PAPER-4 AZwH«$‘m§H$ /
Roll No.
Aptitude Test for Architecture PART-A : Mathematics & Aesthetic Sensitivity PART-B : Drawing Aptitude
àíZnwpñVH$m H$moS>
àíZnwpñVH$m H«$‘m§H$
DC
Question Booklet Sr. No.
Q. Booklet Code
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PAPER-4 AZwH«$‘m§H$ /
32
Aptitude Test for Architecture PART-A : Mathematics & Aesthetic Sensitivity PART-B : Drawing Aptitude
g‘¶ 2.30 K§Q>o Time 2.30 Hours
àíZnwpñVH$m H«$‘m§H$/
A§H$ / Marks 500
nwpñVH$m ‘| àíZm| H$s g§»¶m No. of Questions in Booklet
100 Questions & Drawing Sheet
Question Booklet Sr. No.
Roll No.
H$j {ZarjH$ Ho$ hñVmja
/Signature of the Invigilator àíZnwpñVH$m H$moS>
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narjmWu H$m Zm‘/
Name of Candidate :
narjm{W©¶m| Ho$ {bE {ZX}e /INSTRUCTIONS TO CANDIDATE
Aä¶{W©¶m| hoVw Amdí¶H$ {ZX}e :
1. Amo.E‘.Ama. CÎma n{ÌH$m ‘| Jmobm| VWm g^r à{dpîQ>¶m| H$mo ^aZo Ho$ {bE Ho$db Zrbo ¶m H$mbo ~mb ßdmB§Q> noZ H$m hr Cn¶moJ H$a|& 2. SECURITY SEAL ImobZo Ho$ nhbo Aä¶Wu AnZm Zm‘, AZwH«$‘m§H$ (A§H$m| ‘|) Amo.E‘.Ama. CÎma-erQ> H$m H«$‘m§H$ Bg àíZ-nwpñVH$m Ho$ D$na {X¶o J¶o ñWmZ na {bI|& ¶{X do Bg {ZX}e H$m nmbZ Zht H$a|Jo Vmo CZH$s CÎma-erQ> H$m ‘yë¶m§H$Z Zhr hmo gHo$Jm VWm Eogo Aä¶Wu A¶mo½¶ Kmo{fV hmo Om¶|Jo& 3. à˶oH$ àíZ Mma A§H$m| H$m h¡& {Og àíZ H$m CÎma Zht {X¶m J¶m h¡, Cg na H$moB© A§H$ Zht {X¶m Om¶oJm& JbV CÎma na A§H$ Zht H$mQ>m OmEJm& 4. g^r ~hþ{dH$ënr¶ àíZm| ‘| EH$ hr {dH$ën ghr h¡, {Ogna A§H$ Xo¶ hmoJm& 5. JUH$, bm°J Q>o{~b, ‘mo~mBb ’$moZ, Bbo³Q´>m°{ZH$ CnH$aU VWm ñbmBS> ê$b Am{X H$m à¶moJ d{O©V h¡& 6. Aä¶Wu H$mo narjm H$j N>moS>Zo H$s AZw‘{V narjm Ad{Y H$s g‘mpßV na hr Xr Om¶oJr& 7. ¶{X {H$gr Aä¶Wu Ho$ nmg nwñVH|$ ¶m Aݶ {b{IV ¶m N>nr gm‘J«r, {Oggo do ghm¶Vm bo gH$Vo/gH$Vr h¢, nm¶r Om¶oJr, Vmo Cgo A¶mo½¶ Kmo{fV H$a {X¶m Om gH$Vm h¡& Bgr àH$ma, ¶{X H$moB© Aä¶Wu {H$gr ^r àH$ma H$s ghm¶Vm {H$gr ^r ómoV go XoVm ¶m boVm (¶m XoZo H$m ¶m boZo H$m à¶mg H$aVm) hþAm nm¶m Om¶oJm, Vmo Cgo ^r A¶mo½¶ Kmo{fV {H$¶m Om gH$Vm h¡& 8. {H$gr ^r ^«‘ H$s Xem ‘| àíZ-nwpñVH$m Ho$ A§J«oOr A§e H$mo hr ghr d A§{V‘ ‘mZm Om¶oJm& 9. a’$ H$m¶© Ho$ {bE EH$ Imbr sheet g§½b½Z h¡& 10. OMR sheet Bg Paper Ho$ ^rVa h¡ VWm Bgo ~mha {ZH$mbm Om gH$Vm h¡ naÝVw Paper H$s grb Ho$db nona ewé hmoZo Ho$ g‘¶ na hr Imobm Om¶oJm&
Q. Booklet Code
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PAPER-4
Aptitude Test for Architecture Mathematics & Aesthetic Sensitivity – Part A : Q. 1 to 100 Drawing Aptitude – Part B : Q. 1 & 2
PART-A / ^mJ-A MATHEMATICS & AESTHETICS SENSITIVITY /
J{UV Am¡a EñWo{Q>H$ g|{gQ>r{dQ>r
001.
1 0 1 0 H & I= > H , then If A = > -1 7 0 1
001.
¶{X A = >
find K so that A2 = 8A + KI.
‘mZ ¶{X A2 = 8A + KI.
(A) – 3
(A) – 3
(B) 9
(B) 9
(C) – 5
(C) – 5
(D) – 7
(D) – 7
4 - DC ]
[ 2 ]
1 0 1 0 H& I= > H, -1 7 0 1
Vmo K H$m
[ Contd...
002.
R V S 2 -1W If S 1 0 W A = W S S- 3 4 W T X will be A? 3 2 (A) A = > 7 -4
R V S- 1 - 8 - 10 W S 1 - 2 - 5 W what W S S 9 22 15 W T X -7 2
H
1 - 2 -5 H (B) A = > 3 4 0 (C) None of these 7 -4 0 H (D) A = > -2 6 -2
R V S 2 -1W S 1 0 WA = W S S- 3 4 W T X
002.
¶{X
A H$m
(A) A = >
‘mZ-
R V S- 1 - 8 - 10 W S 1 - 2 - 5 W Vmo W S S 9 22 15 W T X
3 2 -7 H 7 -4 2
1 - 2 -5 H (B) A = > 3 4 0 (C) BZ‘| go H$moB© Zht 7 -4 0 H (D) A = > -2 6 -2
What will be the maximum value of the function f (x) = – (x – 1)2 + 2 on R? (A) 3 (B) 1 (C) 2 (D) 4
003.
’$bZ f (x) = – (x – 1)2 + 2 on R H$m A{YH$V‘ ‘mZ ³¶m hmoJm -
(A) 3 (C) 2
004.
Find the maximum & minimum value of the function f (x) = |sin4x + 3| on R?
004.
(A) Max – 4 Min – 2
(B) Max – 5 Min – 2
(C) Max – 3 Min – 1
(D) None of these
’$bZ f (x) = |sin4x + 3| on R H$m A{YH$V‘ ‘mZ ³¶m hmoJm? (A) A{YH$V‘ – 4 ݶyZV‘ – 2 (B) A{YH$V‘ – 5 ݶyZV‘ – 2 (C) A{YH$V‘ – 3 ݶyZV‘ – 1 (D) BZ‘| go H$moB© Zht
003.
005.
What will be the point of local maximum and local maximum value of the function f (x) = x 1 - x , x >0 1 (A) Point of local max - x = Local 2 2 2 max value 3 2 (B) Point of local max - x = Local 3 2 max value 3 3 3 (C) Point of local max - x = Local 2 3 2 max value 2 1 (D) Point of local max - x = Local 4 4 3 max value 3 4 - DC ]
005.
(B) 1 (D) 4
’$bZ f (x) = x 1 - x , x >0 Ho$ {bE A{YH$V‘ ñWmZr` d A{YH$V‘ ñWmZr` ‘mZ hmoJm-
1 (A) Point of local max - x = Local 2 2 2 max value 3 2 (B) Point of local max - x = Local 3 2 max value 3 3 3 (C) Point of local max - x = Local 2 3 2 max value 2 1 (D) Point of local max - x = Local 4 4 3 max value 3
[ 3 ]
[ PTO
006.
If f (2) = 4 and f´(2) =1, then find
006.
¶{X
lim xf (2) 2f (x) x- 2 x"2
lim xf (2) 2f (x) x- 2 x"2
(A) 1
(B) 0
(A) 1
(B) 0
(C) 2
(D) None of these
(C) 2
(D)
007.
If f (x) = x + 2x + 7 , what will be f (3)
007.
(A) 3
(B) 5
¶{X f (x) = x2 + 2x + 7 , hmo Vmo ³¶m hmoJm -
(C) 4
(D) 8
(A) 3
(B) 5
(C) 4
(D) 8
008.
‘mZm f (x) = | x | d g(x) = | x3|, Vmo -
2
f (2) = 4 Am¡a f´(2) =1, Vmo
H$m ‘mZ hmoJm -
BZ‘| go H$moB© Zht f (3) H$m
‘mZ
008.
Let f (x) = | x | and g(x) = | x3|, then–
(A) f (x) and g (x) both are continous at x=0
(A) f (x) and g (x) both are continous at x=0
(B) f(x) and g(x) both are differentiable at x = 0
(B) f(x) and g(x) both are differentiable at x = 0
(C) f(x) is differentiable but g(x) is not differentiable at x = 0
(C) f(x) is differentiable but g(x) is not differentiable at x = 0
(D) f(x) and g (x) both are not differentiable at x = 0
(D) f(x) and g (x) both are not differentiable at x = 0
009.
Let f (x) = (x + | x |) | x |. Then for all x
009.
‘mZm f (x) = (x + | x |) | x |. Vmo Hw$b x Ho$ {bE-
(A) f is continuous
(A) f is continuous
(B) f is differentiable for some x
(B) f is differentiable for some x
(C) f ′ is continuous
(C) f ′ is continuous
(D) f & f ′ both are continuous
(D) f & f ′ both are continuous
4 - DC ]
[ 4 ]
[ Contd...
010.
ABCD is a parallelogram. If the coordinates of A, B, C are (2, 3), (2, 4) and (0, – 2) respectively, what will the coordinate of D.
010.
ABCD
(A) x = 2, y = – 1
(A) x = 2, y = -1
(B) x = 3, y = – 2
(B) x = 3, y = -2
(C) x = 1, y = – 3
(C) x = 1, y = -3
(D) None of these
(D)
011.
If ` 85 amounts to ` 95 in 3 years, what ` 102 will amount in 5 years at the same rate %?
011.
`{X
(A) 117
(B) 122
(A) 117
(B) 122
(C) 132
(D) 142
(C) 132
(D) 142
012.
If
012.
`{X,
(A) 15
(B) 16
(A) 15
(C) 17
(D) 18
(C) 17
1+
x =9 , than x = ? 64 8
2 1 1 If x + x = 5, then value of x + 2 = ?, x (A) 21 (B) 23
(C) 25
014.
The cube root of 0.00000729 is -
(A) 0.0027
(B) 0.027
(C) 0.0009
(D) 0.009
013.
4 - DC ]
(D) 27
013.
EH$ MVw^w©O h¡ `{X A, B, C Ho$ {ZX}em§H$ H«$‘e: (2, 3), (2, 4) d (0, -2) hmo Vmo D erf© Ho$ {ZX}em§H$ Š`m hm|Jo?
BZ‘| go H$moB© Zht ` 85
H$m {‘lYZ 3 dfm}§ ‘| ` 95 hmo Vmo ` 102 H$m 5 dfm}§ ‘| Cgr ã`mO Xa go {‘lYZ Š`m hmoJm?
1+
x =9 , hmo Vmo x H$m 64 8 (B) 16 (D) 18
`{X, x + 1x = 5, Vmo ~VmAmo-
2 1 x + 2 = ?, x
(A) 21
(B) 23
(C) 25
(D) 27
014.
0.00000729 H$m
(A) 0.0027
(B) 0.027
(C) 0.0009
(D) 0.009
[ 5 ]
‘mZ hmoJm &
H$m ‘mZ
KZ‘yb Š`m hmoJm-
[ PTO
015.
Find the value of x if
015.
`{X d 1 + 256 n = 91 + 16 C hmo Vmo x H$m ‘mZ Š`m hmoJmx
33
d1 +
33 n = + x 91 C 256 16
(A) 1
(B) 2
(A) 1
(B) 2
(C) 4
(D) 3
(C) 4
(D) 3
016.
Which is the Term of 1280 in Series 5, 10, 20, 40, ...............?
016.
loUr 5, 10, 20, 40, ............... H$m H$m¡Z-gm nX 1280 h¡?
(A) 7th
(A) 7th
(B) 10th
(B) 10th
(C) 9th
(C) 9th
(D) None of these
(D)
017.
If (k – 2, (2k +1), (6 k + 3) are in GP, then k=?
017.
`{X (k – 2, (2k +1), (6 k + 3) JwUmoËVa loUr ‘| hmo Vmo k H$m ‘mZ Š`m hmoJm?
(A) 2
(B) 7
(A) 2
(B) 7
(C) 3
(D) 6
(C) 3
(D) 6
018.
The 3rd term of a G.P. is 4. What will be the total sum of the first five terms of this GP?
018.
JwUmoËVa loUr H$m Vrgam nX 4 h¡ Vmo JwUmoËVa loUr Ho$ àW‘ nm±M nXm| H$m `moJ Š`m hmoJm?
(A) 1024
(A) 1024
(B) 1248
(B) 1248
(C) 1368
(C) 1368
(D) 1092
(D) 1092 019.
g‘mÝVa loUr 3, 18, 13, ........ H$m H$m¡Z-gm nX 78 h¡?
019.
Which term of AP 3, 18, 13, ........ is 78? (A) A23 (B) A19
(C) A16
(D) A22
4 - DC ]
BZ‘| go H$moB© Zht
(A) A23 (B) A19
(C) A16
(D) A22
[ 6 ]
[ Contd...
020.
Which term of the AP 3, 15, 27, 39.......... will be 132 more than its 54th term?
020.
g‘mÝVa loUr 3, 15, 27, 39.......... H$m H$m¡Z-gm nX 54d| nX go 132 A{YH$ hmoJm?
(A) 57
(B) 92
(A) 57
(B) 92
(C) 63
(D) 65
(C) 63
(D) 65
021.
Evaluating cos(tan– 1 x) we get :–
021.
cos(tan– 1 x) H$mo
(A)
(A)
(B) 1 + x
(B) 1 + x
(C)
(C)
(D) 1
(D) 1
022.
If x, y, z ∈ [– 1, 1] such that
022.
`{X x, y, z ∈ [– 1, 1] Bgr àH$ma
sin– 1 x + sin– 1 y z =
3p , find the value of 2 2006 2007 2008 9 x + y + z - 2006 2007 2008 x +y +z
sin– 1 x + sin– 1 y z =
x
-1 2 1+ x 2
1 2 1+ x
(A) 0
(B) 1
(C) – 1
(D)
023.
Evaluate tan (
(A)
2
5 -1 1 2 we get – cos 2 3
2006
-1 2 1+ x 2
1 2 1+ x
+y
2007
+z
2008
3p , 2
-
H$m ‘mZ Š`m hmoJm?
(B) 1
(C) – 1
(D)
5 -1 1 2 H$mo cos 2 3
3- 5 2
tan (
hmoJm-
(B)
5+3 2
(A)
(C)
2
(B)
(D) 1
(C)
(D) 1
[ 7 ]
x
hmo, Vmo
2006
(A) 0
023.
4 - DC ]
hb H$aZo na Š`m àmá hmoJm-
9
+y
2007
+z
2008
2
hb H$aZo na Š`m àmá
3- 5 2 5+3 2 2
[ PTO
6 2 a+ b 2 H= > H, find the value of 5 8 5 ab a and b.
(A) 4, 5
(A) 4, 5
(B) 2, 4
(B) 2, 4
(C) 4, 2
(C) 4, 2
(D) 0, 1
(D) 0, 1
025.
Simplify -
025.
gab H$s{OE-
cos q sin q sin q - cos q H + sin q > H cos q > - sin q cos q cos q sin q
cos q sin q sin q - cos q H + sin q > H cos q > - sin q cos q cos q sin q
1 0 H (A) > 1 1
1 0 H (B) > 0 1
1 0 H (A) > 1 1
(B) >
1 0 H 0 1
1 1 H (C) > 1 1
1 1 H (D) > 4 5
1 1 H (C) > 1 1
(D) >
1 1 H 4 5
026.
Find a matrix A, if -
026.
`{X
024.
If >
6 2 a+ b 2 H= > H, hmo 5 8 5 ab
024.
`{X >
‘mZ Š`m hmoJm-
2 3 3 -6 H H= > A=> -1 4 -3 8
H$m ‘mZ Š`m hmoJm-
1 -9 H (A) > -2 4
2 3 3 -6 H H= > A=> -1 4 -3 8
1 -9 H (A) > -2 4
(B) >
1 -4 H 0 2
(B) >
1 1 H (C) > -4 4
1 1 H (C) > -4 4
-2 - 9 H (D) > 1 -4
-2 - 9 H (D) > 1 -4
4 - DC ]
[ 8 ]
Vmo a Am¡a b H$m
hmo Vmo ‘¡{Q´Šg A
1 -4 H 0 2
[ Contd...
027.
x+ a If f (x) = ab ab
2
ab ac 2 x+ b bc , find f (x) 2 bc x + c
x+ a f (x) = ab ab
2
ab ac 2 x+ b bc , hmo 2 bc x + c
027.
`{X
2 2 2 2 (A) 3x + 2x_ a + b + c i
f (x) H$m
2 2 2 (B) 2x + 4x_ a + b i
2 2 2 2 (A) 3x + 2x_ a + b + c i
(C) 4x + 2x + bx
2 2 2 (B) 2x + 4x_ a + b i
(D) 4x + 3x_ a + b + c i
(C) 4x + 2x + bx
(D) 4x + 3x_ a + b + c i
028.
`{X
hmoJm-
(A)
(B) 3, 3
(C) 4, 2
(D) – 3,
029.
`{X 52 Vmg Ho$ nËVm| ‘| go EH$ nËVm {~Zm H«$‘ Ho$ {ZH$mbm OmVm h¡ Vmo amOm `m amZr H$s {H$VZr àm{`H$Vm hmoJr?
(A)
2
2
x- 2 -3 = 3 , find the value of x 3x 2x
028.
If
(A)
1 , – 3 2
(B) 3, 3
(C) 4, 2
(D) – 3,
029.
If from a pack of 52 playing cards, one card is drawn at random. What is the probability that it is either a king or queen?
1 13 2 (B) 13 3 (C) 26 1 (D) 52 (A)
4 - DC ]
[ 9 ]
Vmo
‘mZ Š`m hmoJm-
2
2
x- 2 -3 = 3 , hmo 3x 2x
Vmo x H$m ‘mZ Š`m
1 , – 3 2
1 13 2 (B) 13 3 (C) 26 1 (D) 52
[ PTO
1 2 What is the Value of 2 1 1 + tan 22 2 1 (A) 2 2
030.
1 - tan 22
1 2 2 1 1 + tan 22 2 1 (A) 2 2
030.
1 - tan 22
H$m ‘mZ Š`m hmoJm-
(B)
1 2
(B)
1 2
(C)
3 2
(C)
3 2
(D) 2
(D) 2
031.
What is the value of 3 sin 20º – 4 sin3 20. 1 (A) 1 (B) 2 3 (C) (D) 0 2
031.
3 sin 20º – 4 sin3 20 H$m
(A) 1
(C)
2
2
(B)
3 2
‘mZ Š`m hmoJm? 1 2
(D) 0
032.
If tan q = 1– a then 3 sec q + tan q cosec q = ?
032.
`{X tan 2 q = 1– a 2 Vmo
(A) (2– 3)3/2
(A) (2– 3)3/2
(B) (2– a2)1/2
(B) (2– a2)1/2
(C) (2– a2)2/3
(C) (2– a2)2/3
(D) 1
(D) 1
033.
The lines 2x – 3y & 3x – 4y = 7 are diameters of a circle of are 154 square units. An equator of this circle is (p = 22/7)
033.
`{X aoIm 2x – 3y Am¡a 3x – 4y = 7 EH$ d¥ËV H$m ì`mg h¡ Am¡a joÌ’$b 154 ‘r2 hmo Vmo d¥ËV H$m g‘r. Š`m hmoJm (p = 22/7)
2
2
2
2
2
2
2
2
(A) x + y + 2x – 2y = 62
2
2
(B) x + y + 2x – 2y = 47
2
2
(C) x + y – 2x + 2y = 47
2
2
(D) x + y – 2x + 2y = 62
(A) x + y + 2x – 2y = 62
(C) x + y – 2x + 2y = 47 (D) x + y – 2x + 2y = 62
4 - DC ]
2
‘mZ Š`m hmoJm?
2
(B) x + y + 2x – 2y = 47
3
sec q + tan q cosec q = H$m
[ 10 ]
[ Contd...
034.
035.
dy What will be the value of if dx x – y = p? (A) 1 (C) 1/4
dy , if x = a(q + sin q), dx y = a(1– cosq).
Find
If x
(A) (B) (C) (D)
2
If ax + bx + c = a _ x – p i , then, what is the relation between a, b, c? 2 (A) b = 4ac (B) 2b = a + c 2
2
(C) b = ac (D) abc = 1
038.
(A) x + y
(B) 1
(C) – 1 (D)
4 - DC ]
2
3
2
2
x +y
035.
`{X x = a (q + sin q), y = a(1– cosq) hmo Vmo
y 2xy x x - y + x + y + 2 - 2 will be =? y x
(A) 1 (C) 1/4
3 + 12 = 7 , then x + 13 will be? x x 38 29 18 28
x +y
(D) tan2q 2
`{X
(A) sin2q q (B) cos 2 q (C) tan 2
036.
037.
(B) 3 (D) 1/2
dy H$m ‘mZ dx (B) 3 (D) 1/2
034.
dy dx
x – y = p hmo
Vmo
Š`m hmoJm?
(A) sin2q q (B) cos 2 q (C) tan 2
(D) tan2q
036.
`{X x 2 + hmoJm-
(A) (B) (C) (D)
037.
`{X ax 2 + bx + c = a_ x – c ‘| Š`m g§~§Y hmoJm-
(A) b = 4ac (B) 2b = a + c 2 (C) b = ac (D) abc = 1
1 = 7, 2 x
Vmo
3 1 x + 3 x
hmo Vmo a, b,
2
(B) 1
(C) – 1
[ 11 ]
2
pi ,
H$m ‘mZ Š`m
38 29 18 28
y 2xy x x - y + x + y + 2 - 2 =? y x (A) x + y
038.
Š`m hmoJm?
(D)
2
3
2
2
x +y x +y
[ PTO
1 2 sin q = x + x , then (A) x = ± 1
(B) – 1 < x < 1
(C) x = 1
(D) None of these
039.
040.
1 2 sin q = x + x , V~(A) x = ±1
(B) – 1 < x < 1
(C) x = 1
(D)
040.
`{X x = hmoJm-
(A) 16
(B) 12
(C) 10
(D) 14
039.
If x = tan 15º then what will be the value 2 1 of x + 2 . x (A) 16 (B) 12 (C) 10 (D) 14
BZ‘| go H$moB© Zht tan 15º
2 1 x + 2 x
Vmo
H$m ‘mZ Š`m
4
041.
If
4
cos α sin α + = 1, then 2 2 cos β sin β 4
042.
4
4
cos β
+
2
cos α
sin β 2
sin α
will be -
(A) 4 1 (C) 8 3
(B) 0
041.
`{X
H$m ‘mZ Š`m hmoJm-
(A) 4
(B) 0
(C)
1 8
(D) 1
042.
`{X
(D) 1 3
If x sin q + y cos q = sin q cos q & x sin q = y cos q, then x2 + y2 = ?
(A) 0
(B) 2
(C) 4
(D) 1
043.
1 sin 22 = ? 2
(A)
2- 2 2
(B)
3- 2 2
(C)
2+ 2 2
(D)
2- 2 2
4 - DC ]
4
4 4 cos β sin β cos α sin α + + = 1 Vmo 2 2 2 2 cos β sin β cos α sin α
3
3
x sin q + y cos q = sin q cos q Am¡a x sin q = y cos q V~ x2 + y2 H$m ‘mZ Š`m
hmoJm
(A) 0 (C) 4
043.
1 sin 22 = ? 2
(A)
2- 2 2
(B)
3- 2 2
(C)
2+ 2 2
(D)
[ 12 ]
(B) 2 (D) 1
H$m ‘mZ hmoJm-
2- 2 2
[ Contd...
4
x 2 p , its factors will be a
044.
f 36 -
x x (A) 6 d x - a n f 6 + 2 p a
x x (B) 6 d x + a n d 6 - a n
x x (C) 6 d x - a n d 6 + a n
x x (D) 6 d x - a n d 6 - a n
045.
If a + b + c = ab + bc + ca , then
a + b + c will be equal to?
2
3
2
3
2
2
2
2
2
2
2
2
2
3
2
(A) 3 _ abc i 2
f 36 -
x x (A) 6 d x - a n f 6 + 2 p a
x x (B) 6 d x + a n d 6 - a n
x x (C) 6 d x - a n d 6 + a n
x x (D) 6 d x - a n d 6 - a n
045.
¶{X
a +b +c
2 2
4
x 2 p , H$m a
044.
3
2
JwUZIÊS> hmoJm-
2
2
2
2
2
2
2
2
2
2
a + b + c = ab + bc + ca , hmo 3
3
{H$gHo$ ~am~a hmoJm?
2
(A) 3 _ abc i 2
Vmo
2 2
(B) 3a b c
(C) 3abc
(C) 3abc
(D) None of these
(D)
046.
In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl? 3 1 (A) (B) 10 4 3 1 (C) (D) 5 7
046.
EH$ ñHy$b ‘| 1000 N>mÌm| ‘| go 430 b‹S>{H$`m± h¢& 430 ‘| go 10% b‹S>{H$`m± H$jm ~mah ‘| n‹T>Vr h¢ g§^m{dV b‹S>{H$`m| H$s àm{`H$Vm Š`m hmoJr?
(A)
2
047.
What will be the value of evaluating it? 8 9 2 (B) 5 6 (C) 7 7 (D) 5 (A)
4 - DC ]
# x dx after 2
1
(B) 3a b c
BZ‘| go H$moB© Zht
3 4 1 (C) 5
1 10 3 (D) 7 (B)
2
047.
gab H$aZo na
(A)
(B)
(C)
(D)
[ 13 ]
8 9 2 5 6 7 7 5
# x dx H$m ‘mZ Š`m hmoJm2
1
[ PTO
p 4
048.
What will be
(A) (B) (C) (D)
w
p 4
048.
1 + sin 2x dx ?
0
– 1 1 0 None of these
What will be the value of
w xe
1 + sin 2x dx ? H$m
‘mZ Š`m hmoJm-
0
(A) – 1 (B) 1 (C) 0 (D) BZ‘|
go H$moB© Zht
1
1
049.
w
x
049.
dx?
0
w xe
x
dx H$m
‘mZ ³¶m hmoJm -
0
(A) 1
(B)
1 2
(C) 0
(D)
BZ‘| go H$moB© Zht
(A) 1
1 (B) 2
(C) 0
(D) None of these
050.
050.
¶{X
R VR V S 1 3 2 W S1 W If [1 × 1] S 2 5 1 W S2 W = 0 , then what S WS W S15 3 2 W S x W T XT X will be x?
H$m ‘mZ hmoJm?
(A) – 1 or – 7
(B) – 2 or – 14
(A) – 1 VWm – 7 (B) – 2 VWm – 14
(C) – 3 or – 6
(D) – 4 or – 10
(C) – 3 VWm – 6 (D) – 4 VWm – 10
051.
Select the correct figure from the options to continue the series to replace the question mark.
051.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(A)
(C)
(C)
4 - DC ]
(B)
(D)
[ 14 ]
R VR V S 1 3 2 W S1 W [1 × 1] S 2 5 1 W S2 W = 0 , hmo S WS W S15 3 2 W S x W T XT X
Vmo x
(B)
(D)
[ Contd...
052.
Select the correct figure from the options to continue the series to replace the question mark.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
052.
(A)
(B)
(C)
(D)
053.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
(D)
053.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(C)
4 - DC ]
(A)
(B)
(C)
(D)
(B)
(D)
[ 15 ]
[ PTO
054.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
(D)
055.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
(D)
4 - DC ]
054.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
055.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
[ 16 ]
[ Contd...
056.
Select the correct figure from the options to continue the series to replace the question mark.
056.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(A)
(B)
(C)
(D)
(C)
(D)
057.
Select the correct figure from the options to continue the series to replace the question mark.
057.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(A)
(B)
(C)
(D)
(B)
(C)
(D)
4 - DC ]
[ 17 ]
[ PTO
058.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(C)
(D)
059.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(C)
4 - DC ]
(B)
058.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(C)
(D)
059.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
(B)
(B)
(D)
[ 18 ]
[ Contd...
060.
Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
061.
Write the missing numeral.
(A) 14
(B) 21
(C) 28
(D) 18
4 - DC ]
(D)
060.
{dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
061.
bwßV g§»`m kmV H$a|&
(A) 14
(B) 21
(C) 28
(D) 18
[ 19 ]
[ PTO
062.
Write the missing numeral.
062.
bwßV g§»`m kmV H$a|&
(A) 3
(B) 2
(A) 3
(B) 2
(C) 1
(D) 8
(C) 1
(D) 8
063.
How many faces/surfaces does this object have?
063.
(A) 12
(A) 12
(B) 10
(B) 10
(C) 13
(C) 13
(D) 15
(D) 15
064.
How many faces/surfaces does this object have?
064.
ZrMo Xr JB© dñVw Ho$ Vbm| H$s Hw$b g§»`m kmV H$a|&
(A) 14
(A) 14
(B) 15
(B) 15
(C) 12
(C) 12
(D) 13
(D) 13
4 - DC ]
[ 20 ]
ZrMo Xr JB© dñVw Ho$ Vbm| H$s Hw$b g§»`m kmV H$a|&
[ Contd...
065.
The below diagram is the top view of an object. Identify the object with the given top view that cannot have the elevation from the side of the arrow.
065.
àíZ {MÌ EH$ dñVw Ho$ D$na H$m Ñî` Xem©Vm h¡& {X`o JE {dH$ënm| ‘| go CgH$mo A§{H$V H$s{OE Omo Bg dñVw H$m {MpÝhV Ñí` Zht h¢&
(A)
(A)
(B)
(B)
(C)
(C)
(D)
(D)
4 - DC ]
[ 21 ]
[ PTO
066.
The below diagram is the top view of an object. Identify the front elevation of this object.
066.
àíZ {MÌ EH$ dñVw Ho$ D$na H$m Ñî` Xem©Vm h¡& {X`o JE {dH$ënm| go gm‘Zo dmbo ghr Ñí` H$mo nhMmZ| &
(A)
(A)
(B)
(B)
(C)
(C)
(D)
(D)
067.
How many triangles are there in this figure?
067.
ZrMo {X`o J`o {MÌ ‘| {H$VZo {ÌH$moU h¢ ?
(A) 27 (C) 23
(A) 27 (C) 23
4 - DC ]
(B) 25 (D) 21
[ 22 ]
(B) 25 (D) 21
[ Contd...
068.
How many triangles are there in this figure?
(A) 23
(B) 27
(C) 29
(D) 31
069.
How many squares are there in the figure below?
068.
ZrMo {X`o J`o {MÌ ‘| {H$VZo {ÌH$moU h¢ ?
(A) 23
(B) 27
(C) 29
(D) 31
069.
ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢¡ ?
(A) 20
(A) 20
(B) 13
(B) 13
(C) 24
(C) 24
(D) 17
(D) 17
070.
How many squares are there in the figure below?
070.
ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢ ?
(A) 18
(B) 19
(C) 25
(D) 27
(A) 18
(B) 19
(C) 25
(D) 27
4 - DC ]
[ 23 ]
[ PTO
071.
How many squares are there in the figure below?
(A) 11
(B) 21
(C) 24
(D) 26
072.
The figure below is embedded in one of the four alternate figures. Identify it.
(A)
(B)
(C)
(D)
4 - DC ]
071.
ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢ ?
(A) 11
(B) 21
(C) 24
(D) 26
072.
àíZ {MÌ {H$gr EH$ {dH$ën ‘| g‘m{hV h¡& ghr {dH$ën H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
[ 24 ]
[ Contd...
073. The figure below is embedded in one of the four alternate figures. Identify it.
073.
àíZ {MÌ {H$gr EH$ {dH$ën ‘| g‘m{hV h¡& ghr {dH$ën H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
074. Which of the following choices is the exact mirror image of the main figure given. (the mirror is on the right side of the object)
074.
àíZ {MÌ Ho$ ghr Xn©U à{V{~å~ {MÌ H$m M`Z H$a|& (Xn©U dñVw Ho$ Xm{hZo hmW H$s Va’$ h¡)
(A)
(B)
(A)
(B)
(C)
(D)
(C)
(D)
(A)
(B)
(C)
(D)
4 - DC ]
[ 25 ]
[ PTO
075. Which of the following choices is the exact mirror image of the main figure given. (the mirror is on the right side of the object)
(A)
(B)
(C)
(D)
076.
{dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(C)
076.
Identify the odd one.
(B)
(D)
077.
àíZ {MÌ Ho$ ghr Xn©U à{V{~å~ {MÌ H$m M`Z H$a|& (Xn©U dñVw Ho$ Xm{hZo hmW H$s Va’$ h¡)
(A)
075.
(A)
(B)
(C)
(D)
Identify the odd one.
(A)
4 - DC ]
(B)
(C)
077.
(D)
[ 26 ]
(A)
(B)
(C)
(D)
{dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
[ Contd...
078.
Identify the odd one.
(A)
078.
(B)
(C)
079.
Identify the odd one.
(A)
080.
Hamayun’s Tomb is situated in
(A) Punjab
(B) Madhya Pradesh
(C) Uttar Pradesh
(D)
{dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
079.
{dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A)
(D) Delhi
080.
hþ‘mD±° H$m ‘H$~am H$hm° h¡ ? (A) n§Om~ (B) ‘Ü` àXoe (C) CËVa àXoe (D) {Xëbr
081.
Architect B.V. Doshi Designed
081.
(A) IIT Kanpur
(B) IIT Delhi
(C) IIM Ahmedabad
(D) IIM Bengaluru
dmñVw{dX ~mb H¥$îU Xmofr Zo BZ g~ ‘| go Š`m {S>OmBZ {H$`m Wm? (A) AmB©. AmB©. Q>r. H$mZnwa (B) AmB©. AmB©. Q>r. {Xëbr (C) AmB©. AmB©. E‘. Ah‘Xm~mX (D) AmB©. AmB©. E‘. ~|Jmbwê$
082.
Who designed the city of Chandigarh?
(A) Edward Lutyens
(B) Richard Rogers
(C) Le Corbusier
(D) Aldo Rossi
082.
MÊS>rJ‹T> {H$gZo {S>OmBZ {H$¶m Wm? (A) ES>dS©> bw{Q>`Ýg (B) [aMS©> am°Og© (C) b H$ma~y{µO¶a (D) EëS>mo amogr
083.
Which stone is used in Dilwara temples?
(A) Granite
(B) Marble
(C) Sandstone
(D) Kota
083.
{Xbdmam ‘pÝXa H$m¡Z go nËWa go ~Zm h¡? (A) J«oZmBQ> (B) ‘m~©b (C) g¢S>ñQ>moZ (D) H$moQ>m
4 - DC ]
(B)
(C)
(D)
[ 27 ]
(B)
(C)
(D)
[ PTO
084.
Major component of brick is
(A) Silica
(B) Nickel
(C) Carbon
(D) Magnesia
085.
Which of the following is a flowering
084.
BªQ> H$s ~ZmdQ> ‘| A{YH$m§e ^mJ {H$gH$m hmoVm h¡? (A) {g{bH$m (B) {ZŠH$b (C) H$m~©Z (D) ‘¡J{Z{g`m
tree?
085.
BZ ‘| go H$m¡Z go no‹S> na a§JrZ ’y$b AmVo h¢?
(A) Arjun
(A) AO©wZ
(B) Ashok
(B) AemoH$
(C) Teak
(C) Q>rH$
(D) Amaltas
(D) A‘bVmg
086.
Which of the following is rock cut
086.
BZ‘| go H$m¡Z gm "am°H$ H$Q>' ‘pÝXa h¡ ?
temple?
(A) ‘rZmjr
(A) Meenakshi Temple
(B) H$ÝXm[a`m
(B) Kandariya Mahadeo Temple
(C) H¡$bmeZmW
(C) Kailashanath Temple
(D) qbJamO
(D) Lingraja Temple
087.
VrZ ‘m¡{bH$ (àmB©‘ar) a§J H$m¡Z go h¢ ?
(A) bmb,
Zrbm Am¡a nrbm
(B) bmb,
Zrbm Am¡a ham
‘pÝXa ‘hmXod ‘pÝXa ‘pÝXa
‘pÝXa
087.
The three primary colours are
(A) Red, Blue and Yellow
(B) Red, Blue and Green
(C) bmb,
Zrbm Am¡a H$mbm
(C) Red, Blue and Black
(D) bmb,
g’o$X Am¡a H$mbm
(D) Red, White and Black
088.
byd«, n¡[ag' H$m {dñVma (EŠgQ>¡ÝeZ) Omo {H$ EH$ {nam{‘S> H$s Vah h¡, {H$gZo {H$`m Wm ?
form of a pyramid is designed by
(A) E¡amo
(A) Eero Saarinen
(B) AmB©.
(B) I.M.Pei
(C) Om°Z
AQ>OZ
(C) John Utzon
(D) OoZ
S¯>
(D) Jane Drew
088.
The Extension of the Louvre, Paris, in the
4 - DC ]
[ 28 ]
g¡[aZZ E‘. nmB©.
[ Contd...
089.
Which of these does not form part of Reinforced Cement Concrete?
(A) Steel
(B) Sand
(C) Lime
(D) Cement
In questions 90-99, identify the logo and select the correct answer from the options below: 090.
089.
BZ g~ ‘| go H$m¡Z gm [aBZ’$moñS©> {g‘oÝQ> H$mÝH««$rQ (R.C.C.) Ho$ g§`moOZ H$m {hñgm Zht hmoVm ?
(A) ñQ>rb
(B) g¢S>
(C) bmB©‘
(D) gr‘oÝQ> àíZ 90-99 ‘| {X`o J`o bmoJmo H$mo nhMmZ| d {X`o JE {dH$ënm| ‘| go ghr CËVa M`Z H$ao|& 090.
(A) IBM
(B) BSNL
(C) TATA
(D) INTEL
091.
(A) AmB©.
~r. E‘. (B) ~r. Eg. EZ. Eb. (C) Q>mQ>m (D) BZQ>¡b
091.
(A) Facebook
(B) Firefox
(C) Fiat
(D) Fendi
092.
(A) ’o$g~wH$ (B) ’$m`°a’$m°Šg (C) {’$`Q> (D) ’o$ÝS>r
092.
(A) Make in India
(B) Jaguar
(C) King Power
(D) WWF
4 - DC ]
[ 29 ]
(A) ‘oH$
BZ BpÝS>`m (B) O¡½`ma (C) qH$J nmda (D) S>ãë`y. S>ãë`y. E’$.
[ PTO
093.
093.
(A) Adidas
(B) Mahindra
(C) Amazon
(D) Avon
094.
(A) ES>rS>mg (B) ‘{hÝÐm (C) A‘oOm°Z (D) Edm°Z
094.
(A) Surya
(B) Aadhaar
(C) Phillips
(D) ONGC
(A) gy`m©
(B) AmYma
(C) {’${bßg
(D) Amo.
(A) {‘Ëgw~wfr
(B) ‘{hÝÐm
(C) ‘mñQ>af¡’$
(D) ‘¡H$S>m°ZëS>g
EZ. Or. gr.
095.
095.
(A) Mitsubushi (B) Mahendra
(C) Masterchef (D) McDonalds
096.
096.
(A) Chartered Accountant
(B) Council of Auditors
(C) Council of Architecture
(D) Chamber of Auctioneers
(A) MmQ>©S©>
AH$mD$°Q>¢Q> (B) H$mD$pÝgb Am°’$ Am°{S>Q>g© (C) H$mD$pÝgb Am°’$ Am{H©$Q>oŠMa (D) Moå~a Am°’$ H$m°‘g©
097.
097.
(A) Airport Authority of India
(B) Sports Authority of India
(C) Electricity Commission of India
(D) Audit and Accounts Commission
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[ 30 ]
(A) E`anmoQ>©
AWmo[a{Q> Am°’$ BpÝS>`m (B) ñnmoQ>²©g AWmo[a{Q> Am°’$ BpÝS>`m (C) Bb¡pŠQ´{gQ>r H${‘eZ Am°’$ BpÝS>`m (D) Am°{S>Q> EÊS> AH$mD$§Q²g H${‘eZ [ Contd...
098.
098.
(A) Asian Paints
(B) Digital India
(C) Planning Commission
(D) Smart City
(A) E{e`Z
noÝQ²g (B) {S>OrQ>b BpÝS>`m (C) ßb¡qZJ H${‘eZ (D) ñ‘mQ>© {g{Q>
099.
099.
(A) State Bank of India
(A) ñQ>oQ>
(B) Metro
(B) ‘¡Q´mo
(C) Uber
(C) D$~oa
(D) Oriental Bank of Commerce
(D) Amo[aE§Q>b
100.
Select the correct figure from the options to continue the series to replace the question mark.
100.
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~¢H$ Am°’$ BpÝS>`m
~¢H$ Am°’$ H$m°‘g©
(A)
(C)
4 - DC ]
(A)
(B)
(C)
(D)
(B)
(D)
[ 31 ]
[ PTO
SPACE FOR ROUGH WORK /
4 - DC ]
[ 32 ]
H$ÀMo H$m‘ Ho$ {b¶o OJh
