Question Paper Name : B ARCH 1st Sep 2020 Shift 1
Subject Name : B ARCH
Creation Date : 2020-09-01 17:10:16
--- Content provided by FirstRanker.com ---
Duration : 180
Total Marks : 400
Display Marks: Yes
Share Answer Key With Delivery Engine : Yes
Actual Answer Key : Yes
--- Content provided by FirstRanker.com ---
B ARCH
Group Number : 1
Group Id : 40503674
Group Maximum Duration : 0
--- Content provided by FirstRanker.com ---
Group Minimum Duration : 180
Show Attended Group? : No
Edit Attended Group? : No
Break time : 0
Group Marks : 400
--- Content provided by FirstRanker.com ---
Is this Group for Examiner? : No
Mathematics
Section Id : 405036258
Section Number : 1
--- Content provided by FirstRanker.com ---
Section type : Online
Mandatory or Optional : Mandatory
Number of Questions : 25
Number of Questions to be attempted : 25
Section Marks : 100
--- Content provided by FirstRanker.com ---
Display Number Panel : Yes
Group All Questions : Yes
Mark As Answered Required? : Yes
Sub-Section Number : 1
Sub-Section Id : 405036539
--- Content provided by FirstRanker.com ---
Question Shuffling Allowed : Yes
Question Number : 1 Question Id : 4050367312 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let a function, f: R ? R be defined by
f(x)=1+|x|x and let sgn(x) = { 1, if x = 0 -1, if x < 0 }
Then:
Options:
40503626701. f is not invertible
--- Content provided by FirstRanker.com ---
40503626702. f-1(x) = sgn (x-1)vx-1
40503626703. f-1(x) = vx-1
40503626704. f-1(x) = sgn(x)vx-1
Question Number : 2 Question Id : 4050367313 Question Type : MCQ Option Shuffling : Yes Display Ques
--- Content provided by FirstRanker.com ---
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let a be a common root of the equations,
x²-x-12=0 and ?x²+10x+3=0
(where ? is an integer). If ß is the other
--- Content provided by FirstRanker.com ---
root of the second equation, then the
ordered pair (?, ß) is equal to :
Options:
40503626705. (-3, 1/3)
40503626706. (-3, -1/3)
--- Content provided by FirstRanker.com ---
40503626707. (3, 1/3)
40503626708. (3, -1/3)
Question Number : 3 Question Id : 4050367314 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
If z = -1 + iv2, then which one of the
following is not true?
Options:
40503626709. Re(z4) + Re(z³) = -2
--- Content provided by FirstRanker.com ---
40503626710. Im(z4) + Im(z³) = 5v2
40503626711. Im(z4) - Re(z³) = 4v2 - 5
40503626712. Re(z4) - Im(z³) = v2 - 7
Question Number : 4 Question Id : 4050367315 Question Type : MCQ Option Shuffling : Yes Display Ques
--- Content provided by FirstRanker.com ---
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
For ?(0, p/2), ?(p, 2p) and ß?R, the value
of the determinant
| cos2a cos(a + ?) -sin(a + ?) sina sin? cos? ßcosa -cos? sin? | :
--- Content provided by FirstRanker.com ---
Options:
40503626713. is independent of a.
40503626714. is independent of ß.
40503626715. is independent of ?.
40503626716. depends on all a, ß and ?.
--- Content provided by FirstRanker.com ---
Question Number : 5 Question Id : 4050367316 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let A = ( a 1 2 1 2 3 3 1 1 ) , a?R and B = [bij]3×3
--- Content provided by FirstRanker.com ---
such that AB=rI, r?0 in R. If
b32 = -3/2 r and |adjB| =r5, then |adj(AB)|
equals :
Options:
40503626717. 412
--- Content provided by FirstRanker.com ---
40503626718. 212
40503626719. 26
40503626720. 48
Question Number : 6 Question Id : 4050367317 Question Type : MCQ Option Shuffling : Yes Display Ques
--- Content provided by FirstRanker.com ---
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let a1, a2, a3 a4 and a5 be in A.P. with the
common difference greater than 2. If
?5i=1 ai = 30 and a1 a2 a3 a4 a5=3840, then
--- Content provided by FirstRanker.com ---
a1a5 is equal to :
Options:
40503626721. 82
40503626722. -128
40503626723. 128
--- Content provided by FirstRanker.com ---
40503626724. -82
Question Number : 7 Question Id : 4050367318 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let the functions f and g be defined as
f(x) = 2cosx-2+3|x| sin|x| and g(x)=x5+x.
If S be the set of points where the function
(fog)(x) is not differentiable, then S is equal
to :
--- Content provided by FirstRanker.com ---
Options:
40503626725. {1}
40503626726. {0}
40503626727. {0,1}
40503626728. Ø (an empty set)
--- Content provided by FirstRanker.com ---
Question Number : 8 Question Id : 4050367319 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let f be a twice differentiable function on
--- Content provided by FirstRanker.com ---
R such that f(0) = 4 and the function,
g(x) = 1/2 f2(x) + 3x³ - 5 is monotonically
increasing in R. Then f(1) cannot be :
Options:
40503626729. 2v3
--- Content provided by FirstRanker.com ---
40503626730. 3v2
40503626731. 4
40503626732. 2v2
Question Number : 9 Question Id : 4050367320 Question Type : MCQ Option Shuffling : Yes Display Ques
--- Content provided by FirstRanker.com ---
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let f(x) = (2x²-9x+11)ex, -8 < x < 8.
Then f has :
Options:
--- Content provided by FirstRanker.com ---
40503626733. a local maxima at x = 1/2 and a local minima at x=2.
40503626734. a local minima at x = 1/2 and a local maxima at x=2.
40503626735. neither a local maxima nor a local minima at x = 1/2
40503626736. neither a local maxima nor a local minima at x=2.
--- Content provided by FirstRanker.com ---
Question Number : 10 Question Id : 4050367321 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
If for x > 0,
? (evx sin(p/4 + vx) / vx) dx = evx. f(x) + C,
--- Content provided by FirstRanker.com ---
where C is a constant of integration, then
f(x) is equal to:
Options:
40503626737. (3/v2) cosvx
40503626738. (2v2/3) sinvx
--- Content provided by FirstRanker.com ---
40503626739. v2 sinvx
40503626740. v2 cosvx
Question Number : 11 Question Id : 4050367322 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
If y(x) = ?x²/16sinx (sinv? / (1 + cos²v?)) d?, then
y(p/4) is equal to :
Options:
40503626741. p/(3v2)
--- Content provided by FirstRanker.com ---
40503626742. p/12
40503626743. p/6
40503626744. p/3
Question Number : 12 Question Id : 4050367323 Question Type : MCQ Option Shuffling : Yes Display Ques
--- Content provided by FirstRanker.com ---
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
The area (in sq. units) of the region
{(x, y)?R²: 2|x| + |y| =2 and x+y=1} is :
Options:
--- Content provided by FirstRanker.com ---
40503626745. 1/3
40503626746. 2/3
40503626747. 1/2
40503626748. 4/3
--- Content provided by FirstRanker.com ---
Question Number : 13 Question Id : 4050367324 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Let ABC be a triangle such that the vertex
A has coordinates (-3, 1). If the equation
--- Content provided by FirstRanker.com ---
of the median through B be 2x+y-3=0
and the equation of the bisector of angle C
be 7x-4y-1=0, then the equation of the
line BC is:
Options:
--- Content provided by FirstRanker.com ---
40503626749. 15x+y=50
40503626750. 4x-y=7
40503626751. 18x-y=49
40503626752. 7x-3y=6
--- Content provided by FirstRanker.com ---
Question Number : 14 Question Id : 4050367325 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
If the ellipse centered at the origin has a
focus at (0, 3) and the corresponding
--- Content provided by FirstRanker.com ---
directrix is y=9, then which one of the
following is not true for this ellipse?
Options:
40503626753. Length of its minor axis is 6v2
40503626754. Length of its latus rectum is 4v3
--- Content provided by FirstRanker.com ---
40503626755. Point (v6, 2v3) lies on it
40503626756. Point (v6, -3v2) lies on it
Question Number : 15 Question Id : 4050367326 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
If a hyperbola has length of its transverse
axis = v2 and it has the same foci as that of
the ellipse, 4x²+3y²=24, then this
hyperbola also passes through the point
--- Content provided by FirstRanker.com ---
whose coordinates are:
Options:
40503626757. (2v3, 3/v2)
40503626758. (2/v3, 3/2)
40503626759. (1/v6, 1/3)
--- Content provided by FirstRanker.com ---
40503626760. (1/v6, v2/3)
Question Number : 16 Question Id : 4050367327 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let P be the point of intersection of the
plane, 4x-6y+14z=57 with the line
joining the points A(2, 3, 5) and B(1, -1, 4).
If BP = ?AP, then the value of ? is :
Options:
--- Content provided by FirstRanker.com ---
40503626761. 1/9
40503626762. 9
40503626763. 1/3
40503626764. 3
--- Content provided by FirstRanker.com ---
Question Number : 17 Question Id : 4050367328 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
A six faced biased dice is so loaded that in
any of its toss getting any of even scores is
--- Content provided by FirstRanker.com ---
equally likely and the probability of getting
an even score is three times the probability
of getting an odd score. This dice is tossed
repeatedly until a six is obtained. If X
denotes the number of tosses required, then
--- Content provided by FirstRanker.com ---
P(X < 4) is :
Options:
40503626765. 19/3³
40503626766. 37/4³
40503626767. 61/4³
--- Content provided by FirstRanker.com ---
40503626768. 397/(12)³
Question Number : 18 Question Id : 4050367329 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
If 2sinx - cos2x = 1, then :
Options:
40503626769. cos4x - cos²x = 3-v5
40503626770. 2(cos4x - cos²x) = -1
40503626771. sin4x - sin²x = 2 - v5
--- Content provided by FirstRanker.com ---
40503626772. 2(sin4x - sin²x) = 1
Question Number : 19 Question Id : 4050367330 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let a, b, c be any three non-coplanar
vectors. If the points
A(-2a + 3b + 5c),
B(a + 2b + 3c) and C(7a - ?c)
are collinear, then ? is equal to :
--- Content provided by FirstRanker.com ---
Options:
40503626773. 1
40503626774. -1
40503626775. 2
40503626776. -2
--- Content provided by FirstRanker.com ---
Question Number : 20 Question Id : 4050367331 Question Type : MCQ Option Shuffling : Yes Display Ques
Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Which one of the following is a tautology?
--- Content provided by FirstRanker.com ---
Options:
40503626777. ~(p ? q) ? q
40503626778. ~(p ? q) ? ~q
40503626779. ~(p ? q) ? p
40503626780. ~(p ? q) ? p
--- Content provided by FirstRanker.com ---
Sub-Section Number : 2
Sub-Section Id : 405036540
Question Shuffling Allowed : Yes
--- Content provided by FirstRanker.com ---
Question Number : 21 Question Id : 4050367332 Question Type : SA Display Question Number : Yes
Correct Marks : 4 Wrong Marks : 0
If the sum of all possible 4 digit numbers
formed using digits 1, 2, 3, 4 without
repetition, is 1111k, then k is equal to _______
--- Content provided by FirstRanker.com ---
Response Type: Numeric
Evaluation Required For SA : Yes
Show Word Count : Yes
Answers Type : Range
Text Areas: PlainText
--- Content provided by FirstRanker.com ---
Possible Answers : 5 to 5.002
Question Number : 22 Question Id : 4050367333 Question Type : SA Display Question Number : Yes
Correct Marks : 4 Wrong Marks : 0
If x = cosec? - sin? and y=cosec5? - sin5?,
--- Content provided by FirstRanker.com ---
0 < ? < p/2, then (x²+4) (dy/dx)² - 25y²
is equal to ________
Response Type: Numeric
Evaluation Required For SA : Yes
Show Word Count : Yes
--- Content provided by FirstRanker.com ---
Answers Type : Range
Text Areas: PlainText
Possible Answers : 5 to 5.002
Question Number : 23 Question Id : 4050367334 Question Type : SA Display Question Number : Yes
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 0
Let the function f:N?R satisfy
f(x+y)=f(x)f(y) for all x, y ? N and f(1) = 2.
If ?50k=1 f(4 + k) = ?(2ß-1), then ? + ß is
equal to ________
--- Content provided by FirstRanker.com ---
Response Type : Numeric
Evaluation Required For SA : Yes
Show Word Count : Yes
Answers Type : Range
Text Areas: PlainText
--- Content provided by FirstRanker.com ---
Possible Answers : 5 to 5.002
Question Number : 24 Question Id : 4050367335 Question Type : SA Display Question Number : Yes
Correct Marks : 4 Wrong Marks : 0
Let the circle, (x-a)²+(y-b)²=8 and the
--- Content provided by FirstRanker.com ---
parabola, y² = 4x have a common tangent
at the point P(1, 2). If C is the centre of the
circle and S is the focus of the parabola, then
the area (in sq. units) of ACPS is equal to ________
Response Type : Numeric
--- Content provided by FirstRanker.com ---
Evaluation Required For SA : Yes
Show Word Count: Yes
Answers Type : Range
Question Number : 25 Question Id : 4050367336 Question Type : SA Display Question Number : Yes
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 0
If y = y(x) is a solution of the differential
equation, x dy/dx = y(2-3xy), x > 0 with
y(1) = 1, then y(1/4) is equal to ________
Response Type: Numeric
--- Content provided by FirstRanker.com ---
Evaluation Required For SA : Yes
Show Word Count : Yes
Answers Type : Range
Text Areas: PlainText
Possible Answers : 5 to 5.002
--- Content provided by FirstRanker.com ---
Aptitude Test
Section Id : 405036259
Section Number : 2
Section type : Online
--- Content provided by FirstRanker.com ---
Mandatory or Optional : Mandatory
Number of Questions : 50
Number of Questions to be attempted : 50
Section Marks : 200
Display Number Panel : Yes
--- Content provided by FirstRanker.com ---
Group All Questions : Yes
Mark As Answered Required? : Yes
Sub-Section Number : 1
Sub-Section Id : 405036541
Question Shuffling Allowed : Yes
--- Content provided by FirstRanker.com ---
Question Number : 26 Question Id : 4050367337 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
The 3 - D figure shows the view of an object. Identify the correct top view from amongst the
--- Content provided by FirstRanker.com ---
answer figures.
Options:
Question Number : 27 Question Id : 4050367338 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
The 3 - D figure shows the view of an object. Identify the correct top view from amongst the
answer figures.
Options:
--- Content provided by FirstRanker.com ---
Question Number : 28 Question Id : 4050367339 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
The 3 - D figure shows the view of an object. Identify the correct top view from amongst the
answer figures.
--- Content provided by FirstRanker.com ---
Options:
Question Number : 29 Question Id : 4050367340 Question Type : MCQ Option Shuffling : Yes Display Ques
Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
The 3 - D figure shows the view of an object
This download link is referred from the post: JEE-Main Last 10 Years 2011-2021 Previous Question Papers
--- Content provided by FirstRanker.com ---