Download JEE-Main 2019 Paper II EHG 8th Jan 2019 Shift 2a Question Paper

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Question Paper Name: Paper II EHG 8th Jan 2019 Shift 2a

Subject Name: Paper II EHG

Creation Date: 2019-01-08 16:07:24

Duration: 180

Total Marks: 390

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Display Marks: Yes

Paper II

Group Number : 1

Group Id : 416529137

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Group Maximum Duration : 0

Group Minimum Duration : 180

Revisit allowed for view?: No

Revisit allowed for edit?: No

Break time: 0

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Group Marks: 390

Mathematics

Section Id : 416529193

Section Number : 1

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Section type : Online

Mandatory or Optional: Mandatory

Number of Questions: 120

Number of Questions to be attempted:

Section Marks: 390

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Display Number Panel: Yes

Group All Questions: No

Sub-Section Number: 1

Sub-Section Id: 416529255

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Question Shuffling Allowed : Yes

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

The function f: R?R, is given by

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f(x)= x / (1+|x|) is:

Options:

1. one-one and onto
2. onto but not one-one
3. neither one-one nor onto

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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

f: R?R, f(x)= x / (1+|x|) ? ? ? :

Options:

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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

Correct Marks : 4 Wrong Marks : 1

? f : R?R, f(x)= x / (1+|x|) ?

Options:

1. ?-? ? ? ?.

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2. ? ? ? ?-? ?.
3. ?-? ? ? ? ?.
4. ?-? ? ? ? ? ?.

Question Number : 2 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

If z1, z2 and z3 are any three distinct complex

numbers such that |z1| =1, |z2| = 2, |z3| = 4,

arg z2 = arg z1 - p / 2 and arg z3 = arg z1 + p / 2

then z2z3 is equal to :

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Options:

1. 8i / z1^2
2. 8iz1^2
3. -8iz1^2
4. 8i / z1^2

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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

? ? ? ? ? ? z1, z2 ? z3

? ? ? ? |z1| =1, |z2| = 2, |z3| = 4,

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arg z2 = arg z1 - ? / 2 ? arg z3 = arg z1 + p / 2

? z2z3 ? ? :

Options:

1. 8i / z1^2
2. 8iz1^2

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3. -8iz1^2
4. 8i / z1^2

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

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? z1, z2 ? z3 ? ? ? ? ? ?

? ? ? ? |z1| =1, |z2| = 2, |z3| = 4,

arg z2 = arg z1 - p / 2 ? arg z3 = arg z1 + p / 2

?, ? z2z3 =

Options:

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1. 8i / z1^2

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

If 2a is a root of ax²+bx+c=0, ß is a root

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of ax²-2bx-c=0, and the real numbers a,

b, c (a>0), are such that ß < a; then a root ?

of ax²+4bx+2c=0 always satisfies :

Options:

1. a < ? <2ß

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2. ß< ? <a
3. ?<ß<a
4. ß < a <?

Question Number: 3 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks: 4 Wrong Marks : 1

? ax²+bx+c=0 ? ? ? 2a ?,

ax² - 2bx - c = 0 ? ? ? ? ? ? ?

? a, b, c, (a>0) ? ? ? ? ß < a, ?

ax²+4bx + 2c=0 ? ? ? ? ? ? ?

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? :

Options:

1. a < ? <2ß
2. ß< ? <a
3. ?<ß<a

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4. ß < a <?

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

ax²- 2bx-c=0 ? ? ? B ?, ? a, b, c

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(a>0) ? ? ? ? ? ? ? B < a

?, ? ax²+4bx +2c=0 ? ? ? ? ?

? ?.

Options:

1. a < ? <2ß

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2. ß< ? <a
3. ?<ß<a
4. ß < a <?

Question Number : 4 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

If B = [-2 -2] and A is a matrix such

[-1 0]

that A?¹B=B?¹ and kA?¹=2B?¹+I,

where k is some scalar and I is the 2×2

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identity matrix, then the value of k is :

Options:

1. -2
2. -1
3. 1

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4. 2

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

? B = [-2 -2] ? ? A ? ? ?

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[-1 0]

? A?¹B = B?¹ ? kA?¹=2B?¹+I, ? k

? ? (scalar) ? ? I, 2×2 ? ?

(identity) ? ?, ? k ? ? ? :

Options:

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1. -2

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

? B = [-2 -2] ? A ? ? ? ? ?

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[-1 0]

? A?¹B = B?¹ ? kA?¹=2B?¹+I, ?

k ? ? ? I ? 2X2 ? ? ? ?,

? k ? ? ?.

Options:

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

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

If for positive real numbers a, b and c, the

system of linear equations

x=a(y+z), y=b(z+x), z= c(x + y)

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has non-trivial solutions, then

1 / (1+a) + 1 / (1+b) + 1 / (1+c) is equal to :

Options:

1. 3 / 2
2. 3

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3. 2
4. 1 / 2

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

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? ? ? ? a, b ? c ?

? ? ? ? x = a (y+z),

y=b(z+x), z=c(x + y) ? ? (non-trivial)

? ?, ? 1 / (1+a) + 1 / (1+b) + 1 / (1+c) ? ? :

Options:

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1. 3 / 2
2. 3
3. 2
4. 1 / 2

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

? ? ? a, b ? c ?, ? ?

? ? x = a(y+z), y=b(z+x),

z=c(x+y) ? ? ? (non-trivial

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solutions) ?, ? 1 / (1+a) + 1 / (1+b) + 1 / (1+c) =

Options:

1. 3 / 2
2. 3
3. 2

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4. 1 / 2

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

n

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where C1 = nCr and (C0 + C1) (C1 + C2)....

(Cn-1+Cn) = AC0C1C2....Cn. Then for n=5,

A is equal to:

Options:

1. 324/5

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2. 3125/24
3. 128/3
4. 625/24

Question Number: 6 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks: 4 Wrong Marks : 1

? (1+x)n = C0+ C1x + C2x² + ... + C?xn ,

? C? = nC? ? (C0 + C1) (C1 + C2)....

(C?1+C?) = AC0C1C2....C? ? n=5 ? ?

A ? ? :

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Options:

1. 324/5
2. 3125/24
3. 128/3
4. 625/24

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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

? ? (1+x)n = C0+ C1x + C2x² + .... + C?xn

? C? = nC? ? (C0 + C1) (C1 + C2)....

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(C?1+C?) = AC0C1C2....C? ? ? n = 5 ?

A=

Options:

1. 324/5
2. 3125/24

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3. 128/3
4. 625/24

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

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For ß?0, if the coefficient of x³ in the

binomial expansion of (1 + ßx)6 and the

coefficient of x4 in the binomial expansion

of (1-ßx)8 are equal, then the value of ß

is:

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Options:

1. 1/7
2. -2/7
3. 2/7
4. -1/7

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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

B?0 ? ?, ? (1 + ßx) 6 ? ? ? ? x³

? ? ? (1-ßx) 8 ? ? ? ? x4 ?

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? ? ?, ? ß ? ? ? :

Options:

1. 1/7
2. -2/7
3. 2/7

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4. -1/7

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

B?0 ? ? (1 + ßx)6 ? ? ? x³

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? ? ? (1 – ßx)8 ? ? ? x4

? ? ? ? ? B ? ?

?.

Options:

1. 1/7

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2. -2/7

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

For distinct positive numbers a, b and c, if

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a², b², c² are in A.P., then which one of the

following triplets is also in A.P.?

Options:

1. 1 / (b-c), 1 / (c-a), 1 / (a-b)
2. 1 / (b-c), 1 / (a-b), 1 / (c-a)

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3. 1 / (b+c), 1 / (c+a), 1 / (a+b)
4. 1 / (b+2c), 1 / (c+2a), 1 / (a+2b)

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

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? ? ? ? a, b ? c ?

?, ? a², b², c² ? ? ? ?, ? ? ?

? ? ? ? (triplet) ? ? ? ? ?

Options:

1. 1 / (b-c), 1 / (c-a), 1 / (a-b)

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2. 1 / (b-c), 1 / (a-b), 1 / (c-a)
3. 1 / (b+c), 1 / (c+a), 1 / (a+b)
4. 1 / (b+2c), 1 / (c+2a), 1 / (a+2b)

Question Number: 8 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

? ? (A.P.) ? ?, ? ? ? ?

? ? ? (A.P.) ? ?

Options:

1. 1 / (b-c), 1 / (c-a), 1 / (a-b)

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2. 1 / (b-c), 1 / (a-b), 1 / (c-a)
3. 1 / (b+c), 1 / (c+a), 1 / (a+b)
4. 1 / (b+2c), 1 / (c+2a), 1 / (a+2b)

Question Number : 9 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

Let S? be the sum of the first n terms of

the series

1²+2·5²+3²+2·7²+5²+2·9²+ .....

If S20 = 20 A, then A is equal to :

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Note: For this question, discrepancy is found in question/answer. Full Marks is being awarded to all

candidates.

Options:

1. 1851
2. 1951

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3. 2001
4. 2019

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

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? ? 1²+ 2·5²+3²+2·7²+5²+2·9²+.....

? ? n ? ? ? S? ? ? S20 = 20A, ?

A ? ? :

Note: For this question, discrepancy is found in question/answer. Full Marks is being awarded to all

candidates.

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Options:

1. 1851

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

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? ? 1²+2·5²+3²+2·7²+5² +2·9²+.....

? ? n ? ? S? ?. ? S20 = 20 A

?, ? A =

Note: For this question, discrepancy is found in question/answer. Full Marks is being awarded to all

candidates.

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Options:

1. 1851
2. 1951
3. 2001
4. 2019

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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

Let m and k be positive integers (m?k).

Then

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lim n? [ (1+1/n)? + (1+2/n)? + ..... + (1+k/n)? ] - k is :

n?8

Options:

1. 0
2. k(k+1) / 2 * m

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3. m(m+1)k / 2
4. km

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

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? m ? k ? ? ? (m?k), ?

lim n? [ (1+1/n)? + (1+2/n)? + ..... + (1+k/n)? ] - k

n?8

Options:

1. 0

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2. k(k+1) / 2 * m
3. m(m+1)k / 2
4. km

Question Number : 11 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

For f(x) = (e^(x?¹) - e^(-x?¹)) / (e^(x?¹) + e^(-x?¹)), x ? 0

0 , x = 0

Options:

1. f'(0)=1

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

Question Number: 11 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks: 4 Wrong Marks : 1

f(x) = (e^(x?¹) - e^(-x?¹)) / (e^(x?¹) + e^(-x?¹)), x ? 0 ? ? :

0 , x = 0

Options:

1. f'(0)=1

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2. f'(0)=0
3. x = 0 ? f ? ? ?
4. x = 0 ? f ? ? ?

Question Number: 11 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

f(x) = (e^(x?¹) - e^(-x?¹)) / (e^(x?¹) + e^(-x?¹)), x ? 0 ?

0 , x = 0

Options:

1. f'(0)=1

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2. f'(0)=0
3. f ? 0 ? ? ?.
4. f ? 0 ? ? ?.

Question Number : 12 Question Type : MCQ Option Shuffling: Yes Display Question Number : Yes Single Line Question Option : No Option Orientation : Vertical

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Correct Marks : 4 Wrong Marks : 1

Let F(x) = ? f(t) dt, If

0

f(x)=2+ sinx - cosx. If

F(x)-F(y) = k|x-y| for all x and y in R,

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then a possible value of k is :

Options:

1. 2 + v2
2. 2-v2
3. 1 + 1/v2

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4. v2-1

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

? F(x) = ? f(t) dt, ?

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0

f(x) = 2+ sinx - cosx. ? R ? ? x ? y

? ? |F(x) - F(y)| = k|x-y|, ? k ? ?

? ? ? :

Options:

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1. 2 + v2
2. 2-v2
3. 1 + 1/v2
4. v2-1

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

? ? F(x) = ? f(t) dt ?

0

f(x) = 2+ sinx - cosx ?. ? R ? ? x

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? y ? |F(x) - F(y)| = k|x-y| ?, ? k ?

? ? ?.

Options:

1. 2 + v2
2. 
   

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