  How many two digit prime numbers are there 
between 10 to 100 which remains prime 
numbers when the order of their digits is 
reversed ?  
  10 mes 100 kesâ yeerÛe oes DebkeâeW keâer Ssmeer efkeâleveer DeYeepÙe 
mebKÙee nw efpevekesâ DebkeâeW kesâ ›eâce keâes heuešves hej Yeer Jes 
Skeâ DeYeepÙe mebKÙee ner jnsieer? 
 (a) 8  (b) 9  
 (c) 10 (d) 12 
2.  How many perfect cubes are there between 1 
and 100000 which are divisible by 7.  
  1 mes 100000 kesâ yeerÛe efkeâleves hetCe& Ieve nQ pees 7 mes 
efJeYeeefpele nw? 
 (a) 5  (b) 6  
 (c) 7 (d) 15 
3.  If A = 0.142857142857 ...... and B = 0.16666...., 
then what is the value of (A+B)/AB ?  
  Ùeefo A = 0.142857142857 ...... leLee B = 
0.16666.......... nw, lees (A+B)/AB keâe ceeve keäÙee nw? 
 (a) 10 (b) 11  
 (c) 12 (d) 13 
4.  If A = 0.abcabc....., then by what number A 
should be multiplied so as to get an integeral 
value ?  
  Ùeefo A = 0.abcabc..... nw, lees A keâes efkeâme mebKÙee mes 
iegCee efkeâÙee peeS leeefkeâ Skeâ hetCeeËkeâ ceeve Øeehle nes? 
 (a) 2997  
 (b) 1000 
 (c) 1998 
 (d) Both 2997 and 1998/2997 leLee 1998 oesveeW 
5.  What is the sum of 
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 
upto 20 terms ?  
  
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 kesâ 20 heoeW lekeâ keâe 
Ùeesie keäÙee nw? 
 (a) 12410/21 (b) 12412/21 
 (c) 12433/21 (d) 1179/2 
6.  If (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k, then 
what is the value of k ?  
  Ùeefo (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k nw, lees 
k keâe ceeve keäÙee nw? 
 (a) 512/511  (b) 1024/1023 
 (c) 511/512 (d) 1023/1024 
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
2 3 4
1 + 2 + 3 > 8
3 4 5
 
  II. 
1 3 1
6 - 5 + 4 > 5
2 4 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 
8.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. Highest common factor of (3
2002
–1) and  
(3
2002
 + 1) is 4/(3
2002
–1) leLee (3
2002
 + 1) keâe cenòece 
meceeheJeòe&keâ 4 nw~ 
  II. (4
84
 –1) is exactly divisible by 5/(4
84
 –1), 5 mes 
hetCe&le: efJeYeeefpele nw~ 
 (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 
9.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 is exactly divisible by 
5./ 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 mes hetCe&le: efJeYeeefpele nw~ 
  II. 31
11
 > 17
14
 
 (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 
10.  N = 2
48
 – 1 and N are exactly divisible by two 
numbers between 60 and 70. What is the sum 
of those two numbers ?  
  N = 2
48
 – 1 leLee N, 60 leLee 70 kesâ yeerÛe oes mebKÙee mes 
hetCe&le: efJeYeeefpele nw~ Gve oes mebKÙeeDeeW keâe Ùeesie keäÙee nw? 
 (a) 128 (b) 256 
 (c) 64 (d) 512 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  How many two digit prime numbers are there 
between 10 to 100 which remains prime 
numbers when the order of their digits is 
reversed ?  
  10 mes 100 kesâ yeerÛe oes DebkeâeW keâer Ssmeer efkeâleveer DeYeepÙe 
mebKÙee nw efpevekesâ DebkeâeW kesâ ›eâce keâes heuešves hej Yeer Jes 
Skeâ DeYeepÙe mebKÙee ner jnsieer? 
 (a) 8  (b) 9  
 (c) 10 (d) 12 
2.  How many perfect cubes are there between 1 
and 100000 which are divisible by 7.  
  1 mes 100000 kesâ yeerÛe efkeâleves hetCe& Ieve nQ pees 7 mes 
efJeYeeefpele nw? 
 (a) 5  (b) 6  
 (c) 7 (d) 15 
3.  If A = 0.142857142857 ...... and B = 0.16666...., 
then what is the value of (A+B)/AB ?  
  Ùeefo A = 0.142857142857 ...... leLee B = 
0.16666.......... nw, lees (A+B)/AB keâe ceeve keäÙee nw? 
 (a) 10 (b) 11  
 (c) 12 (d) 13 
4.  If A = 0.abcabc....., then by what number A 
should be multiplied so as to get an integeral 
value ?  
  Ùeefo A = 0.abcabc..... nw, lees A keâes efkeâme mebKÙee mes 
iegCee efkeâÙee peeS leeefkeâ Skeâ hetCeeËkeâ ceeve Øeehle nes? 
 (a) 2997  
 (b) 1000 
 (c) 1998 
 (d) Both 2997 and 1998/2997 leLee 1998 oesveeW 
5.  What is the sum of 
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 
upto 20 terms ?  
  
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 kesâ 20 heoeW lekeâ keâe 
Ùeesie keäÙee nw? 
 (a) 12410/21 (b) 12412/21 
 (c) 12433/21 (d) 1179/2 
6.  If (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k, then 
what is the value of k ?  
  Ùeefo (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k nw, lees 
k keâe ceeve keäÙee nw? 
 (a) 512/511  (b) 1024/1023 
 (c) 511/512 (d) 1023/1024 
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
2 3 4
1 + 2 + 3 > 8
3 4 5
 
  II. 
1 3 1
6 - 5 + 4 > 5
2 4 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 
8.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. Highest common factor of (3
2002
–1) and  
(3
2002
 + 1) is 4/(3
2002
–1) leLee (3
2002
 + 1) keâe cenòece 
meceeheJeòe&keâ 4 nw~ 
  II. (4
84
 –1) is exactly divisible by 5/(4
84
 –1), 5 mes 
hetCe&le: efJeYeeefpele nw~ 
 (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 
9.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 is exactly divisible by 
5./ 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 mes hetCe&le: efJeYeeefpele nw~ 
  II. 31
11
 > 17
14
 
 (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 
10.  N = 2
48
 – 1 and N are exactly divisible by two 
numbers between 60 and 70. What is the sum 
of those two numbers ?  
  N = 2
48
 – 1 leLee N, 60 leLee 70 kesâ yeerÛe oes mebKÙee mes 
hetCe&le: efJeYeeefpele nw~ Gve oes mebKÙeeDeeW keâe Ùeesie keäÙee nw? 
 (a) 128 (b) 256 
 (c) 64 (d) 512 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
 
  I. 
4
625 + 1296 + 1024 > 90 
  II. 
( ) ( )
3 4
729 + 256 = 5 
 (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.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1 + 2 + 3 + 4 + 5 + 6 > 10 
  II. ( ) ( ) ( ) ( ) 10 + 12 + 14 > 3 12 
 (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 
13.  If y
2
 = y + 7, then what is the value of y
3 
? 
  Ùeefo y
2
 = y + 7 nw, lees y
3
 keâe ceeve keäÙee nw? 
 (a) 8y + 7 (b) y + 14  
 (c) y + 2 (d) 4y + 7 
14.  If f(x) = (x–2)/(x
2
 + Px + 4) and (x–3) is a factor 
of f(x), then what is the value of P ? 
  Ùeefo f(x) = (x–2) (x
2
 + Px + 4) leLee (x–3) f(x) keâe 
iegCeveKeC[ nw, lees P keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) –13/3 (d) 13/3 
15.  If [x–(1/x)] = 2, then what is the value of [x
6
 – 
(1/x
6
)] ? 
  Ùeefo [x–(1/x)] = 2 nw, lees [x
6
 – (1/x
6
)] keâe ceeve keäÙee 
nw? 
 (a) 114 3 1 + (b) 134 2 
 (c) 142 2 3 + (d) 140 2 
16.  x, y and z all are positive number. If 3
x
 > 9
y
 and 
2
y
 > 4
z
, then which of the following is TRUE ?  
   x, y leLee z meYeer Oeveelcekeâ mebKÙee nw~ Ùeefo 3
x
 > 9
y
 
leLee 2
y
 > 4
z
 nw, lees efvecveefueefKele ceW mes keâewve melÙe nw? 
 (a) x > y > z (b) x > z > y 
 (c) z > y > x (d) y > x > z 
17.  If x = (1/8), which of the following has the 
largest values ?  
  Ùeefo x = (1/8) nw, lees efvecveefueefKele ceW mes efkeâmekeâe ceeve 
meyemes yeÌ[e nw? 
 (a) x/2  (b) x
2
 
 (c) x (d) 1/x 
18.  If 
1
X =
1
1 +
1 + X
and 
2
y =
1
2 +
1 + Y
 then which 
of the following can be the value of X + Y ?  
  Ùeefo 
1
X =
1
1 +
1 + X
 leLee
2
y =
1
2 +
1 + Y
nw, lees 
efvecveefueefKele ceW mes keâewve mee X + Y keâe ceeve nes mekeâlee 
nw? 
 (a) 
( )
5 17 3 / 4 - - + (b) 
( )
2 5 17 3 / 4 + - 
 (c) 
( )
5 17 1 / 4 - + + (d) 
( )
5 17 1 / 4 + - 
19.  If P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 × 
3
22
 × 5
8
 and S = 2
25
 × 3
22
 × 5
9
, then which of the 
following is TRUE ?  
  Ùeefo P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 
× 3
22
 × 5
8
 leLee S = 2
25
 × 3
22
 × 5
9
 nw, lees efvecveefueefKele 
ceW mes keâewve melÙe nw? 
 (a) P > S > R > Q (b) S > P > R > Q  
 (c) P > R > S > Q (d) S > P > Q > R 
20.  If A = 125 and B = 8, then what is the value of 
(A+B)
3
 – (A–B)
3
 – 6B (A
2
 – B
2
) ?  
  Ùeefo A = 125 leLee B = 8, nw, lees (A+B)
3
 – (A–B)
3
 – 
6B (A
2
 – B
2
) keâe ceeve keäÙee nw? 
 (a) 4096 (b) 4608 
 (c) 4224 (d) 3456 
21.  If 
z x
y z
x = 1, y = 125 and 
x
y
z = 243 (x, y and z 
are natural numbers), then what is the value of 
9x + 10y – 18z ?  
  Ùeefo 
z x
y z
x = 1, y = 125leLee 
x
y
z = 243nw (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees 9x + 10y – 18z keâe ceeve 
keäÙee nw? 
 (a) 18  (b) 15  
 (c) 12 (d) 5 
22.  If 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
and 18x 
+ 27y – z 
113
=
9
, then what is the value of 75x + 
113y ?  
  Ùeefo 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
 leLee 
18x + 27y – z 
113
=
9
nw, lees 75x + 113y keâe ceeve 
keäÙee nw? 
 (a) 163/3 (b) 143/6 
 (c) 218/9 (d) 311/3 
23.  If sides of a triangle are 12 cm, 15 cm and 21 
cm, then what is the inradius (in cm) of the 
triangle ? 
  Ùeefo Skeâ ef$eYegpe keâer YegpeeSB 12 mes.ceer., 15 mes.ceer. leLee 
21 mes.ceer. nw, lees ef$eYegpe keâer Deble: ef$epÙee (mes.ceer. ceW) 
keäÙee nw? 
 (a) 
( )
5 3 / 2  (b) 4 3 
 (c) 
( )
3 6 / 2 (d) 3 3 
24.  In a triangle ABC, AB = 12, BC = 18 and AC = 
15. The medians AX and BY intersect sides BC 
and AC at X and Y respectively. If AX and BY 
intersect each other at O, then what is the value 
of OX ?  
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  How many two digit prime numbers are there 
between 10 to 100 which remains prime 
numbers when the order of their digits is 
reversed ?  
  10 mes 100 kesâ yeerÛe oes DebkeâeW keâer Ssmeer efkeâleveer DeYeepÙe 
mebKÙee nw efpevekesâ DebkeâeW kesâ ›eâce keâes heuešves hej Yeer Jes 
Skeâ DeYeepÙe mebKÙee ner jnsieer? 
 (a) 8  (b) 9  
 (c) 10 (d) 12 
2.  How many perfect cubes are there between 1 
and 100000 which are divisible by 7.  
  1 mes 100000 kesâ yeerÛe efkeâleves hetCe& Ieve nQ pees 7 mes 
efJeYeeefpele nw? 
 (a) 5  (b) 6  
 (c) 7 (d) 15 
3.  If A = 0.142857142857 ...... and B = 0.16666...., 
then what is the value of (A+B)/AB ?  
  Ùeefo A = 0.142857142857 ...... leLee B = 
0.16666.......... nw, lees (A+B)/AB keâe ceeve keäÙee nw? 
 (a) 10 (b) 11  
 (c) 12 (d) 13 
4.  If A = 0.abcabc....., then by what number A 
should be multiplied so as to get an integeral 
value ?  
  Ùeefo A = 0.abcabc..... nw, lees A keâes efkeâme mebKÙee mes 
iegCee efkeâÙee peeS leeefkeâ Skeâ hetCeeËkeâ ceeve Øeehle nes? 
 (a) 2997  
 (b) 1000 
 (c) 1998 
 (d) Both 2997 and 1998/2997 leLee 1998 oesveeW 
5.  What is the sum of 
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 
upto 20 terms ?  
  
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 kesâ 20 heoeW lekeâ keâe 
Ùeesie keäÙee nw? 
 (a) 12410/21 (b) 12412/21 
 (c) 12433/21 (d) 1179/2 
6.  If (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k, then 
what is the value of k ?  
  Ùeefo (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k nw, lees 
k keâe ceeve keäÙee nw? 
 (a) 512/511  (b) 1024/1023 
 (c) 511/512 (d) 1023/1024 
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
2 3 4
1 + 2 + 3 > 8
3 4 5
 
  II. 
1 3 1
6 - 5 + 4 > 5
2 4 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 
8.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. Highest common factor of (3
2002
–1) and  
(3
2002
 + 1) is 4/(3
2002
–1) leLee (3
2002
 + 1) keâe cenòece 
meceeheJeòe&keâ 4 nw~ 
  II. (4
84
 –1) is exactly divisible by 5/(4
84
 –1), 5 mes 
hetCe&le: efJeYeeefpele nw~ 
 (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 
9.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 is exactly divisible by 
5./ 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 mes hetCe&le: efJeYeeefpele nw~ 
  II. 31
11
 > 17
14
 
 (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 
10.  N = 2
48
 – 1 and N are exactly divisible by two 
numbers between 60 and 70. What is the sum 
of those two numbers ?  
  N = 2
48
 – 1 leLee N, 60 leLee 70 kesâ yeerÛe oes mebKÙee mes 
hetCe&le: efJeYeeefpele nw~ Gve oes mebKÙeeDeeW keâe Ùeesie keäÙee nw? 
 (a) 128 (b) 256 
 (c) 64 (d) 512 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
 
  I. 
4
625 + 1296 + 1024 > 90 
  II. 
( ) ( )
3 4
729 + 256 = 5 
 (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.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1 + 2 + 3 + 4 + 5 + 6 > 10 
  II. ( ) ( ) ( ) ( ) 10 + 12 + 14 > 3 12 
 (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 
13.  If y
2
 = y + 7, then what is the value of y
3 
? 
  Ùeefo y
2
 = y + 7 nw, lees y
3
 keâe ceeve keäÙee nw? 
 (a) 8y + 7 (b) y + 14  
 (c) y + 2 (d) 4y + 7 
14.  If f(x) = (x–2)/(x
2
 + Px + 4) and (x–3) is a factor 
of f(x), then what is the value of P ? 
  Ùeefo f(x) = (x–2) (x
2
 + Px + 4) leLee (x–3) f(x) keâe 
iegCeveKeC[ nw, lees P keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) –13/3 (d) 13/3 
15.  If [x–(1/x)] = 2, then what is the value of [x
6
 – 
(1/x
6
)] ? 
  Ùeefo [x–(1/x)] = 2 nw, lees [x
6
 – (1/x
6
)] keâe ceeve keäÙee 
nw? 
 (a) 114 3 1 + (b) 134 2 
 (c) 142 2 3 + (d) 140 2 
16.  x, y and z all are positive number. If 3
x
 > 9
y
 and 
2
y
 > 4
z
, then which of the following is TRUE ?  
   x, y leLee z meYeer Oeveelcekeâ mebKÙee nw~ Ùeefo 3
x
 > 9
y
 
leLee 2
y
 > 4
z
 nw, lees efvecveefueefKele ceW mes keâewve melÙe nw? 
 (a) x > y > z (b) x > z > y 
 (c) z > y > x (d) y > x > z 
17.  If x = (1/8), which of the following has the 
largest values ?  
  Ùeefo x = (1/8) nw, lees efvecveefueefKele ceW mes efkeâmekeâe ceeve 
meyemes yeÌ[e nw? 
 (a) x/2  (b) x
2
 
 (c) x (d) 1/x 
18.  If 
1
X =
1
1 +
1 + X
and 
2
y =
1
2 +
1 + Y
 then which 
of the following can be the value of X + Y ?  
  Ùeefo 
1
X =
1
1 +
1 + X
 leLee
2
y =
1
2 +
1 + Y
nw, lees 
efvecveefueefKele ceW mes keâewve mee X + Y keâe ceeve nes mekeâlee 
nw? 
 (a) 
( )
5 17 3 / 4 - - + (b) 
( )
2 5 17 3 / 4 + - 
 (c) 
( )
5 17 1 / 4 - + + (d) 
( )
5 17 1 / 4 + - 
19.  If P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 × 
3
22
 × 5
8
 and S = 2
25
 × 3
22
 × 5
9
, then which of the 
following is TRUE ?  
  Ùeefo P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 
× 3
22
 × 5
8
 leLee S = 2
25
 × 3
22
 × 5
9
 nw, lees efvecveefueefKele 
ceW mes keâewve melÙe nw? 
 (a) P > S > R > Q (b) S > P > R > Q  
 (c) P > R > S > Q (d) S > P > Q > R 
20.  If A = 125 and B = 8, then what is the value of 
(A+B)
3
 – (A–B)
3
 – 6B (A
2
 – B
2
) ?  
  Ùeefo A = 125 leLee B = 8, nw, lees (A+B)
3
 – (A–B)
3
 – 
6B (A
2
 – B
2
) keâe ceeve keäÙee nw? 
 (a) 4096 (b) 4608 
 (c) 4224 (d) 3456 
21.  If 
z x
y z
x = 1, y = 125 and 
x
y
z = 243 (x, y and z 
are natural numbers), then what is the value of 
9x + 10y – 18z ?  
  Ùeefo 
z x
y z
x = 1, y = 125leLee 
x
y
z = 243nw (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees 9x + 10y – 18z keâe ceeve 
keäÙee nw? 
 (a) 18  (b) 15  
 (c) 12 (d) 5 
22.  If 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
and 18x 
+ 27y – z 
113
=
9
, then what is the value of 75x + 
113y ?  
  Ùeefo 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
 leLee 
18x + 27y – z 
113
=
9
nw, lees 75x + 113y keâe ceeve 
keäÙee nw? 
 (a) 163/3 (b) 143/6 
 (c) 218/9 (d) 311/3 
23.  If sides of a triangle are 12 cm, 15 cm and 21 
cm, then what is the inradius (in cm) of the 
triangle ? 
  Ùeefo Skeâ ef$eYegpe keâer YegpeeSB 12 mes.ceer., 15 mes.ceer. leLee 
21 mes.ceer. nw, lees ef$eYegpe keâer Deble: ef$epÙee (mes.ceer. ceW) 
keäÙee nw? 
 (a) 
( )
5 3 / 2  (b) 4 3 
 (c) 
( )
3 6 / 2 (d) 3 3 
24.  In a triangle ABC, AB = 12, BC = 18 and AC = 
15. The medians AX and BY intersect sides BC 
and AC at X and Y respectively. If AX and BY 
intersect each other at O, then what is the value 
of OX ?  
 
  Skeâ ef$eYegpe ABC ceW, AB = 12, BC = 18 leLee AC = 
15 nw~ ceeOÙe jsKee AX leLee BY Yegpee BC leLee AC keâes 
›eâceMe: X leLee Y hej ØeefleÛÚso keâjleer nw~ Ùeefo AX leLee 
BY, O hej ØeefleÛÚsove keâjles nQ, lees OX keâe ceeve keäÙee 
nw? 
 (a) 4 23  (b) 23 
 (c) 2 23 (d) 
( ) ( )
23 / 2 
25.  In a triangle PQR, PX bisects QR, PX is the 
angle bisector of angle P. If PQ = 12 cm and 
QX = 3 cm, then what is the area (in cm
2
) of 
triangle PQR ? 
  Skeâ ef$eYegpe PQR ceW, PX, QR keâe efÉYeepekeâ nw~ PX, 
keâesCe P keâe efÉYeepekeâ nw~ Ùeefo PQ = 12 mes.ceer. leLee 
QX = 3 mes.ceer. nw, lees ef$eYegpe PQR keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 12 3 (b) 8 15 
 (c) 18 2 (d) 9 15 
26.  In the given figure PT : TS : SR = 2 : 1 : 1 and 
SU is parallel to TQ. If RU = 10 cm, RS = 8 cm 
and SU = 6 cm, then what is the value (in cm) 
of PQ ?  
  oer ieF& Deeke=âefle ceW, PT : TS : SR = 2 : 1 : 1 leLee 
SU, TQ kesâ meceeveevlej nw~ Ùeefo RU = 10 mes.ceer., RS = 
8 mes.ceer. leLee SU = 6 mes.ceer. nw, lees PQ keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 
 (a) 12 (b) 10  
 (c) 20 (d) 30 
27.  PQ and RS are two chords of a circle. PQ = 20 
cm, RS = 48 cm and PQ is parallel to RS. If the 
distance between PQ and RS is 34 cm, then 
what is the area (in cm
2
) of the circle ?  
  PQ leLee RS Skeâ Je=òe keâer oes peerJeeSB nw~ PQ = 20 
mes.ceer., RS = 48 mes.ceer. leLee PQ, RS kesâ meceeveevlej nw~ 
Ùeefo PQ leLee RS kesâ ceOÙe otjer 34 mes.ceer. nw, lees Je=òe 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw?  
 (a) 729p (b) 900p 
 (c) 676p (d) 784p 
28.  Centre of two concentric circles is O. The area 
of two circles is 616 cm
2
 and 154 cm
2
 
respectively. A tangent is drawn through point 
A on the larger circle to the smaller circle. This 
tangent touches smaller circle at B and 
intersects larger circle at C. What is the length 
(in cm) of AC ?  
  oes mebkeWâefvõle Je=òe keâe kesâvõ O nw~ oesveeW Je=òeeW keâe 
#es$eHeâue 616 mes.ceer.
2
  leLee 154 mes.ceer.
2
 nw~ yeÌ[s Je=òe kesâ 
efyevog A mes Úesšs Je=òe hej Skeâ mheMe& jsKee KeeRÛeer ieF& nw~ 
Ùen mheMe& jsKee Úesšs Je=òe keâes efyevog B hej mheMe& keâjleer nw 
leLee yeÌ[s Je=òe keâes efyevog C hej ØeefleÛÚso keâjleer nw~ AC 
keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 12 3 (b) 14 3 
 (c) 10 6 (d) 18 2 
29.  PA and PB are two tangents drawn to two 
circles of radius 3 cm and 5 cm respectively. PA 
touches the smaller and larger circles at points 
X and Y respectively. PB touches the smaller 
and larger circle at point U and V respectively. 
The centres of the smaller and larger circles O 
and N respectively. If ON = 12 cm, then what is 
the value (in cm) of PY ?  
  PA leLee PB ›eâceMe: 3 mes.ceer. leLee 5 mes.ceer. Jeeues oes 
Je=òeeW hej mheMe& jsKeeSB yeveeF& ieF& nw~ PA Úesšs leLee yeÌ[s 
Je=òeeW keâes ›eâceMe: X leLee Y efyevog hej mheMe& keâjleer nw~ 
PB Úesšs leLee yeÌ[s Je=òe keâes ›eâceMe: U leLee V efyevog hej 
mheMe& keâjleer nw~ O leLee N ›eâceMe: Úesšs leLee yeÌ[s Je=òe kesâ 
kesâvõ nQ~ Ùeefo ON = 12 mes.ceer. nw, lees PY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 5 35 (b) 7 15 
 (c) 9 15 (d) 12 5 
30.  XR is a tangent to the circle. O is the centre of 
the circle. If ?XRP = 120
0
, then what is the 
value (in degrees) of ?QOR ?  
  XR Je=òe hej Skeâ mheMe& jsKee nw~ O Je=òe keâe kesâvõ nw~ 
Ùeefo ?XRP = 120
0
 nw, lees ?QOR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
   
 (a) 80 (b) 70  
 (c) 60 (d) 40 
31.  O is the centre of the circle. A tangent is drawn 
which touches the circle at C. If ?AOC = 80
0
, 
then what is the value (in degrees) of ?BCX ?  
  O Je=òe keâe kesâvõ nw~ Skeâ mheMe& jsKee yeveeF& ieF& nw pees 
Je=òe keâes C hej mheMe& keâjleer nw~ Ùeefo ?AOC = 80
0
 nw, 
lees ?BCX keâe ceeve (ef[«eer ceW) keäÙee nesiee? 
 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  How many two digit prime numbers are there 
between 10 to 100 which remains prime 
numbers when the order of their digits is 
reversed ?  
  10 mes 100 kesâ yeerÛe oes DebkeâeW keâer Ssmeer efkeâleveer DeYeepÙe 
mebKÙee nw efpevekesâ DebkeâeW kesâ ›eâce keâes heuešves hej Yeer Jes 
Skeâ DeYeepÙe mebKÙee ner jnsieer? 
 (a) 8  (b) 9  
 (c) 10 (d) 12 
2.  How many perfect cubes are there between 1 
and 100000 which are divisible by 7.  
  1 mes 100000 kesâ yeerÛe efkeâleves hetCe& Ieve nQ pees 7 mes 
efJeYeeefpele nw? 
 (a) 5  (b) 6  
 (c) 7 (d) 15 
3.  If A = 0.142857142857 ...... and B = 0.16666...., 
then what is the value of (A+B)/AB ?  
  Ùeefo A = 0.142857142857 ...... leLee B = 
0.16666.......... nw, lees (A+B)/AB keâe ceeve keäÙee nw? 
 (a) 10 (b) 11  
 (c) 12 (d) 13 
4.  If A = 0.abcabc....., then by what number A 
should be multiplied so as to get an integeral 
value ?  
  Ùeefo A = 0.abcabc..... nw, lees A keâes efkeâme mebKÙee mes 
iegCee efkeâÙee peeS leeefkeâ Skeâ hetCeeËkeâ ceeve Øeehle nes? 
 (a) 2997  
 (b) 1000 
 (c) 1998 
 (d) Both 2997 and 1998/2997 leLee 1998 oesveeW 
5.  What is the sum of 
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 
upto 20 terms ?  
  
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 kesâ 20 heoeW lekeâ keâe 
Ùeesie keäÙee nw? 
 (a) 12410/21 (b) 12412/21 
 (c) 12433/21 (d) 1179/2 
6.  If (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k, then 
what is the value of k ?  
  Ùeefo (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k nw, lees 
k keâe ceeve keäÙee nw? 
 (a) 512/511  (b) 1024/1023 
 (c) 511/512 (d) 1023/1024 
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
2 3 4
1 + 2 + 3 > 8
3 4 5
 
  II. 
1 3 1
6 - 5 + 4 > 5
2 4 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 
8.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. Highest common factor of (3
2002
–1) and  
(3
2002
 + 1) is 4/(3
2002
–1) leLee (3
2002
 + 1) keâe cenòece 
meceeheJeòe&keâ 4 nw~ 
  II. (4
84
 –1) is exactly divisible by 5/(4
84
 –1), 5 mes 
hetCe&le: efJeYeeefpele nw~ 
 (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 
9.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 is exactly divisible by 
5./ 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 mes hetCe&le: efJeYeeefpele nw~ 
  II. 31
11
 > 17
14
 
 (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 
10.  N = 2
48
 – 1 and N are exactly divisible by two 
numbers between 60 and 70. What is the sum 
of those two numbers ?  
  N = 2
48
 – 1 leLee N, 60 leLee 70 kesâ yeerÛe oes mebKÙee mes 
hetCe&le: efJeYeeefpele nw~ Gve oes mebKÙeeDeeW keâe Ùeesie keäÙee nw? 
 (a) 128 (b) 256 
 (c) 64 (d) 512 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
 
  I. 
4
625 + 1296 + 1024 > 90 
  II. 
( ) ( )
3 4
729 + 256 = 5 
 (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.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1 + 2 + 3 + 4 + 5 + 6 > 10 
  II. ( ) ( ) ( ) ( ) 10 + 12 + 14 > 3 12 
 (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 
13.  If y
2
 = y + 7, then what is the value of y
3 
? 
  Ùeefo y
2
 = y + 7 nw, lees y
3
 keâe ceeve keäÙee nw? 
 (a) 8y + 7 (b) y + 14  
 (c) y + 2 (d) 4y + 7 
14.  If f(x) = (x–2)/(x
2
 + Px + 4) and (x–3) is a factor 
of f(x), then what is the value of P ? 
  Ùeefo f(x) = (x–2) (x
2
 + Px + 4) leLee (x–3) f(x) keâe 
iegCeveKeC[ nw, lees P keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) –13/3 (d) 13/3 
15.  If [x–(1/x)] = 2, then what is the value of [x
6
 – 
(1/x
6
)] ? 
  Ùeefo [x–(1/x)] = 2 nw, lees [x
6
 – (1/x
6
)] keâe ceeve keäÙee 
nw? 
 (a) 114 3 1 + (b) 134 2 
 (c) 142 2 3 + (d) 140 2 
16.  x, y and z all are positive number. If 3
x
 > 9
y
 and 
2
y
 > 4
z
, then which of the following is TRUE ?  
   x, y leLee z meYeer Oeveelcekeâ mebKÙee nw~ Ùeefo 3
x
 > 9
y
 
leLee 2
y
 > 4
z
 nw, lees efvecveefueefKele ceW mes keâewve melÙe nw? 
 (a) x > y > z (b) x > z > y 
 (c) z > y > x (d) y > x > z 
17.  If x = (1/8), which of the following has the 
largest values ?  
  Ùeefo x = (1/8) nw, lees efvecveefueefKele ceW mes efkeâmekeâe ceeve 
meyemes yeÌ[e nw? 
 (a) x/2  (b) x
2
 
 (c) x (d) 1/x 
18.  If 
1
X =
1
1 +
1 + X
and 
2
y =
1
2 +
1 + Y
 then which 
of the following can be the value of X + Y ?  
  Ùeefo 
1
X =
1
1 +
1 + X
 leLee
2
y =
1
2 +
1 + Y
nw, lees 
efvecveefueefKele ceW mes keâewve mee X + Y keâe ceeve nes mekeâlee 
nw? 
 (a) 
( )
5 17 3 / 4 - - + (b) 
( )
2 5 17 3 / 4 + - 
 (c) 
( )
5 17 1 / 4 - + + (d) 
( )
5 17 1 / 4 + - 
19.  If P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 × 
3
22
 × 5
8
 and S = 2
25
 × 3
22
 × 5
9
, then which of the 
following is TRUE ?  
  Ùeefo P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 
× 3
22
 × 5
8
 leLee S = 2
25
 × 3
22
 × 5
9
 nw, lees efvecveefueefKele 
ceW mes keâewve melÙe nw? 
 (a) P > S > R > Q (b) S > P > R > Q  
 (c) P > R > S > Q (d) S > P > Q > R 
20.  If A = 125 and B = 8, then what is the value of 
(A+B)
3
 – (A–B)
3
 – 6B (A
2
 – B
2
) ?  
  Ùeefo A = 125 leLee B = 8, nw, lees (A+B)
3
 – (A–B)
3
 – 
6B (A
2
 – B
2
) keâe ceeve keäÙee nw? 
 (a) 4096 (b) 4608 
 (c) 4224 (d) 3456 
21.  If 
z x
y z
x = 1, y = 125 and 
x
y
z = 243 (x, y and z 
are natural numbers), then what is the value of 
9x + 10y – 18z ?  
  Ùeefo 
z x
y z
x = 1, y = 125leLee 
x
y
z = 243nw (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees 9x + 10y – 18z keâe ceeve 
keäÙee nw? 
 (a) 18  (b) 15  
 (c) 12 (d) 5 
22.  If 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
and 18x 
+ 27y – z 
113
=
9
, then what is the value of 75x + 
113y ?  
  Ùeefo 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
 leLee 
18x + 27y – z 
113
=
9
nw, lees 75x + 113y keâe ceeve 
keäÙee nw? 
 (a) 163/3 (b) 143/6 
 (c) 218/9 (d) 311/3 
23.  If sides of a triangle are 12 cm, 15 cm and 21 
cm, then what is the inradius (in cm) of the 
triangle ? 
  Ùeefo Skeâ ef$eYegpe keâer YegpeeSB 12 mes.ceer., 15 mes.ceer. leLee 
21 mes.ceer. nw, lees ef$eYegpe keâer Deble: ef$epÙee (mes.ceer. ceW) 
keäÙee nw? 
 (a) 
( )
5 3 / 2  (b) 4 3 
 (c) 
( )
3 6 / 2 (d) 3 3 
24.  In a triangle ABC, AB = 12, BC = 18 and AC = 
15. The medians AX and BY intersect sides BC 
and AC at X and Y respectively. If AX and BY 
intersect each other at O, then what is the value 
of OX ?  
 
  Skeâ ef$eYegpe ABC ceW, AB = 12, BC = 18 leLee AC = 
15 nw~ ceeOÙe jsKee AX leLee BY Yegpee BC leLee AC keâes 
›eâceMe: X leLee Y hej ØeefleÛÚso keâjleer nw~ Ùeefo AX leLee 
BY, O hej ØeefleÛÚsove keâjles nQ, lees OX keâe ceeve keäÙee 
nw? 
 (a) 4 23  (b) 23 
 (c) 2 23 (d) 
( ) ( )
23 / 2 
25.  In a triangle PQR, PX bisects QR, PX is the 
angle bisector of angle P. If PQ = 12 cm and 
QX = 3 cm, then what is the area (in cm
2
) of 
triangle PQR ? 
  Skeâ ef$eYegpe PQR ceW, PX, QR keâe efÉYeepekeâ nw~ PX, 
keâesCe P keâe efÉYeepekeâ nw~ Ùeefo PQ = 12 mes.ceer. leLee 
QX = 3 mes.ceer. nw, lees ef$eYegpe PQR keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 12 3 (b) 8 15 
 (c) 18 2 (d) 9 15 
26.  In the given figure PT : TS : SR = 2 : 1 : 1 and 
SU is parallel to TQ. If RU = 10 cm, RS = 8 cm 
and SU = 6 cm, then what is the value (in cm) 
of PQ ?  
  oer ieF& Deeke=âefle ceW, PT : TS : SR = 2 : 1 : 1 leLee 
SU, TQ kesâ meceeveevlej nw~ Ùeefo RU = 10 mes.ceer., RS = 
8 mes.ceer. leLee SU = 6 mes.ceer. nw, lees PQ keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 
 (a) 12 (b) 10  
 (c) 20 (d) 30 
27.  PQ and RS are two chords of a circle. PQ = 20 
cm, RS = 48 cm and PQ is parallel to RS. If the 
distance between PQ and RS is 34 cm, then 
what is the area (in cm
2
) of the circle ?  
  PQ leLee RS Skeâ Je=òe keâer oes peerJeeSB nw~ PQ = 20 
mes.ceer., RS = 48 mes.ceer. leLee PQ, RS kesâ meceeveevlej nw~ 
Ùeefo PQ leLee RS kesâ ceOÙe otjer 34 mes.ceer. nw, lees Je=òe 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw?  
 (a) 729p (b) 900p 
 (c) 676p (d) 784p 
28.  Centre of two concentric circles is O. The area 
of two circles is 616 cm
2
 and 154 cm
2
 
respectively. A tangent is drawn through point 
A on the larger circle to the smaller circle. This 
tangent touches smaller circle at B and 
intersects larger circle at C. What is the length 
(in cm) of AC ?  
  oes mebkeWâefvõle Je=òe keâe kesâvõ O nw~ oesveeW Je=òeeW keâe 
#es$eHeâue 616 mes.ceer.
2
  leLee 154 mes.ceer.
2
 nw~ yeÌ[s Je=òe kesâ 
efyevog A mes Úesšs Je=òe hej Skeâ mheMe& jsKee KeeRÛeer ieF& nw~ 
Ùen mheMe& jsKee Úesšs Je=òe keâes efyevog B hej mheMe& keâjleer nw 
leLee yeÌ[s Je=òe keâes efyevog C hej ØeefleÛÚso keâjleer nw~ AC 
keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 12 3 (b) 14 3 
 (c) 10 6 (d) 18 2 
29.  PA and PB are two tangents drawn to two 
circles of radius 3 cm and 5 cm respectively. PA 
touches the smaller and larger circles at points 
X and Y respectively. PB touches the smaller 
and larger circle at point U and V respectively. 
The centres of the smaller and larger circles O 
and N respectively. If ON = 12 cm, then what is 
the value (in cm) of PY ?  
  PA leLee PB ›eâceMe: 3 mes.ceer. leLee 5 mes.ceer. Jeeues oes 
Je=òeeW hej mheMe& jsKeeSB yeveeF& ieF& nw~ PA Úesšs leLee yeÌ[s 
Je=òeeW keâes ›eâceMe: X leLee Y efyevog hej mheMe& keâjleer nw~ 
PB Úesšs leLee yeÌ[s Je=òe keâes ›eâceMe: U leLee V efyevog hej 
mheMe& keâjleer nw~ O leLee N ›eâceMe: Úesšs leLee yeÌ[s Je=òe kesâ 
kesâvõ nQ~ Ùeefo ON = 12 mes.ceer. nw, lees PY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 5 35 (b) 7 15 
 (c) 9 15 (d) 12 5 
30.  XR is a tangent to the circle. O is the centre of 
the circle. If ?XRP = 120
0
, then what is the 
value (in degrees) of ?QOR ?  
  XR Je=òe hej Skeâ mheMe& jsKee nw~ O Je=òe keâe kesâvõ nw~ 
Ùeefo ?XRP = 120
0
 nw, lees ?QOR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
   
 (a) 80 (b) 70  
 (c) 60 (d) 40 
31.  O is the centre of the circle. A tangent is drawn 
which touches the circle at C. If ?AOC = 80
0
, 
then what is the value (in degrees) of ?BCX ?  
  O Je=òe keâe kesâvõ nw~ Skeâ mheMe& jsKee yeveeF& ieF& nw pees 
Je=òe keâes C hej mheMe& keâjleer nw~ Ùeefo ?AOC = 80
0
 nw, 
lees ?BCX keâe ceeve (ef[«eer ceW) keäÙee nesiee? 
 
 
 (a) 80 (b) 30  
 (c) 40 (d) 50 
32.  The distance between the centres of two circles 
is 24 cm. If the radius of the two circles are 4 
cm and 8 cm, then what is the sum of the 
lengths (in cm) of the direct common tangent 
and the transverse common tangent ?  
  oes Je=òeeW kesâ kesâvõ kesâ ceOÙe keâer otjer 24 mes.ceer. nw~ Ùeefo 
oes Je=òe keâer ef$epÙee 4 mes.ceer. leLee 8 mes.ceer. nw, lees 
GYeÙeefve<" DevegmheMe& jsKee leLee efleÙe&keâ GYeÙeefve<" 
DevegmheMe& jsKee (mes.ceer. ceW) keâe Ùeesie keäÙee nw? 
 (a) 
( )
4 3 3 35 +  (b) 
( )
4 4 35 3 3 +  
 (c) 
( )
4 35 3 3 + (d) 
( )
4 3 35 3 3 + 
33.  ABC is triangle. AB = 10 cm and BC = 16 cm. 
AD = 8 cm and is perpendicular to side BC. 
What is the length (in cm) of side AC ?  
  ABC Skeâ ef$eYegpe nw~ AB = 10 mes.ceer. leLee BC = 16 
mes.ceer. nw~ AD = 8 mes.ceer. nw leLee Ùen Yegpee BC kesâ 
meceuecye nw~ Yegpee AC keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 4 41 (b) 2 41 
 (c) 2 82 (d) 4 82 
34.  An equilateral triangle of side 12 cm is drawn. 
What is the area (in cm
2
) of the largest square 
which can be drawn inside it ?  
  12 mes.ceer. Yegpee Jeeuee Skeâ meceyeeng ef$eYegpe yeveeÙee ieÙee~ 
FmeceW yeveeÙes pee mekeâves Jeeues meyemes yeÌ[s Jeie& keâe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 1512 864 3 - (b) 3024 1728 3 - 
 (c) 3024 1728 3 + (d) 1512 864 3 + 
35.  PQRS is a rectangle. The ratio of the sides PQ 
and QR is 3 : 1. If the length of the diagonal PR 
is 10 cm, then what is the area (in cm
2
) of the 
rectangle ?  
  PQRS Skeâ DeeÙele nw~ Yegpee PQ leLee QR keâe Devegheele 
3 : 1 nw~ Ùeefo efJekeâCe& PR keâer uecyeeF& 10 mes.ceer. nw, lees 
DeeÙele keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw?  
 (a) 15 (b) 30  
 (c) 45 (d) 20 
36.  ABCDEF is a regular hexagon. What is the 
ratio of the area of triangle ACE and area of 
triangle AEF ?  
  ABCDEF Skeâ mece<ešYegpe nw~ ef$eYegpe ACE kesâ 
#es$eHeâue leLee ef$eYegpe AEF kesâ #es$eHeâue keâe Devegheele 
keäÙee nw? 
 (a) 6 : 1 (b) 4 : 1  
 (c) 3 : 1 (d) 5 : 1 
37.  ABCD is trapezium. Sides AB and CD are 
parallel to each other. AB = 6 cm, CD = 18 cm, 
BC = 8 cm and AD = 12 cm. A line parallel to 
AB divides the trapezium in two parts of equal 
perimeter. This line cuts BC at E and AD at F. 
If BE/EC = AF/FD, then what is the value of 
BE/EC ?  
  ABCD Skeâ meceuecye nw~ YegpeeSB AB leLee CD Skeâ 
otmejs kesâ meceevlej nw~ AB = 6 mes.ceer., CD = 18 mes.ceer., 
BC = 8 mes.ceer. leLee AD = 12 mes.ceer. nw~ AB kesâ 
meceevlej Skeâ jsKee meceuecye keâes oes yejeyej heefjceehe Jeeues 
efnmmeeW ceW keâešlee nw~ Ùen jsKee Yegpee BC keâes E hej leLee 
AD keâes F hej keâešleer nw~ Ùeefo BE/EC=AF/FD nw, lees 
BE/EC keâe ceeve keäÙee nw? 
 (a) 1/2 (b) 2  
 (c) 4 (d) 1/4 
38.  A rectangular sheet of length 42 cm and 
breadth 14 cm is cut from a circular sheet. 
What is the minimum area (in cm
2
) of circular 
sheet ?  
  Skeâ Je=òeekeâej Ûeeoj mes 42 mes.ceer. uecyeer leLee 14 
mes.ceer. ÛeewÌ[er Skeâ DeeÙeleekeâej Ûeeoj keâešer ieF& nw~ 
Je=òeekeâej Ûeeoj keâe #es$eHeâue (mes.ceer.
2
 ceW) keâce mes keâce 
keäÙee nw? 
 (a) 3080 (b) 1540 
 (c) 770 (d) 1030 
39.  An equilateral triangle ABC is inscribed in a 
circle as shown in figure. A square of largest 
possible area is made inside this triangle as 
shown. Another circle made inscribing the 
square. What is the ratio of large circle and the 
small circle ?  
  pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw, Skeâ mece ef$eYegpe 
ABC Skeâ Je=òe ceW yeveeÙee ieÙee nw~ pewmee oMee&Ùee ieÙee 
nw, meyemes yeÌ[s mebYeeefJele #es$eHeâue Jeeuee Jeie& Fme ef$eYegpe 
kesâ Deboj yeveeÙee ieÙee nw~ Skeâ Deewj Je=òe Jeie& kesâ Deboj 
yeveeÙee ieÙee nw~ yeÌ[s Je=òe leLee Úesšs Je=òe kesâ #es$eHeâue keâe 
Devegheele keäÙee nw? 
 
 (a) 
( )
15 12 3 :1 - (b) 
( )
4 : 63 36 3 - 
 (c) 
( )
7 4 3 : 8 - (d) 
( )
18 3 : 2 - 
40.  A prism has a regular hexagonal base whose 
side is 12 cm. The height of the prism is 24 cm. 
It is cut into 4 equal parts by 2 perpendicular 
cuts as shown in figure. What is the sum of the 
total surface area of the four parts ?  
  Skeâ efØepce keâe DeeOeej Skeâ mece <ešYegpe nw efpemekeâer Yegpee 
12 mes.ceer. nw~ efØepce keâer TBÛeeF& 24 mes.ceer. nw~ Fmes 2 
uecyeJele keâšeJe Éeje 4 yejeyej YeeieeW ceW keâeše peelee nw 
pewmee efkeâ efÛe$e ceW oMee&Ùee ieÙee nw~ ÛeejeW YeeieeW kesâ kegâue 
he=<"erÙe #es$eHeâue keâe Ùeesie keäÙee nw? 
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
 (Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
[Exam Date : 9-03-2018, Shift-I  
1.  How many two digit prime numbers are there 
between 10 to 100 which remains prime 
numbers when the order of their digits is 
reversed ?  
  10 mes 100 kesâ yeerÛe oes DebkeâeW keâer Ssmeer efkeâleveer DeYeepÙe 
mebKÙee nw efpevekesâ DebkeâeW kesâ ›eâce keâes heuešves hej Yeer Jes 
Skeâ DeYeepÙe mebKÙee ner jnsieer? 
 (a) 8  (b) 9  
 (c) 10 (d) 12 
2.  How many perfect cubes are there between 1 
and 100000 which are divisible by 7.  
  1 mes 100000 kesâ yeerÛe efkeâleves hetCe& Ieve nQ pees 7 mes 
efJeYeeefpele nw? 
 (a) 5  (b) 6  
 (c) 7 (d) 15 
3.  If A = 0.142857142857 ...... and B = 0.16666...., 
then what is the value of (A+B)/AB ?  
  Ùeefo A = 0.142857142857 ...... leLee B = 
0.16666.......... nw, lees (A+B)/AB keâe ceeve keäÙee nw? 
 (a) 10 (b) 11  
 (c) 12 (d) 13 
4.  If A = 0.abcabc....., then by what number A 
should be multiplied so as to get an integeral 
value ?  
  Ùeefo A = 0.abcabc..... nw, lees A keâes efkeâme mebKÙee mes 
iegCee efkeâÙee peeS leeefkeâ Skeâ hetCeeËkeâ ceeve Øeehle nes? 
 (a) 2997  
 (b) 1000 
 (c) 1998 
 (d) Both 2997 and 1998/2997 leLee 1998 oesveeW 
5.  What is the sum of 
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 
upto 20 terms ?  
  
1 1 1 1
1 + 4 + 7 +10 .......
2 6 12 20
 kesâ 20 heoeW lekeâ keâe 
Ùeesie keäÙee nw? 
 (a) 12410/21 (b) 12412/21 
 (c) 12433/21 (d) 1179/2 
6.  If (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k, then 
what is the value of k ?  
  Ùeefo (1/2
1
) + (1/2
2
) + (1/2
3
) .... (1/2
10
) = 1/k nw, lees 
k keâe ceeve keäÙee nw? 
 (a) 512/511  (b) 1024/1023 
 (c) 511/512 (d) 1023/1024 
7.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
2 3 4
1 + 2 + 3 > 8
3 4 5
 
  II. 
1 3 1
6 - 5 + 4 > 5
2 4 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 
8.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. Highest common factor of (3
2002
–1) and  
(3
2002
 + 1) is 4/(3
2002
–1) leLee (3
2002
 + 1) keâe cenòece 
meceeheJeòe&keâ 4 nw~ 
  II. (4
84
 –1) is exactly divisible by 5/(4
84
 –1), 5 mes 
hetCe&le: efJeYeeefpele nw~ 
 (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 
9.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 is exactly divisible by 
5./ 1
99
 + 2
99
 + 3
99
 + 4
99
 + 5
99
 mes hetCe&le: efJeYeeefpele nw~ 
  II. 31
11
 > 17
14
 
 (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 
10.  N = 2
48
 – 1 and N are exactly divisible by two 
numbers between 60 and 70. What is the sum 
of those two numbers ?  
  N = 2
48
 – 1 leLee N, 60 leLee 70 kesâ yeerÛe oes mebKÙee mes 
hetCe&le: efJeYeeefpele nw~ Gve oes mebKÙeeDeeW keâe Ùeesie keäÙee nw? 
 (a) 128 (b) 256 
 (c) 64 (d) 512 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
 
  I. 
4
625 + 1296 + 1024 > 90 
  II. 
( ) ( )
3 4
729 + 256 = 5 
 (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.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 1 + 2 + 3 + 4 + 5 + 6 > 10 
  II. ( ) ( ) ( ) ( ) 10 + 12 + 14 > 3 12 
 (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 
13.  If y
2
 = y + 7, then what is the value of y
3 
? 
  Ùeefo y
2
 = y + 7 nw, lees y
3
 keâe ceeve keäÙee nw? 
 (a) 8y + 7 (b) y + 14  
 (c) y + 2 (d) 4y + 7 
14.  If f(x) = (x–2)/(x
2
 + Px + 4) and (x–3) is a factor 
of f(x), then what is the value of P ? 
  Ùeefo f(x) = (x–2) (x
2
 + Px + 4) leLee (x–3) f(x) keâe 
iegCeveKeC[ nw, lees P keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) –13/3 (d) 13/3 
15.  If [x–(1/x)] = 2, then what is the value of [x
6
 – 
(1/x
6
)] ? 
  Ùeefo [x–(1/x)] = 2 nw, lees [x
6
 – (1/x
6
)] keâe ceeve keäÙee 
nw? 
 (a) 114 3 1 + (b) 134 2 
 (c) 142 2 3 + (d) 140 2 
16.  x, y and z all are positive number. If 3
x
 > 9
y
 and 
2
y
 > 4
z
, then which of the following is TRUE ?  
   x, y leLee z meYeer Oeveelcekeâ mebKÙee nw~ Ùeefo 3
x
 > 9
y
 
leLee 2
y
 > 4
z
 nw, lees efvecveefueefKele ceW mes keâewve melÙe nw? 
 (a) x > y > z (b) x > z > y 
 (c) z > y > x (d) y > x > z 
17.  If x = (1/8), which of the following has the 
largest values ?  
  Ùeefo x = (1/8) nw, lees efvecveefueefKele ceW mes efkeâmekeâe ceeve 
meyemes yeÌ[e nw? 
 (a) x/2  (b) x
2
 
 (c) x (d) 1/x 
18.  If 
1
X =
1
1 +
1 + X
and 
2
y =
1
2 +
1 + Y
 then which 
of the following can be the value of X + Y ?  
  Ùeefo 
1
X =
1
1 +
1 + X
 leLee
2
y =
1
2 +
1 + Y
nw, lees 
efvecveefueefKele ceW mes keâewve mee X + Y keâe ceeve nes mekeâlee 
nw? 
 (a) 
( )
5 17 3 / 4 - - + (b) 
( )
2 5 17 3 / 4 + - 
 (c) 
( )
5 17 1 / 4 - + + (d) 
( )
5 17 1 / 4 + - 
19.  If P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 × 
3
22
 × 5
8
 and S = 2
25
 × 3
22
 × 5
9
, then which of the 
following is TRUE ?  
  Ùeefo P = 2
29
 × 3
21
 × 5
8
, Q = 2
27
 × 3
21
 × 5
8
, R = 2
26
 
× 3
22
 × 5
8
 leLee S = 2
25
 × 3
22
 × 5
9
 nw, lees efvecveefueefKele 
ceW mes keâewve melÙe nw? 
 (a) P > S > R > Q (b) S > P > R > Q  
 (c) P > R > S > Q (d) S > P > Q > R 
20.  If A = 125 and B = 8, then what is the value of 
(A+B)
3
 – (A–B)
3
 – 6B (A
2
 – B
2
) ?  
  Ùeefo A = 125 leLee B = 8, nw, lees (A+B)
3
 – (A–B)
3
 – 
6B (A
2
 – B
2
) keâe ceeve keäÙee nw? 
 (a) 4096 (b) 4608 
 (c) 4224 (d) 3456 
21.  If 
z x
y z
x = 1, y = 125 and 
x
y
z = 243 (x, y and z 
are natural numbers), then what is the value of 
9x + 10y – 18z ?  
  Ùeefo 
z x
y z
x = 1, y = 125leLee 
x
y
z = 243nw (x, y leLee 
z Øeeke=âeflekeâ mebKÙeeSB nQ), lees 9x + 10y – 18z keâe ceeve 
keäÙee nw? 
 (a) 18  (b) 15  
 (c) 12 (d) 5 
22.  If 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
and 18x 
+ 27y – z 
113
=
9
, then what is the value of 75x + 
113y ?  
  Ùeefo 3x + 6y + 9z 
20
=
3
, 6x + 9y + 3z 
17
=
3
 leLee 
18x + 27y – z 
113
=
9
nw, lees 75x + 113y keâe ceeve 
keäÙee nw? 
 (a) 163/3 (b) 143/6 
 (c) 218/9 (d) 311/3 
23.  If sides of a triangle are 12 cm, 15 cm and 21 
cm, then what is the inradius (in cm) of the 
triangle ? 
  Ùeefo Skeâ ef$eYegpe keâer YegpeeSB 12 mes.ceer., 15 mes.ceer. leLee 
21 mes.ceer. nw, lees ef$eYegpe keâer Deble: ef$epÙee (mes.ceer. ceW) 
keäÙee nw? 
 (a) 
( )
5 3 / 2  (b) 4 3 
 (c) 
( )
3 6 / 2 (d) 3 3 
24.  In a triangle ABC, AB = 12, BC = 18 and AC = 
15. The medians AX and BY intersect sides BC 
and AC at X and Y respectively. If AX and BY 
intersect each other at O, then what is the value 
of OX ?  
 
  Skeâ ef$eYegpe ABC ceW, AB = 12, BC = 18 leLee AC = 
15 nw~ ceeOÙe jsKee AX leLee BY Yegpee BC leLee AC keâes 
›eâceMe: X leLee Y hej ØeefleÛÚso keâjleer nw~ Ùeefo AX leLee 
BY, O hej ØeefleÛÚsove keâjles nQ, lees OX keâe ceeve keäÙee 
nw? 
 (a) 4 23  (b) 23 
 (c) 2 23 (d) 
( ) ( )
23 / 2 
25.  In a triangle PQR, PX bisects QR, PX is the 
angle bisector of angle P. If PQ = 12 cm and 
QX = 3 cm, then what is the area (in cm
2
) of 
triangle PQR ? 
  Skeâ ef$eYegpe PQR ceW, PX, QR keâe efÉYeepekeâ nw~ PX, 
keâesCe P keâe efÉYeepekeâ nw~ Ùeefo PQ = 12 mes.ceer. leLee 
QX = 3 mes.ceer. nw, lees ef$eYegpe PQR keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 12 3 (b) 8 15 
 (c) 18 2 (d) 9 15 
26.  In the given figure PT : TS : SR = 2 : 1 : 1 and 
SU is parallel to TQ. If RU = 10 cm, RS = 8 cm 
and SU = 6 cm, then what is the value (in cm) 
of PQ ?  
  oer ieF& Deeke=âefle ceW, PT : TS : SR = 2 : 1 : 1 leLee 
SU, TQ kesâ meceeveevlej nw~ Ùeefo RU = 10 mes.ceer., RS = 
8 mes.ceer. leLee SU = 6 mes.ceer. nw, lees PQ keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 
 (a) 12 (b) 10  
 (c) 20 (d) 30 
27.  PQ and RS are two chords of a circle. PQ = 20 
cm, RS = 48 cm and PQ is parallel to RS. If the 
distance between PQ and RS is 34 cm, then 
what is the area (in cm
2
) of the circle ?  
  PQ leLee RS Skeâ Je=òe keâer oes peerJeeSB nw~ PQ = 20 
mes.ceer., RS = 48 mes.ceer. leLee PQ, RS kesâ meceeveevlej nw~ 
Ùeefo PQ leLee RS kesâ ceOÙe otjer 34 mes.ceer. nw, lees Je=òe 
keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw?  
 (a) 729p (b) 900p 
 (c) 676p (d) 784p 
28.  Centre of two concentric circles is O. The area 
of two circles is 616 cm
2
 and 154 cm
2
 
respectively. A tangent is drawn through point 
A on the larger circle to the smaller circle. This 
tangent touches smaller circle at B and 
intersects larger circle at C. What is the length 
(in cm) of AC ?  
  oes mebkeWâefvõle Je=òe keâe kesâvõ O nw~ oesveeW Je=òeeW keâe 
#es$eHeâue 616 mes.ceer.
2
  leLee 154 mes.ceer.
2
 nw~ yeÌ[s Je=òe kesâ 
efyevog A mes Úesšs Je=òe hej Skeâ mheMe& jsKee KeeRÛeer ieF& nw~ 
Ùen mheMe& jsKee Úesšs Je=òe keâes efyevog B hej mheMe& keâjleer nw 
leLee yeÌ[s Je=òe keâes efyevog C hej ØeefleÛÚso keâjleer nw~ AC 
keâer uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 12 3 (b) 14 3 
 (c) 10 6 (d) 18 2 
29.  PA and PB are two tangents drawn to two 
circles of radius 3 cm and 5 cm respectively. PA 
touches the smaller and larger circles at points 
X and Y respectively. PB touches the smaller 
and larger circle at point U and V respectively. 
The centres of the smaller and larger circles O 
and N respectively. If ON = 12 cm, then what is 
the value (in cm) of PY ?  
  PA leLee PB ›eâceMe: 3 mes.ceer. leLee 5 mes.ceer. Jeeues oes 
Je=òeeW hej mheMe& jsKeeSB yeveeF& ieF& nw~ PA Úesšs leLee yeÌ[s 
Je=òeeW keâes ›eâceMe: X leLee Y efyevog hej mheMe& keâjleer nw~ 
PB Úesšs leLee yeÌ[s Je=òe keâes ›eâceMe: U leLee V efyevog hej 
mheMe& keâjleer nw~ O leLee N ›eâceMe: Úesšs leLee yeÌ[s Je=òe kesâ 
kesâvõ nQ~ Ùeefo ON = 12 mes.ceer. nw, lees PY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 5 35 (b) 7 15 
 (c) 9 15 (d) 12 5 
30.  XR is a tangent to the circle. O is the centre of 
the circle. If ?XRP = 120
0
, then what is the 
value (in degrees) of ?QOR ?  
  XR Je=òe hej Skeâ mheMe& jsKee nw~ O Je=òe keâe kesâvõ nw~ 
Ùeefo ?XRP = 120
0
 nw, lees ?QOR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
   
 (a) 80 (b) 70  
 (c) 60 (d) 40 
31.  O is the centre of the circle. A tangent is drawn 
which touches the circle at C. If ?AOC = 80
0
, 
then what is the value (in degrees) of ?BCX ?  
  O Je=òe keâe kesâvõ nw~ Skeâ mheMe& jsKee yeveeF& ieF& nw pees 
Je=òe keâes C hej mheMe& keâjleer nw~ Ùeefo ?AOC = 80
0
 nw, 
lees ?BCX keâe ceeve (ef[«eer ceW) keäÙee nesiee? 
 
 
 (a) 80 (b) 30  
 (c) 40 (d) 50 
32.  The distance between the centres of two circles 
is 24 cm. If the radius of the two circles are 4 
cm and 8 cm, then what is the sum of the 
lengths (in cm) of the direct common tangent 
and the transverse common tangent ?  
  oes Je=òeeW kesâ kesâvõ kesâ ceOÙe keâer otjer 24 mes.ceer. nw~ Ùeefo 
oes Je=òe keâer ef$epÙee 4 mes.ceer. leLee 8 mes.ceer. nw, lees 
GYeÙeefve<" DevegmheMe& jsKee leLee efleÙe&keâ GYeÙeefve<" 
DevegmheMe& jsKee (mes.ceer. ceW) keâe Ùeesie keäÙee nw? 
 (a) 
( )
4 3 3 35 +  (b) 
( )
4 4 35 3 3 +  
 (c) 
( )
4 35 3 3 + (d) 
( )
4 3 35 3 3 + 
33.  ABC is triangle. AB = 10 cm and BC = 16 cm. 
AD = 8 cm and is perpendicular to side BC. 
What is the length (in cm) of side AC ?  
  ABC Skeâ ef$eYegpe nw~ AB = 10 mes.ceer. leLee BC = 16 
mes.ceer. nw~ AD = 8 mes.ceer. nw leLee Ùen Yegpee BC kesâ 
meceuecye nw~ Yegpee AC keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 4 41 (b) 2 41 
 (c) 2 82 (d) 4 82 
34.  An equilateral triangle of side 12 cm is drawn. 
What is the area (in cm
2
) of the largest square 
which can be drawn inside it ?  
  12 mes.ceer. Yegpee Jeeuee Skeâ meceyeeng ef$eYegpe yeveeÙee ieÙee~ 
FmeceW yeveeÙes pee mekeâves Jeeues meyemes yeÌ[s Jeie& keâe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 1512 864 3 - (b) 3024 1728 3 - 
 (c) 3024 1728 3 + (d) 1512 864 3 + 
35.  PQRS is a rectangle. The ratio of the sides PQ 
and QR is 3 : 1. If the length of the diagonal PR 
is 10 cm, then what is the area (in cm
2
) of the 
rectangle ?  
  PQRS Skeâ DeeÙele nw~ Yegpee PQ leLee QR keâe Devegheele 
3 : 1 nw~ Ùeefo efJekeâCe& PR keâer uecyeeF& 10 mes.ceer. nw, lees 
DeeÙele keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw?  
 (a) 15 (b) 30  
 (c) 45 (d) 20 
36.  ABCDEF is a regular hexagon. What is the 
ratio of the area of triangle ACE and area of 
triangle AEF ?  
  ABCDEF Skeâ mece<ešYegpe nw~ ef$eYegpe ACE kesâ 
#es$eHeâue leLee ef$eYegpe AEF kesâ #es$eHeâue keâe Devegheele 
keäÙee nw? 
 (a) 6 : 1 (b) 4 : 1  
 (c) 3 : 1 (d) 5 : 1 
37.  ABCD is trapezium. Sides AB and CD are 
parallel to each other. AB = 6 cm, CD = 18 cm, 
BC = 8 cm and AD = 12 cm. A line parallel to 
AB divides the trapezium in two parts of equal 
perimeter. This line cuts BC at E and AD at F. 
If BE/EC = AF/FD, then what is the value of 
BE/EC ?  
  ABCD Skeâ meceuecye nw~ YegpeeSB AB leLee CD Skeâ 
otmejs kesâ meceevlej nw~ AB = 6 mes.ceer., CD = 18 mes.ceer., 
BC = 8 mes.ceer. leLee AD = 12 mes.ceer. nw~ AB kesâ 
meceevlej Skeâ jsKee meceuecye keâes oes yejeyej heefjceehe Jeeues 
efnmmeeW ceW keâešlee nw~ Ùen jsKee Yegpee BC keâes E hej leLee 
AD keâes F hej keâešleer nw~ Ùeefo BE/EC=AF/FD nw, lees 
BE/EC keâe ceeve keäÙee nw? 
 (a) 1/2 (b) 2  
 (c) 4 (d) 1/4 
38.  A rectangular sheet of length 42 cm and 
breadth 14 cm is cut from a circular sheet. 
What is the minimum area (in cm
2
) of circular 
sheet ?  
  Skeâ Je=òeekeâej Ûeeoj mes 42 mes.ceer. uecyeer leLee 14 
mes.ceer. ÛeewÌ[er Skeâ DeeÙeleekeâej Ûeeoj keâešer ieF& nw~ 
Je=òeekeâej Ûeeoj keâe #es$eHeâue (mes.ceer.
2
 ceW) keâce mes keâce 
keäÙee nw? 
 (a) 3080 (b) 1540 
 (c) 770 (d) 1030 
39.  An equilateral triangle ABC is inscribed in a 
circle as shown in figure. A square of largest 
possible area is made inside this triangle as 
shown. Another circle made inscribing the 
square. What is the ratio of large circle and the 
small circle ?  
  pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw, Skeâ mece ef$eYegpe 
ABC Skeâ Je=òe ceW yeveeÙee ieÙee nw~ pewmee oMee&Ùee ieÙee 
nw, meyemes yeÌ[s mebYeeefJele #es$eHeâue Jeeuee Jeie& Fme ef$eYegpe 
kesâ Deboj yeveeÙee ieÙee nw~ Skeâ Deewj Je=òe Jeie& kesâ Deboj 
yeveeÙee ieÙee nw~ yeÌ[s Je=òe leLee Úesšs Je=òe kesâ #es$eHeâue keâe 
Devegheele keäÙee nw? 
 
 (a) 
( )
15 12 3 :1 - (b) 
( )
4 : 63 36 3 - 
 (c) 
( )
7 4 3 : 8 - (d) 
( )
18 3 : 2 - 
40.  A prism has a regular hexagonal base whose 
side is 12 cm. The height of the prism is 24 cm. 
It is cut into 4 equal parts by 2 perpendicular 
cuts as shown in figure. What is the sum of the 
total surface area of the four parts ?  
  Skeâ efØepce keâe DeeOeej Skeâ mece <ešYegpe nw efpemekeâer Yegpee 
12 mes.ceer. nw~ efØepce keâer TBÛeeF& 24 mes.ceer. nw~ Fmes 2 
uecyeJele keâšeJe Éeje 4 yejeyej YeeieeW ceW keâeše peelee nw 
pewmee efkeâ efÛe$e ceW oMee&Ùee ieÙee nw~ ÛeejeW YeeieeW kesâ kegâue 
he=<"erÙe #es$eHeâue keâe Ùeesie keäÙee nw? 
 
 
 (a) 1728 432 3 +  (b) 2880 1008 3 + 
 (c) 2880 432 3 + (d) 1728 1008 3 + 
41.  Four identical cones each of radius 10.5 cm and 
height 14 cm are cut from a cuboid of 
dimensions 30 cm × 32 cm × 40 cm (base of 
each cone lies on the surface of cuboid). What 
is the total surface area (in cm
2
) of the 
remaining solid ?  
  10.5 mes.ceer. ef$epÙee leLee 14 mes.ceer. TBÛeeF& Jeeues Ûeej 
meceeve MebkegâDeeW keâes Skeâ IeveeYe ceW mes keâeše ieÙee nw 
efpemekesâ DeeÙeece 30 mes.ceer. × 32 mes.ceer. × 40 mes.ceer. 
nw (ØelÙeskeâ Mebkegâ keâe DeeOeej IeveeYe keâer melen hej nw) 
yeÛes ngS "esme keâe kegâue he=<"erÙe (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 6528  (b) 7804 
 (c) 5926 (d) 6824 
42.  A hollow cylinder of thickness 0.7 cm and 
height 15 cm is made of iron. If inner radius of 
cylinder is 3.5 cm, then what is the total surface 
area (in cm
2
) of the hollow cylinder ?  
  Skeâ ueesns mes yeves Keeueer yesueve keâer ÛeewÌ[eF& 0.7 mes.ceer. 
leLee TBÛeeF& 15 mes.ceer. nw~ Ùeefo yesueve keâer Deebleefjkeâ 
ef$epÙee 3.5 mes.ceer. nw, lees Keeueer yesueve keâe kegâue he=<"erÙe 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 812.12 (b) 768.42 
 (c) 759.88 (d) 828.42 
43.  A hollow cylinder has height 90 cm and the 
outer curved surface area is 11880 cm
2
. It can 
hold 55440 cm
3
 of air inside it. What is the 
thickness (in cm) of this cylinder ?  
  Skeâ Keeueer yesueve keâer TBÛeeF& 90 mes.ceer. leLee Jee¢e Je›eâ 
he=<"erÙe #es$eHeâue 11880 mes.ceer.
2
 nw~ Ùen 55440 mes.ceer.
3
 
JeeÙeg Deheves Deboj jKe mekeâlee nw~ yesueve keâer ceesšeF& 
(mes.ceer. ceW) keäÙee nw? 
 (a) 10.5  (b) 14 
 (c) 7 (d) 3.5 
44.  A hollow sphere is melted to form small 
identical hollw spheres. Inner and outer radius 
of the bigger sphere are 4 cm and 6 cm 
respectively. If inner and outer radii of the 
smaller sphere are 2 cm and 3 cm respectively, 
then how many smaller spheres can be formed?  
  Skeâ Keeueer ieesues keâes efheIeueekeâj meceeve Keeueer Úesšs 
ieesues yeveeS ieS nQ~ yeÌ[s ieesues keâer Deelebefjkeâ leLee yee¢e 
ef$epÙee ›eâceMe: 4 mes.ceer. leLee 6mes.ceer. nw~ Ùeefo Úesšs 
ieesues keâer Deebleefjkeâ leLee yee¢e ef$epÙee ›eâceMe: 2 mes.ceer. 
leLee 3 mes.ceer. nw, lees efkeâleves Úesšs ieesues yeve mekeâles nQ? 
 (a) 4  (b) 8  
 (c) 6 (d) 12 
45.  A hemispherical dome is open from its base 
and is made of iron. Thickness of dome is 3.5 
meter. Total cost of painting domes outer 
curved surface is Rs. 2464. If the rate of 
painting is Rs. 8 per meter
2
, then what is the 
volume (in meter
3
) of iron used in making 
dome ?  
  Skeâ DeOe&ieesueekeâej iegcyeo Deheves DeeOeej mes Keguee nw 
leLee ueesns mes yevee nw~ iegcyeo keâer ceesšeF& 3.5 ceeršj nw~ 
iegcyeo kesâ yeenj keâer Je›eâerÙe melen keâes heWš keâjves ceW kegâue 
2464®. keâe KeÛee& neslee nw~ Ùeefo heWefšbie keâer oj 8 ®. 
Øeefle ceeršj
2
 nw, lees iegcyeo keâes yeveeves ceW ØeÙeesie ngS ueesns 
keâe DeeÙeleve (ceeršj
3
 ceW) keäÙee nesiee? 
 (a) 656.42 (b) 614.21 
 (c) 524.46 (d) 628.83 
46.  A solid cuboid has dimensions 14 cm × 18 cm × 
24 cm. A hemisphere of radius 3.5 cm is cut 
from the centre of each face of cuboid. What is 
the total surface area (in cm
2
)  of the remaining 
solid ?  
  Skeâ "esme IeveeYe kesâ DeeÙeece 14 mes.ceer.×18 mes.ceer. × 
24 mes.ceer. nw~ IeveeYe kesâ ØelÙeskeâ melen kesâ kesâvõ mes 3.5 
mes.ceer. ef$epÙee Jeeuee Skeâ DeOe&ieesuee keâeše ieÙee~ Mes<e 
"esme keâe kegâue he=<"erÙe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee 
nesiee? 
 (a) 1902 (b) 1809 
 (c) 1706 (d) 2271 
47.  A right pyramid with square base has side of 
base 12 cm and height 40 cm. It is kept on its 
base. It is cut into 4 parts of equal heights by 3 
cuts parallel to its base. What is the ratio of 
volume of the four parts ?  
  Skeâ Jeie& DeeOeej Jeeues efhejeefce[ kesâ DeeOeej keâer Yegpee 
12 mes.ceer. leLee TBÛeeF& 40 mes.ceer. nw~ Fmes Fmekesâ DeeOeej 
hej jKee ieÙee nw~ Fmes 3 keâšeJeeW mes Fmekesâ DeeOeej kesâ 
meceevlej yejeyej TBÛeeF& Jeeues 4 YeeieeW ceW keâeše ieÙee~ 
ÛeejeW YeeieeW kesâ DeeÙeleve keâe Devegheele keäÙee nw? 
 (a) 1 : 8 : 27 : 70 (b) 1 : 7 : 19 : 47 
 (c) 1 : 7 : 19 : 37 (d) 1 : 8 : 27 : 64 
48.  What is the value of 2 sin 15
0
 cos 15
0
 – 4 sin
3
 15
0
 
cos 15
0
 ?  
  2 sin 15
0
 cos 15
0
 – 4 sin
3
 15
0
 cos 15
0
 keâe ceeve keäÙee 
nw? 
 (a) 3/ 2 (b) 3 / 2 
 (c) 3 / 4 (d) 1/2 
49.  If sin x = 1/2 and sin y = 2/3, then what is the 
value of [(6cos
2
x–4 cos
4
x)/(18 cos
2
y–27cos
4
y)]?  
  Ùeefo sin x = 1/2 leLee sin y = 2/3 nw, lees [(6 cos
2
x – 
4 cos
4
x)/(18 cos
2
y–27 cos
4
y)] keâe ceeve keäÙee nw? 
 (a) 27/20 (b) 15/14 
 (c) 25/21 (d) 17/14 
50.  What is the value of cos 15
0
 + cos 105
0
 ?  
  cos 15
0
 + cos 105
0
 keâe ceeve keäÙee nw?