JEE Main Sample Paper B.Arch Set A

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. If the shortest distance between the lines x+2λ=2y=−12z, x=y+4λ=6z−12λ is 4√2 units, then a
value of λ is :
1. 2
2. √2
3. 2√2
√2
4. 2

Q2. 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

→, →b and c→ are such that
Q3. Three vectors a
→ → →
|a| = 1, | b| = 2, |c | = 4 and
→
→ → →
a + b + c = 0 Then the value of

→ ⋅ →b + 3→b ⋅ c→ + 3c→ ⋅ a
4a → is equal to :
1. −68
2. −26
3. −34
4. 27

Q4. If A and B are two independent events such that P( a ) = 3/10 and P(A∪B) = 4/5 , then P(A∩B) is
equal to :
1. 1/5
2. 1/10

3. 3/14
4. 3/35

Correct. 3

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. If any tangent to the parabola x² = 4y intersects the hyperbola xy = 2 at two points P and Q,
then the mid - point of line segment PQ lies on a parabola with axis along:
1. x-axis and focus on positive x-axis
2. y-axis and focus on positive y-axis
3. y-axis and focus on negative y-axis
4. x-axis and focus on negative x-axis

Correct. 3

Q7. The distance of the point (1, 2, 3) from the plane x+y+z=2 measured parallel to the line
is :
x+1 y z−3
= =
−1 −2 1

1. √23
2. √22
3. √24
4. √21

Correct. 3

→ = 2^i + ^j − 2k
Q8. Let a ^ → ^ ^ c be a vector such that a
and b = i + j . If →
→ −a
→ ⋅ c→ = |c→|, |c →| = 2√2 and
→ × →b and c→ is 30°, then the value of |(a
the angle between a → × →b) × c→| is:
1. 3
2. 3/2
3. 1/2
4. 6

x ′
3f (3)
Q9. If f (x) = ∫ , then the value of is:
e x
loge ( )dt
e loge t e

1. −3 log 3 e

2. 3 log 3 e

3. e 2
− 1

4. e 3
− e

Correct. 3

−2 −2
Q10. If B = [ ] and A is a matrix such that A⁻¹B = B⁻¹ and kA⁻¹= 2B⁻¹+I, where k is
−1 0

some scalar and I is the 2x2 identity matrix, then the value of k is:
1. -2
2. -1
3. 1
4. 2

Correct. 4

Q11. Let x₁, x₂....,x₂₀ be 20 observations and dί = 2(xί - 5), i=1,2,..., 20. If the mean and variance of
d₁, d₂.....d₂₀ are 20 and 12 respectively, then the mean and variance of x₁, x₂....,x₂₀ are
respectively,
1. 10 and 3
2. 10 and 4
3. 15 and 3
4. 15 and 4

Correct. 3

z̄ (1−z)
Q12. 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

Q13. The set of all real values of ∝ for which the equation, |x+2|*|x-2|= ∝2-2∝ has real solutions for
x is:
1. ([-∞,0]∪[2,∞])
2. ([-∞,0]∪[2, 1+√5])
3. ([-1-√5, 1-√5]∪[1+√5, ∞])
4. ([1-√5,0], ∪[2, 1+√5])

Correct. 4

Q14. Let f:[0,5]⇾R be a continuous function such that |f (x)| ≤ 3 for all xє[0,5] and ∫
5
f (t)dt = 3
0

3
. Then the value of ∫ 0
f (t)dt :
1. -4
2. 6
3. 10
4. 12

Q15. Let the abscissae of two points A and B on a circle be the roots of x + 2x − 4 = 0 and the
2

ordinates of A and B be the roots of $y^{2}+4 y-16=0$. If AB is a diameter of this circle, then the
radius of this circle is ::
1. 5
2. 6
3. 2√6
4. 2√10

Correct. 1

Q16. Let the ellipse x + 16y = 16 be inscribed in a rectangle whose sides are parallel to the
2 2

coordinate axes. If the rectangle is inscribed in another ellipse that passes through the point (16,
0), then the equation of the outer ellipse is :
1. x + 256y = 16
2 2 2

2. x + 248y = 16
2 2 2

3. x 2 2 2
+ 240y = 16

4. x 2 2 2
+ 232y = 16

Correct. 3

Q17. Let the planes x -2y +kz-0 and x + 5y -z = 0 be perpendicular. Then the plane through the
point (2, -2, -2) and perpendicular to the given planes also passes through the point :
1. (0,5,8)
2. (0,5,-8)
3. (-1,0,-7)
4. (1,0,7)

Correct. 4

Q18. If for two event A and B , in random experiment P (A|B) = 4

5
and P (B|A) =
1
then
4

P(A|A ∪ B) is equal to
1.
5

16

2. 5

17

3.
16

17

4.
11

16

Correct. 3

Q19. If a , b and c (all distinct) are the sides of a triangle ABC opposite angles a , b and c
csin(A−B) b sin(C−A)
respectively then 2 2
− 2 2
is equal to
a −b c −a

1. 0
2. 1
3. 2
4. -1

Correct. 1

Q20. The expression ∼ (p ↔ q) is equivalent to
1. (p∧ ∼ q) ∧ (q∧ ∼ p)
2. p ∨ q
3. p∧ ∼ q
4. (∼ p ∧ q) ∨ (∼ q ∧ p)

Correct. 4

Q21. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and
3 boys that can be formed from this class, if there are two speci c boys A and B, who refuse to be
the members of the same team, is _________?

Correct. 300

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. The intercepts on x-axis made by tangents to the curve, y= 0∫x |t| dt, x ∈ R, which are parallel
to the line y = 2x, are equal to (±)___________.

Correct. 1

Q24. In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics
course, those whose number is divisible by 3 opted Physics course and those whose number is
divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the
three courses is _____ ?

Correct. 38

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.

Q2. Problem Figures

1.

2.

3.

4.

Q3. 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

Q4. 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.

Q5. 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

Q6. 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

Q7. 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. 1

Q8. 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.

Q9. The problem gure shows the elevation of an object. Identify the correct top view from
amongst the answer gures.

1.

2.

3.

4.

Q10. Find the odd gure out of the problem gures given below.

1.

2.

3.

4.

Correct. 4

Q11. Salim Chisti mosque is located in :
1. Gwalior
2. Fatehpur Sikri
3. Hyderabad
4. Delhi

Q12. Temperature of the Earth due to the ‘Greenhouse Effect’ :
1. Increases

2. Decreases
3. Remains constant
4. Keeps increasing/decreasing

Correct. 1

Q13. Which type of roof will provide maximum protection from heat radiation in a building ?
1. Painted aluminium sheeting
2. Concrete slab with plaster
3. Concrete slab with mud and brick tiles
4. Concrete slab, water proofed and covered with a roof garden

Correct. 4

Q14. Buland Darwaza is located in :
1. Fatehpur Sikri
2. Red Fort
3. Agra Fort
4. Golconda

Correct. 1

Q15. IGBC stands for :
1. International Great Beautiful City
2. Indian Green Building Council
3. Indian Great Building Center
4. Indian Government Biological Center

Q16. Solar energy is converted to electrical energy by :
1. Photovoltaic cells
2. Electro magnets
3. Bio technology
4. Rain water

Correct. 1

Q17. 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.

Q18. 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. 4

Q19. 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

Q20. 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.

Q21. 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

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. 3

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.

Correct. 1

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: 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. 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.

Q28. 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

Q29. Directions : Find the odd gure out of the answer gures given below:

1.

2.

3.

4.

Q30. Directions : Find the odd gure out of the answer gures given

1.

2.

3.

4.

Q31. 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.

Q32. 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

Q33. Chajjas above windows are meant to protect the building from which of the following ?
1. Sun
2. Birds
3. Typhoon
4. Wind

Correct. 1

Q34. What does the abbreviation NASA stand for amongst the following ?

1. National Art and Science Association
2. National Architecture and Science Association
3. National Archeology Studies Academy
4. National Aeronautics and Space Administration

Correct. 4

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. Cement Plaster is used for which of the following ?
1. Covering Walls
2. Making roofs
3. Making Staircase
4. Making Floors

Correct. 1

Q39. Helical staircases are which one of the following ?
1. Dog leg staircases
2. Curving Staircases
3. Straight Flights
4. Staircase with no railings

Q40. Zaha Hadid was born in which country amongst the following ?
1. Iran
2. Iraq
3. Afghanistan

4. Turkistan

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 : Which one Of the answer gure will complete the sequence Of the three problem
gures ?

1.

2.

3.

4.

Correct. 1

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.

Correct. 1

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

1.

2.

3.

4.

Q47.

1.

2.

3.

4.

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. 3

Drawing

1. In the space provided in the answer sheet for this question, draw margin lines to form a frame.
In this frame create an aesthetic composition using only curved lines. The shapes created by these
curved lines can be of any size, and may be placed separate, overlapping or within each other. The

idea is to produce an aesthetic and visually exciting composition of these shapes in the frame
without making it represent any realistic form like house face etc. The composition should be
lled with some colors Of your choice so that the visual quality of the composition is enhanced.

2. Draw the graphic image shown below to double its size in the space provided for the answer of
this question. Each component line should be drawn double its length and correctly positioned
direction wise as shown in the question gure.