JEE Main Sample Paper B.Plan

JEE MAIN
SAMPLE
PAPER
B.Plan

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

Maths

Q1. If A and B be two nite sets such that the total number of subsets of A is 960 more than the
total number of subsets of B, then n( a )−n( b ) (where n(X) denotes the number of elements in set
X) is equal to :
1. 2
2. 3
3. 4
4. 6

Correct. 3

Q2. For all real numbers x, y and z, the determinant
∣ 2x xy − xz y ∣
∣ 2 ∣
∣ 2x + z + 1 xy − xz + yz − z 1 + y∣
∣ ∣
∣ 3x + 1 2xy − 2xz 1 + y∣

is equal to :
1. zero
2. (x−y) (y−z) (z−x)
3. (x−yz) (y−z)
4. (y−xz) (z−x)

Q3. 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

ax, x < 2
Q4. If the function f : R → R, de ned by f (x) = { 2
is differentiable, then
ax − bx + 3, x ≥ 2

the value of f (−3) + f (c) is equal to :
′ ′

1. 3

2. 4
3. 15/2
4. 0

Correct. 1

Q5. The order and the degree of the differential equation of all ellipses with centre at the origin,
√3
major axis along x-axis and eccentricity 2
are, respectively :
1. 1, 1
2. 2, 1
3. 1, 2
4. 2, 2

Correct. 1

2 2

Q6. The product of the perpendiculars drawn from the foci of the ellipse, upon the
x y
+ = 1
9 25

5√3
tangent to it at the point ( is :
3
, )
2 2

1. 9
2. 189/13
3. 18
4. 3√13

Correct. 1

Q7. A bag contains three coins, one of which has head on both sides, another is a biased coin that
shows up heads 90% of the time and the third one is an unbiased coin. A coin is taken out from the
bag at random and tossed. If it shows up a head, then the probability that it is the unbiased coin, is
:
1. 5/12
2. 5/24
3. 1/3
4. ⅜

Q8. Which one of the following statements is a tautology ?
1. (p ∨ q) → q
2. p ∨ (p → q)
3. p ∨ (q → p)
4. p → (p → q)

Q9. The solution of the differential equation
dy sin 2y
3 2
+ = x cos y,
dx x

(where C is a constant of integration)
1. x sin 2y =
6
2 x
+ C
6
4

2. x tan y =
2 x

4
+ C
6

3. x cos 2y =
2 x

6
+ C

4. x tan y =
6
2 x
+ C
6

Correct. 4

sin(3x/2)
Q10. The value of the integral ∫ is:
π
dx
π/2 sin(x/2)

1. π/2
2. π/2 - 2
3. π/2 - 1
4. π/2 + 2

Q11. 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

Q12. 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

Q13. For β∈0, if the coef cient of x³ in the binomial expansion of (1 + βx) and the coef cient of
6

x⁴ in the binomial expansion of (1 − βx) are equal, then the value of β is:
8

is :
1. 2/7
2. -2/7
3. 1/7

4. -1/7

Correct. 1

Q14. If an ellipse has its foci at (2,0) and (-2,0) and its length of the latus rectum is 6, then the

equation of the ellipse is:
2

1.
2 y
x
+ = 1
16 12
2 2

2. x y
+ = 1
24 64
2

3.
2 y
x
+ = 1
64 24
2 2
y
4.
x
+ = 1
36 18

Correct. 1

Q15. 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

1/x −1/x
e −e
x , x ≠ 0
Q16. For f (x) = {
1/x −1/x
e +e

0 ,x = 0

1. f'(0) = 1
2. f is not continuous at 0
3. f'(0) = 0
4. f is not differentiable at 0

Correct. 4

Q17. If the system of linear equations x+4y-3z=2, 2x+7y-4z=∝, and -x-5y+5z=β has in nitely many
solutions, then the ordered pair (∝,β) can’t take the value:
1. (4, -2)
2. (2, -4)
3. (3,-3)
4. (-3,3)

Correct. 4

Q18. If r is the remainder obtained by dividing (98)5 by 12, then the coef cient of x3 in the
2r

binomial expansion of (1 + is:
x
)
2

1. 55/2

2. 91/2
3. 102
4. 70

Correct. 4

Q19. 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 + y 2 1 ∣

Q20. Let y be an implicit function of x de ned ∣ 1 x + y 2
∣
+ 12y = 0 . If y(0)=-1,
∣ ∣
∣ 1 2 x + y∣

then dx/dy at x=0 is :
1. 1/2
2. -1/2
3. 5/4
4. -4/5

Correct. 1

Q21. 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

Q22. 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

Q23. If for two event A and B , in random experiment P (A|B) = then
4 1
and P (B|A) =
5 4

P(A|A ∪ B) is equal to

1. 5

16

2.
5

17

3.
16

17

4. 11

16

Correct. 3

Q24. If 6 cos θ − 2 cos 2θ − 3 = 0, then tan 3θ is equal to
2 2

1. 1

3

2. 1
3. 3
4. 9

2

Q25. 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
a −b
2
− 2
c −a
2
is equal to
1. 0
2. 1
3. 2
4. -1

Correct. 1

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. 1

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. 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.

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.

Correct. 1

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.

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. From the top view given in the problem gure identify the correct 3-D gure from amongst
the answer gures.

1.

2.

3.

4.

Q13. Find the odd gure out of the problem gures given below.

1.

2.

3.

4.

Correct. 3

Q14. Salim Chisti mosque is located in :
1. Gwalior
2. Fatehpur Sikri
3. Hyderabad
4. Delhi

Q15. Temperature of the Earth due to the ‘Greenhouse Effect’ :
1. Increases
2. Decreases
3. Remains constant
4. Keeps increasing/decreasing

Correct. 1

Q16. Vertical sun protectors over wall openings help in cutting off summer sun rays on :
1. South side
2. West side
3. North side
4. On all sides

Q17. Big Ben is a :
1. Clock Tower

2. Palace
3. Mosque
4. Temple

Correct. 1

Q18. Solar energy is converted to electrical energy by :
1. Photovoltaic cells
2. Electro magnets
3. Bio technology
4. Rain water

Correct. 1

Q19. What is Venice famous for ?
1. Canals
2. Mountains
3. Valleys
4. Springs

Correct. 1

Q20. 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.

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. 3

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.

Q23. 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

Q24. 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

Q25. Directions : Find the odd gure out of the answer gures given below:

1.

2.

3.

4.

Correct. 3

Q26. 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.

Correct. 3

Q27. 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.

Correct. 3

Q28. 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

Q29. Which one of the following is a primary color?
1. Green
2. Orange
3. Red
4. Purple

Correct. 3

Q30. Which one of the following is not a planned city ?
1. Gandhi nagar
2. Kanpur
3. Bhubaneshwar
4. Chandigarh

Q31. Chajjas above windows are meant to protect the building from which of the following ?
1. Sun
2. Birds
3. Typhoon

4. Wind

Correct. 1

Q32. 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

Q33. Helical staircases are which one of the following ?
1. Dog leg staircases
2. Curving Staircases
3. Straight Flights
4. Staircase with no railings

Q34. An escalator moves in which of the following direction ?
1. Only Vertically
2. Only Horizontally
3. Vertically and Horizontally
4. In Steps

Correct. 3

Q35. Zaha Hadid was born in which country amongst the following ?
1. Iran
2. Iraq
3. Afghanistan
4. Turkistan

Q36. 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

Q37. Directions : Which one Of the answer gure will complete the sequence Of the three problem
gures ?

1.

2.

3.

4.

Correct. 3

Q38. Directions : Which one Of the answer gure will complete the sequence Of the three problem
gures ?

1.

2.

3.

4.

Q39. Directions : Which one Of the answer gure will complete the sequence Of the three problem
gures ?

1.

2.

3.

4.

Correct. 1

Q40. 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

Q41. 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.

Q42. 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. 3

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.

Q44. 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

Q45. Directions : The 3D gure shows the view of an object. Identify the correct top view from
amongst the answer gures.

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.

Correct. 1

Q47. Directions : The 3D gure shows the view of an object. Identify the correct top view from

amongst the answer gures.

1.

2.

3.

4.

Q48. Directions : The 3D gure shows the view of an object. Identify the correct top view from

amongst the answer gures.

1.

2.

3.

4.

Correct. 4

Q49.

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. Draw a picture of your favorite lm stars face as realistic as possible.

2. 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.