SSC CGL Tier 2 (21 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 : 21-2-2018] [Time : 10 AM to 12 PM 
1.  If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... upto 60 
terms, then what is the value of A ?  
  Ùeefo A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... 60 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) –360 (b) –310 
 (c) –240 (d) –270 
2.  How many natural numbers are there between 
1000 to 2000, which when divided by 341 leaves 
remainder 5 ?  
  1000 mes 2000 kesâ ceOÙe Ssmeer efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nQ efpevnW 341 mes efJeYeeefpele keâjves hej 
Mes<eHeâue 5 yeÛelee nw? 
 (a) 3 (b) 2  
 (c) 4 (d) 1 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. ( ) ( ) ( ) ( ) 64 + 0.0064 + 0.81 + 0.0081 = 9.07 
  II. ( ) ( ) ( ) 0.010201 + 98.01 + 0.25 = 11.51 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
4.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve-mee/mes keâLeve melÙe nw/nQ? 
  I. (0.7)
2
 + (0.07)
2
 + (11.1)
2
 > 123.8 
  II. (1.12)
2
 + (10.3)
2
 + (1.05)
2
 > 108.3 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II  
5.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
1 1 1 1 12
+ + + ... + =
1× 3 3×5 5×7 11×13 13
 
  II. 
1 1 1 1 12
+ + + ... + =
1× 2 2× 3 3× 4 12×13 13
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
6.  Which of the following statement(s) is/are 
TRUE?   
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 3/71 < 5/91 < 7/99 
  II. 11/135 > 12/157 > 13/181 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
7.  If 1 + (1/2) + (1/3) +....+ (1/20) = k, then what is 
the value of (1/4) + (1/6) + (1/8) + ....+ (1/40) ?  
  Ùeefo 1 + (1/2) + (1/3) +....+ (1/20) = k nw, lees (1/4) 
+ (1/6) + (1/8) + ....+ (1/40) keâe ceeve keäÙee nw? 
 (a) k/2  (b) 2k 
 (c) (k – 1)/2 (d) (k + 1)/2 
8.  If A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 and C = 3
15
 
+ 3
14
 + 3
13
 + ....+ 3
0
, then which of the following 
option is TRUE ? 
  Ùeefo A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 leLee C = 
3
15
 + 3
14
 + 3
13
 + ....+ 3
0
 nw, lees efvecveefueefKele ceW mes 
keâewve mee efJekeâuhe melÙe nw? 
 (a) C > B > A (b) C > A > B 
 (c) A > B > C (d) A > C > B 
9.  If x + y = 10 and xy = 4, then what is the value 
of x
4
 + y
4
 ? 
  Ùeefo x + y = 10 leLee xy = 4 nQ, lees x
4
 + y
4
 keâe ceeve 
keäÙee nw? 
 (a) 8464 (b) 8432 
 (c) 7478 (d) 6218 
10.  M is the largest three digit number which when 
divided by 6 and 5 leaves remainder 5 and 3 
respectively. What will be the remainder when 
M is divided by 11 ?  
  M leerve DebkeâeW keâer meyemes yeÌ[er mebKÙee nw efpemes, peye 6 
leLee 5 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue ›eâceMe: 
5 leLee 3 Deelee nw~ peye M keâes 11 mes efJeYeeefpele efkeâÙee 
peeÙes lees Mes<eHeâue keäÙee nesiee? 
 (a) 1 (b) 2  
 (c) 3 (d) 4 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 5 + 5 > 7 + 3 
  II. 6 + 7 > 8 + 5 
  III. 3 + 9 > 6 + 6 
Page 2


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 21-2-2018] [Time : 10 AM to 12 PM 
1.  If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... upto 60 
terms, then what is the value of A ?  
  Ùeefo A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... 60 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) –360 (b) –310 
 (c) –240 (d) –270 
2.  How many natural numbers are there between 
1000 to 2000, which when divided by 341 leaves 
remainder 5 ?  
  1000 mes 2000 kesâ ceOÙe Ssmeer efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nQ efpevnW 341 mes efJeYeeefpele keâjves hej 
Mes<eHeâue 5 yeÛelee nw? 
 (a) 3 (b) 2  
 (c) 4 (d) 1 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. ( ) ( ) ( ) ( ) 64 + 0.0064 + 0.81 + 0.0081 = 9.07 
  II. ( ) ( ) ( ) 0.010201 + 98.01 + 0.25 = 11.51 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
4.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve-mee/mes keâLeve melÙe nw/nQ? 
  I. (0.7)
2
 + (0.07)
2
 + (11.1)
2
 > 123.8 
  II. (1.12)
2
 + (10.3)
2
 + (1.05)
2
 > 108.3 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II  
5.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
1 1 1 1 12
+ + + ... + =
1× 3 3×5 5×7 11×13 13
 
  II. 
1 1 1 1 12
+ + + ... + =
1× 2 2× 3 3× 4 12×13 13
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
6.  Which of the following statement(s) is/are 
TRUE?   
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 3/71 < 5/91 < 7/99 
  II. 11/135 > 12/157 > 13/181 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
7.  If 1 + (1/2) + (1/3) +....+ (1/20) = k, then what is 
the value of (1/4) + (1/6) + (1/8) + ....+ (1/40) ?  
  Ùeefo 1 + (1/2) + (1/3) +....+ (1/20) = k nw, lees (1/4) 
+ (1/6) + (1/8) + ....+ (1/40) keâe ceeve keäÙee nw? 
 (a) k/2  (b) 2k 
 (c) (k – 1)/2 (d) (k + 1)/2 
8.  If A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 and C = 3
15
 
+ 3
14
 + 3
13
 + ....+ 3
0
, then which of the following 
option is TRUE ? 
  Ùeefo A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 leLee C = 
3
15
 + 3
14
 + 3
13
 + ....+ 3
0
 nw, lees efvecveefueefKele ceW mes 
keâewve mee efJekeâuhe melÙe nw? 
 (a) C > B > A (b) C > A > B 
 (c) A > B > C (d) A > C > B 
9.  If x + y = 10 and xy = 4, then what is the value 
of x
4
 + y
4
 ? 
  Ùeefo x + y = 10 leLee xy = 4 nQ, lees x
4
 + y
4
 keâe ceeve 
keäÙee nw? 
 (a) 8464 (b) 8432 
 (c) 7478 (d) 6218 
10.  M is the largest three digit number which when 
divided by 6 and 5 leaves remainder 5 and 3 
respectively. What will be the remainder when 
M is divided by 11 ?  
  M leerve DebkeâeW keâer meyemes yeÌ[er mebKÙee nw efpemes, peye 6 
leLee 5 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue ›eâceMe: 
5 leLee 3 Deelee nw~ peye M keâes 11 mes efJeYeeefpele efkeâÙee 
peeÙes lees Mes<eHeâue keäÙee nesiee? 
 (a) 1 (b) 2  
 (c) 3 (d) 4 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 5 + 5 > 7 + 3 
  II. 6 + 7 > 8 + 5 
  III. 3 + 9 > 6 + 6 
 
 (a) Only I/ kesâJeue I  
 (b) Only I and II/kesâJeue I leLee II  
 (c) Only II and III/kesâJeue II leLee III 
 (d) Only I and III/ kesâJeue I leLee III 
12.  If 
3 + 2
a =
3 - 2
 and 
3 - 2
b =
3 + 2
 then what is 
the value of a
2
 + b
2
 – ab ?  
  Ùeefo 
3 + 2
a =
3 - 2
 leLee 
3 - 2
b =
3 + 2
 nQ, lees a
2
 + 
b
2
 – ab keâe ceeve keäÙee nw? 
 (a) 97  (b) 
( )
2 3 2 +  
 (c) 
( )
4 6 1 + (d) 98 
13.  If the difference between the roots of the 
equation Ax
2
 – Bx + C = 0 is 4, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 – Bx + C = 0 kesâ cetueeW keâe Deblej 
4 nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) B
2
 – 16 A
2
 = 4AC + 4B
2
 
 (b) B
2
 – 10 A
2
 = 4AC + 6A
2
 
 (c) B
2
 – 8A
2
 = 4AC + 10A
2
 
 (d) B
2
 – 16 A
2
 = 4AC + 8B
2
 
14.  a and ß are the roots of quadratic equation. If  
a + ß = 8 and a–ß = 2 5 , then which of the 
following equation will have roots a
4 
and ß
4
 ?  
  a leLee ß efÉIeele meceerkeâjCe kesâ cetue nQ~ Ùeefo a + ß = 8 
leLee a–ß = 2 5 nQ, lees a
4
 leLee ß
4
 efvecveefueefKele ceW 
mes efkeâme meceerkeâjCe kesâ cetue nQ? 
 (a) x
2
 – 1522x + 14641 = 0  
 (b) x
2
 – 1921x + 14641 = 0 
 (c) x
2
 – 1764x + 14641 = 0 
 (d) x
2
 – 2520x + 14641 = 0 
15.  If a and b are the roots of the equation Px
2
 – 
Qx + R = 0, then what is the value of (1/a
2
) + 
(1/b
2
) + (a/b) + (b/a) ?  
  Ùeefo a leLee b meceerkeâjCe Px
2
 – Qx + R = 0 kesâ 
cetue nQ, lees (1/a
2
) + (1/b
2
) + (a/b) + (b/a) keâe 
ceeve keäÙee nw? 
 (a) 
( )( )
2
2
Q 2P 2R P
PR
- +
  
 (b) 
( )( )
2
2
Q 2PR R P
PR
- +
  
 (c) 
( )( )
2
2 2
Q 2R 2P R
P R
- +
 
 (d) 
( )( )
2
2 2
Q 2PR 2R 2P
P R
- +
 
16.  If x
2
 – 16x + 59 = 0, then what is the value of 
(x–6)
2
 + [1/(x–6)
2
] ?  
  Ùeefo x
2
 – 16x + 59 = 0, nw, lees (x–6)
2
 + [1/(x–6)
2
] 
keâe ceeve keäÙee nw? 
 (a) 14 (b) 18  
 (c) 16 (d) 20 
17.  If A and B are the roots of the equation Ax
2 
– 
A
2
x + AB = 0, then what is the value of A and B 
respectively ?  
  Ùeefo A leLee B meceerkeâjCe Ax
2 
– A
2
x + AB = 0, kesâ 
cetue nQ, lees ›eâceMe: A leLee B keâe ceeve keäÙee nw? 
 (a) 1, 0 (b) 1, 1 
 (c) 0, 2 (d) 0, 1 
18.  a and ß are the roots of the quadratic equation 
x
2
 – x–1 = 0. What is the value of a
8
 + ß
8
 ?  
  a leLee ß efÉIeele meceerkeâjCe x
2
 – x–1 = 0 kesâ cetue nQ~ 
a
8
 + ß
8
 keâe ceeve keäÙee nw? 
 (a) 47 (b) 54  
 (c) 59 (d) 68 
19.  If a + b + c = 9, ab + bc + ca = 26, a
3
 + b
3
 = 91, 
b
3
 + c
3
 = 72 and c
3
 + a
3
 = 35, then what is the 
value of abc ?  
  Ùeefo a + b + c = 9, ab + bc + ca = 27, a
3
 + b
3
 = 
91, b
3
 + c
3
 = 72 leLee c
3
 + a
3
 = 35 nQ, lees abc keâe 
ceeve keäÙee nw? 
 (a) 48 (b) 24  
 (c) 36 (d) 42 
20.  If x
3
 – 4x
2
 + 19 = 6(x–1), then what is the value 
of [x
2
 + (1/x – 4)] ?  
  Ùeefo x
3
 – 4x
2
 + 19 = 6(x–1) nw, lees [x
2
 + (1/x – 4)] 
keâe ceeve keäÙee nw? 
 (a) 3  (b) 5  
 (c) 6 (d) 8 
21.  Cost of 8 pencils, 5 pens and 3 erasers is Rs. 
111. Cost of 9 pencils, 6 pens and 5 erasers is 
Rs. 130. Cost of 16 pencils, 11 pens and 3 
erasers is Rs. 221. What is the cost (in Rs.) of 39 
pencils 26 pens and 13 erasers ?  
  8 heWefmeue, 5 keâuece leLee 3 jyeÌ[ keâe cetuÙe 111 ® nw~ 
9 heWefmeue, 6 keâuece leLee 5 jyeÌ[ keâe cetuÙe 130 ® nw~ 
16 heWefmeue, 11 keâuece leLee 3 jyeÌ[ keâe cetuÙe 221 ® 
nw~ 39 heWefmeue, 26 keâuece leLee 13 jyeÌ[ keâe cetuÙe (® 
ceW) keäÙee nw? 
 (a) 316 (b) 546  
 (c) 624 (d) 482 
22.  If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 
3z = 17, then what is the value of xy + yz + zx ?  
  Ùeefo 2x + 3y – 5z = 18, 3x + 2y + z = 29 leLee x + y 
+ 3z = 17, nQ, lees xy + yz + zx keâe ceeve keäÙee nw? 
 (a) 32 (b) 52 
 (c) 64 (d) 46 
23.  PQR is an equilateral triangle whose side is 10 
cm. What is the value (in cm) of the inradius of 
triangle PQR ?  
  PQR Skeâ meceyeeng ef$eYegpe nQ efpemekeâer Yegpee 10 mesceer. 
nQ~ ef$eYegpe PQR  keâer Deble: ef$epÙee keâe ceeve (mes.ceer. ceW) 
keäÙee nw? 
 (a) 5/ 3 (b) 10/ 3 
 (c) 10/ 3 (d) 5/ 2 
24.  What is the area (in cm
2
) of the circumcircle of 
a triangle whose sides are 6 cm, 8 cm and 10 cm 
respectively ? 
Page 3


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 21-2-2018] [Time : 10 AM to 12 PM 
1.  If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... upto 60 
terms, then what is the value of A ?  
  Ùeefo A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... 60 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) –360 (b) –310 
 (c) –240 (d) –270 
2.  How many natural numbers are there between 
1000 to 2000, which when divided by 341 leaves 
remainder 5 ?  
  1000 mes 2000 kesâ ceOÙe Ssmeer efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nQ efpevnW 341 mes efJeYeeefpele keâjves hej 
Mes<eHeâue 5 yeÛelee nw? 
 (a) 3 (b) 2  
 (c) 4 (d) 1 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. ( ) ( ) ( ) ( ) 64 + 0.0064 + 0.81 + 0.0081 = 9.07 
  II. ( ) ( ) ( ) 0.010201 + 98.01 + 0.25 = 11.51 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
4.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve-mee/mes keâLeve melÙe nw/nQ? 
  I. (0.7)
2
 + (0.07)
2
 + (11.1)
2
 > 123.8 
  II. (1.12)
2
 + (10.3)
2
 + (1.05)
2
 > 108.3 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II  
5.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
1 1 1 1 12
+ + + ... + =
1× 3 3×5 5×7 11×13 13
 
  II. 
1 1 1 1 12
+ + + ... + =
1× 2 2× 3 3× 4 12×13 13
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
6.  Which of the following statement(s) is/are 
TRUE?   
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 3/71 < 5/91 < 7/99 
  II. 11/135 > 12/157 > 13/181 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
7.  If 1 + (1/2) + (1/3) +....+ (1/20) = k, then what is 
the value of (1/4) + (1/6) + (1/8) + ....+ (1/40) ?  
  Ùeefo 1 + (1/2) + (1/3) +....+ (1/20) = k nw, lees (1/4) 
+ (1/6) + (1/8) + ....+ (1/40) keâe ceeve keäÙee nw? 
 (a) k/2  (b) 2k 
 (c) (k – 1)/2 (d) (k + 1)/2 
8.  If A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 and C = 3
15
 
+ 3
14
 + 3
13
 + ....+ 3
0
, then which of the following 
option is TRUE ? 
  Ùeefo A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 leLee C = 
3
15
 + 3
14
 + 3
13
 + ....+ 3
0
 nw, lees efvecveefueefKele ceW mes 
keâewve mee efJekeâuhe melÙe nw? 
 (a) C > B > A (b) C > A > B 
 (c) A > B > C (d) A > C > B 
9.  If x + y = 10 and xy = 4, then what is the value 
of x
4
 + y
4
 ? 
  Ùeefo x + y = 10 leLee xy = 4 nQ, lees x
4
 + y
4
 keâe ceeve 
keäÙee nw? 
 (a) 8464 (b) 8432 
 (c) 7478 (d) 6218 
10.  M is the largest three digit number which when 
divided by 6 and 5 leaves remainder 5 and 3 
respectively. What will be the remainder when 
M is divided by 11 ?  
  M leerve DebkeâeW keâer meyemes yeÌ[er mebKÙee nw efpemes, peye 6 
leLee 5 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue ›eâceMe: 
5 leLee 3 Deelee nw~ peye M keâes 11 mes efJeYeeefpele efkeâÙee 
peeÙes lees Mes<eHeâue keäÙee nesiee? 
 (a) 1 (b) 2  
 (c) 3 (d) 4 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 5 + 5 > 7 + 3 
  II. 6 + 7 > 8 + 5 
  III. 3 + 9 > 6 + 6 
 
 (a) Only I/ kesâJeue I  
 (b) Only I and II/kesâJeue I leLee II  
 (c) Only II and III/kesâJeue II leLee III 
 (d) Only I and III/ kesâJeue I leLee III 
12.  If 
3 + 2
a =
3 - 2
 and 
3 - 2
b =
3 + 2
 then what is 
the value of a
2
 + b
2
 – ab ?  
  Ùeefo 
3 + 2
a =
3 - 2
 leLee 
3 - 2
b =
3 + 2
 nQ, lees a
2
 + 
b
2
 – ab keâe ceeve keäÙee nw? 
 (a) 97  (b) 
( )
2 3 2 +  
 (c) 
( )
4 6 1 + (d) 98 
13.  If the difference between the roots of the 
equation Ax
2
 – Bx + C = 0 is 4, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 – Bx + C = 0 kesâ cetueeW keâe Deblej 
4 nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) B
2
 – 16 A
2
 = 4AC + 4B
2
 
 (b) B
2
 – 10 A
2
 = 4AC + 6A
2
 
 (c) B
2
 – 8A
2
 = 4AC + 10A
2
 
 (d) B
2
 – 16 A
2
 = 4AC + 8B
2
 
14.  a and ß are the roots of quadratic equation. If  
a + ß = 8 and a–ß = 2 5 , then which of the 
following equation will have roots a
4 
and ß
4
 ?  
  a leLee ß efÉIeele meceerkeâjCe kesâ cetue nQ~ Ùeefo a + ß = 8 
leLee a–ß = 2 5 nQ, lees a
4
 leLee ß
4
 efvecveefueefKele ceW 
mes efkeâme meceerkeâjCe kesâ cetue nQ? 
 (a) x
2
 – 1522x + 14641 = 0  
 (b) x
2
 – 1921x + 14641 = 0 
 (c) x
2
 – 1764x + 14641 = 0 
 (d) x
2
 – 2520x + 14641 = 0 
15.  If a and b are the roots of the equation Px
2
 – 
Qx + R = 0, then what is the value of (1/a
2
) + 
(1/b
2
) + (a/b) + (b/a) ?  
  Ùeefo a leLee b meceerkeâjCe Px
2
 – Qx + R = 0 kesâ 
cetue nQ, lees (1/a
2
) + (1/b
2
) + (a/b) + (b/a) keâe 
ceeve keäÙee nw? 
 (a) 
( )( )
2
2
Q 2P 2R P
PR
- +
  
 (b) 
( )( )
2
2
Q 2PR R P
PR
- +
  
 (c) 
( )( )
2
2 2
Q 2R 2P R
P R
- +
 
 (d) 
( )( )
2
2 2
Q 2PR 2R 2P
P R
- +
 
16.  If x
2
 – 16x + 59 = 0, then what is the value of 
(x–6)
2
 + [1/(x–6)
2
] ?  
  Ùeefo x
2
 – 16x + 59 = 0, nw, lees (x–6)
2
 + [1/(x–6)
2
] 
keâe ceeve keäÙee nw? 
 (a) 14 (b) 18  
 (c) 16 (d) 20 
17.  If A and B are the roots of the equation Ax
2 
– 
A
2
x + AB = 0, then what is the value of A and B 
respectively ?  
  Ùeefo A leLee B meceerkeâjCe Ax
2 
– A
2
x + AB = 0, kesâ 
cetue nQ, lees ›eâceMe: A leLee B keâe ceeve keäÙee nw? 
 (a) 1, 0 (b) 1, 1 
 (c) 0, 2 (d) 0, 1 
18.  a and ß are the roots of the quadratic equation 
x
2
 – x–1 = 0. What is the value of a
8
 + ß
8
 ?  
  a leLee ß efÉIeele meceerkeâjCe x
2
 – x–1 = 0 kesâ cetue nQ~ 
a
8
 + ß
8
 keâe ceeve keäÙee nw? 
 (a) 47 (b) 54  
 (c) 59 (d) 68 
19.  If a + b + c = 9, ab + bc + ca = 26, a
3
 + b
3
 = 91, 
b
3
 + c
3
 = 72 and c
3
 + a
3
 = 35, then what is the 
value of abc ?  
  Ùeefo a + b + c = 9, ab + bc + ca = 27, a
3
 + b
3
 = 
91, b
3
 + c
3
 = 72 leLee c
3
 + a
3
 = 35 nQ, lees abc keâe 
ceeve keäÙee nw? 
 (a) 48 (b) 24  
 (c) 36 (d) 42 
20.  If x
3
 – 4x
2
 + 19 = 6(x–1), then what is the value 
of [x
2
 + (1/x – 4)] ?  
  Ùeefo x
3
 – 4x
2
 + 19 = 6(x–1) nw, lees [x
2
 + (1/x – 4)] 
keâe ceeve keäÙee nw? 
 (a) 3  (b) 5  
 (c) 6 (d) 8 
21.  Cost of 8 pencils, 5 pens and 3 erasers is Rs. 
111. Cost of 9 pencils, 6 pens and 5 erasers is 
Rs. 130. Cost of 16 pencils, 11 pens and 3 
erasers is Rs. 221. What is the cost (in Rs.) of 39 
pencils 26 pens and 13 erasers ?  
  8 heWefmeue, 5 keâuece leLee 3 jyeÌ[ keâe cetuÙe 111 ® nw~ 
9 heWefmeue, 6 keâuece leLee 5 jyeÌ[ keâe cetuÙe 130 ® nw~ 
16 heWefmeue, 11 keâuece leLee 3 jyeÌ[ keâe cetuÙe 221 ® 
nw~ 39 heWefmeue, 26 keâuece leLee 13 jyeÌ[ keâe cetuÙe (® 
ceW) keäÙee nw? 
 (a) 316 (b) 546  
 (c) 624 (d) 482 
22.  If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 
3z = 17, then what is the value of xy + yz + zx ?  
  Ùeefo 2x + 3y – 5z = 18, 3x + 2y + z = 29 leLee x + y 
+ 3z = 17, nQ, lees xy + yz + zx keâe ceeve keäÙee nw? 
 (a) 32 (b) 52 
 (c) 64 (d) 46 
23.  PQR is an equilateral triangle whose side is 10 
cm. What is the value (in cm) of the inradius of 
triangle PQR ?  
  PQR Skeâ meceyeeng ef$eYegpe nQ efpemekeâer Yegpee 10 mesceer. 
nQ~ ef$eYegpe PQR  keâer Deble: ef$epÙee keâe ceeve (mes.ceer. ceW) 
keäÙee nw? 
 (a) 5/ 3 (b) 10/ 3 
 (c) 10/ 3 (d) 5/ 2 
24.  What is the area (in cm
2
) of the circumcircle of 
a triangle whose sides are 6 cm, 8 cm and 10 cm 
respectively ? 
 
  Skeâ ef$eYegpe efpemekeâer YegpeeSB ›eâceMe: 6 mes.ceer., 8 mesceer, 
leLee 10 mes.ceer. nw, kesâ heefjJe=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) 
keäÙee nw? 
 (a) 275/7  (b) 550/7 
 (c) 2200/7 (d) 1100/7 
25.  In the given figure, MNOP is a parallelogram. 
PM is extended to Z. OZ intersects MN and PN 
at Y and X respectively. If OX = 27 cm and XY 
= 18 cm, then what is the length (in cm) of YZ ? 
  oer ieF& Deeke=âefle ceW, MNOP Skeâ meceeblej ÛelegYeg&pe nw~ 
PM keâes Z lekeâ yeÌ{eÙee ieÙee nw~ OZ, MN leLee PN 
keâes ›eâceMe: Y leLee X hej ØeefleÛÚso keâjleer nw~ Ùeefo OX 
= 27 mes.ceer. leLee XY = 18 mes.ceer. nQ, lees YZ keâer 
uecyeeF& (mes.ceer. ceW) keäÙee nw?  
 
 (a) 21.4 (b) 22.5 
 (c) 23.8 (d) 24.5 
26.  ABCD is a trapezium in which AB is parallel to 
CD and AB = 4 (CD). The diagonals of the 
trapezium intersects at O. What is the ratio of 
area of triangle DCO to the area of the triangle 
ABO ?  
  ABCD Skeâ meceuecye nw efpemeceW AB, CD kesâ meceeblej nw 
leLee AB = 4 (CD) nw~ meceuecye kesâ efJekeâCe& O hej 
ØeefleÛÚsove keâjles nw~ ef$eYegpe DCO kesâ #es$eHeâue keâe 
ef$eYegpe ABO kesâ #es$eHeâue mes keäÙee Devegheele nw? 
 (a) 1 : 4  (b) 1 : 2 
 (c) 1 : 8 (d) 1 : 16 
27.  In the given figure, ABC is an equilateral 
triangle. Two circles of radius 4 cm and 12 cm 
are inscribed in the triangle. What is the side 
(in cm) of an equilateral triangle ?  
  oer ieF& Deeke=âefle ceW, ABC Skeâ meceyeeng ef$eYegpe nw~ 4 
mes.ceer. leLee 12 mes.ceer. ef$epÙee Jeeues oes Je=òe ef$eYegpe 
ceW Debefkeâle nw~ mecekeâesCe ef$eYegpe keâer Yegpee (mes.ceer. ceW) 
keäÙee nw?  
 
  
 (a) 32/ 3 (b) 32 3 
 (c) 64/ 3 (d) 64 2 
28.  In the given figure, SX is tangent. SX = OX = 
OR. If QX = 3 cm and PQ = 9 cm, then what is 
the value (in cm) of OS ?  
  oer ieF& Deeke=âefle ceW, SX  Skeâ mheMe& jsKee nw~ SX = OX 
= OR nQ~ Ùeefo QX = 3 mes.ceer. leLee PQ = 9 mes.ceer. nQ, 
lees OS keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 6 (b) 5  
 (c) 4 (d) 3 
29.  PAB and PCD are two secants to a circle. If PA 
= 10 cm, AB = 12 cm and PC = 11 cm, then 
what is the value (in cm) of PD ?  
  PAB leLee PCD Skeâ Je=le hej oes Úsove jsKeeSB nQ~ Ùeefo 
PA = 10 mes.ceer., AB = 12 mes.ceer. leLee PC = 11 mes.ceer. 
nes lees, PD keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 18 (b) 9 
 (c) 20 (d) 12 
30.  Triangle PQR is inscribed in a circle such that 
P, Q and R lie on the circumference. If PQ is 
the diameter of the circle and ?PQR = 40
0
, 
then what is the value (in degrees) of ?QPR ?  
  Skeâ Je=òe ceW ef$eYegpe PQR Fme Øekeâej Debefkeâle nw, efkeâ P, 
Q leLee R heefjefOe hej efmLele nw~ Ùeefo PQ Je=òe keâe JÙeeme 
nw leLee ?PQR = 40
0
 nw, lees ?QPR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 (a) 40 (b) 45  
 (c) 50 (d) 55 
31.  In the given figure, ?QRU = 72
0
, ? TRS = 15
0
 
and ?PSR = 95
0
, then what is the value (in 
degrees) of ?PQR ? 
  oer ieF& Deeke=âefle ceW, ?QRU = 72
0
, ? TRS = 15
0
 
leLee ?PSR = 95
0
 nQ, lees ?PQR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 
 (a) 85 (b) 95  
 (c) 75 (d) 90 
32.  What can be the maximum number of common 
tangent which can be drawn to two non-
intersecting circles? 
  oes iewj–ØeefleÛÚsoer Je=òeeW ceW DeefOekeâlece efkeâleveer DevegmheMe& 
jsKee KeeRÛeer pee mekeâleer nw? 
 (a) 2 (b) 4 
 (c) 3 (d) 6 
Page 4


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 21-2-2018] [Time : 10 AM to 12 PM 
1.  If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... upto 60 
terms, then what is the value of A ?  
  Ùeefo A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... 60 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) –360 (b) –310 
 (c) –240 (d) –270 
2.  How many natural numbers are there between 
1000 to 2000, which when divided by 341 leaves 
remainder 5 ?  
  1000 mes 2000 kesâ ceOÙe Ssmeer efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nQ efpevnW 341 mes efJeYeeefpele keâjves hej 
Mes<eHeâue 5 yeÛelee nw? 
 (a) 3 (b) 2  
 (c) 4 (d) 1 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. ( ) ( ) ( ) ( ) 64 + 0.0064 + 0.81 + 0.0081 = 9.07 
  II. ( ) ( ) ( ) 0.010201 + 98.01 + 0.25 = 11.51 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
4.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve-mee/mes keâLeve melÙe nw/nQ? 
  I. (0.7)
2
 + (0.07)
2
 + (11.1)
2
 > 123.8 
  II. (1.12)
2
 + (10.3)
2
 + (1.05)
2
 > 108.3 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II  
5.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
1 1 1 1 12
+ + + ... + =
1× 3 3×5 5×7 11×13 13
 
  II. 
1 1 1 1 12
+ + + ... + =
1× 2 2× 3 3× 4 12×13 13
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
6.  Which of the following statement(s) is/are 
TRUE?   
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 3/71 < 5/91 < 7/99 
  II. 11/135 > 12/157 > 13/181 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
7.  If 1 + (1/2) + (1/3) +....+ (1/20) = k, then what is 
the value of (1/4) + (1/6) + (1/8) + ....+ (1/40) ?  
  Ùeefo 1 + (1/2) + (1/3) +....+ (1/20) = k nw, lees (1/4) 
+ (1/6) + (1/8) + ....+ (1/40) keâe ceeve keäÙee nw? 
 (a) k/2  (b) 2k 
 (c) (k – 1)/2 (d) (k + 1)/2 
8.  If A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 and C = 3
15
 
+ 3
14
 + 3
13
 + ....+ 3
0
, then which of the following 
option is TRUE ? 
  Ùeefo A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 leLee C = 
3
15
 + 3
14
 + 3
13
 + ....+ 3
0
 nw, lees efvecveefueefKele ceW mes 
keâewve mee efJekeâuhe melÙe nw? 
 (a) C > B > A (b) C > A > B 
 (c) A > B > C (d) A > C > B 
9.  If x + y = 10 and xy = 4, then what is the value 
of x
4
 + y
4
 ? 
  Ùeefo x + y = 10 leLee xy = 4 nQ, lees x
4
 + y
4
 keâe ceeve 
keäÙee nw? 
 (a) 8464 (b) 8432 
 (c) 7478 (d) 6218 
10.  M is the largest three digit number which when 
divided by 6 and 5 leaves remainder 5 and 3 
respectively. What will be the remainder when 
M is divided by 11 ?  
  M leerve DebkeâeW keâer meyemes yeÌ[er mebKÙee nw efpemes, peye 6 
leLee 5 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue ›eâceMe: 
5 leLee 3 Deelee nw~ peye M keâes 11 mes efJeYeeefpele efkeâÙee 
peeÙes lees Mes<eHeâue keäÙee nesiee? 
 (a) 1 (b) 2  
 (c) 3 (d) 4 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 5 + 5 > 7 + 3 
  II. 6 + 7 > 8 + 5 
  III. 3 + 9 > 6 + 6 
 
 (a) Only I/ kesâJeue I  
 (b) Only I and II/kesâJeue I leLee II  
 (c) Only II and III/kesâJeue II leLee III 
 (d) Only I and III/ kesâJeue I leLee III 
12.  If 
3 + 2
a =
3 - 2
 and 
3 - 2
b =
3 + 2
 then what is 
the value of a
2
 + b
2
 – ab ?  
  Ùeefo 
3 + 2
a =
3 - 2
 leLee 
3 - 2
b =
3 + 2
 nQ, lees a
2
 + 
b
2
 – ab keâe ceeve keäÙee nw? 
 (a) 97  (b) 
( )
2 3 2 +  
 (c) 
( )
4 6 1 + (d) 98 
13.  If the difference between the roots of the 
equation Ax
2
 – Bx + C = 0 is 4, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 – Bx + C = 0 kesâ cetueeW keâe Deblej 
4 nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) B
2
 – 16 A
2
 = 4AC + 4B
2
 
 (b) B
2
 – 10 A
2
 = 4AC + 6A
2
 
 (c) B
2
 – 8A
2
 = 4AC + 10A
2
 
 (d) B
2
 – 16 A
2
 = 4AC + 8B
2
 
14.  a and ß are the roots of quadratic equation. If  
a + ß = 8 and a–ß = 2 5 , then which of the 
following equation will have roots a
4 
and ß
4
 ?  
  a leLee ß efÉIeele meceerkeâjCe kesâ cetue nQ~ Ùeefo a + ß = 8 
leLee a–ß = 2 5 nQ, lees a
4
 leLee ß
4
 efvecveefueefKele ceW 
mes efkeâme meceerkeâjCe kesâ cetue nQ? 
 (a) x
2
 – 1522x + 14641 = 0  
 (b) x
2
 – 1921x + 14641 = 0 
 (c) x
2
 – 1764x + 14641 = 0 
 (d) x
2
 – 2520x + 14641 = 0 
15.  If a and b are the roots of the equation Px
2
 – 
Qx + R = 0, then what is the value of (1/a
2
) + 
(1/b
2
) + (a/b) + (b/a) ?  
  Ùeefo a leLee b meceerkeâjCe Px
2
 – Qx + R = 0 kesâ 
cetue nQ, lees (1/a
2
) + (1/b
2
) + (a/b) + (b/a) keâe 
ceeve keäÙee nw? 
 (a) 
( )( )
2
2
Q 2P 2R P
PR
- +
  
 (b) 
( )( )
2
2
Q 2PR R P
PR
- +
  
 (c) 
( )( )
2
2 2
Q 2R 2P R
P R
- +
 
 (d) 
( )( )
2
2 2
Q 2PR 2R 2P
P R
- +
 
16.  If x
2
 – 16x + 59 = 0, then what is the value of 
(x–6)
2
 + [1/(x–6)
2
] ?  
  Ùeefo x
2
 – 16x + 59 = 0, nw, lees (x–6)
2
 + [1/(x–6)
2
] 
keâe ceeve keäÙee nw? 
 (a) 14 (b) 18  
 (c) 16 (d) 20 
17.  If A and B are the roots of the equation Ax
2 
– 
A
2
x + AB = 0, then what is the value of A and B 
respectively ?  
  Ùeefo A leLee B meceerkeâjCe Ax
2 
– A
2
x + AB = 0, kesâ 
cetue nQ, lees ›eâceMe: A leLee B keâe ceeve keäÙee nw? 
 (a) 1, 0 (b) 1, 1 
 (c) 0, 2 (d) 0, 1 
18.  a and ß are the roots of the quadratic equation 
x
2
 – x–1 = 0. What is the value of a
8
 + ß
8
 ?  
  a leLee ß efÉIeele meceerkeâjCe x
2
 – x–1 = 0 kesâ cetue nQ~ 
a
8
 + ß
8
 keâe ceeve keäÙee nw? 
 (a) 47 (b) 54  
 (c) 59 (d) 68 
19.  If a + b + c = 9, ab + bc + ca = 26, a
3
 + b
3
 = 91, 
b
3
 + c
3
 = 72 and c
3
 + a
3
 = 35, then what is the 
value of abc ?  
  Ùeefo a + b + c = 9, ab + bc + ca = 27, a
3
 + b
3
 = 
91, b
3
 + c
3
 = 72 leLee c
3
 + a
3
 = 35 nQ, lees abc keâe 
ceeve keäÙee nw? 
 (a) 48 (b) 24  
 (c) 36 (d) 42 
20.  If x
3
 – 4x
2
 + 19 = 6(x–1), then what is the value 
of [x
2
 + (1/x – 4)] ?  
  Ùeefo x
3
 – 4x
2
 + 19 = 6(x–1) nw, lees [x
2
 + (1/x – 4)] 
keâe ceeve keäÙee nw? 
 (a) 3  (b) 5  
 (c) 6 (d) 8 
21.  Cost of 8 pencils, 5 pens and 3 erasers is Rs. 
111. Cost of 9 pencils, 6 pens and 5 erasers is 
Rs. 130. Cost of 16 pencils, 11 pens and 3 
erasers is Rs. 221. What is the cost (in Rs.) of 39 
pencils 26 pens and 13 erasers ?  
  8 heWefmeue, 5 keâuece leLee 3 jyeÌ[ keâe cetuÙe 111 ® nw~ 
9 heWefmeue, 6 keâuece leLee 5 jyeÌ[ keâe cetuÙe 130 ® nw~ 
16 heWefmeue, 11 keâuece leLee 3 jyeÌ[ keâe cetuÙe 221 ® 
nw~ 39 heWefmeue, 26 keâuece leLee 13 jyeÌ[ keâe cetuÙe (® 
ceW) keäÙee nw? 
 (a) 316 (b) 546  
 (c) 624 (d) 482 
22.  If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 
3z = 17, then what is the value of xy + yz + zx ?  
  Ùeefo 2x + 3y – 5z = 18, 3x + 2y + z = 29 leLee x + y 
+ 3z = 17, nQ, lees xy + yz + zx keâe ceeve keäÙee nw? 
 (a) 32 (b) 52 
 (c) 64 (d) 46 
23.  PQR is an equilateral triangle whose side is 10 
cm. What is the value (in cm) of the inradius of 
triangle PQR ?  
  PQR Skeâ meceyeeng ef$eYegpe nQ efpemekeâer Yegpee 10 mesceer. 
nQ~ ef$eYegpe PQR  keâer Deble: ef$epÙee keâe ceeve (mes.ceer. ceW) 
keäÙee nw? 
 (a) 5/ 3 (b) 10/ 3 
 (c) 10/ 3 (d) 5/ 2 
24.  What is the area (in cm
2
) of the circumcircle of 
a triangle whose sides are 6 cm, 8 cm and 10 cm 
respectively ? 
 
  Skeâ ef$eYegpe efpemekeâer YegpeeSB ›eâceMe: 6 mes.ceer., 8 mesceer, 
leLee 10 mes.ceer. nw, kesâ heefjJe=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) 
keäÙee nw? 
 (a) 275/7  (b) 550/7 
 (c) 2200/7 (d) 1100/7 
25.  In the given figure, MNOP is a parallelogram. 
PM is extended to Z. OZ intersects MN and PN 
at Y and X respectively. If OX = 27 cm and XY 
= 18 cm, then what is the length (in cm) of YZ ? 
  oer ieF& Deeke=âefle ceW, MNOP Skeâ meceeblej ÛelegYeg&pe nw~ 
PM keâes Z lekeâ yeÌ{eÙee ieÙee nw~ OZ, MN leLee PN 
keâes ›eâceMe: Y leLee X hej ØeefleÛÚso keâjleer nw~ Ùeefo OX 
= 27 mes.ceer. leLee XY = 18 mes.ceer. nQ, lees YZ keâer 
uecyeeF& (mes.ceer. ceW) keäÙee nw?  
 
 (a) 21.4 (b) 22.5 
 (c) 23.8 (d) 24.5 
26.  ABCD is a trapezium in which AB is parallel to 
CD and AB = 4 (CD). The diagonals of the 
trapezium intersects at O. What is the ratio of 
area of triangle DCO to the area of the triangle 
ABO ?  
  ABCD Skeâ meceuecye nw efpemeceW AB, CD kesâ meceeblej nw 
leLee AB = 4 (CD) nw~ meceuecye kesâ efJekeâCe& O hej 
ØeefleÛÚsove keâjles nw~ ef$eYegpe DCO kesâ #es$eHeâue keâe 
ef$eYegpe ABO kesâ #es$eHeâue mes keäÙee Devegheele nw? 
 (a) 1 : 4  (b) 1 : 2 
 (c) 1 : 8 (d) 1 : 16 
27.  In the given figure, ABC is an equilateral 
triangle. Two circles of radius 4 cm and 12 cm 
are inscribed in the triangle. What is the side 
(in cm) of an equilateral triangle ?  
  oer ieF& Deeke=âefle ceW, ABC Skeâ meceyeeng ef$eYegpe nw~ 4 
mes.ceer. leLee 12 mes.ceer. ef$epÙee Jeeues oes Je=òe ef$eYegpe 
ceW Debefkeâle nw~ mecekeâesCe ef$eYegpe keâer Yegpee (mes.ceer. ceW) 
keäÙee nw?  
 
  
 (a) 32/ 3 (b) 32 3 
 (c) 64/ 3 (d) 64 2 
28.  In the given figure, SX is tangent. SX = OX = 
OR. If QX = 3 cm and PQ = 9 cm, then what is 
the value (in cm) of OS ?  
  oer ieF& Deeke=âefle ceW, SX  Skeâ mheMe& jsKee nw~ SX = OX 
= OR nQ~ Ùeefo QX = 3 mes.ceer. leLee PQ = 9 mes.ceer. nQ, 
lees OS keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 6 (b) 5  
 (c) 4 (d) 3 
29.  PAB and PCD are two secants to a circle. If PA 
= 10 cm, AB = 12 cm and PC = 11 cm, then 
what is the value (in cm) of PD ?  
  PAB leLee PCD Skeâ Je=le hej oes Úsove jsKeeSB nQ~ Ùeefo 
PA = 10 mes.ceer., AB = 12 mes.ceer. leLee PC = 11 mes.ceer. 
nes lees, PD keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 18 (b) 9 
 (c) 20 (d) 12 
30.  Triangle PQR is inscribed in a circle such that 
P, Q and R lie on the circumference. If PQ is 
the diameter of the circle and ?PQR = 40
0
, 
then what is the value (in degrees) of ?QPR ?  
  Skeâ Je=òe ceW ef$eYegpe PQR Fme Øekeâej Debefkeâle nw, efkeâ P, 
Q leLee R heefjefOe hej efmLele nw~ Ùeefo PQ Je=òe keâe JÙeeme 
nw leLee ?PQR = 40
0
 nw, lees ?QPR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 (a) 40 (b) 45  
 (c) 50 (d) 55 
31.  In the given figure, ?QRU = 72
0
, ? TRS = 15
0
 
and ?PSR = 95
0
, then what is the value (in 
degrees) of ?PQR ? 
  oer ieF& Deeke=âefle ceW, ?QRU = 72
0
, ? TRS = 15
0
 
leLee ?PSR = 95
0
 nQ, lees ?PQR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 
 (a) 85 (b) 95  
 (c) 75 (d) 90 
32.  What can be the maximum number of common 
tangent which can be drawn to two non-
intersecting circles? 
  oes iewj–ØeefleÛÚsoer Je=òeeW ceW DeefOekeâlece efkeâleveer DevegmheMe& 
jsKee KeeRÛeer pee mekeâleer nw? 
 (a) 2 (b) 4 
 (c) 3 (d) 6 
 
33.  Triangle PQR is inscribed in the circle whose 
radius is 14 cm. If PQ is the diameter of the 
circle and PR = 10 cm, then what is the area of 
the triangle PQR ? 
  ef$eYegpe PQR Je=òe efpemekeâer ef$epÙee 14 mes.ceer. nw, ceW 
Debefkeâle nw~ Ùeefo PQ Je=òe keâe JÙeeme nw leLee PR = 10 
mes.ceer. nw, lees ef$eYegpe PQR keâe #es$eHeâue keäÙee nw? 
 (a) 196 (b) 30 19 
 (c) 40 17 (d) 35 21 
34.  PQR is a right angled triangle in which PQ = 
QR. If the hypotenuse of the triangle is 20 cm, 
then what is the area (in cm
2
) of the triangle 
PQR ?  
  PQR Skeâ mecekeâesCe ef$eYegpe nw efpemeceW PQ = QR nw~ 
Ùeefo ef$eYegpe keâe keâCe& 20 mes.ceer. nw, lees ef$eYegpe PQR  
keâe keäÙee #es$eHeâue (mes.ceer.
2
 ceW) ceW keäÙee nw? 
 (a) 100 2  (b) 100 
 (c) 50 2 (d) 50 
35.  PQRS is a square whose side is 20 cm. By 
joining opposite vertices of PQRS are get four 
triangles. What is the sum of the perimeters 
ofthe four triangles ?  
  PQRS Skeâ Jeie& nw efpemekeâer Yegpee 20 mes.ceer. nw~ PQRS 
kesâ efJehejerle Meer<eeX keâes efceueeves hej Ûeej ef$eYegpe Øeehle nesles 
nQ~ Ûeejes ef$eYegpeeW kesâ heefjceeheeW keâe Ùeesie keäÙee nw? 
 (a) 40 2  (b) 80 2 80 + 
 (c) 40 2 40 + (d) 40 2 80 + 
36.  If ABCDEF is a regular hexagon, then what is 
the value (in degrees) of ?ADB ? 
  Ùeefo ABCDEF Skeâ mece <ešdYegpe nw, lees ?ADB keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 15 (b) 30  
 (c) 45 (d) 60 
37.  ABCD is square and CDE is an equilateral 
triangle outside the square. What is the value 
(in degrees) of ?BEC ?  
  ABCD Skeâ Jeie& nw leLee CDE Jeie& kesâ yeenj Skeâ 
meceyeeng ef$eYegpe nw~ ?BEC keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 15 (b) 30  
 (c) 45 (d) 60 
38.  There is a circular garden of radius 21 metres. 
A path of width 3.5 metres is constructed just 
outside the garden. What is the area (in 
metres
2
) of the path ? 
  21 ceeršj ef$epÙee Jeeuee Skeâ Je=òeekeâej GÅeeve nw~ GÅeeve  
kesâ "erkeâ yeenj 3.5 ceeršj ÛeewÌ[eF& Jeeues Skeâ heLe keâe 
efvecee&Ce efkeâÙee ieÙee nw~ heLe keâe #es$eHeâue (ceeršj
2
 ceW) 
keäÙee nw? 
 (a) 50.05 (b) 57.56 
 (c) 52.12 (d) 56.07 
39.  In the given figure, PQRS is a square whose 
side is 8 cm. PQS and QPR are two quadrants. 
A circle is placed touching both the quadrants 
and the square as shown in the figure. What is 
the are (in cm
2
) of the circle ?  
  oer ieF& Deeke=âefle ceW, PQRS Skeâ Jeie& nw efpemekeâer Yegpee 8 
mes.ceer. nw~ PQS leLee QPR Je=òe kesâ oes ÛelegLe& Yeeie nQ~ 
Skeâ Je=òe, Je=òe kesâ oesveeW ÛelegLe& YeeieeW leLee Jeie& keâes mheMe& 
keâj jne nw pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw~ Je=òe keâe 
#es$eHeâue (mes.ceer.
2 
ceW) keäÙee nw? 
 
 (a) 13/17 (b) 11/14 
 (c) 19/31 (d) 15/19 
40.  The base of a prism is in the shape of an 
equilateral triangle. If the perimeter of the base 
is 18 cm and the height of the prism is 20 cm, 
then what is the volume (in cm
3
) of the prism ?  
  Skeâ efØepce keâe DeeOeej meceyeeng ef$eYegpe kesâ Deekeâej ceW nw~ 
Ùeefo DeeOeej keâer heefjefOe 18 mes.ceer. nw leLee efØepce keâer 
TBÛeeF& 20 mes.ceer. nw, lees efØepce keâe DeeÙeleve (mes.ceer.
3
 ceW) 
keäÙee nw? 
 (a) 60 3  (b) 30 6 
 (c) 60 2 (d) 120 3 
41.  The height of a cone is 24 cm and the area of 
the base is 154 cm
2
. What is the curved surface 
area (in cm
2
) of the cone ?  
  Skeâ Mebkegâ keâer TBÛeeF& 24 mes.ceer. nw leLee DeeOeej keâe 
#es$eHeâue 154 mes.ceer.
2
 nw~ Mebkegâ kesâ Je›eâ he=<"erÙe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 484 (b) 550 
 (c) 525 (d) 515 
42.  A right circular solid cylinder has radius of 
base 7 cm and height is 28 cm. It is melted to 
form a cuboid such that the ratio of its side is 
2:3:6. What is the total surface area (in cm
2
) of 
cuboid ?  
  Skeâ mece Je=òeekeâej "esme yesueve kesâ DeeOeej keâer ef$epÙee 7 
mes.ceer. leLee TBÛeeF& 28 mes.ceer. nw~ Fmes efheIeueekeâj Skeâ 
IeveeYe Fme Øekeâej yeveeÙee peelee nw keâer Gmekeâer Yegpee keâe 
Devegheele 2:3:6 nw~ IeveeYe keâe kegâue he=<"erÙe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 
3
2156
3
 (b) 
3
2156
9
 
 (c) 
3
2148
3
 (d) 
3
2048
3
 
43.  A right circular cylinder is formed A = sum of 
total surface area and the area of the two bases. 
B = the curved surface area of this cylinder. If 
A : B = 3 : 2 and the volume of cylinder is 4312 
cm
3
, then what is the sum of area (in cm
2
) of 
the two bases of this cylinder ?  
  Skeâ mece Je=òeekeâej yesueve yeveeÙee peelee nw~ A = kegâue 
he=<"erÙe #es$eHeâue leLee oes DeeOeejeW kesâ #es$eHeâue keâe Ùeesie~ 
Page 5


 
mebÙegòeâ mveelekeâ mlejerÙe hejer#ee, 2018 
(Tier-II) 
ieefCele (MATH) 
JÙeeKÙee meefnle nue ØeMve he$e 
Exam Date : 21-2-2018] [Time : 10 AM to 12 PM 
1.  If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... upto 60 
terms, then what is the value of A ?  
  Ùeefo A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + ....... 60 
heoeW lekeâ nQ, lees A keâe ceeve keäÙee nw? 
 (a) –360 (b) –310 
 (c) –240 (d) –270 
2.  How many natural numbers are there between 
1000 to 2000, which when divided by 341 leaves 
remainder 5 ?  
  1000 mes 2000 kesâ ceOÙe Ssmeer efkeâleveer Øeeke=âeflekeâ 
mebKÙeeSB nQ efpevnW 341 mes efJeYeeefpele keâjves hej 
Mes<eHeâue 5 yeÛelee nw? 
 (a) 3 (b) 2  
 (c) 4 (d) 1 
3.  Which of the following statement(s) is/are 
TRUE ? 
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. ( ) ( ) ( ) ( ) 64 + 0.0064 + 0.81 + 0.0081 = 9.07 
  II. ( ) ( ) ( ) 0.010201 + 98.01 + 0.25 = 11.51 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
4.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve-mee/mes keâLeve melÙe nw/nQ? 
  I. (0.7)
2
 + (0.07)
2
 + (11.1)
2
 > 123.8 
  II. (1.12)
2
 + (10.3)
2
 + (1.05)
2
 > 108.3 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II  
5.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 
1 1 1 1 12
+ + + ... + =
1× 3 3×5 5×7 11×13 13
 
  II. 
1 1 1 1 12
+ + + ... + =
1× 2 2× 3 3× 4 12×13 13
 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
6.  Which of the following statement(s) is/are 
TRUE?   
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 3/71 < 5/91 < 7/99 
  II. 11/135 > 12/157 > 13/181 
 (a) Only I/kesâJeue I  
 (b) Only II/kesâJeue II  
 (c) Both I and II/I leLee II oesveeW 
 (d) Neither I nor II/ve lees I ve ner II 
7.  If 1 + (1/2) + (1/3) +....+ (1/20) = k, then what is 
the value of (1/4) + (1/6) + (1/8) + ....+ (1/40) ?  
  Ùeefo 1 + (1/2) + (1/3) +....+ (1/20) = k nw, lees (1/4) 
+ (1/6) + (1/8) + ....+ (1/40) keâe ceeve keäÙee nw? 
 (a) k/2  (b) 2k 
 (c) (k – 1)/2 (d) (k + 1)/2 
8.  If A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 and C = 3
15
 
+ 3
14
 + 3
13
 + ....+ 3
0
, then which of the following 
option is TRUE ? 
  Ùeefo A = 2
32
, B = 2
31
 + 2
30
 + 2
29
 +...+ 2
0
 leLee C = 
3
15
 + 3
14
 + 3
13
 + ....+ 3
0
 nw, lees efvecveefueefKele ceW mes 
keâewve mee efJekeâuhe melÙe nw? 
 (a) C > B > A (b) C > A > B 
 (c) A > B > C (d) A > C > B 
9.  If x + y = 10 and xy = 4, then what is the value 
of x
4
 + y
4
 ? 
  Ùeefo x + y = 10 leLee xy = 4 nQ, lees x
4
 + y
4
 keâe ceeve 
keäÙee nw? 
 (a) 8464 (b) 8432 
 (c) 7478 (d) 6218 
10.  M is the largest three digit number which when 
divided by 6 and 5 leaves remainder 5 and 3 
respectively. What will be the remainder when 
M is divided by 11 ?  
  M leerve DebkeâeW keâer meyemes yeÌ[er mebKÙee nw efpemes, peye 6 
leLee 5 mes efJeYeeefpele efkeâÙee peelee nw lees Mes<eHeâue ›eâceMe: 
5 leLee 3 Deelee nw~ peye M keâes 11 mes efJeYeeefpele efkeâÙee 
peeÙes lees Mes<eHeâue keäÙee nesiee? 
 (a) 1 (b) 2  
 (c) 3 (d) 4 
11.  Which of the following statement(s) is/are 
TRUE ?  
  efvecveefueefKele ceW mes keâewve mee/mes keâLeve melÙe nw/nQ? 
  I. 5 + 5 > 7 + 3 
  II. 6 + 7 > 8 + 5 
  III. 3 + 9 > 6 + 6 
 
 (a) Only I/ kesâJeue I  
 (b) Only I and II/kesâJeue I leLee II  
 (c) Only II and III/kesâJeue II leLee III 
 (d) Only I and III/ kesâJeue I leLee III 
12.  If 
3 + 2
a =
3 - 2
 and 
3 - 2
b =
3 + 2
 then what is 
the value of a
2
 + b
2
 – ab ?  
  Ùeefo 
3 + 2
a =
3 - 2
 leLee 
3 - 2
b =
3 + 2
 nQ, lees a
2
 + 
b
2
 – ab keâe ceeve keäÙee nw? 
 (a) 97  (b) 
( )
2 3 2 +  
 (c) 
( )
4 6 1 + (d) 98 
13.  If the difference between the roots of the 
equation Ax
2
 – Bx + C = 0 is 4, then which of 
the following is TRUE ?  
  Ùeefo meceerkeâjCe Ax
2
 – Bx + C = 0 kesâ cetueeW keâe Deblej 
4 nw, lees efvecveefueefKele ceW mes keâewve mee melÙe nw? 
 (a) B
2
 – 16 A
2
 = 4AC + 4B
2
 
 (b) B
2
 – 10 A
2
 = 4AC + 6A
2
 
 (c) B
2
 – 8A
2
 = 4AC + 10A
2
 
 (d) B
2
 – 16 A
2
 = 4AC + 8B
2
 
14.  a and ß are the roots of quadratic equation. If  
a + ß = 8 and a–ß = 2 5 , then which of the 
following equation will have roots a
4 
and ß
4
 ?  
  a leLee ß efÉIeele meceerkeâjCe kesâ cetue nQ~ Ùeefo a + ß = 8 
leLee a–ß = 2 5 nQ, lees a
4
 leLee ß
4
 efvecveefueefKele ceW 
mes efkeâme meceerkeâjCe kesâ cetue nQ? 
 (a) x
2
 – 1522x + 14641 = 0  
 (b) x
2
 – 1921x + 14641 = 0 
 (c) x
2
 – 1764x + 14641 = 0 
 (d) x
2
 – 2520x + 14641 = 0 
15.  If a and b are the roots of the equation Px
2
 – 
Qx + R = 0, then what is the value of (1/a
2
) + 
(1/b
2
) + (a/b) + (b/a) ?  
  Ùeefo a leLee b meceerkeâjCe Px
2
 – Qx + R = 0 kesâ 
cetue nQ, lees (1/a
2
) + (1/b
2
) + (a/b) + (b/a) keâe 
ceeve keäÙee nw? 
 (a) 
( )( )
2
2
Q 2P 2R P
PR
- +
  
 (b) 
( )( )
2
2
Q 2PR R P
PR
- +
  
 (c) 
( )( )
2
2 2
Q 2R 2P R
P R
- +
 
 (d) 
( )( )
2
2 2
Q 2PR 2R 2P
P R
- +
 
16.  If x
2
 – 16x + 59 = 0, then what is the value of 
(x–6)
2
 + [1/(x–6)
2
] ?  
  Ùeefo x
2
 – 16x + 59 = 0, nw, lees (x–6)
2
 + [1/(x–6)
2
] 
keâe ceeve keäÙee nw? 
 (a) 14 (b) 18  
 (c) 16 (d) 20 
17.  If A and B are the roots of the equation Ax
2 
– 
A
2
x + AB = 0, then what is the value of A and B 
respectively ?  
  Ùeefo A leLee B meceerkeâjCe Ax
2 
– A
2
x + AB = 0, kesâ 
cetue nQ, lees ›eâceMe: A leLee B keâe ceeve keäÙee nw? 
 (a) 1, 0 (b) 1, 1 
 (c) 0, 2 (d) 0, 1 
18.  a and ß are the roots of the quadratic equation 
x
2
 – x–1 = 0. What is the value of a
8
 + ß
8
 ?  
  a leLee ß efÉIeele meceerkeâjCe x
2
 – x–1 = 0 kesâ cetue nQ~ 
a
8
 + ß
8
 keâe ceeve keäÙee nw? 
 (a) 47 (b) 54  
 (c) 59 (d) 68 
19.  If a + b + c = 9, ab + bc + ca = 26, a
3
 + b
3
 = 91, 
b
3
 + c
3
 = 72 and c
3
 + a
3
 = 35, then what is the 
value of abc ?  
  Ùeefo a + b + c = 9, ab + bc + ca = 27, a
3
 + b
3
 = 
91, b
3
 + c
3
 = 72 leLee c
3
 + a
3
 = 35 nQ, lees abc keâe 
ceeve keäÙee nw? 
 (a) 48 (b) 24  
 (c) 36 (d) 42 
20.  If x
3
 – 4x
2
 + 19 = 6(x–1), then what is the value 
of [x
2
 + (1/x – 4)] ?  
  Ùeefo x
3
 – 4x
2
 + 19 = 6(x–1) nw, lees [x
2
 + (1/x – 4)] 
keâe ceeve keäÙee nw? 
 (a) 3  (b) 5  
 (c) 6 (d) 8 
21.  Cost of 8 pencils, 5 pens and 3 erasers is Rs. 
111. Cost of 9 pencils, 6 pens and 5 erasers is 
Rs. 130. Cost of 16 pencils, 11 pens and 3 
erasers is Rs. 221. What is the cost (in Rs.) of 39 
pencils 26 pens and 13 erasers ?  
  8 heWefmeue, 5 keâuece leLee 3 jyeÌ[ keâe cetuÙe 111 ® nw~ 
9 heWefmeue, 6 keâuece leLee 5 jyeÌ[ keâe cetuÙe 130 ® nw~ 
16 heWefmeue, 11 keâuece leLee 3 jyeÌ[ keâe cetuÙe 221 ® 
nw~ 39 heWefmeue, 26 keâuece leLee 13 jyeÌ[ keâe cetuÙe (® 
ceW) keäÙee nw? 
 (a) 316 (b) 546  
 (c) 624 (d) 482 
22.  If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 
3z = 17, then what is the value of xy + yz + zx ?  
  Ùeefo 2x + 3y – 5z = 18, 3x + 2y + z = 29 leLee x + y 
+ 3z = 17, nQ, lees xy + yz + zx keâe ceeve keäÙee nw? 
 (a) 32 (b) 52 
 (c) 64 (d) 46 
23.  PQR is an equilateral triangle whose side is 10 
cm. What is the value (in cm) of the inradius of 
triangle PQR ?  
  PQR Skeâ meceyeeng ef$eYegpe nQ efpemekeâer Yegpee 10 mesceer. 
nQ~ ef$eYegpe PQR  keâer Deble: ef$epÙee keâe ceeve (mes.ceer. ceW) 
keäÙee nw? 
 (a) 5/ 3 (b) 10/ 3 
 (c) 10/ 3 (d) 5/ 2 
24.  What is the area (in cm
2
) of the circumcircle of 
a triangle whose sides are 6 cm, 8 cm and 10 cm 
respectively ? 
 
  Skeâ ef$eYegpe efpemekeâer YegpeeSB ›eâceMe: 6 mes.ceer., 8 mesceer, 
leLee 10 mes.ceer. nw, kesâ heefjJe=òe keâe #es$eHeâue (mes.ceer.
2
 ceW) 
keäÙee nw? 
 (a) 275/7  (b) 550/7 
 (c) 2200/7 (d) 1100/7 
25.  In the given figure, MNOP is a parallelogram. 
PM is extended to Z. OZ intersects MN and PN 
at Y and X respectively. If OX = 27 cm and XY 
= 18 cm, then what is the length (in cm) of YZ ? 
  oer ieF& Deeke=âefle ceW, MNOP Skeâ meceeblej ÛelegYeg&pe nw~ 
PM keâes Z lekeâ yeÌ{eÙee ieÙee nw~ OZ, MN leLee PN 
keâes ›eâceMe: Y leLee X hej ØeefleÛÚso keâjleer nw~ Ùeefo OX 
= 27 mes.ceer. leLee XY = 18 mes.ceer. nQ, lees YZ keâer 
uecyeeF& (mes.ceer. ceW) keäÙee nw?  
 
 (a) 21.4 (b) 22.5 
 (c) 23.8 (d) 24.5 
26.  ABCD is a trapezium in which AB is parallel to 
CD and AB = 4 (CD). The diagonals of the 
trapezium intersects at O. What is the ratio of 
area of triangle DCO to the area of the triangle 
ABO ?  
  ABCD Skeâ meceuecye nw efpemeceW AB, CD kesâ meceeblej nw 
leLee AB = 4 (CD) nw~ meceuecye kesâ efJekeâCe& O hej 
ØeefleÛÚsove keâjles nw~ ef$eYegpe DCO kesâ #es$eHeâue keâe 
ef$eYegpe ABO kesâ #es$eHeâue mes keäÙee Devegheele nw? 
 (a) 1 : 4  (b) 1 : 2 
 (c) 1 : 8 (d) 1 : 16 
27.  In the given figure, ABC is an equilateral 
triangle. Two circles of radius 4 cm and 12 cm 
are inscribed in the triangle. What is the side 
(in cm) of an equilateral triangle ?  
  oer ieF& Deeke=âefle ceW, ABC Skeâ meceyeeng ef$eYegpe nw~ 4 
mes.ceer. leLee 12 mes.ceer. ef$epÙee Jeeues oes Je=òe ef$eYegpe 
ceW Debefkeâle nw~ mecekeâesCe ef$eYegpe keâer Yegpee (mes.ceer. ceW) 
keäÙee nw?  
 
  
 (a) 32/ 3 (b) 32 3 
 (c) 64/ 3 (d) 64 2 
28.  In the given figure, SX is tangent. SX = OX = 
OR. If QX = 3 cm and PQ = 9 cm, then what is 
the value (in cm) of OS ?  
  oer ieF& Deeke=âefle ceW, SX  Skeâ mheMe& jsKee nw~ SX = OX 
= OR nQ~ Ùeefo QX = 3 mes.ceer. leLee PQ = 9 mes.ceer. nQ, 
lees OS keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 
 (a) 6 (b) 5  
 (c) 4 (d) 3 
29.  PAB and PCD are two secants to a circle. If PA 
= 10 cm, AB = 12 cm and PC = 11 cm, then 
what is the value (in cm) of PD ?  
  PAB leLee PCD Skeâ Je=le hej oes Úsove jsKeeSB nQ~ Ùeefo 
PA = 10 mes.ceer., AB = 12 mes.ceer. leLee PC = 11 mes.ceer. 
nes lees, PD keâe ceeve (mes.ceer. ceW) keäÙee nw? 
 (a) 18 (b) 9 
 (c) 20 (d) 12 
30.  Triangle PQR is inscribed in a circle such that 
P, Q and R lie on the circumference. If PQ is 
the diameter of the circle and ?PQR = 40
0
, 
then what is the value (in degrees) of ?QPR ?  
  Skeâ Je=òe ceW ef$eYegpe PQR Fme Øekeâej Debefkeâle nw, efkeâ P, 
Q leLee R heefjefOe hej efmLele nw~ Ùeefo PQ Je=òe keâe JÙeeme 
nw leLee ?PQR = 40
0
 nw, lees ?QPR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 (a) 40 (b) 45  
 (c) 50 (d) 55 
31.  In the given figure, ?QRU = 72
0
, ? TRS = 15
0
 
and ?PSR = 95
0
, then what is the value (in 
degrees) of ?PQR ? 
  oer ieF& Deeke=âefle ceW, ?QRU = 72
0
, ? TRS = 15
0
 
leLee ?PSR = 95
0
 nQ, lees ?PQR keâe ceeve (ef[«eer 
ceW) keäÙee nw? 
 
 (a) 85 (b) 95  
 (c) 75 (d) 90 
32.  What can be the maximum number of common 
tangent which can be drawn to two non-
intersecting circles? 
  oes iewj–ØeefleÛÚsoer Je=òeeW ceW DeefOekeâlece efkeâleveer DevegmheMe& 
jsKee KeeRÛeer pee mekeâleer nw? 
 (a) 2 (b) 4 
 (c) 3 (d) 6 
 
33.  Triangle PQR is inscribed in the circle whose 
radius is 14 cm. If PQ is the diameter of the 
circle and PR = 10 cm, then what is the area of 
the triangle PQR ? 
  ef$eYegpe PQR Je=òe efpemekeâer ef$epÙee 14 mes.ceer. nw, ceW 
Debefkeâle nw~ Ùeefo PQ Je=òe keâe JÙeeme nw leLee PR = 10 
mes.ceer. nw, lees ef$eYegpe PQR keâe #es$eHeâue keäÙee nw? 
 (a) 196 (b) 30 19 
 (c) 40 17 (d) 35 21 
34.  PQR is a right angled triangle in which PQ = 
QR. If the hypotenuse of the triangle is 20 cm, 
then what is the area (in cm
2
) of the triangle 
PQR ?  
  PQR Skeâ mecekeâesCe ef$eYegpe nw efpemeceW PQ = QR nw~ 
Ùeefo ef$eYegpe keâe keâCe& 20 mes.ceer. nw, lees ef$eYegpe PQR  
keâe keäÙee #es$eHeâue (mes.ceer.
2
 ceW) ceW keäÙee nw? 
 (a) 100 2  (b) 100 
 (c) 50 2 (d) 50 
35.  PQRS is a square whose side is 20 cm. By 
joining opposite vertices of PQRS are get four 
triangles. What is the sum of the perimeters 
ofthe four triangles ?  
  PQRS Skeâ Jeie& nw efpemekeâer Yegpee 20 mes.ceer. nw~ PQRS 
kesâ efJehejerle Meer<eeX keâes efceueeves hej Ûeej ef$eYegpe Øeehle nesles 
nQ~ Ûeejes ef$eYegpeeW kesâ heefjceeheeW keâe Ùeesie keäÙee nw? 
 (a) 40 2  (b) 80 2 80 + 
 (c) 40 2 40 + (d) 40 2 80 + 
36.  If ABCDEF is a regular hexagon, then what is 
the value (in degrees) of ?ADB ? 
  Ùeefo ABCDEF Skeâ mece <ešdYegpe nw, lees ?ADB keâe 
ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 15 (b) 30  
 (c) 45 (d) 60 
37.  ABCD is square and CDE is an equilateral 
triangle outside the square. What is the value 
(in degrees) of ?BEC ?  
  ABCD Skeâ Jeie& nw leLee CDE Jeie& kesâ yeenj Skeâ 
meceyeeng ef$eYegpe nw~ ?BEC keâe ceeve (ef[«eer ceW) keäÙee nw? 
 (a) 15 (b) 30  
 (c) 45 (d) 60 
38.  There is a circular garden of radius 21 metres. 
A path of width 3.5 metres is constructed just 
outside the garden. What is the area (in 
metres
2
) of the path ? 
  21 ceeršj ef$epÙee Jeeuee Skeâ Je=òeekeâej GÅeeve nw~ GÅeeve  
kesâ "erkeâ yeenj 3.5 ceeršj ÛeewÌ[eF& Jeeues Skeâ heLe keâe 
efvecee&Ce efkeâÙee ieÙee nw~ heLe keâe #es$eHeâue (ceeršj
2
 ceW) 
keäÙee nw? 
 (a) 50.05 (b) 57.56 
 (c) 52.12 (d) 56.07 
39.  In the given figure, PQRS is a square whose 
side is 8 cm. PQS and QPR are two quadrants. 
A circle is placed touching both the quadrants 
and the square as shown in the figure. What is 
the are (in cm
2
) of the circle ?  
  oer ieF& Deeke=âefle ceW, PQRS Skeâ Jeie& nw efpemekeâer Yegpee 8 
mes.ceer. nw~ PQS leLee QPR Je=òe kesâ oes ÛelegLe& Yeeie nQ~ 
Skeâ Je=òe, Je=òe kesâ oesveeW ÛelegLe& YeeieeW leLee Jeie& keâes mheMe& 
keâj jne nw pewmee efkeâ Deeke=âefle ceW oMee&Ùee ieÙee nw~ Je=òe keâe 
#es$eHeâue (mes.ceer.
2 
ceW) keäÙee nw? 
 
 (a) 13/17 (b) 11/14 
 (c) 19/31 (d) 15/19 
40.  The base of a prism is in the shape of an 
equilateral triangle. If the perimeter of the base 
is 18 cm and the height of the prism is 20 cm, 
then what is the volume (in cm
3
) of the prism ?  
  Skeâ efØepce keâe DeeOeej meceyeeng ef$eYegpe kesâ Deekeâej ceW nw~ 
Ùeefo DeeOeej keâer heefjefOe 18 mes.ceer. nw leLee efØepce keâer 
TBÛeeF& 20 mes.ceer. nw, lees efØepce keâe DeeÙeleve (mes.ceer.
3
 ceW) 
keäÙee nw? 
 (a) 60 3  (b) 30 6 
 (c) 60 2 (d) 120 3 
41.  The height of a cone is 24 cm and the area of 
the base is 154 cm
2
. What is the curved surface 
area (in cm
2
) of the cone ?  
  Skeâ Mebkegâ keâer TBÛeeF& 24 mes.ceer. nw leLee DeeOeej keâe 
#es$eHeâue 154 mes.ceer.
2
 nw~ Mebkegâ kesâ Je›eâ he=<"erÙe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 484 (b) 550 
 (c) 525 (d) 515 
42.  A right circular solid cylinder has radius of 
base 7 cm and height is 28 cm. It is melted to 
form a cuboid such that the ratio of its side is 
2:3:6. What is the total surface area (in cm
2
) of 
cuboid ?  
  Skeâ mece Je=òeekeâej "esme yesueve kesâ DeeOeej keâer ef$epÙee 7 
mes.ceer. leLee TBÛeeF& 28 mes.ceer. nw~ Fmes efheIeueekeâj Skeâ 
IeveeYe Fme Øekeâej yeveeÙee peelee nw keâer Gmekeâer Yegpee keâe 
Devegheele 2:3:6 nw~ IeveeYe keâe kegâue he=<"erÙe #es$eHeâue 
(mes.ceer.
2
 ceW) keäÙee nw? 
 (a) 
3
2156
3
 (b) 
3
2156
9
 
 (c) 
3
2148
3
 (d) 
3
2048
3
 
43.  A right circular cylinder is formed A = sum of 
total surface area and the area of the two bases. 
B = the curved surface area of this cylinder. If 
A : B = 3 : 2 and the volume of cylinder is 4312 
cm
3
, then what is the sum of area (in cm
2
) of 
the two bases of this cylinder ?  
  Skeâ mece Je=òeekeâej yesueve yeveeÙee peelee nw~ A = kegâue 
he=<"erÙe #es$eHeâue leLee oes DeeOeejeW kesâ #es$eHeâue keâe Ùeesie~ 
 
B = Fme yesueve keâe Je›eâ he=<"erÙe #es$eHeâue~ Ùeefo A : B = 
3 : 2 leLee yesueve keâe DeeÙeleve 4312 mes.ceer.3 nw, lees Fme 
yesueve kesâ oesveeW DeeOeejeW kesâ #es$eHeâue (mes.ceer.
2
 ceW) keâe 
Ùeesie keäÙee nw? 
 (a) 154 (b) 308 
 (c) 462 (d) 616 
44.  A solid sphere has a radius 21 cm. It is melted 
to form a cube. 20% material is wasted in this 
process. The cube is melted to form 
hemisphere. In this process 20% material is 
wasted. The hemisphere is melted to form two 
spheres of equal radius. 20% material was also 
wasted in this process. What is the radius (in 
cm) of each new sphere ?  
  Skeâ "esme ieesues keâer ef$epÙee 21 mes.ceer. nw~ Fmes efheIeueekeâj 
Skeâ Ieve yeveeÙee peelee nw~ Fme Øeef›eâÙee ceW 20³ meece«eer 
JÙeLe& nes peeleer nw~ Ieve keâes efheIeueekeâj Skeâ DeOe&ieesuee 
yeveeÙee peelee nw~ Fme Øeef›eâÙee ceW 20³ meece«eer JÙeLe& nes 
peeleer nw~ DeOe&ieesues keâes efheIeueekeâj oes meceeve ef$epÙee 
Jeeues oes ieesues yeveeÙes peeles nQ~ Fme Øeef›eâÙee ceW Yeer 20³ 
meece«eer Yeer JÙeLe& nes ieF& Leer~ ØelÙeskeâ veS ieesues keâer 
ef$epÙee (mes.ceer. ceW) keäÙee nw? 
 (a) 
( )
3
4.2 2 (b) 
( )
3
2.1 2 
 (c) 
( )
3
2.1 4 (d) 
( )
3
4.2 4 
45.  A solid hemisphere has radius 14 cm. It is 
melted to form a cylinder such that the ratio of 
its curved surface area and total surface area is 
2:3. What is the radius (in cm) of its base ?  
  Skeâ "esme DeOe&ieesues keâer ef$epÙee 14 mes.ceer. nw~ Fmes 
efheIeueekeâj Skeâ yesueve Fme Øekeâej yeveeÙee peelee nw efkeâ 
Gmekesâ Je›eâ he=<"erÙe #es$eHeâue leLee kegâue he=‰erÙe #es$eheâue 
keâe Devegheele 2:3 nw~ Fmekesâ DeeOeej keâer ef$epÙee (mes.ceer. 
ceW) keäÙee nw? 
 (a) 
3
10
3
 (b) 
3
14
3
 
 (c) 
3
7
3
 (d) 
3
21
3
 
46.  A cuboid has dimensions 8 cm × 10 cm × 12 cm. 
It is cut into small cubes of side 2 cm. What is 
the percentage increase in the total surface 
area ?  
  Skeâ IeveeYe keâe DeeÙeece 8 mes.ceer. × 10 mes.ceer. × 12 
mes.ceer. nw~ Fmes 2 mes.ceer. Yegpee Jeeues Úesšs IeveeW ceW keâeše 
peelee nw~ kegâue he=<"erÙe #es$eHeâue ceW efkeâleves ØeefleMele keâer 
Je=efæ ngF&?  
 (a) 286.2 (b) 314.32  
 (c) 250.64 (d) 386.5 
47.  A pyramid has a square base. The side of 
square is 12 cm and height of pyramid is 21 cm. 
The pyramid is cut into 3 parts by 2 cuts 
parallel to its base. The cuts are at height of 
7cm and 14cm respectively from the base. 
What is the difference (in cm
3
) in the volume of 
top most and bottom most part?    
  Skeâ efhejeefce[ keâe DeeOeej Skeâ Jeie& nw~ Jeie& keâer Yegpee 12 
mes.ceer. leLee efhejeefce[ keâer TBÛeeF& 21 mes.ceer. nw~ efhejeefce[ 
keâes Gmekesâ DeeOeej kesâ meceeblej 2 keâšeJeeW mes 3 YeeieeW ceW 
keâeše peelee nw~ keâšeJe DeeOeej mes ›eâceMe: 7 mes.ceer. leLee 
14 mes.ceer. keâer TBÛeeF& hej nw~ meyemes Thej leLee meyemes veerÛes 
kesâ Yeeie kesâ DeeÙeleve keâe Deblej (mes.ceer.
3
 ceW) keäÙee nw? 
 (a) 872 (b) 944 
 (c) 786 (d) 918 
48.  What is the value of {(sin 4x + sin 4y) [(tan (2x 
– 2y)]}/(sin 4x–sin 4y) ?  
  {(sin 4x + sin 4y) [(tan (2x – 2y)]}/(sin 4x–sin 
4y) keâe ceeve keäÙee nw? 
 (a) tan 2 (2x + 2y)  (b) tan
2
  
 (c) cot (x–y) (d) tan (2x + 2y) 
49.  What is the value of (32 cos
6
 x – 48 cos
4
 x + 18 
cos
2
x–1)/ [4 sin x cosx sin (60 –x) cos (60–x) sin 
(60 + x) cos (60 + x) ? 
  (32 cos
6
 x – 48 cos
4
 x + 18 cos
2
x–1)/ [4 sin x cosx 
sin (60 –x) cos (60–x) sin (60 + x) cos (60 + x) 
keâe ceeve keäÙee nw? 
 (a) 4 tan 6x (b) 4 cot 6x 
 (c) 8 cot 6x (d) 8 tan 6x 
50.  What is the value of [2 cot(p – A)/2]/[1 + tan
2 
(2p–A)/2] ? 
  [2 cot(p – A)/2]/[1 + tan
2
(2p–A)/2] keâe ceeve keäÙee 
nw? 
 (a) 2 sin
2
A/2  (b) cos A 
 (c) sin A (d) 2 cos
2
A/2 
51.  If tan ? + sec? = (x–2)/(x+2), then what is the 
value of cos ? ?  
  Ùeefo tan ? + sec? = (x–2)/(x+2) nw, lees cos ? keâe 
ceeve keäÙee nw? 
 (a) (x
2
 – 1)/ (x
2
 + 1)  
 (b) (2x
2
 – 4)/ (2x
2
 + 4) 
 (c) (x
2
 – 4)/(x
2
 + 4) 
 (d) (x
2 
– 2)/(x
2
 + 2) 
52.  What is the value of (cos 40
0
 – cos 140
0
)/(sin 80
0
 
+ sin 20
0
) ?  
  (cos 40
0
 – cos 140
0
)/(sin 80
0
 + sin 20
0
) keâe ceeve 
keäÙee nw? 
 (a) 2 3  (b) 2/ 3 
 (c) 1/ 3 (d) 3 
53.  What is the value of [1–tan (90–?) + sec (90 – 
?)]/[tan (90–?) + sec (90 –?) + 1] ? 
  [1–tan (90–?) + sec (90 – ?)]/[tan (90–?) + sec 
(90 –?) + 1] keâe ceeve keäÙee nw? 
 (a) cot (?/2)  (b) tan (?/2)  
 (c) sin ? (d) cos ? 
54.  What is the value of [sin (90–A) + cos (180–
2A)]/[cos (90–2A) + sin (180–A]?  
  [sin (90–A) + cos (180–2A)]/[cos (90–2A) + sin 
(180–A] keâe ceeve keäÙee nw? 
 (a) sin (A/2) cosA (b) cot (A/2) 
 (c) tan (A/2) (d) sin A cos (A/2)