JEE Main Sample Paper B.Arch Set B

JEE MAIN
SAMPLE
PAPER
Paper 2 for B.Arch

SET B
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Jee Main Paper 2 (B.Arch) Sample Paper

Maths

Q1. Let S be the set of all real values of ‘a’ for which the following system of linear equations
ax+2y+5z=1
2x+y+3z=1
3y+7z=1
is consistent. Then the set S is :
1. equal to R
2. equal to R−{1}
3. equal to {1}
4. an empty set

Correct. 1

Q2. An urn contains 5 red, 4 black and 3 white marbles. Then the number of ways in which 4
marbles can be drawn from it so that at most 3 of them are red, is :
1. 455
2. 460
3. 490
4. 495

Correct. 3

Q3. The perpendicular distance from the point (3, 1, 1) on the plane passing through the point (1,
→
2, 3) and containing the line, r = ^i + ^
j + λ(2 i + j + 4k) is :
^ ^ ^

1.
1

√11

2.
4

√41

3. 0
4. 3

√11

Correct. 3

Q4. The value of 1
∘
+
1

∘
is:
cos 285 √3 sin 255

1. 2√2
4√2
2.
√3

2√2
3.
√3

4. √3 − √2

Q5. An observer standing at a point P on the top of a hill near the sea-shore notices that the angle
of depression of a ship moving towards the hill in a straight line at a constant speed is 30°. After
45° minutes, this angle becomes 45°. If T (in minutes) is the total time taken by the ship to move
to a point in the sea where the angle of depression from P of the ship is 60°, then T is equal to :
1. 45(1 + √3)
2. 45 (1 + 2
)
√3

3. 45 (2 +
1
)
√3

4. 45 (1 +
1
)
√3

Correct. 4

Q6. A and B try to hit a target. The probability that A hits the target is 7/10 and the probability
that B hits the target is 4/10. If these two events are independent, the probability that B hits the
target, given that the target is hit, is:
1. 17/41
2. 18/41
3. 20/41
4. 19/41

Correct. 3

Q7. The compound statement (~C∧A∧B) v (~C∧~A∧B) v (C∧B)
is equivalent to:
1. B
2. A
3. ~A
4. C

Correct. 1

Q8. For distinct positive numbers a, b and c, if a², b², c² are in A.P., then which one of the
following triplets is also in A.P. ?
1. 1
,
b+2c
,
c+2a
1

a+2b
1

2. 1

b−c
,
1

a−b
,
c−a
1

3.

1 1 1
, ,
b+c c+a a+b

4.
1 1 1
, ,
b−c c−a a−b

Correct. 3

Q9. The distance of the point (1, 2, 3) from the plane x+y+z=2 measured parallel to the line
y
is :
x+1 z−3
= =
−1 −2 1

1. √23
2. √22
3. √24
4. √21

Correct. 3

x ′
3f (3)
Q10. If f (x) = ∫ , then the value of is:
e x
loge ( )dt
e log t e
e

1. −3 log 3 e

2. 3 log 3 e

3. e − 1
2

4. e − e
3

Correct. 3

Q11. The value of α for which the shortest distance between the lines represented by y+z=0, z+x=0
and x+y=0, x+y+z=α is 1, is :
1. √ 3

5

2. √ 2

3

3. √ 5

3

4. √ 3

2

Correct. 4

Q12. If z₁, z₂ and z₃ are any three distinct complex numbers such that |z | = 1, |z | = 2, |z | = 4, 1 2 3

arg z₂ = arg z₁ - π and arg z₃ = arg z₁ + π/2, then z₁z₃ is equal to :
1.
8i

2
z
1

2. −8iz 2
1

3. −
8i

2
z
1

4. 8iz 2

1

z̄ (1−z)
Q13. Let z(≠ -1) be any complex number such that |z|=1. Then the imaginary part of z(1+z̄ )
is:

1. -tan(θ/2) Sinθ
2. tan(θ/2) Cosθ
3. -tan(θ/2) Cosθ
4. tan(θ/2) Sinθ

Correct. 3

Q14. Let A be a 2x2 matrix such that A2+A+1=0 where I=I2. Then |adj((I-A) 6)| is equal to:
1. 33
2. 34
3. 36
4. 39

Correct. 3

Q15. Let A be the set of all 3 digit natural numbers and B={xЄA: H.C.F. (x,15)=1}. Then the number
of elements in B is:
1. 420
2. 360
3. 480
4. 240

Correct. 3

Q16. The sum of the in nite series 1 + 2 + 2

3
+
6
2
+
10
3
+
14
4
+ … … … . is : :
3 3 3

1. 4
2. 5
3. 6
4. 9/2

√x+6−sin(x−3)−3
Q17. lim x→3 is equal to :
(x−3) cos(x−3)

1. 5/6
2. 1/6
3. -2/3
4. -5/6

Correct. 4

Q18. Let P be a point on the parabola y = 3x such that OP makes an angle of π/6 with the x-axis,
2

where O is the origin. A normal is drawn to the parabola at P intersecting the axis of the parabola
at Q. If S is the focus Of the parabola, then SQ is equal to :
1. 39/2
2. 39/4

3. 9
4. 41/4

y y
Q19. If the two lines and are parallel for some m Є R,
x−2m z−4 x−2 z−2m
= = = =
2m+5 8m 2 m−2 −1 1−3m

then the distance between them is:
1. √10
2. 2√5
3. √29
4. √34

Correct. 4

→
Q20. If three vectors v 1
^ ^ ^
= αi + j + k ,
→
^ ^ ^
V 2 = i + β j − 2k , and
→
^ ^
V3 = i + j are coplanar,
→
v 1 and
→ →
v 3 are perpendicular, then the vector V (\times \overrightarrow{\mathrm{V}_{2}}\) is:
1

1. ^ ^ ^
− i + j + 2k

2. ^i − ^ ^
j + 2k

3. ^i + ^
j

4. 2^i − 2^ ^
j + k

Q21. Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular
polygon. If Tn+1 − Tn = 10, then the value of n is ________?

Correct. 5

Q22. Let A and B be two sets containing 2 elements and 4 elements respectively. The number of
subsets of A × B having 3 or more elements is ____?

Correct. 219

Q23. If the tangent at (1, 7) to the curve x²=y−6 touches the circle x²+y²+16x+12y+c=0 then the
value of c is _______?

Correct. 95

Q24. The sum of the following series
2 2 2 2 2 2 2 2 2 2
9(1 +2 +3 ) 12(1 +2 +3 +4 ) 15(1 +2 +…+5 )
1 + 6 +
7
+
9
+
11
+ ⋯ upto 15 terms is _______?

Correct. 7820

6
3

Q25. The coef cient of t in the expansion of ( is _______?
4 1−t
)
1−t

Correct. 15

Aptitude

Q1. The problem gure shows the top view of an object. Identify the correct elevation from
amongst the answer gures looking in the direction of the arrow.

1.

2.

3.

4.

Correct. 3

Q2. Which one of the answer gures is the correct mirror image of the problem gure with respect
to X - X ?

1.

2.

3.

4.

Correct. 1

Q3. Problem Figures

1.

2.

3.

4.

Q4. Which one of the answer gures shows the correct view of the 3–D problem gure after the
problem gure is opened up ?

1.

2.

3.

4.

Correct. 1

Q5. Which one of the answer gures shows the correct view of the 3–D problem gure after the
problem gure is opened up ?

1.

2.

3.

4.

Q6. The 3-D gure shows the view of an object. Identify the correct top view from amongst the
answer gures.

1.

2.

3.

4.

Q7. The 3-D gure shows the view of an object. Identify the correct top view from amongst the
answer gures.

1.

2.

3.

4.

Correct. 3

Q8. The 3–D problem gure shows a view of an object. Identify the correct front view, from
amongst the answer gures, looking in the direction of arrow.

1.

2.

3.

4.

Correct. 3

Q9. The 3–D problem gure shows a view of an object. Identify the correct front view, from
amongst the answer gures, looking in the direction of arrow.

1.

2.

3.

4.

Q10. The problem gure shows the top view of objects. Looking in the direction of the arrow,
identify the correct elevation, from amongst the answer gures.

1.

2.

3.

4.

Correct. 3

Q11. The problem gure shows the top view of objects. Looking in the direction of the arrow,
identify the correct elevation, from amongst the answer gures.

1.

2.

3.

4.

Q12. The problem gure shows the top view of objects. Looking in the direction of the arrow,
identify the correct elevation, from amongst the answer gures.

1.

2.

3.

4.

Correct. 1

Q13. The problem gure shows the elevation of an object. Identify the correct top view from
amongst the answer gures.

1.

2.

3.

4.

Q14. The problem gure shows the elevation of an object. Identify the correct top view from
amongst the answer gures.

1.

2.

3.

4.

Q15. Find the odd gure out of the problem gures given below.

1.

2.

3.

4.

Correct. 4

Q16. Which color is obtained by mixing red and yellow colors ?
1. Purple
2. Pink
3. Orange

4. Brown

Correct. 3

Q17. Temperature of the Earth due to the ‘Greenhouse Effect’ :
1. Increases
2. Decreases
3. Remains constant
4. Keeps increasing/decreasing

Correct. 1

Q18. Gol Gumbaj of Bijapur is :
1. A Fort
2. A Mausoleum
3. A Palace
4. A Mosque

Q19. IGBC stands for :
1. International Great Beautiful City
2. Indian Green Building Council
3. Indian Great Building Center
4. Indian Government Biological Center

Q20. What is Venice famous for ?
1. Canals
2. Mountains
3. Valleys
4. Springs

Correct. 1

Q21. Pyramids are located in :
1. Rome
2. Egypt
3. Greece
4. Ethiopia

Q22. Directions : The 3-D gure shows the view of an object. Identify the correct front view in the
direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Correct. 4

Q23. Directions : The 3-D gure shows the view of an object. Identify the correct front view in the
direction of the arrow', from amongst the answer gures.

1.

2.

3.

4.

Q24. Directions : The 3-D gure shows the view of an object. Identify the correct front view in the

direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Q25. Directions: The 3-D gure shows the view of an object. Identify the correct top view from
amongst the answer gures.

1.

2.

3.

4.

Correct. 3

Q26. Directions : Which one of the answer gure is the correct mirror image of the problem gure
with respect to X-X?

1.

2.

3.

4.

Correct. 4

Q27. Directions : Which one of the answer gure is the correct mirror image of the problem gure
with respect to X-X?

1.

2.

3.

4.

Correct. 3

Q28. Directions : Find the odd gure out of the answer gures given below:

1.

2.

3.

4.

Q29. Directions: One of the following answer gure is hidden in the problem gure in the same
size and direction Select the correct one.

1.

2.

3.

4.

Q30. What does the abbreviation ISRO stand for amongst the following?
1. Indian Studies and Result Of ce
2. International Settlements and Relief Organization
3. Indian Space Research Organization

4. International Sea and Rain Of ce

Correct. 3

Q31. Frame structure in high rise building pertains to which one of the following?

1. Structure with squares on the facade
2. Columns and Beams structure
3. Load bearing wall structure
4. A square building

Q32. A byte is which one of the following ?
1. A unit of digital memory
2. An act of an acrobat
3. A group of stars
4. A unit of sound

Correct. 1

Q33. Which one of the following is a primary color?
1. Green
2. Orange
3. Red
4. Purple

Correct. 3

Q34. Chajjas above windows are meant to protect the building from which of the following ?
1. Sun
2. Birds
3. Typhoon
4. Wind

Correct. 1

Q35. A small lift for carrying small loads only is known as which of the following ?
1. A Deaf Bearer
2. A Dump Waiter
3. A Jockey Boy
4. A Push Upper

Q36. Parquet ooring is usually made of which of the following ?
1. Granite
2. Marble
3. Cement

4. Wood

Correct. 4

Q37. The fort in Hyderabad is known as which of the following ?
1. Bahubali
2. Golconda
3. Siladhari
4. Virbanda

Q38. The Sas Bahu Temple is located in which of the following ?
1. Red Fort
2. Jhansi Fort
3. Gwalior Fort
4. Jaipur Fort

Correct. 3

Q39. The Lotus Temple is located in which one of the following city ?
1. New Delhi
2. Nagpur
3. Kanpur
4. Lucknow

Correct. 1

Q40. Directions : One of the following answer gures is hidden in the problem gure in the same
size and direction. Select the correct one.

1.

2.

3.

4.

Correct. 3

Q41. Directions : One of the following answer gures is hidden in the problem gure in the same
size and direction. Select the correct one.

1.

2.

3.

4.

Correct. 1

Q42. Directions : One of the following answer gures is hidden in the problem gure in the same
size and direction. Select the correct one.

1.

2.

3.

4.

Correct. 4

Q43. Directions : The 3D gure shows the view of an object. Identify the correct front view looking
in the direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Correct. 1

Q44. Directions : The 3D gure shows the view of an object. Identify the correct front view looking
in the direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Q45. Directions : The problem gure shows the top view of an object. Identify the correct
elevation from amongst the answer gures looking in the direction of the arrow.

1.

2.

3.

4.

Correct. 3

Q46. Directions : The problem gure shows the top view of an object. Identify the correct
elevation from amongst the answer gures looking in the direction of the arrow. AglaSem Admission

1.

2.

3.

4.

Correct. 3

Q47. Directions : The problem gure shows the top view of an object. Identify the correct elevation
from amongst the answer gures looking in the direction of the arrow.

1.

2.

3.

4.

Correct. 1

Q48. Directions : The 3D gure shows the view of an object. Identify the correct side view looking
in the direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Correct. 3

Q49. Directions : The 3D gure shows the view of an object. Identify the correct side view looking
in the direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Q50. Directions : The 3D gure shows the view of an object. Identify the correct side view looking
in the direction of the arrow, from amongst the answer gures.

1.

2.

3.

4.

Correct. 1

Drawing

1. Design an appropriate pattern for a curtain for a small girl's room. Draw and color it.

2. Draw from imagination a picture of some people sitting around a bon re.