Question Paper Name: Paper II EHG 7th April 2019 S1 S2
Subject Name: Paper II EHG
Creation Date: 2019-04-07 14:22:38
--- Content provided by FirstRanker.com ---
Duration: 180
Total Marks: 390
Display Marks: Yes
Paper II
Group Number : 1
--- Content provided by FirstRanker.com ---
Group Id : 416529185
Group Maximum Duration : 0
Group Minimum Duration : 180
Revisit allowed for view?: No
Revisit allowed for edit?: No
--- Content provided by FirstRanker.com ---
Break time: 0
Group Marks: 390
Mathematics
Section Id : 416529349
Section Number : 1
--- Content provided by FirstRanker.com ---
Section type : Online
Mandatory or Optional: Mandatory
Number of Questions: 120
Number of Questions to be attempted:
Section Marks: 390
--- Content provided by FirstRanker.com ---
Display Number Panel: Yes
Group All Questions: No
Sub-Section Number: 1
Sub-Section Id: 416529529
Question Shuffling Allowed : Yes
--- Content provided by FirstRanker.com ---
Question Number : 1 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? Z X Z ? ? ? R ? ? ? ?:
(a, b) R (c, d) = a-d=b-c, ? Z ? ? ? ? ?, ? ? R :
Options:
--- Content provided by FirstRanker.com ---
1. ? ? ? ? ? ? ? ? ? ? ?
2. ? ? ? ? ? ? ? ? ? ? ?
3. ? ? ? ? ? ? ? ? ? ? ?
4. ? ? ? ? ? ? ? ?
--- Content provided by FirstRanker.com ---
Question Number : 1 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? R ? Z X Z ?
(a, b) R (c, d) = a-d=b-c, i Z ? ? ? ? ? ?. ? R ?
Options:
--- Content provided by FirstRanker.com ---
1. ? ? ? ? ? ? ? ? ?.
2. ? ? ? ? ? ? ? ? ?.
3. ? ? ? ? ? ? ? ? ?.
4. ? ? ? ? ? ? ?
Question Number : 1 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
Let R be a relation defined on ZXZ by
(a, b) R (c, d) = a-d=b-c, where Z is the set of all integers, then R is:
Options:
1. reflexive but neither symmetric nor transitive.
--- Content provided by FirstRanker.com ---
2. transitive.
3. transitive but neither reflexive nor symmetric.
4. symmetric and transitive but not reflexive.
Question Number: 2 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let z(-1) be any complex number such that |z| = 1. Then the imaginary part of
z(1-z)
is:
z(1 + z)
(Here 0 = arg z)
--- Content provided by FirstRanker.com ---
Options:
1. -tan(?/2)sin?
2. tan(?/2)cos?
3. -tan(?/2)cos?
4. tan(?/2)sin?
--- Content provided by FirstRanker.com ---
Question Number : 2 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
? z (? -1) ? ? ? ?, ? |z| = 1 ?, ? Im (z(1-z)/(1+z)) ? ? :
(? 0 = arg z)
Options:
--- Content provided by FirstRanker.com ---
1. tan(?/2)cos?
2. -tan(?/2)cos?
3. tan(?/2)sin?
Question Number: 2 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
? ? z (#-1) ? ? ? ? ? ? ? |z/ = 1 ?. ? z(1-z)/(1+z) ? ? ? ?.
(? 0 = arg z.)
Options:
1. -tan(?/2)sin?
2. tan(?/2)cos?
--- Content provided by FirstRanker.com ---
3. -tan(?/2)cos?
4. tan(?/2)sin?
Question Number: 3 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
The set of all real values of a for which the equation, |x+2|-|x-2| = a²-2x has real solutions for x, is:
--- Content provided by FirstRanker.com ---
Options:
2. (-8,0] ? [2,1+v5]
3. [-1-v5,1-v5] ? [1+v5, 8)
4. [1-v5,0] ? [2,1+v5]
Question Number: 3 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
a ? ? ? ? ?, ? ? ? |x+2|-|x-2| = a²-2x, ? x ? ? ? ?, ? ? ? :
Options:
1. (-8,0] ? [2,8)
2. (-8,0] ? [2,1 + v5]
--- Content provided by FirstRanker.com ---
3. [-1-v5,1-v5] ? [1+v5, 8)
4. [1-v5,0] ? [2,1+v5]
Question Number: 3 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
x ? ? |x+ 2|-|x-2| = a²- 2x ? ? ? ? ? ? @ ? ? ? ? ? ?.
--- Content provided by FirstRanker.com ---
Options:
1. (-8,0] ? [2,8)
2. (-8,0] ? [2,1 + v5]
3. [-1-v5,1-v5] ? [1+ v5, 8)
4. [1-v5,0] ? [2,1+v5]
--- Content provided by FirstRanker.com ---
Question Number : 4 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
Let A be a 2x2 matrix such that A²+A+I=0, where I=I2. Then |adj(I-A)6)| is equal to:
Options:
1. 3³
--- Content provided by FirstRanker.com ---
2. 34
3. 36
4. 3?
Question Number : 4 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
? A ? 2×2 ?, ? ? A²+A+I=0, ? I=I2 ?, ? |adj (I-A)6)| ? ? :
Options:
1. 3³
2. 34
3. 36
--- Content provided by FirstRanker.com ---
4. 3?
Question Number : 4 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? A ? ? 2×2 ? ? ? ? A²+A+I=0 ?, ? I = I2. ? |adj (I – A)6) | ? ?.
Options:
--- Content provided by FirstRanker.com ---
1. 3³
3. 36
4. 3?
Question Number: 5 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
If the system of linear equations
x+4y-3z=2
2x+7y-4z=a
-x-5y+5z=ß
--- Content provided by FirstRanker.com ---
has infinitely many solutions, then the ordered pair (a, ß) cannot take the value :
Options:
1. (4,-2)
2. (2,-4)
3. (3, -3)
--- Content provided by FirstRanker.com ---
4. (-3,3)
Question Number: 5 Question Type : MCQ Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? ? ?
x+4y-3z=2
--- Content provided by FirstRanker.com ---
2x+7y-4z = a
-x-5y+5z=ß
? ? ? ?, ? ? ? (a, (B) ? ? ? ? ? ? ? ? ? ?
Options:
1. (4,-2)
--- Content provided by FirstRanker.com ---
2. (2,-4)
4. (-3,3)
Question Number : 5 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
? ? ? ?
x+4y-3z=2
2x+7y-4z = a
-x-5y+5z=ß
? ? ? ?, ? ? ? (a, B) ? ? ? ? ?.
--- Content provided by FirstRanker.com ---
Options:
1. (4,-2)
2. (2,-4)
3. (3, -3)
4. (-3,3)
--- Content provided by FirstRanker.com ---
Question Number: 6 Question Type : MCQ Option Shuffling Es Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
Let A be the set of all 3-digit natural numbers and B = {x ? A : H.C.F. (x, 15) =1}. Then the number of elements in B is:
Options:
1. 420
--- Content provided by FirstRanker.com ---
2. 360
3. 480
4. 240
Question Number : 6 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Options:
1. 420
2. 360
3. 480
--- Content provided by FirstRanker.com ---
4. 240
Question Number : 6 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? A ? 3-? ? ? ? ? ? ? B = {x ? A : H.C.F. (x, 15) =1}. ? B ? ? ? ?.
Options:
--- Content provided by FirstRanker.com ---
1. 420
2. 360
3. 480
4. 240
Question Number: 7 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option: No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
If r is the remainder obtained on dividing (98)5 by 12, then the coefficient of x³ in the Binomial expansion of (1 + x/2)²r is:
Options:
1. 55/2
2. 91/2
--- Content provided by FirstRanker.com ---
4. 70
Question Number : 7 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? (98)5 ? 12 ? ? ? ? ? 1 ?, ? (1+x/2)²r ? ? ? ?, x³ ? ? ?:
--- Content provided by FirstRanker.com ---
Options:
1. 55/2
2. 91/2
3. 102
4. 70
--- Content provided by FirstRanker.com ---
Question Number: 7 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? (98)5 ? 12 ? ? ? ? x ?, ? (1+x/2)²r ? ? ? 3 ? ? ?.
Options:
1. 55/2
--- Content provided by FirstRanker.com ---
2. 91/2
3. 102
4. 70
Question Number : 8 Question Type : MCQ Option www.FirstRanker.com
No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
4. 128
Question Number : 8 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? ? ? ?, ? ? ? ? ? ? 66 ? ? ? ? ? ? ? ? 128 ?, ? ? ? ? 6 ? ? ? ? :
--- Content provided by FirstRanker.com ---
Options:
1. 127
2. 129
3. 126
4. 128
--- Content provided by FirstRanker.com ---
Question Number: 8 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
? ? ? ? ? ? ? ? ? 66 ? ? ? ? ? ? 128 ?. ? ? ? ? 6 ? ? ?.
Options:
1. 127
--- Content provided by FirstRanker.com ---
3. 126
4. 128
Question Number: 9 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
The sum of the infinite series 1 + 2/3 + 6/3² + 10/3³ + 14/34 + ......: is:
Options:
1. 4
2. 5
3. 6
--- Content provided by FirstRanker.com ---
4. 9/2
Question Number: 9 Question Type: MCQ Option Shuffling: Yo Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? 1 + 2/3 + 6/3² + 10/3³ + 14/34 + ? ? ? ? :
Options:
--- Content provided by FirstRanker.com ---
1. 4
2. 5
3. 6
4. 9/2
Question Number : 9 Question Type: MCQ Option www.FirstRanker.com
--- Content provided by FirstRanker.com ---
No Option Orientation : Vertical
1+ 2/3 + 6/3² + 10/3³ + 14/34 + ? ? ?.
Options:
1. 4
2. 5
--- Content provided by FirstRanker.com ---
3. 6
4. 9/2
Question Number : 10 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
lim (vx + 6 - sin(x - 3) - 3) / ((x-3)cos(x - 3)) is equal to:
--- Content provided by FirstRanker.com ---
x?3
Options:
1. 5/6
2. 1/6
3. 2/3
--- Content provided by FirstRanker.com ---
4. 5/6
Question Number: 10 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
lim (vx + 6 - sin(x - 3) - 3) / ((x-3)cos(x - 3)) ? ? :
x?3
--- Content provided by FirstRanker.com ---
Options:
2. 1/6
3. 2/3
4. 5/6
--- Content provided by FirstRanker.com ---
Question Number : 11 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
Question Number : 11 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? f ?
--- Content provided by FirstRanker.com ---
a sin2x - b cosx, x > p/2
f(x) = 4, x = p/2
2b cosx, x < p/2
? ? ? ? ?, ? a + b ? ? ?.
Options:
--- Content provided by FirstRanker.com ---
1. 1
2. 4
3. 5
4. 8
Question Number: 12 Question Type: MCQ Option Shuffling: Wag: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
Let y be an implicit function of x defined by
(x+y)/2 - 1/(x+y) + 12y = 0.
If y(0) = -1, then dy/dx at x = 0 is:
Options:
--- Content provided by FirstRanker.com ---
1. 1/2
3. 5/4
4. -4/5
Question Number : 12 Question Type : MCQ Option Shuffling : Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks: 4 Wrong Marks : 1
? ? ? ? ? :
? y, x ? ? (implicit) ?
(x+y)/2 - 1/(x+y) + 12y = 0.
? y(0) = - 1, ? x = 0 ? dy/dx ? ? ? :
--- Content provided by FirstRanker.com ---
Options:
1. 1/2
2. -1/2
3. 5/4
4. -4/5
--- Content provided by FirstRanker.com ---
Question Number : 12 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? ?. ?y(0) = -1, ? x = 0 ? dy/dx =
Options:
1. 1/2
--- Content provided by FirstRanker.com ---
2. -1/2
3. 5/4
4. -4/5
Question Number : 13 Question Type : MCQ Option Shuffling: Yes Displa Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Let f: R-{0} ? R be defined by
f(x) = a loge |x| +bx3+x2.
If x=-1 and x = 1 are the critical points of f(x), then:
Options:
1. f"(1)+f"(-1)=0
--- Content provided by FirstRanker.com ---
2. f"(1)-f"(-1)=4
3. both x=1 and x= 1 are local minima of f(x)
4. x=1 is a local minima and x = -1 is a local maxima of f(x)
Question Number : 13 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks: 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
Options:
1. f"(1)+f"(-1)=0
2. f"(1)-f"(-1)=4
3. x = 1 ? x = 1, ? f(x) ? ? ? ? ?
--- Content provided by FirstRanker.com ---
4. f(x) ? x = 1, ? ? ? ? ? ? x = - 1, ? ? ? ? ?
Question Number : 13 Question Type : MCQ Option Shuffling : Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? ? f : R- {0} ? R ? f(x)=a loge |x| +bx3 + x2 ? ? ?. ? x=-1 ? x = 1 ? f(x) ? ? ? ?, ?
Options:
--- Content provided by FirstRanker.com ---
1. f"(1)+f"(-1)=0
2. f"(1)-f"(-1)=4
3. x=1 ? x =-1 ? ? /(x) ? ? ?.
4. x=1 ? f(x) ? ? ? x= - 1 ? f(x) ? ? ?.
Question Number : 14 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
--- Content provided by FirstRanker.com ---
Correct Marks : 4 Wrong Marks : 1
such that f(x) = 3 for all x ? [0, 5] and if ?05 f(t)dt = 3. Then the value of ?03 f(t)dt can be :
Options:
1. -4
2. 6
--- Content provided by FirstRanker.com ---
3. 10
4. 12
Question Number : 14 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? f: [0, 5] ? R ? ? ? ? ? ? ? ? x ? [0, 5] ? ? |f(x)| = 3 ? ?05 f(t)dt = 3 ?, ? ?03 f(t)dt ? ? ? ? ? ? ? ?
--- Content provided by FirstRanker.com ---
Options:
1. -4
2. 6
3. 10
4. 12
--- Content provided by FirstRanker.com ---
Question Number : 14 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
? x € [0, 5] ? |f(x) = 3 ? ?05 f (t)dt = 3 ?. ? ?03 f(t)dt ? ? ? ?.
Options:
1. -4
--- Content provided by FirstRanker.com ---
2. 6
3. 10
4. 12
Question Number : 15 Question Type : MCQ Option Shuffling: Yes Display Question Number: Yes Single Line Question Option : No Option Orientation : Vertical
Correct Marks : 4 Wrong Marks : 1
--- Content provided by FirstRanker.com ---
? secx / v(sinx.cosx) dx is equal to : (where C is a constant of integration)
Options:
1. 2(tanx)^(1/2) + (2/5)(tanx)^(5/2) + C
2. (1/2)(tanx)^(1/2) + (2/5)(tanx)^(5/2) + C
3. 2(tanx)^(1/2) + (1/5)(tanx)^(5/2) + C
--- Content provided by FirstRanker.com ---
4. (1/2)(tan.x)^(2) + (2/5)(tanx)^(5/2) + C
This download link is referred from the post: JEE-Main Last 10 Years 2011-2021 Previous Question Papers