SSC CGL Tier 2 (18 Feb) Past Year Paper (2018) | SSC CGL (Hindi) Tier - 1 Mock Test Series PDF Download

 Page 1


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 18-2-2018] [Time : 10 AM to 12 PM 
1.  How many three digit numbers are there in 
which all the digits are odd ?  
  leerve DebkeâeW Jeeueer Ssmeer efkeâleveer mebKÙeeSB nQ efpemeceW meYeer 
Debkeâ efJe<ece nQ? 
 (a) 100 (b) 125 
 (c) 500 (d) 250 
2.  If the sum of ten different positive integers is 
100, then what is the greatest possible number 
among these 10 numbers ?  
  Ùeefo ome efJeefYeVe Oeveelcekeâ hetCeeËkeâeW keâe Ùeesie 100 nw, 
lees Fve 10 mebKÙeeDeeW ceW meyemes yeÌ[er mebYeeefJele mebKÙee 
keäÙee nw? 
 (a) 45 (b) 91  
 (c) 55 (d) 64 
3.  If N = 0.369369369369..... and M = 
0.531531531531...., then what is the value of 
(1/N) + (1/M) ?  
  Ùeefo N = 0.369369369369.... leLee M = 
0.531531531531.... nQ, lees (1/N) + (1/M) keâe ceeve 
keäÙee nw? 
 (a) 11100/2419 (b) 111/100 
 (c) 1897/3162 (d) 2419/11100 
4.  If 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 and 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 
then what is the value of (A
2
 + B
2
) ?  
  Ùeefo 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 leLee 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 nes, lees (A
2
 + B
2
) keâe ceeve 
keäÙee nw? 
 (a) 0.8 (b) 1 
 (c) 1.4 (d) 2.2 
5.  If 
1 1 1 1 1
A = + + + +
1× 2 1×4 2× 3 4× 7 3× 4
 
1
+ ...
7×10
  
upto 20 terms, then what is the value of A ?  
  Ùeefo 
1 1 1 1 1
A = + + + +
1× 2 1× 4 2× 3 4× 7 3× 4
 
............
1
+
7×10
  heoeW lekeâ nes, lees A keâe ceeve keäÙee 
nw? 
 (a) 379/308  (b) 171/140 
 (c) 379/310 (d) 420/341 
6.  If 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
, 
then what is the value of [(p+q)/s]+r ?  
  Ùeefo 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
. 
nes, lees [(p+q)/s]+r keâe ceeve keäÙee nw? 
 (a) 6  (b) 8  
 (c) 12 (d) 10 
7.  If 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 and 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
 then what is the value of 
A–B ?  
  Ùeefo 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 leLee 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
nes, lees A – B keâe ceeve keäÙee 
nw? 
 (a) 5/8  (b) 1 
 (c) 0 (d) 3/8 
8.  What is the sum of all natural numbers 
between 100 and 400 which are divisible by 13?  
  100 leLee 400 kesâ ceOÙe meYeer Øeeke=âeflekeâ mebKÙeeDeeW keâe 
Ùeesie keäÙee nw pees 13 mes efJeYeepÙe nw? 
 (a) 5681 (b) 5334 
 (c) 5434 (d) 5761 
9.  If the least common multiple of two numbers, 
1728 and K is 5184, then how many values of K 
are possible ?  
  Ùeefo oes mebKÙeeDeeW 1728 leLee K keâe ueIegòece meceeheJelÙe& 
5184 nw, lees K kesâ efkeâleves ceeve mebYeJe nw? 
 (a) 11  (b) 8  
 (c) 6 (d) 7 
10.  If (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 then what is 
the value of ?  
  Ùeefo (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 nes, lees x keâe 
ceeve keäÙee nw? 
 (a) 34  (b) 35  
 (c) 33 (d) 33.5 
11.  Which of the following statement(s) is/are true?  
  efvecveefueefKele keâLeve/keâLeveeW ceW mes keâewve mee/mes mener 
nw/nQ? 
  I. (65)
1/6
 > (17)
1/4
 > (12)
1/3
 
  II. (17)
1/4
 > (65)
1/6
 > (12)
1/3
 
  III. (12)
1/3
 > (17)
1/4
 > (65)
1/6
 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 18-2-2018] [Time : 10 AM to 12 PM 
1.  How many three digit numbers are there in 
which all the digits are odd ?  
  leerve DebkeâeW Jeeueer Ssmeer efkeâleveer mebKÙeeSB nQ efpemeceW meYeer 
Debkeâ efJe<ece nQ? 
 (a) 100 (b) 125 
 (c) 500 (d) 250 
2.  If the sum of ten different positive integers is 
100, then what is the greatest possible number 
among these 10 numbers ?  
  Ùeefo ome efJeefYeVe Oeveelcekeâ hetCeeËkeâeW keâe Ùeesie 100 nw, 
lees Fve 10 mebKÙeeDeeW ceW meyemes yeÌ[er mebYeeefJele mebKÙee 
keäÙee nw? 
 (a) 45 (b) 91  
 (c) 55 (d) 64 
3.  If N = 0.369369369369..... and M = 
0.531531531531...., then what is the value of 
(1/N) + (1/M) ?  
  Ùeefo N = 0.369369369369.... leLee M = 
0.531531531531.... nQ, lees (1/N) + (1/M) keâe ceeve 
keäÙee nw? 
 (a) 11100/2419 (b) 111/100 
 (c) 1897/3162 (d) 2419/11100 
4.  If 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 and 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 
then what is the value of (A
2
 + B
2
) ?  
  Ùeefo 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 leLee 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 nes, lees (A
2
 + B
2
) keâe ceeve 
keäÙee nw? 
 (a) 0.8 (b) 1 
 (c) 1.4 (d) 2.2 
5.  If 
1 1 1 1 1
A = + + + +
1× 2 1×4 2× 3 4× 7 3× 4
 
1
+ ...
7×10
  
upto 20 terms, then what is the value of A ?  
  Ùeefo 
1 1 1 1 1
A = + + + +
1× 2 1× 4 2× 3 4× 7 3× 4
 
............
1
+
7×10
  heoeW lekeâ nes, lees A keâe ceeve keäÙee 
nw? 
 (a) 379/308  (b) 171/140 
 (c) 379/310 (d) 420/341 
6.  If 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
, 
then what is the value of [(p+q)/s]+r ?  
  Ùeefo 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
. 
nes, lees [(p+q)/s]+r keâe ceeve keäÙee nw? 
 (a) 6  (b) 8  
 (c) 12 (d) 10 
7.  If 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 and 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
 then what is the value of 
A–B ?  
  Ùeefo 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 leLee 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
nes, lees A – B keâe ceeve keäÙee 
nw? 
 (a) 5/8  (b) 1 
 (c) 0 (d) 3/8 
8.  What is the sum of all natural numbers 
between 100 and 400 which are divisible by 13?  
  100 leLee 400 kesâ ceOÙe meYeer Øeeke=âeflekeâ mebKÙeeDeeW keâe 
Ùeesie keäÙee nw pees 13 mes efJeYeepÙe nw? 
 (a) 5681 (b) 5334 
 (c) 5434 (d) 5761 
9.  If the least common multiple of two numbers, 
1728 and K is 5184, then how many values of K 
are possible ?  
  Ùeefo oes mebKÙeeDeeW 1728 leLee K keâe ueIegòece meceeheJelÙe& 
5184 nw, lees K kesâ efkeâleves ceeve mebYeJe nw? 
 (a) 11  (b) 8  
 (c) 6 (d) 7 
10.  If (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 then what is 
the value of ?  
  Ùeefo (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 nes, lees x keâe 
ceeve keäÙee nw? 
 (a) 34  (b) 35  
 (c) 33 (d) 33.5 
11.  Which of the following statement(s) is/are true?  
  efvecveefueefKele keâLeve/keâLeveeW ceW mes keâewve mee/mes mener 
nw/nQ? 
  I. (65)
1/6
 > (17)
1/4
 > (12)
1/3
 
  II. (17)
1/4
 > (65)
1/6
 > (12)
1/3
 
  III. (12)
1/3
 > (17)
1/4
 > (65)
1/6
 
 
 (a) Only I/kesâJeue I  
 (b) Only III/kesâJeue III 
 (c) Only II/kesâJeue II 
 (d) None of these/FveceW mes keâesF& veneR 
12.  If P = 7 + 4 3 and PQ =1, then what is the 
value of (1/P
2
) + (1/Q
2
) ?  
  Ùeefo P = 7 + 4 3 leLee PQ = 1 nQ, lees (1/P
2
) + 
(1+Q
2
) keâe ceeve keäÙee nw? 
 (a) 148 (b) 189  
 (c) 194 (d) 204 
13.  If 
( )
x = 5 + 1 and 
( )
y = 5 - 1 then what is 
the value of (x
2
/y
2
) + (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
 + 6 ?  
  Ùeefo 
( )
x = 5 + 1 leLee 
( )
y = 5 - 1 nQ, lees (x
2
/y
2
) 
+ (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
+ 6 keâe ceeve keäÙee nw? 
 (a) 31 (b) 23 5  
 (c) 27 5 (d) 25 
14.  If , x = 2 + 3 y = 2 - 3 and z = 1, then what is 
the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + 
(1/y) + (1/z)] ?  
  Ùeefo , x = 2 + 3 y = 2 - 3 leLee z = 1 nQ, lees (x/yz) 
+ (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)] keâe 
ceeve keäÙee nw? 
 (a) 25 (b) 22  
 (c) 17 (d) 43 
15.  A root of equation ax
2
 + bx + c = 0 (where a, b 
and c are rational numbers) is 5 + 3 3 . What 
is the value of (a
2
 + b
2
 + c
2
)/(a+b+c) ?  
  meceerkeâjCe ax
2
 + bx + c = 0 (peneB a, b leLee c heefjcesÙe 
mebKÙeeSB nw) keâe cetue 5 + 3 3 nw~ (a
2
 + b
2
 + c
2
)/(a + b 
+ c) keâe ceeve keäÙee nw? 
 (a) 35/3  (b) 37/3 
 (c) –105/11 (d) –105/13 
16.  If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) 
+ (a/c), then what is the value of xyz – x
2
 – y
2
 – 
z
2
 ?  
  Ùeefo x = (a/b) + (b/a), y = (b/c) + (c/b) leLee z = 
(c/a) + (a/c) nQ, lees xyz – x
2
 – y
2
 – z
2
 keâe ceeve keäÙee 
nw? 
 (a) –4 (b) 2  
 (c) –1 (d) –6 
17.  If [a+(1/a)]
2
 – 2[a–(1/a)] = 12, then which of the 
following is a value of 'a' ?  
  Ùeefo [a+(1/a)]
2
–2[a–(1/a)] = 12 nes, lees efvecveefueefKele 
ceW mes keâewve mee 'a' keâe Skeâ ceeve nw? 
 (a) 8 3 - +  
 (b) 8 3 - - 
 (c) 8 5 - + 
 (d) None of these/FveceW mes keâesF& veneR 
18.  If x
2
 – 4x + 1 = 0, then what is the value of  
x
9
 + x
7
 – 194x
5
 – 194x
3
 ?  
  Ùeefo x
2
 – 4x + 1 = 0 nes, lees x
9
 + x
7
 – 194x
5
 – 194x
3
 
keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) 1 (d) –1 
19.  If x+y= 3, then what is the value of x
3
+y
3
+9xy?  
  Ùeefo x+y= 3 nes, lees x
3
+y
3
+9xy keâe ceeve keäÙee nw? 
 (a) 15  (b) 81  
 (c) 27 (d) 9 
20.  A = (x
8 
–1)/(x
4
 + 1) and B = (y
4
 –1)/(y
2
 + 1). If x 
= 2 and y = 9, the what is the value of A
2
 + 2AB 
+ AB
2
 ?  
  A = (x
8 
–1)/(x
4
 + 1) leLee B = (y
4
 –1)/(y
2
 + 1) nQ~ 
Ùeefo x = 2 leLee y = 9 nQ, lees A
2
 + 2AB + AB
2
 keâe 
ceeve keäÙee nw? 
 (a) 96475 (b) 98625 
 (c) 92425 (d) 89125 
21.  If x–4y = 0 and x + 2y = 24, then what is the 
value of (2x + 3y)/(2x–3y) ?  
  Ùeefo x – 4y = 0 leLee x + 2y = 24 nQ, lees 
(2x+3y)/(2x–3y) keâe ceeve keäÙee nw? 
 (a) 9/5  (b) 11/5 
 (c) 13/7 (d) 9/7 
22.  If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then 
what is the value of x/y ?  
  Ùeefo (x/a) + (y/b) = 3 leLee (x/b)–(y/a) = 9 nQ, lees 
x/y keâe ceeve keäÙee nw? 
 (a) (b+3a)/(a–3b)  (b) (a+3b)/(b–3a) 
 (c) (1+3a)/(a+3b) (d) (a+3b
2
)/(b–3a
2
) 
23.  In the given figure, OX, OY and OZ are 
perpendicular bisectors of the three sides of the 
triangle. If ?QPR = 65
0
 and ?PQR = 60
0
, then 
what is the value (in degrees) of ?QOR + 
?POR ?  
  oer ieF& Deeke=âefle ceW, OX, OY leLee OZ ef$eYegpe keâer 
leerveeW YegpeeDeeW kesâ uebye efÉYeepekeâ nQ~ Ùeefo ?QPR = 65
0
 
leLee ?PQR = 60
0
 nes, lees ?QOR + ?POR keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 250 (b) 180  
 (c) 210 (d) 125 
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 18-2-2018] [Time : 10 AM to 12 PM 
1.  How many three digit numbers are there in 
which all the digits are odd ?  
  leerve DebkeâeW Jeeueer Ssmeer efkeâleveer mebKÙeeSB nQ efpemeceW meYeer 
Debkeâ efJe<ece nQ? 
 (a) 100 (b) 125 
 (c) 500 (d) 250 
2.  If the sum of ten different positive integers is 
100, then what is the greatest possible number 
among these 10 numbers ?  
  Ùeefo ome efJeefYeVe Oeveelcekeâ hetCeeËkeâeW keâe Ùeesie 100 nw, 
lees Fve 10 mebKÙeeDeeW ceW meyemes yeÌ[er mebYeeefJele mebKÙee 
keäÙee nw? 
 (a) 45 (b) 91  
 (c) 55 (d) 64 
3.  If N = 0.369369369369..... and M = 
0.531531531531...., then what is the value of 
(1/N) + (1/M) ?  
  Ùeefo N = 0.369369369369.... leLee M = 
0.531531531531.... nQ, lees (1/N) + (1/M) keâe ceeve 
keäÙee nw? 
 (a) 11100/2419 (b) 111/100 
 (c) 1897/3162 (d) 2419/11100 
4.  If 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 and 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 
then what is the value of (A
2
 + B
2
) ?  
  Ùeefo 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 leLee 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 nes, lees (A
2
 + B
2
) keâe ceeve 
keäÙee nw? 
 (a) 0.8 (b) 1 
 (c) 1.4 (d) 2.2 
5.  If 
1 1 1 1 1
A = + + + +
1× 2 1×4 2× 3 4× 7 3× 4
 
1
+ ...
7×10
  
upto 20 terms, then what is the value of A ?  
  Ùeefo 
1 1 1 1 1
A = + + + +
1× 2 1× 4 2× 3 4× 7 3× 4
 
............
1
+
7×10
  heoeW lekeâ nes, lees A keâe ceeve keäÙee 
nw? 
 (a) 379/308  (b) 171/140 
 (c) 379/310 (d) 420/341 
6.  If 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
, 
then what is the value of [(p+q)/s]+r ?  
  Ùeefo 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
. 
nes, lees [(p+q)/s]+r keâe ceeve keäÙee nw? 
 (a) 6  (b) 8  
 (c) 12 (d) 10 
7.  If 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 and 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
 then what is the value of 
A–B ?  
  Ùeefo 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 leLee 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
nes, lees A – B keâe ceeve keäÙee 
nw? 
 (a) 5/8  (b) 1 
 (c) 0 (d) 3/8 
8.  What is the sum of all natural numbers 
between 100 and 400 which are divisible by 13?  
  100 leLee 400 kesâ ceOÙe meYeer Øeeke=âeflekeâ mebKÙeeDeeW keâe 
Ùeesie keäÙee nw pees 13 mes efJeYeepÙe nw? 
 (a) 5681 (b) 5334 
 (c) 5434 (d) 5761 
9.  If the least common multiple of two numbers, 
1728 and K is 5184, then how many values of K 
are possible ?  
  Ùeefo oes mebKÙeeDeeW 1728 leLee K keâe ueIegòece meceeheJelÙe& 
5184 nw, lees K kesâ efkeâleves ceeve mebYeJe nw? 
 (a) 11  (b) 8  
 (c) 6 (d) 7 
10.  If (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 then what is 
the value of ?  
  Ùeefo (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 nes, lees x keâe 
ceeve keäÙee nw? 
 (a) 34  (b) 35  
 (c) 33 (d) 33.5 
11.  Which of the following statement(s) is/are true?  
  efvecveefueefKele keâLeve/keâLeveeW ceW mes keâewve mee/mes mener 
nw/nQ? 
  I. (65)
1/6
 > (17)
1/4
 > (12)
1/3
 
  II. (17)
1/4
 > (65)
1/6
 > (12)
1/3
 
  III. (12)
1/3
 > (17)
1/4
 > (65)
1/6
 
 
 (a) Only I/kesâJeue I  
 (b) Only III/kesâJeue III 
 (c) Only II/kesâJeue II 
 (d) None of these/FveceW mes keâesF& veneR 
12.  If P = 7 + 4 3 and PQ =1, then what is the 
value of (1/P
2
) + (1/Q
2
) ?  
  Ùeefo P = 7 + 4 3 leLee PQ = 1 nQ, lees (1/P
2
) + 
(1+Q
2
) keâe ceeve keäÙee nw? 
 (a) 148 (b) 189  
 (c) 194 (d) 204 
13.  If 
( )
x = 5 + 1 and 
( )
y = 5 - 1 then what is 
the value of (x
2
/y
2
) + (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
 + 6 ?  
  Ùeefo 
( )
x = 5 + 1 leLee 
( )
y = 5 - 1 nQ, lees (x
2
/y
2
) 
+ (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
+ 6 keâe ceeve keäÙee nw? 
 (a) 31 (b) 23 5  
 (c) 27 5 (d) 25 
14.  If , x = 2 + 3 y = 2 - 3 and z = 1, then what is 
the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + 
(1/y) + (1/z)] ?  
  Ùeefo , x = 2 + 3 y = 2 - 3 leLee z = 1 nQ, lees (x/yz) 
+ (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)] keâe 
ceeve keäÙee nw? 
 (a) 25 (b) 22  
 (c) 17 (d) 43 
15.  A root of equation ax
2
 + bx + c = 0 (where a, b 
and c are rational numbers) is 5 + 3 3 . What 
is the value of (a
2
 + b
2
 + c
2
)/(a+b+c) ?  
  meceerkeâjCe ax
2
 + bx + c = 0 (peneB a, b leLee c heefjcesÙe 
mebKÙeeSB nw) keâe cetue 5 + 3 3 nw~ (a
2
 + b
2
 + c
2
)/(a + b 
+ c) keâe ceeve keäÙee nw? 
 (a) 35/3  (b) 37/3 
 (c) –105/11 (d) –105/13 
16.  If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) 
+ (a/c), then what is the value of xyz – x
2
 – y
2
 – 
z
2
 ?  
  Ùeefo x = (a/b) + (b/a), y = (b/c) + (c/b) leLee z = 
(c/a) + (a/c) nQ, lees xyz – x
2
 – y
2
 – z
2
 keâe ceeve keäÙee 
nw? 
 (a) –4 (b) 2  
 (c) –1 (d) –6 
17.  If [a+(1/a)]
2
 – 2[a–(1/a)] = 12, then which of the 
following is a value of 'a' ?  
  Ùeefo [a+(1/a)]
2
–2[a–(1/a)] = 12 nes, lees efvecveefueefKele 
ceW mes keâewve mee 'a' keâe Skeâ ceeve nw? 
 (a) 8 3 - +  
 (b) 8 3 - - 
 (c) 8 5 - + 
 (d) None of these/FveceW mes keâesF& veneR 
18.  If x
2
 – 4x + 1 = 0, then what is the value of  
x
9
 + x
7
 – 194x
5
 – 194x
3
 ?  
  Ùeefo x
2
 – 4x + 1 = 0 nes, lees x
9
 + x
7
 – 194x
5
 – 194x
3
 
keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) 1 (d) –1 
19.  If x+y= 3, then what is the value of x
3
+y
3
+9xy?  
  Ùeefo x+y= 3 nes, lees x
3
+y
3
+9xy keâe ceeve keäÙee nw? 
 (a) 15  (b) 81  
 (c) 27 (d) 9 
20.  A = (x
8 
–1)/(x
4
 + 1) and B = (y
4
 –1)/(y
2
 + 1). If x 
= 2 and y = 9, the what is the value of A
2
 + 2AB 
+ AB
2
 ?  
  A = (x
8 
–1)/(x
4
 + 1) leLee B = (y
4
 –1)/(y
2
 + 1) nQ~ 
Ùeefo x = 2 leLee y = 9 nQ, lees A
2
 + 2AB + AB
2
 keâe 
ceeve keäÙee nw? 
 (a) 96475 (b) 98625 
 (c) 92425 (d) 89125 
21.  If x–4y = 0 and x + 2y = 24, then what is the 
value of (2x + 3y)/(2x–3y) ?  
  Ùeefo x – 4y = 0 leLee x + 2y = 24 nQ, lees 
(2x+3y)/(2x–3y) keâe ceeve keäÙee nw? 
 (a) 9/5  (b) 11/5 
 (c) 13/7 (d) 9/7 
22.  If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then 
what is the value of x/y ?  
  Ùeefo (x/a) + (y/b) = 3 leLee (x/b)–(y/a) = 9 nQ, lees 
x/y keâe ceeve keäÙee nw? 
 (a) (b+3a)/(a–3b)  (b) (a+3b)/(b–3a) 
 (c) (1+3a)/(a+3b) (d) (a+3b
2
)/(b–3a
2
) 
23.  In the given figure, OX, OY and OZ are 
perpendicular bisectors of the three sides of the 
triangle. If ?QPR = 65
0
 and ?PQR = 60
0
, then 
what is the value (in degrees) of ?QOR + 
?POR ?  
  oer ieF& Deeke=âefle ceW, OX, OY leLee OZ ef$eYegpe keâer 
leerveeW YegpeeDeeW kesâ uebye efÉYeepekeâ nQ~ Ùeefo ?QPR = 65
0
 
leLee ?PQR = 60
0
 nes, lees ?QOR + ?POR keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 250 (b) 180  
 (c) 210 (d) 125 
 
24.  In a triangle PQR, ?PQR = 90
0
, PQ = 10 cm 
and PR = 26 cm, then what is the value (in cm) 
of inradius of incircle ?  
  ef$eYegpe PQR ceW, ?PQR = 90
0
, PQ = 10 mes.ceer. leLee 
PR = 26 mes.ceer. nQ, lees Deble: Je=òe keâer Deble:ef$epÙee keâe 
ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 9 (b) 4  
 (c) 8 (d) 6 
25.  In the given figure, if 
QR 14
=
XY 9
 and PY = 18 
cm, then what is the value (in cm) of PQ ?  
  oer ieF& Deeke=âefle ceW, Ùeefo 
QR 14
=
XY 9
 leLee PY = 18 
mes.ceer. nes, lees PQ keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 28 (b) 18  
 (c) 21 (d) 24 
26.  In a triangle PQR, PX, QY and RZ be altitudes 
intersecting at O. If PO = 6 cm, PX = 8 cm and 
QO = 4 cm, then what is the value (in cm) of 
QY?  
  ef$eYegpe PQR ceW, PX, QY leLee RZ, O hej ØeefleÛÚso 
keâjleer ngF& TBÛeeF&ÙeeB nQ~ Ùeefo PO = 6 mes.ceer., PX = 8 
mes.ceer., leLee QO = 4 mes.ceer. nQ, lees QY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 6.3  (b) 5.8 
 (c) 6 (d) 7 
27.  A line cuts two concentric circles. The lengths 
of chords formed by that line on the two circles 
are 4 cm and 16 cm. What is the difference (in 
cm
2
) in squares of radii of two circles ?  
  Skeâ jsKee oes mebkesâefvõle Je=òeeW keâes keâešleer nw~ Gme jsKee 
Éeje Je=òeeW hej yeveeF& ieF& peerJeeDeeW keâer uecyeeF& 4 mes.ceer. 
leLee 16 mes.ceer. nQ~ oesveeW Je=òeeW keâer ef$epÙeeDeeW kesâ JeieeX keâe 
Deblej (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 240 (b) 120 
 (c) 60 (d) 90 
28.  In the given figure, a circle touches the sides of 
the quadrilateral PQRS. The radius of the 
circle is 9 cm. ?RSP = ?SRQ = 60
0
 and ?PQR 
= ?QPS = 120
0
. What is the perimeter (in cm) 
of the quadrilateral ?  
  oer ieF& Deeke=âefle ceW, Skeâ Je=òe ÛelegYeg&pe PQRS keâer 
YegpeeDeeW keâes mheMe& keâj jne nw~ Je=òe keâer ef$epÙee 9 mes.ceer. 
nw~ ?RSP = ?SRQ = 60
0
 leLee ?PQR = ?QPS = 
120
0
 nw~ ÛelegYeg&pe keâe heefjceehe (mes.ceer. ceW) keäÙee nw? 
 
 (a) 36 3 (b) 24 3 
 (c) 48 3 (d) 32 
29.  In the given figure, from the point P two 
tangents PA and PB are drawn to a circle with 
centre O and radius 5 cm. From the point O, 
OC and OD are drawn parallel to PA and PB 
respectively. If the length of the chord AB is 5 
cm, then what is the value (in degrees) of 
?COD ?  
  oer ieF& Deeke=âefle ceW, efyevog P mes Skeâ Je=òe efpemekeâe kesâvõ 
O nw leLee ef$epÙee 5 mes.ceer. nw, hej PA leLee PB oes mheMe& 
jsKeeSB KeeRÛeer ieF& nw~ efyevog O mes OC leLee OD keâes 
›eâceMe: PA leLee PB kesâ meceeveeblej KeeRÛee ieÙee nw~ Ùeefo 
peerJee AB keâer uebyeeF& 5 mes.ceer. nw, lees ?COD keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 90 (b) 120  
 (c) 150 (d) 135 
30.  In the given figure, AB is a diameter of the 
circle with centre O and XY is the tangent at a 
point C. If ?ACX = 35
0
, then what is the value 
(in degrees) of ?CAB ?  
  oer ieF& Deeke=âefle ceW, AB Skeâ Je=òe efpemekeâe kesâvõ O nw, 
keâe JÙeeme nw leLee XY, efyevog C hej Skeâ mheMe& jsKee nw~ 
Ùeefo ?ACX = 35
0 
nw, lees ?CAB keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 
 (a) 45 (b) 35  
 (c) 55 (d) 65 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 18-2-2018] [Time : 10 AM to 12 PM 
1.  How many three digit numbers are there in 
which all the digits are odd ?  
  leerve DebkeâeW Jeeueer Ssmeer efkeâleveer mebKÙeeSB nQ efpemeceW meYeer 
Debkeâ efJe<ece nQ? 
 (a) 100 (b) 125 
 (c) 500 (d) 250 
2.  If the sum of ten different positive integers is 
100, then what is the greatest possible number 
among these 10 numbers ?  
  Ùeefo ome efJeefYeVe Oeveelcekeâ hetCeeËkeâeW keâe Ùeesie 100 nw, 
lees Fve 10 mebKÙeeDeeW ceW meyemes yeÌ[er mebYeeefJele mebKÙee 
keäÙee nw? 
 (a) 45 (b) 91  
 (c) 55 (d) 64 
3.  If N = 0.369369369369..... and M = 
0.531531531531...., then what is the value of 
(1/N) + (1/M) ?  
  Ùeefo N = 0.369369369369.... leLee M = 
0.531531531531.... nQ, lees (1/N) + (1/M) keâe ceeve 
keäÙee nw? 
 (a) 11100/2419 (b) 111/100 
 (c) 1897/3162 (d) 2419/11100 
4.  If 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 and 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 
then what is the value of (A
2
 + B
2
) ?  
  Ùeefo 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 leLee 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 nes, lees (A
2
 + B
2
) keâe ceeve 
keäÙee nw? 
 (a) 0.8 (b) 1 
 (c) 1.4 (d) 2.2 
5.  If 
1 1 1 1 1
A = + + + +
1× 2 1×4 2× 3 4× 7 3× 4
 
1
+ ...
7×10
  
upto 20 terms, then what is the value of A ?  
  Ùeefo 
1 1 1 1 1
A = + + + +
1× 2 1× 4 2× 3 4× 7 3× 4
 
............
1
+
7×10
  heoeW lekeâ nes, lees A keâe ceeve keäÙee 
nw? 
 (a) 379/308  (b) 171/140 
 (c) 379/310 (d) 420/341 
6.  If 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
, 
then what is the value of [(p+q)/s]+r ?  
  Ùeefo 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
. 
nes, lees [(p+q)/s]+r keâe ceeve keäÙee nw? 
 (a) 6  (b) 8  
 (c) 12 (d) 10 
7.  If 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 and 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
 then what is the value of 
A–B ?  
  Ùeefo 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 leLee 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
nes, lees A – B keâe ceeve keäÙee 
nw? 
 (a) 5/8  (b) 1 
 (c) 0 (d) 3/8 
8.  What is the sum of all natural numbers 
between 100 and 400 which are divisible by 13?  
  100 leLee 400 kesâ ceOÙe meYeer Øeeke=âeflekeâ mebKÙeeDeeW keâe 
Ùeesie keäÙee nw pees 13 mes efJeYeepÙe nw? 
 (a) 5681 (b) 5334 
 (c) 5434 (d) 5761 
9.  If the least common multiple of two numbers, 
1728 and K is 5184, then how many values of K 
are possible ?  
  Ùeefo oes mebKÙeeDeeW 1728 leLee K keâe ueIegòece meceeheJelÙe& 
5184 nw, lees K kesâ efkeâleves ceeve mebYeJe nw? 
 (a) 11  (b) 8  
 (c) 6 (d) 7 
10.  If (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 then what is 
the value of ?  
  Ùeefo (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 nes, lees x keâe 
ceeve keäÙee nw? 
 (a) 34  (b) 35  
 (c) 33 (d) 33.5 
11.  Which of the following statement(s) is/are true?  
  efvecveefueefKele keâLeve/keâLeveeW ceW mes keâewve mee/mes mener 
nw/nQ? 
  I. (65)
1/6
 > (17)
1/4
 > (12)
1/3
 
  II. (17)
1/4
 > (65)
1/6
 > (12)
1/3
 
  III. (12)
1/3
 > (17)
1/4
 > (65)
1/6
 
 
 (a) Only I/kesâJeue I  
 (b) Only III/kesâJeue III 
 (c) Only II/kesâJeue II 
 (d) None of these/FveceW mes keâesF& veneR 
12.  If P = 7 + 4 3 and PQ =1, then what is the 
value of (1/P
2
) + (1/Q
2
) ?  
  Ùeefo P = 7 + 4 3 leLee PQ = 1 nQ, lees (1/P
2
) + 
(1+Q
2
) keâe ceeve keäÙee nw? 
 (a) 148 (b) 189  
 (c) 194 (d) 204 
13.  If 
( )
x = 5 + 1 and 
( )
y = 5 - 1 then what is 
the value of (x
2
/y
2
) + (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
 + 6 ?  
  Ùeefo 
( )
x = 5 + 1 leLee 
( )
y = 5 - 1 nQ, lees (x
2
/y
2
) 
+ (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
+ 6 keâe ceeve keäÙee nw? 
 (a) 31 (b) 23 5  
 (c) 27 5 (d) 25 
14.  If , x = 2 + 3 y = 2 - 3 and z = 1, then what is 
the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + 
(1/y) + (1/z)] ?  
  Ùeefo , x = 2 + 3 y = 2 - 3 leLee z = 1 nQ, lees (x/yz) 
+ (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)] keâe 
ceeve keäÙee nw? 
 (a) 25 (b) 22  
 (c) 17 (d) 43 
15.  A root of equation ax
2
 + bx + c = 0 (where a, b 
and c are rational numbers) is 5 + 3 3 . What 
is the value of (a
2
 + b
2
 + c
2
)/(a+b+c) ?  
  meceerkeâjCe ax
2
 + bx + c = 0 (peneB a, b leLee c heefjcesÙe 
mebKÙeeSB nw) keâe cetue 5 + 3 3 nw~ (a
2
 + b
2
 + c
2
)/(a + b 
+ c) keâe ceeve keäÙee nw? 
 (a) 35/3  (b) 37/3 
 (c) –105/11 (d) –105/13 
16.  If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) 
+ (a/c), then what is the value of xyz – x
2
 – y
2
 – 
z
2
 ?  
  Ùeefo x = (a/b) + (b/a), y = (b/c) + (c/b) leLee z = 
(c/a) + (a/c) nQ, lees xyz – x
2
 – y
2
 – z
2
 keâe ceeve keäÙee 
nw? 
 (a) –4 (b) 2  
 (c) –1 (d) –6 
17.  If [a+(1/a)]
2
 – 2[a–(1/a)] = 12, then which of the 
following is a value of 'a' ?  
  Ùeefo [a+(1/a)]
2
–2[a–(1/a)] = 12 nes, lees efvecveefueefKele 
ceW mes keâewve mee 'a' keâe Skeâ ceeve nw? 
 (a) 8 3 - +  
 (b) 8 3 - - 
 (c) 8 5 - + 
 (d) None of these/FveceW mes keâesF& veneR 
18.  If x
2
 – 4x + 1 = 0, then what is the value of  
x
9
 + x
7
 – 194x
5
 – 194x
3
 ?  
  Ùeefo x
2
 – 4x + 1 = 0 nes, lees x
9
 + x
7
 – 194x
5
 – 194x
3
 
keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) 1 (d) –1 
19.  If x+y= 3, then what is the value of x
3
+y
3
+9xy?  
  Ùeefo x+y= 3 nes, lees x
3
+y
3
+9xy keâe ceeve keäÙee nw? 
 (a) 15  (b) 81  
 (c) 27 (d) 9 
20.  A = (x
8 
–1)/(x
4
 + 1) and B = (y
4
 –1)/(y
2
 + 1). If x 
= 2 and y = 9, the what is the value of A
2
 + 2AB 
+ AB
2
 ?  
  A = (x
8 
–1)/(x
4
 + 1) leLee B = (y
4
 –1)/(y
2
 + 1) nQ~ 
Ùeefo x = 2 leLee y = 9 nQ, lees A
2
 + 2AB + AB
2
 keâe 
ceeve keäÙee nw? 
 (a) 96475 (b) 98625 
 (c) 92425 (d) 89125 
21.  If x–4y = 0 and x + 2y = 24, then what is the 
value of (2x + 3y)/(2x–3y) ?  
  Ùeefo x – 4y = 0 leLee x + 2y = 24 nQ, lees 
(2x+3y)/(2x–3y) keâe ceeve keäÙee nw? 
 (a) 9/5  (b) 11/5 
 (c) 13/7 (d) 9/7 
22.  If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then 
what is the value of x/y ?  
  Ùeefo (x/a) + (y/b) = 3 leLee (x/b)–(y/a) = 9 nQ, lees 
x/y keâe ceeve keäÙee nw? 
 (a) (b+3a)/(a–3b)  (b) (a+3b)/(b–3a) 
 (c) (1+3a)/(a+3b) (d) (a+3b
2
)/(b–3a
2
) 
23.  In the given figure, OX, OY and OZ are 
perpendicular bisectors of the three sides of the 
triangle. If ?QPR = 65
0
 and ?PQR = 60
0
, then 
what is the value (in degrees) of ?QOR + 
?POR ?  
  oer ieF& Deeke=âefle ceW, OX, OY leLee OZ ef$eYegpe keâer 
leerveeW YegpeeDeeW kesâ uebye efÉYeepekeâ nQ~ Ùeefo ?QPR = 65
0
 
leLee ?PQR = 60
0
 nes, lees ?QOR + ?POR keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 250 (b) 180  
 (c) 210 (d) 125 
 
24.  In a triangle PQR, ?PQR = 90
0
, PQ = 10 cm 
and PR = 26 cm, then what is the value (in cm) 
of inradius of incircle ?  
  ef$eYegpe PQR ceW, ?PQR = 90
0
, PQ = 10 mes.ceer. leLee 
PR = 26 mes.ceer. nQ, lees Deble: Je=òe keâer Deble:ef$epÙee keâe 
ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 9 (b) 4  
 (c) 8 (d) 6 
25.  In the given figure, if 
QR 14
=
XY 9
 and PY = 18 
cm, then what is the value (in cm) of PQ ?  
  oer ieF& Deeke=âefle ceW, Ùeefo 
QR 14
=
XY 9
 leLee PY = 18 
mes.ceer. nes, lees PQ keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 28 (b) 18  
 (c) 21 (d) 24 
26.  In a triangle PQR, PX, QY and RZ be altitudes 
intersecting at O. If PO = 6 cm, PX = 8 cm and 
QO = 4 cm, then what is the value (in cm) of 
QY?  
  ef$eYegpe PQR ceW, PX, QY leLee RZ, O hej ØeefleÛÚso 
keâjleer ngF& TBÛeeF&ÙeeB nQ~ Ùeefo PO = 6 mes.ceer., PX = 8 
mes.ceer., leLee QO = 4 mes.ceer. nQ, lees QY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 6.3  (b) 5.8 
 (c) 6 (d) 7 
27.  A line cuts two concentric circles. The lengths 
of chords formed by that line on the two circles 
are 4 cm and 16 cm. What is the difference (in 
cm
2
) in squares of radii of two circles ?  
  Skeâ jsKee oes mebkesâefvõle Je=òeeW keâes keâešleer nw~ Gme jsKee 
Éeje Je=òeeW hej yeveeF& ieF& peerJeeDeeW keâer uecyeeF& 4 mes.ceer. 
leLee 16 mes.ceer. nQ~ oesveeW Je=òeeW keâer ef$epÙeeDeeW kesâ JeieeX keâe 
Deblej (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 240 (b) 120 
 (c) 60 (d) 90 
28.  In the given figure, a circle touches the sides of 
the quadrilateral PQRS. The radius of the 
circle is 9 cm. ?RSP = ?SRQ = 60
0
 and ?PQR 
= ?QPS = 120
0
. What is the perimeter (in cm) 
of the quadrilateral ?  
  oer ieF& Deeke=âefle ceW, Skeâ Je=òe ÛelegYeg&pe PQRS keâer 
YegpeeDeeW keâes mheMe& keâj jne nw~ Je=òe keâer ef$epÙee 9 mes.ceer. 
nw~ ?RSP = ?SRQ = 60
0
 leLee ?PQR = ?QPS = 
120
0
 nw~ ÛelegYeg&pe keâe heefjceehe (mes.ceer. ceW) keäÙee nw? 
 
 (a) 36 3 (b) 24 3 
 (c) 48 3 (d) 32 
29.  In the given figure, from the point P two 
tangents PA and PB are drawn to a circle with 
centre O and radius 5 cm. From the point O, 
OC and OD are drawn parallel to PA and PB 
respectively. If the length of the chord AB is 5 
cm, then what is the value (in degrees) of 
?COD ?  
  oer ieF& Deeke=âefle ceW, efyevog P mes Skeâ Je=òe efpemekeâe kesâvõ 
O nw leLee ef$epÙee 5 mes.ceer. nw, hej PA leLee PB oes mheMe& 
jsKeeSB KeeRÛeer ieF& nw~ efyevog O mes OC leLee OD keâes 
›eâceMe: PA leLee PB kesâ meceeveeblej KeeRÛee ieÙee nw~ Ùeefo 
peerJee AB keâer uebyeeF& 5 mes.ceer. nw, lees ?COD keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 90 (b) 120  
 (c) 150 (d) 135 
30.  In the given figure, AB is a diameter of the 
circle with centre O and XY is the tangent at a 
point C. If ?ACX = 35
0
, then what is the value 
(in degrees) of ?CAB ?  
  oer ieF& Deeke=âefle ceW, AB Skeâ Je=òe efpemekeâe kesâvõ O nw, 
keâe JÙeeme nw leLee XY, efyevog C hej Skeâ mheMe& jsKee nw~ 
Ùeefo ?ACX = 35
0 
nw, lees ?CAB keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 
 (a) 45 (b) 35  
 (c) 55 (d) 65 
 
31.  In the given figure, PQ is a diameter of the 
Semicircle PABQ and O is its center. ?AOB = 
64
0
. BP cuts AQ at X. What is the value (in 
degrees) of ?AXP ?  
  oer ieF& Deeke=âefle ceW, PQ, DeOe&Je=òe PABQ keâe JÙeeme 
nw, leLee O Fmekeâe kesâvõ nw~ ?AOB = 64
0
 nw~ BP, 
AQ keâes X hej keâešlee nw~ ?AXP keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 
 (a) 36 (b) 32  
 (c) 58 (d) 54 
32.  In the given figure, E and F are the centers of 
two identical circles. What is the ratio of area 
of triangle AOB to the area of triangle DOC ?  
  oer ieF& Deeke=âefle ceW, E leLee F oes mece™he Je=òeeW kesâ kesâvõ 
nQ~ ef$eYegpe AOB kesâ #es$eHeâue keâe ef$eYegpe DOC kesâ 
#es$eHeâue mes keäÙee Devegheele nw? 
 
 (a) 1 : 3 (b) 1 : 9 
 (c) 1 : 8 (d) 1 : 4 
33.  In the given figure, in a right angle triangle 
ABC, AB = 12 cm and AC = 15 cm. A square is 
inscribed in the triangle. One of the vertices of 
square coincides with the vertex of triangle. 
What is the maximum possible area (in cm
2
) of 
the square ?  
  oer ieF& Deeke=âefle ceW, Skeâ mecekeâesCe ef$eYegpe ABC ceW, AB 
= 12 mes.ceer. leLee AC = 15 mes.ceer. nQ~ ef$eYegpe kesâ Yeerlej 
Skeâ Jeie& yeveeÙee ieÙee nw~ Jeie& kesâ Meer<eeX ceW mes Skeâ ef$eYegpe 
kesâ Meer<e& mes mheMe& keâjlee nw~ Jeie& keâe DeefOekeâlece mebYeJe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 1296/49 (b) 25 
 (c) 1225/36 (d) 1225/64 
34.  In the given figure, PQRS is a square of side 8 
cm. ?PQO = 60
0
. What is the area (in cm
2
) of 
the triangle POQ ?  
  oer ieF& Deeke=âefle ceW, PQRS 8 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw~ ?PQO = 60
0
 nw~ ef$eYegpe POQ keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 32 3 (b) 
( )
24 3 1
? ?
-
? ?
 
 (c) 
( )
48 3 1
? ?
-
? ?
 (d) 
( )
16 3 3
? ?
-
? ?
 
35.  In the given figure, two squares of sides 8 cm 
and 20 cm are given. What is the area (in cm
2
) 
of the shaded part ? 
  oer ieF& Deeke=âefle ceW, 8 mes.ceer. leLee 20 mes.ceer. Yegpee Jeeues 
oes Jeie& efoÙes ieÙes nQ~ ÚeÙeebefkeâle Yeeie keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 120/7 (b) 160/7 
 (c) 180/7 (d) 240/13 
36.  The area of a regular hexagon is equal to the 
area of the square. What is the ratio of the 
perimeter of the regular hexagon to the 
perimeter of square ?  
  mece <ešdYegpe keâe #es$eHeâue Jeie& kesâ #es$eHeâue kesâ yejeyej nw~ 
mece <ešdYegpe kesâ heefjceehe keâe Jeie& kesâ heefjceehe mes keäÙee 
Devegheele nw? 
 (a) 6 3 : 3 6 (b) 2 3 : 6 2 
 (c) 6 3 : 2 (d) 6 3 : 2 3 
37.  In the given figure, ABCDEF is a regular 
hexagon of side 12 cm. P, Q and R are the mid 
points of the sides AB, CD and EF respectively. 
What is the area (in cm
2
) of triangle PQR ? 
  oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešdYegpe nw 
efpemekeâer Yegpee 12 mes.ceer. nw~ P, Q leLee R ›eâceMe: 
YegpeeDeeW AB, CD leLee EF kesâ ceOÙe efyevog nw~ ef$eYegpe 
PQR  keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 18-2-2018] [Time : 10 AM to 12 PM 
1.  How many three digit numbers are there in 
which all the digits are odd ?  
  leerve DebkeâeW Jeeueer Ssmeer efkeâleveer mebKÙeeSB nQ efpemeceW meYeer 
Debkeâ efJe<ece nQ? 
 (a) 100 (b) 125 
 (c) 500 (d) 250 
2.  If the sum of ten different positive integers is 
100, then what is the greatest possible number 
among these 10 numbers ?  
  Ùeefo ome efJeefYeVe Oeveelcekeâ hetCeeËkeâeW keâe Ùeesie 100 nw, 
lees Fve 10 mebKÙeeDeeW ceW meyemes yeÌ[er mebYeeefJele mebKÙee 
keäÙee nw? 
 (a) 45 (b) 91  
 (c) 55 (d) 64 
3.  If N = 0.369369369369..... and M = 
0.531531531531...., then what is the value of 
(1/N) + (1/M) ?  
  Ùeefo N = 0.369369369369.... leLee M = 
0.531531531531.... nQ, lees (1/N) + (1/M) keâe ceeve 
keäÙee nw? 
 (a) 11100/2419 (b) 111/100 
 (c) 1897/3162 (d) 2419/11100 
4.  If 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 and 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 
then what is the value of (A
2
 + B
2
) ?  
  Ùeefo 
0.216 + 0.008
A =
0.36 + 0.04 - 0.12
 leLee 
0.729 - 0.027
B =
0.81 + 0.09 + 0.27
 nes, lees (A
2
 + B
2
) keâe ceeve 
keäÙee nw? 
 (a) 0.8 (b) 1 
 (c) 1.4 (d) 2.2 
5.  If 
1 1 1 1 1
A = + + + +
1× 2 1×4 2× 3 4× 7 3× 4
 
1
+ ...
7×10
  
upto 20 terms, then what is the value of A ?  
  Ùeefo 
1 1 1 1 1
A = + + + +
1× 2 1× 4 2× 3 4× 7 3× 4
 
............
1
+
7×10
  heoeW lekeâ nes, lees A keâe ceeve keäÙee 
nw? 
 (a) 379/308  (b) 171/140 
 (c) 379/310 (d) 420/341 
6.  If 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
, 
then what is the value of [(p+q)/s]+r ?  
  Ùeefo 56 × 75 × 60 × 84 × 210 = 2
p
 × 3
q
 × 5
r
 × 7
s
. 
nes, lees [(p+q)/s]+r keâe ceeve keäÙee nw? 
 (a) 6  (b) 8  
 (c) 12 (d) 10 
7.  If 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 and 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
 then what is the value of 
A–B ?  
  Ùeefo 
1 1 47 47
A = 3 × 4 ÷ 34 - +
4 4 32 16
 leLee 
1 1 11
B = 2 + 5 ÷ 55 -
2 2 10
nes, lees A – B keâe ceeve keäÙee 
nw? 
 (a) 5/8  (b) 1 
 (c) 0 (d) 3/8 
8.  What is the sum of all natural numbers 
between 100 and 400 which are divisible by 13?  
  100 leLee 400 kesâ ceOÙe meYeer Øeeke=âeflekeâ mebKÙeeDeeW keâe 
Ùeesie keäÙee nw pees 13 mes efJeYeepÙe nw? 
 (a) 5681 (b) 5334 
 (c) 5434 (d) 5761 
9.  If the least common multiple of two numbers, 
1728 and K is 5184, then how many values of K 
are possible ?  
  Ùeefo oes mebKÙeeDeeW 1728 leLee K keâe ueIegòece meceeheJelÙe& 
5184 nw, lees K kesâ efkeâleves ceeve mebYeJe nw? 
 (a) 11  (b) 8  
 (c) 6 (d) 7 
10.  If (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 then what is 
the value of ?  
  Ùeefo (3
33
 + 3
33
 + 3
33
) (2
33
 + 2
33
) = 6
x
 nes, lees x keâe 
ceeve keäÙee nw? 
 (a) 34  (b) 35  
 (c) 33 (d) 33.5 
11.  Which of the following statement(s) is/are true?  
  efvecveefueefKele keâLeve/keâLeveeW ceW mes keâewve mee/mes mener 
nw/nQ? 
  I. (65)
1/6
 > (17)
1/4
 > (12)
1/3
 
  II. (17)
1/4
 > (65)
1/6
 > (12)
1/3
 
  III. (12)
1/3
 > (17)
1/4
 > (65)
1/6
 
 
 (a) Only I/kesâJeue I  
 (b) Only III/kesâJeue III 
 (c) Only II/kesâJeue II 
 (d) None of these/FveceW mes keâesF& veneR 
12.  If P = 7 + 4 3 and PQ =1, then what is the 
value of (1/P
2
) + (1/Q
2
) ?  
  Ùeefo P = 7 + 4 3 leLee PQ = 1 nQ, lees (1/P
2
) + 
(1+Q
2
) keâe ceeve keäÙee nw? 
 (a) 148 (b) 189  
 (c) 194 (d) 204 
13.  If 
( )
x = 5 + 1 and 
( )
y = 5 - 1 then what is 
the value of (x
2
/y
2
) + (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
 + 6 ?  
  Ùeefo 
( )
x = 5 + 1 leLee 
( )
y = 5 - 1 nQ, lees (x
2
/y
2
) 
+ (y
2
/x
2
) + 
x y
4
y x
? ?
+
? ?
? ?
+ 6 keâe ceeve keäÙee nw? 
 (a) 31 (b) 23 5  
 (c) 27 5 (d) 25 
14.  If , x = 2 + 3 y = 2 - 3 and z = 1, then what is 
the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + 
(1/y) + (1/z)] ?  
  Ùeefo , x = 2 + 3 y = 2 - 3 leLee z = 1 nQ, lees (x/yz) 
+ (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)] keâe 
ceeve keäÙee nw? 
 (a) 25 (b) 22  
 (c) 17 (d) 43 
15.  A root of equation ax
2
 + bx + c = 0 (where a, b 
and c are rational numbers) is 5 + 3 3 . What 
is the value of (a
2
 + b
2
 + c
2
)/(a+b+c) ?  
  meceerkeâjCe ax
2
 + bx + c = 0 (peneB a, b leLee c heefjcesÙe 
mebKÙeeSB nw) keâe cetue 5 + 3 3 nw~ (a
2
 + b
2
 + c
2
)/(a + b 
+ c) keâe ceeve keäÙee nw? 
 (a) 35/3  (b) 37/3 
 (c) –105/11 (d) –105/13 
16.  If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) 
+ (a/c), then what is the value of xyz – x
2
 – y
2
 – 
z
2
 ?  
  Ùeefo x = (a/b) + (b/a), y = (b/c) + (c/b) leLee z = 
(c/a) + (a/c) nQ, lees xyz – x
2
 – y
2
 – z
2
 keâe ceeve keäÙee 
nw? 
 (a) –4 (b) 2  
 (c) –1 (d) –6 
17.  If [a+(1/a)]
2
 – 2[a–(1/a)] = 12, then which of the 
following is a value of 'a' ?  
  Ùeefo [a+(1/a)]
2
–2[a–(1/a)] = 12 nes, lees efvecveefueefKele 
ceW mes keâewve mee 'a' keâe Skeâ ceeve nw? 
 (a) 8 3 - +  
 (b) 8 3 - - 
 (c) 8 5 - + 
 (d) None of these/FveceW mes keâesF& veneR 
18.  If x
2
 – 4x + 1 = 0, then what is the value of  
x
9
 + x
7
 – 194x
5
 – 194x
3
 ?  
  Ùeefo x
2
 – 4x + 1 = 0 nes, lees x
9
 + x
7
 – 194x
5
 – 194x
3
 
keâe ceeve keäÙee nw? 
 (a) 4  (b) –4  
 (c) 1 (d) –1 
19.  If x+y= 3, then what is the value of x
3
+y
3
+9xy?  
  Ùeefo x+y= 3 nes, lees x
3
+y
3
+9xy keâe ceeve keäÙee nw? 
 (a) 15  (b) 81  
 (c) 27 (d) 9 
20.  A = (x
8 
–1)/(x
4
 + 1) and B = (y
4
 –1)/(y
2
 + 1). If x 
= 2 and y = 9, the what is the value of A
2
 + 2AB 
+ AB
2
 ?  
  A = (x
8 
–1)/(x
4
 + 1) leLee B = (y
4
 –1)/(y
2
 + 1) nQ~ 
Ùeefo x = 2 leLee y = 9 nQ, lees A
2
 + 2AB + AB
2
 keâe 
ceeve keäÙee nw? 
 (a) 96475 (b) 98625 
 (c) 92425 (d) 89125 
21.  If x–4y = 0 and x + 2y = 24, then what is the 
value of (2x + 3y)/(2x–3y) ?  
  Ùeefo x – 4y = 0 leLee x + 2y = 24 nQ, lees 
(2x+3y)/(2x–3y) keâe ceeve keäÙee nw? 
 (a) 9/5  (b) 11/5 
 (c) 13/7 (d) 9/7 
22.  If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then 
what is the value of x/y ?  
  Ùeefo (x/a) + (y/b) = 3 leLee (x/b)–(y/a) = 9 nQ, lees 
x/y keâe ceeve keäÙee nw? 
 (a) (b+3a)/(a–3b)  (b) (a+3b)/(b–3a) 
 (c) (1+3a)/(a+3b) (d) (a+3b
2
)/(b–3a
2
) 
23.  In the given figure, OX, OY and OZ are 
perpendicular bisectors of the three sides of the 
triangle. If ?QPR = 65
0
 and ?PQR = 60
0
, then 
what is the value (in degrees) of ?QOR + 
?POR ?  
  oer ieF& Deeke=âefle ceW, OX, OY leLee OZ ef$eYegpe keâer 
leerveeW YegpeeDeeW kesâ uebye efÉYeepekeâ nQ~ Ùeefo ?QPR = 65
0
 
leLee ?PQR = 60
0
 nes, lees ?QOR + ?POR keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 
 (a) 250 (b) 180  
 (c) 210 (d) 125 
 
24.  In a triangle PQR, ?PQR = 90
0
, PQ = 10 cm 
and PR = 26 cm, then what is the value (in cm) 
of inradius of incircle ?  
  ef$eYegpe PQR ceW, ?PQR = 90
0
, PQ = 10 mes.ceer. leLee 
PR = 26 mes.ceer. nQ, lees Deble: Je=òe keâer Deble:ef$epÙee keâe 
ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 9 (b) 4  
 (c) 8 (d) 6 
25.  In the given figure, if 
QR 14
=
XY 9
 and PY = 18 
cm, then what is the value (in cm) of PQ ?  
  oer ieF& Deeke=âefle ceW, Ùeefo 
QR 14
=
XY 9
 leLee PY = 18 
mes.ceer. nes, lees PQ keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 28 (b) 18  
 (c) 21 (d) 24 
26.  In a triangle PQR, PX, QY and RZ be altitudes 
intersecting at O. If PO = 6 cm, PX = 8 cm and 
QO = 4 cm, then what is the value (in cm) of 
QY?  
  ef$eYegpe PQR ceW, PX, QY leLee RZ, O hej ØeefleÛÚso 
keâjleer ngF& TBÛeeF&ÙeeB nQ~ Ùeefo PO = 6 mes.ceer., PX = 8 
mes.ceer., leLee QO = 4 mes.ceer. nQ, lees QY keâe ceeve 
(mes.ceer. ceW) keäÙee nw? 
 (a) 6.3  (b) 5.8 
 (c) 6 (d) 7 
27.  A line cuts two concentric circles. The lengths 
of chords formed by that line on the two circles 
are 4 cm and 16 cm. What is the difference (in 
cm
2
) in squares of radii of two circles ?  
  Skeâ jsKee oes mebkesâefvõle Je=òeeW keâes keâešleer nw~ Gme jsKee 
Éeje Je=òeeW hej yeveeF& ieF& peerJeeDeeW keâer uecyeeF& 4 mes.ceer. 
leLee 16 mes.ceer. nQ~ oesveeW Je=òeeW keâer ef$epÙeeDeeW kesâ JeieeX keâe 
Deblej (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 240 (b) 120 
 (c) 60 (d) 90 
28.  In the given figure, a circle touches the sides of 
the quadrilateral PQRS. The radius of the 
circle is 9 cm. ?RSP = ?SRQ = 60
0
 and ?PQR 
= ?QPS = 120
0
. What is the perimeter (in cm) 
of the quadrilateral ?  
  oer ieF& Deeke=âefle ceW, Skeâ Je=òe ÛelegYeg&pe PQRS keâer 
YegpeeDeeW keâes mheMe& keâj jne nw~ Je=òe keâer ef$epÙee 9 mes.ceer. 
nw~ ?RSP = ?SRQ = 60
0
 leLee ?PQR = ?QPS = 
120
0
 nw~ ÛelegYeg&pe keâe heefjceehe (mes.ceer. ceW) keäÙee nw? 
 
 (a) 36 3 (b) 24 3 
 (c) 48 3 (d) 32 
29.  In the given figure, from the point P two 
tangents PA and PB are drawn to a circle with 
centre O and radius 5 cm. From the point O, 
OC and OD are drawn parallel to PA and PB 
respectively. If the length of the chord AB is 5 
cm, then what is the value (in degrees) of 
?COD ?  
  oer ieF& Deeke=âefle ceW, efyevog P mes Skeâ Je=òe efpemekeâe kesâvõ 
O nw leLee ef$epÙee 5 mes.ceer. nw, hej PA leLee PB oes mheMe& 
jsKeeSB KeeRÛeer ieF& nw~ efyevog O mes OC leLee OD keâes 
›eâceMe: PA leLee PB kesâ meceeveeblej KeeRÛee ieÙee nw~ Ùeefo 
peerJee AB keâer uebyeeF& 5 mes.ceer. nw, lees ?COD keâe ceeve 
(ef[«eer ceW) keäÙee nw? 
 
 (a) 90 (b) 120  
 (c) 150 (d) 135 
30.  In the given figure, AB is a diameter of the 
circle with centre O and XY is the tangent at a 
point C. If ?ACX = 35
0
, then what is the value 
(in degrees) of ?CAB ?  
  oer ieF& Deeke=âefle ceW, AB Skeâ Je=òe efpemekeâe kesâvõ O nw, 
keâe JÙeeme nw leLee XY, efyevog C hej Skeâ mheMe& jsKee nw~ 
Ùeefo ?ACX = 35
0 
nw, lees ?CAB keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 
 (a) 45 (b) 35  
 (c) 55 (d) 65 
 
31.  In the given figure, PQ is a diameter of the 
Semicircle PABQ and O is its center. ?AOB = 
64
0
. BP cuts AQ at X. What is the value (in 
degrees) of ?AXP ?  
  oer ieF& Deeke=âefle ceW, PQ, DeOe&Je=òe PABQ keâe JÙeeme 
nw, leLee O Fmekeâe kesâvõ nw~ ?AOB = 64
0
 nw~ BP, 
AQ keâes X hej keâešlee nw~ ?AXP keâe ceeve (ef[«eer ceW) 
keäÙee nw? 
 
 (a) 36 (b) 32  
 (c) 58 (d) 54 
32.  In the given figure, E and F are the centers of 
two identical circles. What is the ratio of area 
of triangle AOB to the area of triangle DOC ?  
  oer ieF& Deeke=âefle ceW, E leLee F oes mece™he Je=òeeW kesâ kesâvõ 
nQ~ ef$eYegpe AOB kesâ #es$eHeâue keâe ef$eYegpe DOC kesâ 
#es$eHeâue mes keäÙee Devegheele nw? 
 
 (a) 1 : 3 (b) 1 : 9 
 (c) 1 : 8 (d) 1 : 4 
33.  In the given figure, in a right angle triangle 
ABC, AB = 12 cm and AC = 15 cm. A square is 
inscribed in the triangle. One of the vertices of 
square coincides with the vertex of triangle. 
What is the maximum possible area (in cm
2
) of 
the square ?  
  oer ieF& Deeke=âefle ceW, Skeâ mecekeâesCe ef$eYegpe ABC ceW, AB 
= 12 mes.ceer. leLee AC = 15 mes.ceer. nQ~ ef$eYegpe kesâ Yeerlej 
Skeâ Jeie& yeveeÙee ieÙee nw~ Jeie& kesâ Meer<eeX ceW mes Skeâ ef$eYegpe 
kesâ Meer<e& mes mheMe& keâjlee nw~ Jeie& keâe DeefOekeâlece mebYeJe 
#es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 1296/49 (b) 25 
 (c) 1225/36 (d) 1225/64 
34.  In the given figure, PQRS is a square of side 8 
cm. ?PQO = 60
0
. What is the area (in cm
2
) of 
the triangle POQ ?  
  oer ieF& Deeke=âefle ceW, PQRS 8 mes.ceer. Yegpee Jeeuee Skeâ 
Jeie& nw~ ?PQO = 60
0
 nw~ ef$eYegpe POQ keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 32 3 (b) 
( )
24 3 1
? ?
-
? ?
 
 (c) 
( )
48 3 1
? ?
-
? ?
 (d) 
( )
16 3 3
? ?
-
? ?
 
35.  In the given figure, two squares of sides 8 cm 
and 20 cm are given. What is the area (in cm
2
) 
of the shaded part ? 
  oer ieF& Deeke=âefle ceW, 8 mes.ceer. leLee 20 mes.ceer. Yegpee Jeeues 
oes Jeie& efoÙes ieÙes nQ~ ÚeÙeebefkeâle Yeeie keâe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 120/7 (b) 160/7 
 (c) 180/7 (d) 240/13 
36.  The area of a regular hexagon is equal to the 
area of the square. What is the ratio of the 
perimeter of the regular hexagon to the 
perimeter of square ?  
  mece <ešdYegpe keâe #es$eHeâue Jeie& kesâ #es$eHeâue kesâ yejeyej nw~ 
mece <ešdYegpe kesâ heefjceehe keâe Jeie& kesâ heefjceehe mes keäÙee 
Devegheele nw? 
 (a) 6 3 : 3 6 (b) 2 3 : 6 2 
 (c) 6 3 : 2 (d) 6 3 : 2 3 
37.  In the given figure, ABCDEF is a regular 
hexagon of side 12 cm. P, Q and R are the mid 
points of the sides AB, CD and EF respectively. 
What is the area (in cm
2
) of triangle PQR ? 
  oer ieF& Deeke=âefle ceW, ABCDEF Skeâ mece <ešdYegpe nw 
efpemekeâer Yegpee 12 mes.ceer. nw~ P, Q leLee R ›eâceMe: 
YegpeeDeeW AB, CD leLee EF kesâ ceOÙe efyevog nw~ ef$eYegpe 
PQR  keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 
 (a) 27 6 (b) 81 3 
 (c) 54 3 (d) 54 6 
38.  A man is running at the speed of 20 km/hr. 
What is time (in seconds) taken by man to 
cover one round of a circular garden of radius 
350 metres ?  
  Skeâ JÙeefòeâ 20 efkeâceer./Iebše keâer ieefle mes oewÌ[ jne nw~ 
Skeâ Je=òeekeâej yeieerÛee efpemekeâer ef$epÙee 350 ceeršj nw, keâes 
heej keâjves ceW JÙeefòeâ Éeje efkeâlevee meceÙe (meskebâ[ ceW) 
efueÙee peeÙesiee? 
 (a) 412 (b) 336 
 (c) 396 (d) 376 
39.  In the given figure, four identical semicircles 
are drawn in a quadrant. XA = 7 cm. What is 
the area (in cm
2
) of shaded region ?  
  oer ieF& Deeke=âefle ceW, Ûeej mece™he DeOe&Je=òeeW keâes Skeâ Je=òe 
kesâ ÛelegLe& Yeeie ceW yeveeÙee ieÙee nw~ XA = 7 mes.ceer. nw~ 
ÚeÙeebefkeâle Yeeie keâe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 
 (a) 70 (b) 140  
 (c) 77 (d) 84 
40.  A regular hexagonal base prism has height 8 
cm and side of base is 4 cm. What is the total 
surface area (in cm
2
) of the prism ?  
  Skeâ mece <ešdYegpe DeeOeej Jeeues efØe]pce keâer TBÛeeF& 8 
mes.ceer. nw leLee DeeOeej keâer Yegpee 4 mes.ceer. nw~ efØe]pce keâe 
kegâue he=<"erÙe #es$eHeâue (mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 
( )
54 3 3 + (b) 
( )
36 3 3 + 
 (c) 
( )
48 4 3 + (d) 
( )
24 4 3 + 
41.  A cube is placed inside a cone of radius 20 cm 
and height 10 cm, one of its face being on the 
base of the cone and vertices of opposite face 
touching the cone. What is the length (in cm) of 
side of the cube ?  
  Skeâ Ieve keâes Skeâ Mebkegâ efpemekeâer ef$epÙee 20 mesceer. leLee 
TBÛeeF& 10 mesceer. nQ, kesâ Deboj jKee peelee nw, Gmekeâer Skeâ 
melen Mebkegâ kesâ DeeOeej keâer Deesj nw leLee efJehejerle melen kesâ 
Meer<e& Mebkegâ keâes mheMe& keâj jns nQ~ Ieve keâer Yegpee keâer 
uecyeeF& (mes.ceer. ceW) keäÙee nw? 
 (a) 5 (b) 6  
 (c) 8 (d) 9 
42.  A cylinder of radius 4.5 cm and height 12 cm 
just fits in another cylinder completely with 
their axis perpendicular. What is the radius (in 
cm)  of second cylinder ?  
  Skeâ yesueve efpemekeâer ef$epÙee 4.5 mes.ceer. leLee TBÛeeF& 12 
mes.ceer. nw, keâes Skeâ DevÙe yesueve ceW Gvekesâ De#eeW kesâ 
uecyeJele hetjer lejn mes meceeefnle efkeâÙee ieÙee nw~ otmejs 
yesueve keâer ef$epÙee (mes.ceer. ceW) keäÙee nw? 
 (a) 5  (b) 6  
 (c) 15 (d) 7.5 
43.  A right circular cylinder has height 28 cm and 
radius of base 14 cm. Two hemispheres of 
radius 7 cm each are cut from each of the two 
bases of the cylinder. What is the total surface 
area (in cm
2
) of the remaining part ?  
  Skeâ mece ieesueekeâej yesueve keâer TBÛeeF& 28 mes.ceer. leLee 
DeeOeej keâer ef$epÙee 14 mes.ceer. nw~ yesueve kesâ oes DeeOeejeW ceW 
mes ØelÙeskeâ mes 7 mes.ceer. ef$epÙee Jeeues oes DeOe&ieesues keâešs 
peeles nQ~ Mes<e Yeeie keâe kegâue he=<"erÙe #es$eHeâue (mes.ceer.
2
 ceW) 
keäÙee nesiee? 
 (a) 3842 (b) 4312 
 (c) 3296 (d) 4436 
44.  Two spheres of equal radius are taken out by 
cutting from a solid cube of side 
( )
12 + 4 3 cm. 
What is the maximum volume (in cm
3
) eof each 
sphere? 
  meceeve ef$epÙee Jeeues oes ieesues keâes Skeâ "esme Ieve 
efpemekeâer Yegpee 
( )
12 + 4 3 mes.ceer. nw, mes keâeškeâj 
efvekeâeuee ieÙee nw~ ØelÙeskeâ ieesues keâe DeefOekeâlece DeeÙeleve 
(mes.ceer.
3
) keäÙee nw? 
 (a) 1077.31 (b) 905.14 
 (c) 966.07 (d) 1007.24 
45.  Three toys are in a shape of cylinder, 
hemisphere and cone. The three toys have same 
base. Height of each toy is 2 2 cm. What is 
the ratio of the total surface areas of cylinder, 
hemisphere and cone respectively ? 
  leerve efKeueewves yesueve, DeOe&ieesues leLee Mebkegâ kesâ Deekeâej ceW 
nQ~ leerveeW efKeueewveeW keâe DeeOeej meceeve nw~ ØelÙeskeâ efKeueewves 
keâer TBÛeeF& 2 2 mes.ceer. nw~ yesueve, DeOe&ieesues leLee Mebkegâ 
kesâ kegâue he=<"erÙe #es$eHeâue keâe ›eâceMe: Devegheele keäÙee nw? 
 (a) 
( )
4 : 3 : 2 1
? ?
+
? ?
 (b) 
( )
4 : 3: 2 2
? ?
+
? ?
 
 (c) 4 : 3 : 2 2 (d) 
( )
2 :1: 1 2 +