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§â ÂéçSÌ·¤æ ×ð´ 28+4 ×éçÎýÌ ÂëcÆ ãñ´Ð
PAPER - 2
ÂÚUèÿææ ÂéçSÌ·¤æ
OPQ
No. :
: MATHEMATICS & APTITUDE TEST
- 2 : »ç‡æÌ ÌÍæ ¥çÖL¤ç¿ ÂÚUèÿæ‡æ
Do not open this Test Booklet until you are asked to do so.
§â ÂÚèÿææ ÂéçSÌ·¤æ ·¤æð ÌÕ Ì·¤ Ù ¹æðÜð´ ÁÕ Ì·¤ ·¤ãæ Ù Áæ°Ð
Read carefully the Instructions on the Back Cover of this Test Booklet.
§â ÂÚèÿææ ÂéçSÌ·¤æ ·ð¤ çÂÀÜð ¥æßڇæ ÂÚ çΰ »° çÙÎðüàææð´ ·¤æð ŠØæÙ âð Âɸð´Ð
Important Instructions :
×ãžßÂê‡æü çÙÎðüàæ Ñ
1. Immediately fill in the particulars on this page of the Test
Booklet with Blue/Black Ball Point Pen.
2. This Test Booklet consists of three parts - Part I, Part II and
Part III. Part I has 30 objective type questions of Mathematics
consisting of FOUR (4) marks for each correct response.
Part II Aptitude Test has 50 objective type questions
consisting of FOUR (4) marks for each correct response.
Mark your answers for these questions in the appropriate
space against the number corresponding to the question in
the Answer Sheet placed inside this Test Booklet. Use Blue/
Black Ball Point Pen only for writing particulars/marking
responses on Side-1 and Side-2 of the Answer Sheet. Part III
consists of 2 questions carrying 70 marks which are to be
attempted on a separate Drawing Sheet which is also placed
inside the Test Booklet. Marks allotted to each question are
written against each question. Use colour pencils or crayons
only on the Drawing Sheet. Do not use water colours. For
each incorrect response in Part I and Part II, one–fourth (¼)
of the total marks allotted to the question would be deducted
from the total score. No deduction from the total score,
however, will be made if no response is indicated for an item
in the Answer Sheet.
3. There is only one correct response for each question in Part I
and Part II. Filling up more than one response in each question
will be treated as wrong response and marks for wrong response
will be deducted accordingly as per instruction 2 above.
4. The test is of 3 hours duration. The maximum marks are 390.
5. On completion of the test, the candidates must hand over
the Answer Sheet of Mathematics and Aptitude Test-Part I
& II and the Drawing Sheet of Aptitude Test-Part III
alongwith Test Booklet for Part III to the Invigilator in the
Room/Hall. Candidates are allowed to take away with
them the Test Booklet of Aptitude Test-Part I & II.
6. The CODE for this Booklet is
. Make sure that the CODE
printed on Side-2 of the Answer Sheet and on the Drawing
Sheet (Part III) is the same as that on this booklet. Also tally
the Serial Number of the Test Booklet, Answer Sheet and
Drawing Sheet and ensure that they are same. In case of
discrepancy in Code or Serial Number, the candidate should
immediately report the matter to the Invigilator for
replacement of the Test Booklet, Answer Sheet and the
Drawing Sheet.
K
1.
2.
3.
4.
5.
6.
ÂÚèÿææÍèü ·¤æ Ùæ× (ÕǸð ¥ÿæÚæð´ ×ð´) Ñ
¥Ùé·¤ý ×æ´·¤
: in figures
Ñ ¥´·¤æð´ ×ð´
: in words
Ñ àæŽÎæð´ ×ð´
Examination Centre Number :
ÂÚèÿææ ·ð¤‹Îý ِÕÚU Ñ
Centre of Examination (in Capitals) :
ÂÚUèÿææ ·ð¤‹Îý (ÕǸð ¥ÿæÚUæð´ ×ð´ ) Ñ
Candidate’s Signature :
ÂÚèÿææÍèü ·ð¤ ãSÌæÿæÚ Ñ
ÂÚèÿææ ÂéçSÌ·¤æ â´·ð¤Ì
K
ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ §â ÂëcÆU ÂÚU ¥æßàØ·¤ çßßÚU‡æ ÙèÜð/·¤æÜð ÕæòÜ
Â槴ÅU ÂðÙ âð ̈·¤æÜ ÖÚð´Ð
§â ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ ÌèÙ Öæ» ãñ´ - Öæ» I, Öæ» II °ß´ Öæ» III.
ÂéçSÌ·¤æ ·ð¤ Öæ» I ×ð´ »ç‡æÌ ·ð¤ 30 ßSÌéçÙD ÂýàÙ ãñ´ çÁâ×ð´ ÂýˆØð·¤ ÂýàÙ
·ð¤ âãè ©žæÚU ·ð¤ çÜØð ¿æÚU (4) ¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð Öæ» II
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©žæÚU ˜æ ×ð´ â´»Ì ·ý¤× ⴁØæ ·ð¤ »æðÜð ×ð´ »ãÚUæ çÙàææ٠ܻ淤ÚU ÎèçÁ°Ð
©žæÚU Â˜æ ·ð¤ ÂëD-1 °ß´ ÂëD-2 ÂÚU ßæ´çÀUÌ çßßÚU‡æ çܹÙð °ß´ ©žæÚU
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ãñ´Ð Øã ÂýàÙ §âè ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ ¥‹ÎÚU ÚU¹è ÇþU槴» àæèÅU ÂÚU ·¤ÚUÙð ãñ´Ð
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ÂÚU ·ð¤ßÜ Ú´U»èÙ Âð´çâÜ ¥Íßæ ·ýð¤ØæðÙ ·¤æ ãè ÂýØæð» ·¤Úð´UÐ ÂæÙè ·ð¤
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çÜ° ©â ÂýàÙ ·ð¤ çÜ° çÙÏæüçÚUÌ ·é¤Ü ¥´·¤æð́ ×ð́ âð °·¤-¿æñÍæ§ü (¼) ¥´·¤
·é¤Ü Øæð» ×ð́ âð ·¤æÅU çÜ° Áæ°¡»Ðð ØçÎ ©žæÚU ˜æ ×ð́ ç·¤âè ÂýàÙ ·¤æ ·¤æð§ü
©žæÚU Ùãè´ çÎØæ »Øæ ãñ, Ìæð ·é¤Ü Øæð» ×ð́ âð ·¤æð§ü ¥´·¤ Ùãè´ ·¤æÅðU Áæ°¡»Ðð
§â ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ Öæ» I ¥æñÚU Öæ» II ×ð´ ÂýˆØð·¤ ÂýàÙ ·¤æ ·ð¤ßÜ
°·¤ ãè âãè ©žæÚU ãñÐ °·¤ âð ¥çÏ·¤ ©žæÚU ÎðÙð ÂÚU ©âð »ÜÌ ©žæÚU ×æÙæ
ÁæØð»æ ¥æñÚU ©ÂÚUæð€Ì çÙÎðüàæ 2 ·ð¤ ¥ÙéâæÚU ¥´·¤ ·¤æÅU çÜØð ÁæØð´»ðÐ
ÂÚUèÿææ ·¤è ¥ßçÏ 3 ƒæ´ÅðU ãñÐ ¥çÏ·¤Ì× ¥´·¤ 390 ãñ´Ð
ÂÚUèÿææ â×æ# ãæðÙð ÂÚU, ÂÚUèÿææÍèü »ç‡æÌ °ß´ ¥çÖL¤ç¿ ÂÚUèÿæ‡æ-Öæ» I
°ß´ II ·¤æ ©žæÚU Â˜æ °ß´ ¥çÖL¤ç¿ ÂÚUèÿæ‡æ-Öæ» III ·¤è ÇþU槴» àæèÅU
°ß´ ÂÚUèÿææ ÂéçSÌ·¤æ Öæ» III ãæÜ/·¤ÿæ çÙÚUèÿæ·¤ ·¤æð âæñ´Â·¤ÚU ãè
ÂÚUèÿææ ãæÜ/·¤ÿæ ÀUæðǸð´Ð ÂÚUèÿææÍèü ¥çÖL¤ç¿ ÂÚUèÿæ‡æ-Öæ» I °ß´ II
·¤è ÂÚUèÿææ ÂéçSÌ·¤æ ¥ÂÙð âæÍ Üð Áæ â·¤Ìð ãñ´Ð
§â ÂéçSÌ·¤æ ·¤æ â´·ð¤Ì K ãñÐ Øã âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ §â ÂéçSÌ·¤æ
·¤æ â´·ð¤Ì, ©žæÚU Â˜æ ·ð¤ ÂëD-2 °ß´ ÇþU槴» àæèÅU (Öæ»-III) ÂÚU ÀUÂð
â´·ð¤Ì âð ç×ÜÌæ ãñÐ Øã Öè âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ ÂÚUèÿææ ÂéçSÌ·¤æ, ©žæÚU
Â˜æ °ß´ ÇþU 槴» àæèÅU ÂÚU ·ý¤× ⴁØæ ç×ÜÌè ãñÐ ¥»ÚU â´·ð¤Ì Øæ ·ý¤×
ⴁØæ çÖóæ ãæð´, Ìæð ÂÚUèÿææçÍüØæð´ ·¤æð çÙÚUèÿæ·¤ âð ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ,
©žæÚU Â˜æ °ß´ ÇþU槴» àæèÅU ÜðÙð ·ð¤ çÜ° ©‹ãð´ ÌéÚU‹Ì §â ˜æéçÅU âð ¥ß»Ì
·¤ÚUæ°¡Ð
Name of the Candidate (in Capitals) :
Roll Number
Test Booklet Code
Invigilator’s Signature (1) :
çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ (1) Ñ
Invigilator’s Signature (2) :
çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ (2) Ñ
Part I / Öæ» I
Mathematics / »ç‡æÌ
1.
Let N be the set of natural numbers and
1.
for aeN, aN denotes the set {ax : xeN}.
If bN Ç cN5dN, where b, c, d are natural
numbers greater than 1 and the greatest
common divisor of b and c is 1, then d
×æÙæ N Âýæ·ë¤Ì ⴁØæ¥æð´ ·¤æ â×é“æØ ãñ ÌÍæ aeN ·ð¤
çÜ° aN â×é“æØ {ax : xeN} ÎàææüÌæ ãñÐ
ØçÎ bN Ç cN5dN ãñ, Áãæ¡ b, c, d 1 âð ÕǸè
Âýæ·ë¤Ì ⴁØæ°¡ ãñ´ ÌÍæ b ÌÍæ c ·¤æ ×ãžæ× â×æÂßÌü·¤
1 ãñ, Ìæð d ÕÚUæÕÚU ãñ Ñ
equals :
2.
(1)
max { b, c }
(1)
max { b, c }
(2)
min { b, c }
(2)
min { b, c }
(3)
bc
(3)
bc
(4)
b1c
(4)
b1c
If z is a complex number of unit modulus
2.
and argument u, then the real part of
z(1 2 z )
z (1 1 z) is :
3.
ØçÎ z °·¤ âç×Ÿæ ⴁØæ ãñ çÁâ·¤æ ×æÂæ´·¤ 1 ãñ ÌÍæ
z(1 2 z )
z (1 1 z)
·¤æð´‡ææ·¤ u ãñ, Ìæð
(1)
1 1 cos
u
2
(1)
1 1 cos
u
2
(2)
1 2 sin
u
2
(2)
1 2 sin
u
2
(3)
22 sin2
u
2
(3)
22 sin2
u
2
(4)
2 cos 2
u
2
(4)
2 cos 2
u
2
If the roots of the equation
3.
1
1
1
1
5 are equal in magnitude
x1p x1q r
and opposite in sign, then the product of
ØçÎ â×è·¤ÚU‡æ
1
1
1
1
5
x1p x1q r
·ð¤ ×êÜ ÂçÚU×æ‡æ ×ð´ â×æÙ ãñ´ ÌÍæ
çßÂÚUèÌ ç¿‹ãæð´ ·ð¤ ãñ´, Ìæð ×êÜæð´ ·¤æ »é‡æÙÈ¤Ü ãñ Ñ
roots is :
(1)
(p21q2)
(1)
(p21q2)
(2)
1 2
(p 1q 2 )
2
(2)
1 2
(p 1q 2 )
2
(3)
2
1 2
(p 1q 2 )
2
(3)
2
1 2
(p 1q 2 )
2
(4)
2
1 2
(p 2q 2 )
2
(4)
2
1 2
(p 2q 2 )
2
K/Page 2
SPACE FOR ROUGH WORK /
·¤æ ßæSÌçß·¤ Öæ» ãñ Ñ
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
4.
5.
1 k
If Sk = 
 , keN, where N is the set of
0 1
4.
1 k
Sk = 
 , keN
0 1
natural numbers, then (S 2)n (S k)21, for
neN, is :
(S2)n (Sk)21 ãñ
(1)
S2 n 1 k 2 1
(1)
S2 n 1 k 2 1
(2)
S2n1 k 2 1
(2)
S2n1 k 2 1
(3)
S2n2 k
(3)
S2n2 k
(4)
S2 n 2 k
(4)
S2 n 2 k
In
a
DABC,
if
1 a b
1 c a = 0,
1 b c
then
5.
sin2A1sin2B1sin2C is :
6.
ØçÎ Âý æ ·ë ¤ Ì â´  Øæ¥æð ´ ·ð ¤ â×é “ æØ
°·¤
DABC
9
4
(1)
9
4
(2)
5
4
(2)
5
4
(3)
2
(3)
2
(4)
3 3
2
(4)
3 3
2
6.
Madhu and Puja, are having six beds
arranged in a row. Further, suppose that
Madhu does not want a bed adjacent to
Puja. Then the number of ways, the beds
×ð ´ , ØçÎ
(1)
264
(1)
264
(2)
480
(2)
480
(3)
600
(3)
600
(4)
384
(4)
384
SPACE FOR ROUGH WORK /
·ð ¤ çÜ°
1 a b
1 c a= 0
1 b c
ãñ , Ìæð
ãñ Ñ
×æÙæ ÀUÑ çßlæçÍüØæð´, çÁÙ×ð´ ×Ïé ÌÍæ ÂêÁæ âç×çÜÌ
ãñ´, ·ð¤ Âæâ °·¤ ´ç€Ì ×ð´ ÃØßçSÍÌ ÀUÑ çÕSÌÚU ãñ´Ð
¥æñÚU ×Ïé, ÂêÁæ ·ð¤ â´Ü‚Ù ßæÜæ çÕSÌÚU Ùãè´ ¿æãÌè, Ìæð
çÁÌÙð ÌÚUè·¤æð´ âð Øã çÕSÌÚU çßlæçÍüØæð´ ·¤æð çΰ Áæ
â·¤Ìð ãñ, ©Ù ·¤è ⴁØæ ãñ Ñ
can be allotted to students is :
K/Page 3
neN
Ñ
sin2A1sin2B1sin2C
(1)
Suppose that six students, including
ãñ , Ìæð
·ð ¤ çÜ°
N
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
7.
Sum of the last 30 coefficients of powers
of x in the binomial expansion of
7.
(11x)59
(11x)59 ·ð¤
çmÂÎ ÂýâæÚU ×ð´ ¥ç‹Ì× 30 ÂÎæð´ ·ð¤ x ·¤è
ƒææÌæ𴠷𤠻é‡ææ´·¤æð´ ·¤æ Øæð» ãñ Ñ
is :
8.
(1)
2 29
(1)
2 29
(2)
2 28
(2)
2 28
(3)
2592229
(3)
2 592229
(4)
2 58
(4)
2 58
If
8.
48
47
46
2
1
1
1
1⋅⋅⋅ 1
1
2.3
3.4
4.5
48.49
49.50
5
9.
10.
ØçÎ
48
47
46
2
1
1
1
1⋅⋅⋅ 1
1
2.3
3.4
4.5
48.49
49.50
51
1
1
1 

1 K  1 1 1 1 ⋅⋅⋅ 1
 , then
2
2
3
50 

5
51
1
1
1 

1 K  1 1 1 1 ⋅⋅⋅ 1

2
2
3
50 

K equals :
K ÕÚUæÕÚU
(1)
21
(1)
21
(2)
2
1
2
(2)
2
(3)
1
(3)
1
(4)
2
(4)
2
log102, log10 (2x21) and log10 (2x13) are
three consecutive terms of an A. P. for :
(1)
no real x
(2)
exactly one real x
(3)
exactly two real x
(4)
more than two real x.
Let f(x)5(x11)221, x/21, then the set
{x :
f(x)5f21(x)}
ãñ Ñ
1
2
9.
·ð¤ ç·¤ÌÙð ×æÙæð´ ·ð¤ çÜ° log102, log10 (2x21)
ÌÍæ log10 (2x13) °·¤ â×æ´ÌÚU ŸæðÉ¸è ·ð¤ ÌèÙ ·ý¤×æ»Ì
ÂÎ ãñ´?
(1) x ·ð¤ ç·¤âè Öè ßæSÌçß·¤ ×æÙ ·ð¤ çÜ° Ùãè´Ð
(2) x ·ð¤ ·ð¤ßÜ °·¤ ßæSÌçß·¤ ×æÙ ·ð¤ çÜ°Ð
(3) x ·ð¤ ·ð¤ßÜ Îæð ßæSÌçß·¤ ×æÙæð´ ·ð¤ çÜ°Ð
(4) x ·ð¤ Îæð âð ¥çÏ·¤ ßæSÌçß·¤ ×æÙæð´ ·ð¤ çÜ°Ð
10.
×æÙæ
:
x
{x :
(1)
is an empty set
(1)
(2)
contains exactly one element
(2)
(3)
contains exactly two elements
(3)
(4)
contains more than two elements.
(4)
K/Page 4
ãñ, Ìæð
SPACE FOR ROUGH WORK /
f(x)5(x11)221, x/21
f(x)5f21(x)}
:
°·¤ çÚU€Ì â×é“æØ ãñÐ
×ð´ ·ð¤ßÜ °·¤ ¥ßØß ãñÐ
×ð´ ·ð¤ßÜ Îæð ¥ßØß ãñ´Ð
×ð´ Îæð âð ¥çÏ·¤ ¥ßØß ãñ´Ð
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
ãñ, Ìæð â×é“æØ
11.
12.
f(x)5?x log e x?, x > 0, is monotonically
decreasing in :
11.
Oæâ×æÙ ãñ, ßã ãñ Ñ
(1)
1

 0 , 
e
(1)
1

 0 , 
e
(2)
1

 e , 1
(2)
1

 e , 1
(3)
(1 , e)
(3)
(1 , e)
(4)
(e ,:)
(4)
(e ,:)
 1
if x > 2

Let f (x) =  x
,
a 1 bx2 if x ≤ 2

12.
×æÙæ
çÁâ ¥´ÌÚUæÜ ×ð´ °·¤çÎcÅU
1


x
f ( x) = 

2
 a 1 bx
½Ì³
x >2
½Ì³
x ≤ 2
ãñ, Ìæð
x522 ÂÚU f(x) ¥ß·¤ÜÙèØ
3
1
and b = 2
4
16
(1)
a=
1
1
and b =
4
16
(2)
a =2
then f(x) is differentiable at x522 for :
13.
f(x)5?x loge x?, x > 0
3
4
±²Ë b = 2
1
16
1
4
±²Ë b =
1
16
1
4
±²Ë b = 2
1
16
3
4
±²Ë b =
ãñ, ØçÎ Ñ
(1)
a=
(2)
a =2
(3)
a=
1
1
and b = 2
4
16
(3)
a=
(4)
a=
3
1
and b =
4
16
(4)
a=
ØçÎ
f(x)5(x2p)(x2q)(x2r)
If f(x) = (x2p)(x2q)(x2r), where
13.
p < q < r, are real numbers, then the
application of Rolle’s theorem on f leads
1
16
ßæSÌçß·¤ ⴁØæ°¡ ãñ´, Ìæð
Âý×ðØ ·ð¤ ¥ÙéÂýØæð» âð ç×ÜÌæ ãñ Ñ
p<q<r
f
to :
(1)
(p1q1r)253(qr1rp1pq)
(1)
(p1q1r)253(qr1rp1pq)
(2)
(p1q1r)2 > 3(qr1rp1pq)
(2)
(p1q1r)2 > 3(qr1rp1pq)
(3)
(p1q1r)2 < 3(qr1rp1pq)
(3)
(p1q1r)2 < 3(qr1rp1pq)
(4)
(p1q1r)2(qr1rp1pq)53
(4)
(p1q1r)2(qr1rp1pq)53
K/Page 5
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
ãñ , Áãæ¡
ÂÚU ÚUæðÜð ·ð¤
14.
Let f(x)5?x2x1?1?x2x2?, where x1 and x2
are distinct real numbers. Then the
14.
number of points at which f(x) is minimum,
×æÙæ f(x)5?x2x1?1?x2x2? ãñ, Áãæ¡ x1 ÌÍæ x2
çßçÖóæ ßæSÌçß·¤ ⴁØæ°¡ ãñ´, Ìæð ©Ù çÕ´Îé¥æð´ ·¤è ⴁØæ
çÁÙ ÂÚU f(x) ·¤æ ×æÙ ‹ØêÙÌ× ãñ, ãñ Ñ
is :
15.
16.
(1)
1
(1)
1
(2)
2
(2)
2
(3)
3
(3)
3
(4)
more than 3
(4)
3
If
12 5 sin 2 x
∫ cos5 x
2
sin x
dx =
f ( x)
5
cos x
1 C , then
15.
âð ¥çÏ·¤
12 5 sin 2 x
ØçÎ ∫ 5
cos x
2
sin x
f(x) is :
f(x) ÕÚUæÕÚU
(1)
2cosec x
(1)
2cosec x
(2)
cosec x
(2)
cosec x
(3)
cot x
(3)
cot x
(4)
2cot x
(4)
2cot x
If f ( x) =
ex
,
1 1 ex
16.
ØçÎ
f (a)
I1 =
∫
x g{ x (12x )} dx and
I1 =
f (2a)
1C
ãñ , Ìæð
ãñ Ñ
f ( x) =
ex
,
1 1 ex
∫
x g{ x (12x )} dx
ÌÍæ
f (a)
g{ x (12x )} dx ,
where g is not an identity function. Then
I2
the value of I is :
1
I2 =
∫
ãñ´,
Áãæ¡ g °·¤ ̈â×·¤ ȤÜÙ Ùãè´ ãñ, Ìæð
ãñ Ñ
1
2
(1)
1
2
(2)
2
(2)
2
(3)
1
(3)
1
(4)
21
(4)
21
SPACE FOR ROUGH WORK /
g{ x (12x )} dx
f (2a)
(1)
K/Page 6
cos 5 x
f (2a)
f (a)
∫
f (x)
f (a)
f (2a)
I2 =
dx =
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
I2
I1
·¤æ ×æÙ
17.
The area bounded by the curves y2512x
17.
and x2512y is divided by the line x53 in
two parts. The area (in square units) of the
ß·ý¤æð´ y2512x ÌÍæ x2512y ·ð¤ Õè¿ çƒæÚðU ÿæð˜æȤÜ
·¤æð, ÚðU¹æ x53 mæÚUæ Îæð Öæ»æð´ ×ð´ Õæ´ÅUæ »Øæ ãñÐ ÕǸð
Öæ» ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´ ×ð´) ãñ Ñ
larger part is :
18.
(1)
147
(2)
45
(3)
137
(4)
245
(1)
147
(2)
45
4
(3)
137
4
(4)
245
4
4
4
4
4
value 1, then value of x when y54 is :
¥ß·¤ÜÙ â×è·¤ÚU ‡ æ ydx2(x1y2)dy50 ÂÚU
çß¿æÚU ·¤èçÁ°Ð ØçÎ y51 ·ð¤ çÜ° x ·¤æ ×æÙ 1 ãñ,
Ìæð y54 ·ð¤ çÜ° x ·¤æ ×æÙ ãñ Ñ
(1)
9
(1)
9
(2)
16
(2)
16
(3)
36
(3)
36
(4)
64
(4)
64
Consider the differential equation,
18.
ydx2(x1y 2)dy50. If for y51, x takes
19.
4
The locus of the mid points of the chords
of the parabola
x254py
19.
having slope m is
ÂÚUßÜØ x254py ·¤è Áèßæ¥æð´, çÁÙ·¤è ÉUæÜ
·ð¤ ×ŠØ çÕ´Îé¥æð´ ·¤æ çÕ´Îé ÂÍ Ñ
m
ãñ,
a:
(1)
line parallel to x-axis at a distance
(1)
°·¤ ÚðU¹æ ãñ Áæð x-¥ÿæ ·ð¤ â×æ´ÌÚU ãñ ÌÍæ ©ââð
?2pm? ·¤è ÎêÚUè ÂÚU ãñÐ
(2)
°·¤ ÚðU¹æ ãñ Áæð y-¥ÿæ ·ð¤ â×æ´ÌÚU ãñ ÌÍæ ©ââð
?2pm? ·¤è ÎêÚUè ÂÚU ãñÐ
(3)
·ð¤ â×æ´ÌÚU ÚðU¹æ ãñ ÌÍæ ©ââð
?2pm? ·¤è ÎêÚUè ÂÚU ãñÐ
(4)
°·¤ ßëžæ ãñ çÁâ·¤æ ·ð´¤Îý ×êÜ çÕ´Îé ãñ ÌÍæ ç˜æ’Øæ
?2pm? ãñÐ
?2pm? from it.
(2)
line parallel to y-axis at a distance
?2pm? from it.
(3)
line parallel to y5mx, m¹0 at a
distance ?2pm? from it.
(4)
circle with centre at origin and
radius ?2pm?.
K/Page 7
SPACE FOR ROUGH WORK /
y5mx, m¹0
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
20.
If the point (p, 5) lies on the line
20.
parallel to the y-axis and passing through
the
intersection
of
the
2(a 2 11)x1by14(a 3 1a)50
(a 2 11)x23by12(a 3 1a)50,
lines
and
then p is
ØçÎ çÕ´Îé (p, 5) °·¤ ÚðU¹æ ÂÚU çSÍÌ ãñ Áæð y-¥ÿæ ·ð¤
â×æ´ Ì ÚU
ãñ
ÌÍæ
Úð U ¹æ¥æð ´
2(a 2 11)x1by14(a 3 1a)50
ÌÍæ
(a211)x23by12(a31a)50 ·ð¤ Âýç̑ÀðUÎ çÕ´Îé
âð ãæð·¤ÚU ÁæÌè ãñ, Ìæð p ·¤æ ×æÙ ãñ Ñ
equal to :
21.
(1)
22a
(1)
22a
(2)
23a
(2)
23a
(3)
2a
(3)
2a
(4)
3a
(4)
3a
If a circle has two of its diameters along
21.
the lines x1y55 and x2y51 and has
area 9p, then the equation of the circle is :
22.
ØçÎ °·¤ ßëžæ ·ð¤ Îæð ÃØæâ ÚðU¹æ¥æð´ x1y55 ÌÍæ
x2y51 ·ð¤ ¥ÙéçÎàæ ãñ´ ÌÍæ çÁâ·¤æ ÿæð˜æÈ¤Ü 9p ãñ,
Ìæð ©â ßëžæ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
(1)
x 21y 226x24y2350
(1)
x 21y 226x24y2350
(2)
x 21y 226x24y2450
(2)
x 21y 226x24y2450
(3)
x 21y 226x24y1350
(3)
x 21y 226x24y1350
(4)
x 21y 226x24y1450
(4)
x 21y 226x24y1450
Let P be a point in the first quadrant lying
on the ellipse
9x2116y25144,
22.
such that
the tangent at P to the ellipse is inclined at
an angle 1358 to the positive direction of
x-axis. Then the coordinates of P are :
×æÙæ P, ÂýÍ× ¿ÌéÍæZàæ ·¤æ °ðâæ çÕ´Îé ãñ Áæð Îèƒæü ßëžæ
9x2116y25144 ÂÚU çSÍÌ ãñ ÌÍæ Îèƒæü ßëžæ ·ð¤
çÕ´Îé P ÂÚU ¹è´¿è´ »§ü SÂàæü ÚðU¹æ x-¥ÿæ ·¤è ÏÙæˆ×·¤
çÎàææ ·ð¤ âæÍ 1358 ·¤æ ·¤æð‡æ ÕÙæÌè ãñ, Ìæð P ·ð¤
çÙÎðüàææ´·¤ ãñ´ Ñ
(1)
 143 1 
, 

4
 3
(1)
 143 1 
, 

4
 3
(2)
8
 ,
9
77 

3 
(2)
8
 ,
9
(3)
3 
 4
,


2
 2
(3)
3 
 4
,


2
 2
(4)
 16 9 
, 

 5 5
(4)
 16 9 
, 

 5 5
K/Page 8
SPACE FOR ROUGH WORK /
77 

3 
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
23.
A variable plane is at a constant distance
23.
p from the origin O and meets the set of
rectangular axes OXi (i = 1, 2, 3) at points
Ai (i = 1, 2, 3) , respectively. If planes are
drawn through A 1 , A 2 , A 3 , which are
parallel to the coordinate planes, then the
°·¤ ¿ÚU â×ÌÜ ×êÜçÕ´Îé O âð °·¤ ¥¿ÚU ÎêÚUè p ÂÚU
ÚUãÌæ ãñ ¥æñÚU â×·¤æðç‡æ·¤ çÙÎðüàææ´·¤æ𴠷𤠰·¤ â×é“æØ
OXi (i = 1, 2, 3) ·¤æð çÕ´Îé¥æð´ Ai (i = 1, 2, 3) ÂÚU
·ý¤×àæÑ Âýç̑ÀðUÎ ·¤ÚUÌæ ãñÐ ØçÎ A1 , A2 , A3 âð
çÙÎðüàææ´·¤ â×ÌÜæð´ ·ð¤ â×æ´ÌÚU â×ÌÜ ¹è´¿ð ÁæÌð ã´ñ, Ìæð
©Ù·ð¤ Âýç̑ÀðUÎ çÕ´Îé ·¤æ çÕ´Îé ÂÍ ãñ Ñ
locus of their point of intersection is :
(1)
(2)
24.
1
1
1 1
=
1
1
x1
x2
x3 p
1
x12
1
(2)
1
1
1
1 3 1 3 = 3
x2
x3 p
(3)
x13
(4)
x12 1 x22 1 x32 = p 2
x22
1
1
1
1
1 1
1
1
=
x1
x2
x3 p
1
= 2
p
1
1
(1)
x32
(3)
x13
(4)
x12 1 x22 1 x32 = p 2
If the lines
y22
x24
z2 l
=
=
and
1
1
3
24.
1
x12
1
ØçÎ Úð¹æ°¡
1
1
x22
1
1
x32
1
1
1
1 3 1 3 = 3
x2
x3 p
y22
x24
z2 l
=
=
1
1
3
y12
x
z
=
=
intersect each other, then
1
2
4
l lies in the interval :
¥´ÌÚUæÜ ×ð´ çSÍÌ ãñ, ßã ãñ Ñ
(1)
(25,23)
(1)
(25,23)
(2)
(13, 15)
(2)
(13, 15)
(3)
(11, 13)
(3)
(11, 13)
(4)
(9, 11)
(4)
(9, 11)
K/Page 9
SPACE FOR ROUGH WORK /
1
= 2
p
y12
x
z
=
=
1
2
4
ÌÍæ
ÂÚUSÂÚU Âýç̑ÀðUÎè ãñ´, Ìæð l çÁâ
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
25.
→ → →
Unit vectors a , b , c
are coplanar.
25.
→
( →a 3 →b )3( →c 3 →d ) 5 1 ∧i 2 1 ∧j 1 1 ∧k
6
→
3
3
→
ÌÍæ
→
(1)
(2)
∧
∧
 ∧
2i 1 j 2 k


3




(3)
∧
∧
 ∧
2i 1 2 j 2 2 k 

±


3




(4)
∧
∧
∧

 22 i 2 2 j 1 k 


3




coin
with
probability
26.
p, 0 < p < 1, of heads is tossed until a head
appears for the first time. If the probability
that the number of tosses required is even
is 2 5 , then p is equal to :
(1)
1
(2)
1
(3)
1
(4)
2
K/Page 10
â×ÌÜèØ ãñ´Ð °·¤ ×æ˜æ·¤
©Ù ÂÚU Ü´ Õ ßÌ ãñ Ð
ØçÎ
→
a
ÌÍæ
→
b
·ð¤ Õè¿ ·¤æ ·¤æð‡æ
3
308
3
ãñ, Ìæð
ãñ
→
c
ãñ/ãñ´ Ñ
∧
∧
 ∧
2
i
2
2
j
1
2
k
±


3




biased
a, b , c
6
then c is/are :
A
d
→ → →
( →a 3 →b )3( →c 3 →d ) 5 1 ∧i 2 1 ∧j 1 1 ∧k
and the angle between a and b is 308,
26.
→
âçÎàæ
A unit vector d is perpendicular to them.
If
×æ˜æ·¤ âçÎàæ
(1)
∧
∧
 ∧
2 i 22 j 1 2 k 

±


3




(2)
∧
∧
 ∧
2i 1 j 2 k


3




(3)
∧
∧
 ∧
2i 1 2 j 2 2 k 

±


3




(4)
∧
∧
∧

 22 i 2 2 j 1 k 


3




°·¤ ¥çÖÙÌ ç‷¤æ, çÁâ×ð ´ ç¿žæ ¥æÙð ·¤è
ÂýæçØ·¤Ìæ p, 0 < p < 1 ãñ, ÌÕ Ì·¤ ©ÀUæÜæ ÁæÌæ ãñ,
ÁÕ Ì·¤ ç·¤ ÂãÜè ÕæÚU 翞æ Ù ¥æ Áæ°Ð ØçÎ ©ÀUæÜð
»° Âý Ø æâæð ´ ·¤è â´  Øæ â× ãæð Ù ð ·¤è Âý æ çØ·¤Ìæ
2
5
ãñ, Ìæð p ÕÚUæÕÚU ãñ Ñ
2
(1)
1
3
(2)
1
4
(3)
1
3
(4)
2
SPACE FOR ROUGH WORK /
2
3
4
3
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
27.
If the mean and the standard deviation of
27.
10 observations x1, x2, ......, x10 are 2 and 3
respectively,
then
the
mean
of
(x111)2, (x211)2, ......, (x1011)2 is equal
to :
28.
ØçÎ 10 Âýðÿæ‡ææð´ x1, x2, ......, x10 ·¤æ ×æŠØ ÌÍæ
×æÙ·¤ çß¿ÜÙ ·ý ¤ ×àæÑ 2 ÌÍæ 3 ãñ , Ìæð
(x111)2, (x211)2, ......, (x1011)2 ·¤æ ×æŠØ
ãñ Ñ
(1)
13.5
(1)
13.5
(2)
14.4
(2)
14.4
(3)
16.0
(3)
16.0
(4)
18.0
(4)
18.0
A vertical pole stands at a point A on the
28.
boundary of a circular park of radius a and
subtends an angle a at another point B on
the boundary. If the chord AB subtends
an angle a at the centre of the park, the
a ç˜æ’Øæ
ßæÜð °·¤ ßëžæèØ Âæ·ü¤ ·¤è ÂçÚUâè×æ ÂÚU çSÍÌ
çÕ´Îé A ÂÚU °·¤ ©ŠßæüÏÚU ¹Õæ ¹Ç¸æ ãñ Áæð ÂçÚUâè×æ
·ð¤ °·¤ ¥‹Ø çÕ´Îé B ÂÚU ·¤æð‡æ a ¥´ÌçÚUÌ ·¤ÚUÌæ ãñÐ
ØçÎ Áèßæ AB ßëžæèØ Âæ·ü¤ ·ð¤ ·ð´¤Îý ÂÚU ·¤æð‡æ a ¥´ÌçÚUÌ
·¤ÚUÌè ãñ, Ìæ𠹐Öð ·¤è ª¡¤¿æ§ü ãñ Ñ
height of the pole is :
(1)
2 a sin
a
tana
2
(1)
2 a sin
a
tana
2
(2)
2 a cos
a
tana
2
(2)
2 a cos
a
tana
2
(3)
2 a sin
a
cot a
2
(3)
2 a sin
a
cot a
2
(4)
2 a cos
a
cot a
2
(4)
2 a cos
a
cot a
2
K/Page 11
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
29.
Let
3p
< u < p and
4
2 cot u1
30.
1
2
sin u
29.
= K 2 cot u ,
×æÙæ
3p
<u<p
4
2 cot u1
1
sin2 u
then K is equal to :
Ìæð K ÕÚUæÕÚU ãñ Ñ
(1)
21
(1)
21
(2)
0
(2)
0
(3)
1
(3)
1
(4)
1
(4)
1
2
Let p and q be any two propositions.
30.
Statement 1 : (p ® q) « q Ú ~p is a
ãñ ÌÍæ
= K 2 cot u
ãñ,
2
×æÙæ p ÌÍæ q ·¤æð§ü Îæð âæŠØ ãñ´Ð
·¤ÍÙ 1 : (p ® q) « q Ú ~p °·¤ ÂéÙL¤ç€Ì ãñÐ
tautology.
fallacy.
·¤ÍÙ 2 : ~(~p Ù q) Ù (p Ú q) « p °·¤ ãðˆßæÖæâ
ãñÐ
(1)
(1)
·¤ÍÙ 1 ÌÍæ ·¤ÍÙ 2 ÎæðÙæð´ âˆØ ãñ´Ð
(2)
·¤ÍÙ 1 ÌÍæ ·¤ÍÙ 2 ÎæðÙæð´ ¥âˆØ ãñ´Ð
(3)
·¤ÍÙ 1 âˆØ ãñ ÌÍæ ·¤ÍÙ 2 ¥âˆØ ãñÐ
(4)
·¤ÍÙ 1 ¥âˆØ ãñ ÌÍæ ·¤ÍÙ 2 âˆØ ãñÐ
Statement 2 : ~(~p Ù q) Ù (p Ú q) « p is a
Both statement 1 and statement 2 are
true.
(2)
Both statement 1 and statement 2 are
false.
(3)
Statement 1 is true and statement 2
is false.
(4)
Statement 1 is false and statement 2
is true.
K/Page 12
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Part II / Öæ» II
Aptitude Test / ¥çÖL¤ç¿
ÂÚUèÿæ‡æ
Directions : (For Q. 31 to 34).
Find the odd figure out in the problem figures given below :
çÙÎðüàæ Ñ (Âý.
Ùè¿ð Îè »§ü ÂýàÙ ¥æ·ë¤çÌØæð´ ×ð´ âð çßá× ¥æ·ë¤çÌ ÕÌæ°¡Ð
31
âð
34
·ð¤ çÜ°)Ð
31.
(1)
(2)
(3)
(4)
32.
(1)
(2)
(3)
(4)
33.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
34.
Directions : (For Q. 35 to 37). The 3 - D problem figure shows the view of an object. Identify, its correct
top view, from amongst the answer figures.
çÙÎðüàæ Ñ (Âý. 35 âð 37 ·ð¤ çÜ°)Ð
3 - D ÂýàÙ
¥æ·ë¤çÌ ×ð´ °·¤ ßSÌé ·¤æð çιæØæ »Øæ ãñÐ §â·¤æ âãè ª¤ÂÚUè ÎëàØ, ©žæÚU
¥æ·ë¤çÌØæð´ ×ð´ âð Âã¿æçÙ°Ð
Problem Figure / ÂýàÙ ¥æ·ë¤çÌ
Answer Figures / ©žæÚU ¥æ·ë¤çÌØæ¡
35.
(1)
K/Page 13
(2)
SPACE FOR ROUGH WORK /
(3)
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
(4)
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
36.
37.
Directions : (For Q. 38 and 39).
The problem figure shows the top view of an object. Identify the
correct elevation, from amongst the answer figures, looking in the
direction of arrow.
çÙÎðüàæ Ñ (Âý. 38 ¥æñÚU 39 ·ð¤ çÜ°)Ð
ÂýàÙ ¥æ·ë¤çÌ ×ð´ ç·¤âè ßSÌé ·¤æ ª¤ÂÚUè ÎëàØ çιæØæ »Øæ ãñÐ ÌèÚU ·¤è çÎàææ ×ð´
Îð¹Ìð ãé° ©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð §â·¤æ âãè â×é¹ ÎëàØ Âã¿æçÙ°Ð
Problem Figure /
Answer Figures /
ÂýàÙ ¥æ·ë¤çÌ
©žæÚU ¥æ·ë¤çÌØæ¡
38.
(1)
(2)
(3)
(4)
(2)
(3)
(4)
39.
(1)
K/Page 14
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Directions : (For Q. 40 and 41).
çÙÎðüàæ Ñ (Âý.
40
How many minimum number of straight lines are required to draw
the problem figure ?
¥æñÚU 41 ·ð¤ çÜ°)Ð
Problem Figure /
Ùè¿ð Îè »§ü ÂýàÙ ¥æ·ë¤çÌ ·¤æð ÕÙæÙð ·ð¤ çÜ° ·¤× âð ·¤×, ç·¤ÌÙè âèÏè ÚðU¹æ¥æð´
·¤è ¥æßàØ·¤Ìæ ãñ?
ÂýàÙ ¥æ·ë¤çÌ
40.
(1)
11
(2)
10
(3)
9
(4)
12
(1)
18
(2)
19
(3)
20
(4)
21
41.
Directions : (For Q. 42 to 45).
çÙÎðüàæ Ñ (Âý.
42
âð
Problem Figure /
45
·ð¤ çÜ°)Ð
ÂýàÙ ¥æ·ë¤çÌ
The 3 - D problem figure shows a view of an object. Identify the
correct front view, from amongst the answer figures, looking in the
direction of arrow.
3 - D ÂýàÙ ¥æ·ë¤çÌ ×ð´ °·¤ ßSÌé ·ð¤ °·¤ ÎëàØ ·¤æð çιæØæ »Øæ ãñÐ ÌèÚU ·¤è çÎàææ
×ð´ Îð¹Ìð ãé° , §â·ð¤ âãè â×é¹ ÎëàØ ·¤æ𠩞æÚU ¥æ·ë¤çÌØæð´ ×ð´ âð Âã¿æçÙ°Ð
Answer Figures / ©žæÚU ¥æ·ë¤çÌØæ¡
42.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
43.
K/Page 15
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
44.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
45.
Directions : (For Q. 46 and 47).
How many total number of triangles are there in the problem figure
given below ?
çÙÎðüàæ Ñ (Âý. 46 ¥æñÚU
Ùè¿ð Îè »§ü ÂýàÙ ¥æ·ë¤çÌ ×ð´ ç˜æÖéÁæð´ ·¤è ·é¤Ü ⴁØæ ç·¤ÌÙè ãñ?
47
·ð¤ çÜ°)Ð
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
46.
(1)
11
(2)
12
(3)
10
(4)
9
(1)
12
(2)
13
(3)
11
(4)
14
47.
K/Page 16
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Directions : (For Q. 48 to 50).
çÙÎðüàæ Ñ (Âý.
48
âð
Problem Figure /
50
·ð¤ çÜ°)Ð
ÂýàÙ ¥æ·ë¤çÌ
Which one of the answer figures is the correct mirror image of the
problem figure with respect to X - X ?
©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð ·¤æñÙâè ¥æ·ë¤çÌ Îè »§ü ÂýàÙ ¥æ·ë¤çÌ ·¤æ X - X âð â´Õ´çÏÌ
âãè ÎÂü‡æ ÂýçÌçÕÕ ãñ?
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
48.
(1)
(2)
(3)
(4)
49.
(1)
(2)
(3)
(4)
50.
(1)
Directions : (For Q. 51 and 52).
çÙÎðüàæ Ñ (Âý.
51
¥æñÚU 52 ·ð¤ çÜ°)Ð
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
(2)
(3)
(4)
The problem figure shows the elevation of an object. Identify the
correct top view from amongst the answer figures.
ÂýàÙ ¥æ·ë¤çÌ ×ð´ ç·¤âè ßSÌé ·¤æ â×é¹ ÎëàØ çιæØæ »Øæ ãñÐ ©žæÚU ¥æ·ë¤çÌØæð´ ×ð´
âð §â·¤æ âãè ª¤ÂÚUè ÎëàØ Âã¿æçÙ°Ð
Answer Figures / ©žæÚU ¥æ·ë¤çÌØæ¡
51.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
52.
K/Page 17
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Directions : (For Q. 53).
Which one of the answer figures will complete the sequence of the three
problem figures ?
çÙÎðüàæ Ñ (Âý.
©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð ·¤æñÙ âè ¥æ·ë¤çÌ ·¤æð ÌèÙ ÂýàÙ ¥æ·ë¤çÌØæð´ ×ð´ Ü»æÙð âð ¥Ùé·ý¤×
(sequence) ÂêÚUæ ãæð Áæ°»æ?
53
·ð¤ çÜ°)Ð
Problem Figures /
ÂýàÙ ¥æ·ë¤çÌØæ¡
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
53.
(1)
(2)
(3)
(4)
Directions : (For Q. 54 and 55).
Which one of the answer figures, shows the correct view of the 3 - D
problem figure, after the problem figure is opened up ?
çÙÎðüàæ Ñ (Âý. 54 ¥æñÚU 55 ·ð¤ çÜ°)Ð
3 - D ÂýàÙ
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
¥æ·ë¤çÌ ·¤æð ¹æðÜÙð ÂÚU, ©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð âãè ÎëàØ ·¤æñÙ âæ ãñ?
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
54.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
55.
K/Page 18
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Directions : (For Q. 56 to 61).
Find out the total number of surfaces of the object, given below in the
problem figure.
çÙÎðüàæ Ñ (Âý.
ÂýàÙ ¥æ·ë¤çÌ ×ð´ çِÙæ´ç·¤Ì ßSÌé ×ð´ âÌãæð´ ·¤è ·é¤Ü ⴁØæ ™ææÌ ·¤èçÁ°Ð
56
âð
61
·ð¤ çÜ°)Ð
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
56.
(1)
14
(2)
15
(3)
17
(4)
16
(1)
15
(2)
16
(3)
14
(4)
13
(1)
15
(2)
12
(3)
13
(4)
14
(1)
11
(2)
12
(3)
14
(4)
15
57.
58.
59.
K/Page 19
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
60.
(1)
15
(2)
16
(3)
14
(4)
13
(1)
13
(2)
12
(3)
11
(4)
10
61.
Directions : (For Q. 62 and 63).
One of the following answer figures is hidden in the problem figure,
in the same size and direction. Select, which one is correct ?
çÙÎðüàæ Ñ (Âý. 62 ¥æñÚU 63 ·ð¤ çÜ°)Ð
Ùè¿ð Îè »§ü ©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð °·¤ ¥æ·ë¤çÌ ×æ ¥æñÚU çÎàææ ×ð´ â×æÙ M¤Â âð
ÂýàÙ ¥æ·ë¤çÌ ×ð´ çÀUÂè ãñÐ ·¤æñÙ âè âãè ãñ, ¿éçÙ°Ð
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
62.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
63.
K/Page 20
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Directions : (For Q. 64 and 65).
The problem figure shows the top view of objects. Looking in the
direction of arrow, identify the correct elevation, from amongst the
answer figures.
çÙÎðüàæ Ñ (Âý. 64 ¥æñÚU 65 ·ð¤ çÜ°)Ð
ÂýàÙ ¥æ·ë¤çÌ ×ð´ ßSÌé¥æð´ ·¤æ ª¤ÂÚUè ÎëàØ çιæØæ »Øæ ãñÐ ÌèÚU ·¤è çÎàææ ×ð´ Îð¹Ìð
ãé° ©žæÚU ¥æ·ë¤çÌØæð´ ×ð´ âð §â·¤æ âãè â×é¹ ÎëàØ Âã¿æçÙ°Ð
Problem Figure /
ÂýàÙ ¥æ·ë¤çÌ
Answer Figures /
©žæÚU ¥æ·ë¤çÌØæ¡
64.
(1)
(2)
(3)
(4)
65.
K/Page 21
(1)
(2)
(3)
(4)
SPACE FOR ROUGH WORK /
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
66.
§Ù×ð´ âð ·¤æñÙ-âæ ßæSÌé·¤æÚU Ùãè´ ãñ?
Who among the following is not an
architect ?
(1) Zaha Hadid
(2) M.F. Hussain
(3) Hafiz Contractor
(4) Raj Rewal
66.
67.
Fatehpur Sikri was built by :
(1) Jahangir
(2) Akbar
(3) Humayun
(4) Shah Jahan
67.
ȤÌðãÂéÚU âè·¤ÚUè ·¤æð ÕÙæØæ Íæ Ñ
(1) Áãæ´»èÚU Ùð
(2) ¥·¤ÕÚU Ùð
(3) ãé×æØé´ Ùð
(4) àææãÁãæ¡ Ùð
68.
Which one of the following is a sound
reflecting material ?
(1) Thermocol
(2) Jute cloth
(3) Glass
(4) Fabric
68.
§Ù×ð´ âð ·¤æñÙ-âæ, ŠßçÙ ÂÚUæßÌèü ÂÎæÍü ãñ?
69.
Buckingham Palace is located in :
(1) Paris
(2) London
(3) Geneva
(4) Singapore
69.
Õç·´¤ƒæ× ÂñÜðâ ·¤ãæ¡ çSÍÌ ãñ?
(1) ÂñçÚUâ ×ð´
(2) Ü´ÎÙ ×ð´
(3) ÁðÙðßæ ×ð´
(4) çâ´»æÂéÚU ×ð´
70.
What secondary colour is obtained by
mixing blue and red colours ?
(1) Pink
(2) Purple
(3) Orange
(4) Brown
70.
ÙèÜð ¥æñÚU ÜæÜ Ú´U»æð´ ·¤æð ¥æÂâ ×ð´ ç×ÜæÙð âð ·¤æñÙâæ
»æñ‡æ (secondary) Ú´U» ç×Üð»æ?
(1) »éÜæÕè
(2) Õñ´»Ùè
(3) ÙæÚ´U»è
(4) ÖêÚUæ
71.
Lotus Temple in Delhi was built by :
(1) Jews
(2) Jains
(3) Bahais
(4) Muslims
71.
çÎËÜè ·¤æ ÜæðÅUâ ×ç‹ÎÚU ç·¤âÙð ÕÙæØæ Íæ?
(1) ØãêçÎØæð´ Ùð
(2) ÁñçÙØæð´ Ùð
(3) Õæã§Øæð´ Ùð
(4) ×éâçÜ×æð´ Ùð
K/Page 22
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
SPACE FOR ROUGH WORK /
$Áæãæ ãÎèÎ
°×.°È¤. ãéâñÙ
ãȤè$Á ·¤æò‹ÅþñU€ÅUÚU
ÚUæÁ ÚðUßæÜ
Í×æðü·¤æðÜ
ÂÅUâÙ ·¤æ ·¤ÂǸæ
·¤æ¡¿
·¤ÂǸæ
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
72.
73.
74.
75.
76.
Which one of the following material
cannot be used in its original form for
construction of walls ?
(1)
Fly ash
(2)
Basalt
(3)
Laterite
(4)
Granite
Green architecture is promoted these days
because :
(1)
It costs less initially
(2)
It is environment friendly
(3)
It lasts longer
(4)
Green is a good colour
What is texture ?
(1)
A solid colour
(2)
A type of shape
(3)
Lines drawn in one colour
(4)
The way a surface looks and feels
Which one of the following is not an
earthquake resistant structure ?
72.
ÎèßæÚUæð´ ·¤æð ÕÙæÙð ·ð¤ çÜ°, çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ
ÂÎæÍü ¥ÂÙè ×êÜ ¥æ·¤æÚU ×ð´ §SÌð×æÜ Ùãè´ ç·¤Øæ Áæ
â·¤Ìæ?
(1) Üæ§ °ðàæ
(2) ÕðâæËÅU
(3) ×¹ÚUÜæ (ÜñÅðUÚUæ§ÅU)
(4) »ýðÙæ§ÅU
73.
§Ù çÎÙæð´ ãçÚUÌ ßæSÌé·¤Üæ ·¤æð ÂýæðˆâæãÙ çÎØæ ÁæÌæ ãñ
€Øæð´ç·¤ Ñ
(1) §â×ð´ ¥æÚUÖ ×ð´ ·¤× ¹¿ü ãæðÌæ ãñ
(2) Øã ÂØæüßÚU‡æ ·ð¤ ¥Ùé·ê¤Ü ãñ
(3) Øã ÎðÚU Ì·¤ ¿ÜÌæ ãñ
(4) ãÚUæ °·¤ ¥‘ÀUæ Ú´U» ãñ
74.
â´ÃØêçÌ €Øæ ãñ?
(1) °·¤ ÆUæðâ Ú´U»
(2) °·¤ ÌÚUã ·¤æ ¥æ·¤æÚU
(3) °·¤ Ú´U» ×ð´ Ü»æ§ü »§ü ÚðU¹æ°¡
(4) çÁâ ÌÚUã °·¤ âÌã çιÌè ¥æñÚU ×ãâêâ ãæðÌè
ãñ
75.
çِÙæ´ç·¤Ì ÉUæ¡¿æð´ ×ð´ âð ·¤æñÙ-âæ Öê·´¤Â çßÚUæðÏ·¤ ãñ?
(1)
RCC framed structure
(1)
(2)
Load bearing brick walls building
(2)
(3)
Steel framed building
(3)
(4)
Timber framed building
(4)
Which one of the following is an odd
match ?
76.
çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ â×é“æØ ×ðÜ Ùãè´ ¹æÌæ?
(1)
Deforestation - Climate change
(1)
(2)
Ozone layer - UV rays
(2)
(3)
Shrinking Polar Caps - Earthquake
(3)
(4)
Tsunami - Oceanic Earthquake
(4)
K/Page 23
SPACE FOR ROUGH WORK /
¥æÚU.âè.âè. Èýð¤× ·¤æ ÉUæ¡¿æ
ÖæÚU ÚUæð·¤Ùð ßæÜè §ZÅUæð´ ·¤è ÎèßæÚU ·¤è §×æÚUÌ
SÅUèÜ ·ð¤ Èýð¤× âð ÕÙè §×æÚUÌ
Ü·¤Ç¸è ·ð¤ Èýð¤× âð ÕÙè §×æÚUÌ
ßÙ-¥ÂÚUæð‡æ - ÁÜßæØé ÂçÚUßÌüÙ
¥æð$ÁæðÙ ·¤è ÂÚUÌ - Øê.ßè. ç·¤ÚU‡æð´
ÏýéßèØ ÅUæðÂè ·¤è çâ·é¤Ç¸Ù - Öê·´¤Â
âéÙæ×è - ×ãæâæ»ÚUèØ Öê·´¤Â
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
77.
78.
79.
80.
Why do large industrial buildings have
high located glazing on the North side ?
77.
ÕÇ¸è ¥æñlæðç»·¤ §×æÚUÌæð´ ×ð´ àæèàæð ·¤æ𠩞æÚU çÎàææ ×ð´ ©“æ
SÌÚU ÂÚU €Øæð´ Ü»æØæ ÁæÌæ ãñ?
(1) ÂêÚUæ çÎÙ âêØü ·¤è Ìð$Á ÚUæðàæÙè ÂæÙð ·ð¤ çÜ°
(1)
To get bright sunlight throughout the
day.
(2)
To stop the workers from looking
outside.
(2)
(3)
To get uniform shadow - less light
through the day.
(3)
(4)
Because the sun stays on the North
side throughout the day.
(4)
Which one of the following is an odd
match ?
78.
§Ù×ð´ âð ·¤æñÙ-âæ â×é“æØ ×ðÜ Ùãè´ ¹æÌæ?
(1)
Hot and Humid - Chennai
(1)
(2)
Cold and Dry - Ladakh
(2)
(3)
Temperate - Shimla
(3)
(4)
Hot and Dry - Jaisalmer
(4)
Which one of the following is not a
matching set ?
79.
Sundarbans - Mangroves
(1)
(2)
Varanasi - Ghats
(2)
(3)
Jaipur - Canals
(3)
(4)
Udaipur - Lakes
(4)
80.
San Francisco - Golden Gate Bridge
(1)
(2)
Washington - White House
(2)
(3)
Egypt - Mississippi River
(3)
(4)
England - 10 Downing Street
(4)
K/Page 24
SPACE FOR ROUGH WORK /
âé‹ÎÚUÕÙ - ×ñÙ»ýæðß
ßæÚUæ‡æâè - ƒææÅU
ÁØÂéÚU - ÙãÚð´U
©ÎØÂéÚU - ÛæèÜð´
çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ-âæ â×é“æØ ×ðÜ Ùãè´ ¹æÌæ?
(1)
-o0o-
»ÚU× ¥æñÚU Ù× - ¿ðóæ§ü
Æ´UÇUæ ¥æñÚU âê¹æ - ÜÎæ$¹
àæèÌæðc‡æ (Temperate) - çàæ×Üæ
»ÚU× ¥æñÚU âê¹æ - ÁñâÜ×ðÚU
çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ-âæ â×é“æØ ×ðÜ Ùãè´ ¹æÌæ?
(1)
Which one of the following is not a
matching set ?
·¤æ× ·¤ÚUÙð ßæÜæð´ ·¤æð ÕæãÚU Îð¹Ùð âð ÚUæð·¤Ùð ·ð¤
çÜ°
âæÚUæ çÎÙ °·¤ â×æÙ çÕÙ ÀUæØæ ·ð¤ ÚUæðàæÙè ÂæÙð
·ð¤ çÜ°
€Øæð´ç·¤ âêØü ©žæÚU çÎàææ ×ð´ âæÚUæ çÎÙ ÚUãÌæ ãñ
âðÙ Èý¤æ´çââ·¤æð - »æðËÇUÙ »ðÅU çÕýÁ
ßæçàæ´»ÅUÙ - Ããæ§ÅU ã檤â
ç×d - ç×âèçâÂè ÎçÚUØæ
§´»Üñ´ÇU - 10 ÇUª¤çÙ´» SÅþUèÅU
-o0o-
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Space For Rough Work / ÚȤ ·¤æØü ·ð¤ çÜ° Á»ã
K/Page 25
Space For Rough Work / ÚȤ ·¤æØü ·ð¤ çÜ° Á»ã
K/Page 26
Space For Rough Work / ÚȤ ·¤æØü ·ð¤ çÜ° Á»ã
K/Page 27
Read the following instructions carefully :
çِÙçÜç¹Ì çÙÎðüàæ ŠØæÙ âð Âɸð´ Ñ
1. Part I has 30 objective type questions of Mathematics
consisting of FOUR (4) marks each for each correct
response. Part II (Aptitude Test) has 50 objective type
questions consisting of FOUR (4) marks for each
correct response. Part III consists of 2 questions
carrying 70 marks which are to be attempted on a
separate Drawing Sheet which is also placed inside
this Test Booklet. Marks allotted to each question are
written against each question. For each incorrect
response in Part I and Part II, one–fourth (¼) of the
total marks allotted to the question would be deducted
from the total score. No deduction from the total score,
however, will be made if no response is indicated for an
item in the Answer Sheet.
2. Handle the Test Booklet, Answer Sheet and Drawing
Sheet with care, as under no circumstances (except for
discrepancy in Test Booklet Code and Answer Sheet
Code), another set will be provided.
3. The candidates are not allowed to do any rough work
or writing work on the Answer Sheet. All calculations/
writing work are to be done on the space provided for
this purpose in the Test Booklet itself, marked ‘Space
for Rough Work’. This space is given at the bottom of
each page and in 3 pages (pages 25 - 27)at the end of the
booklet.
4. Each candidate must show on demand his/her Admit
Card to the Invigilator.
5. No candidate, without special permission of the
Superintendent or Invigilator, should leave his/her
seat.
6. On completion of the test, the candidates should not
leave the examination hall without handing over their
Answer Sheet of Mathematics and Aptitude Test-Part I
& II and Drawing Sheet of Aptitude Test-Part III to the
Invigilator on duty and sign the Attendance Sheet at
the time of handing over the same. Cases where a
candidate has not signed the Attendance Sheet the
second time will be deemed not have handed over
these documents and dealt with as an unfair means
case. The candidates are also required to put their left
hand THUMB impression in the space provided in the
Attendance Sheet. However, the candidates are
allowed to take away with them the Test Booklet of
Mathematics and Aptitude Test - Part I & II.
7. Use of Electronic/Manual Calculator or drawing
instruments (such as scale, compass etc.) is not allowed.
8. The candidates are governed by all Rules and
Regulations of the JAB/Board with regard to their
conduct in the Examination Hall. All cases of unfair
means will be dealt with as per Rules and Regulations
of the JAB/Board.
9. No part of the Test Booklet, Answer Sheet and Drawing
Sheet shall be detached/folded or defaced under any
circumstances.
10. The candidates will write the Test Booklet Number as
given in the Test Booklet, Answer Sheet and Drawing
Sheet in the Attendance Sheet also.
11. Candidates are not allowed to carry any textual
material, printed or written, bits of papers, pager,
mobile phone, electronic device or any other material
except the Admit Card inside the examination
hall/room.
1.
K/Page 28
ÂéçSÌ·¤æ ·ð¤ Öæ» I ×ð´ »ç‡æÌ ·ð¤ 30 ßSÌéçÙD ÂýàÙ ãñ´ çÁâ×ð´ ÂýˆØð·¤
ÂýàÙ ·ð¤ âãè ©žæÚU ·ð¤ çÜ° ¿æÚU (4) ¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð
Öæ» II (¥çÖL¤ç¿ ÂÚUèÿæ‡æ) ×ð´ 50 ßSÌéçÙD ÂýàÙ ãñ´ çÁÙ×ð´ ÂýˆØð·¤
âãè ©žæÚU ·ð¤ çÜ° ¿æÚU (4) ¥´·¤ ãñ´Ð ÂéçSÌ·¤æ ·ð¤ Öæ» III ×ð´ 2 ÂýàÙ
ãñ´ çÁÙ·ð¤ çÜ° 70 ¥´·¤ çÙÏæüçÚUÌ ãñ´Ð Øã ÂýàÙ §âè ÂÚUèÿææ ÂéçSÌ·¤æ
·ð¤ ¥‹ÎÚU ÚU¹è ÇþU槴» àæèÅU ÂÚU ·¤ÚUÙð ãñ´Ð ÂýˆØð·¤ ÂýàÙ ãðÌé çÙÏæüçÚUÌ
¥´·¤ ÂýàÙ ·ð¤ â×é¹ ¥´ç·¤Ì ãñ´Ð Öæ» I ¥æñÚU Öæ» II ×ð´ ÂýˆØð·¤
»ÜÌ ©žæÚU ·ð¤ çÜ° ©â ÂýàÙ ·ð¤ çÜ° çÙÏæüçÚUÌ ·é¤Ü ¥´·¤æð´ ×ð´ âð
°·¤-¿æñÍæ§ü (¼) ¥´·¤ ·é¤Ü Øæð» ×ð´ âð ·¤æÅU çÜ° Áæ°¡»ðÐ ØçÎ
©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ·¤æð§ü ©žæÚU Ùãè´ çÎØæ »Øæ ãñ, Ìæð ·é¤Ü
Øæð» ×ð´ âð ·¤æð§ü ¥´·¤ Ùãè´ ·¤æÅðU Áæ°¡»ðÐ
2. ÂÚUèÿææ ÂéçSÌ·¤æ, ©žæÚU Â˜æ °ß´ ÇþU槴» àæèÅU ·¤æ ŠØæÙÂêßü·¤ ÂýØæð»
·¤Úð´U, €Øæð´ç·¤ ç·¤âè Öè ÂçÚUçSÍçÌ ×ð´ (·ð¤ßÜ ÂÚUèÿææ ÂéçSÌ·¤æ °ß´
©žæÚU Â˜æ ·ð¤ ·¤æðÇU ×ð´ çÖóæÌæ ·¤è çSÍçÌ ·¤æð ÀUæðǸ·¤ÚU) ÎêâÚUè ÂÚUèÿææ
ÂéçSÌ·¤æ ©ÂÜŽÏ Ùãè´ ·¤ÚUæØè Áæ°»èÐ
3. ÂÚUèÿææçÍüØæð́ ·¤æ𠩞æÚU ˜æ ÂÚU ·¤æð§ü Öè ÚUȤ ·¤æØü Øæ çܹæ§ü ·¤æ ·¤æ×
·¤ÚUÙð ·¤è ¥Ùé×çÌ Ùãè´ ãñÐ âÖè »‡æÙæ °ß´ çܹæ§ü ·¤æ ·¤æ×, ÂÚUèÿææ
ÂéçSÌ·¤æ ×ð́ çÙÏæüçÚUÌ Á»ã Áæð ç·¤ ÒÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãÓ mæÚUæ
Ùæ×æ´ç·¤Ì ãñ, ÂÚU ãè ç·¤Øæ ÁæØð»æÐ Øã Á»ã ÂýˆØð·¤ ÂëcÆU ÂÚU Ùè¿ð ·¤è
¥æðÚU ÌÍæ ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð́ 3 ÂëDæð́ (ÂëD 25 - 27) ÂÚU Îè »§ü ãñÐ
4. ÂêÀðU ÁæÙð ÂÚU ÂýˆØð·¤ ÂÚUèÿææÍèü çÙÚUèÿæ·¤ ·¤æð ¥ÂÙæ Âýßðàæ ·¤æÇüU
çι氡Ð
5. ¥Ïèÿæ·¤ Øæ çÙÚUèÿæ·¤ ·¤è çßàæðá ¥Ùé×çÌ ·ð¤ çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü
¥ÂÙæ SÍæÙ Ù ÀUæðǸð´Ð
6. ÂÚU è ÿææ â×æ# ãæð Ù ð ÂÚU , ÂÚU è ÿææÍèü çÙÚU è ÿæ·¤æð ´ ·¤æð ¥ÂÙð
»ç‡æÌ - Öæ» I °ß´ ¥çÖL¤ç¿ ÂÚUèÿæ‡æ - Öæ» II ·¤æ ©žæÚU Â˜æ °ß´
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