Download JEE-Main 2020 B.Tech 6th Jan 2020 Shift 2 Set 2 Question Paper

Question Paper Name: B ARCH 6th Jan 2020 Shift 2 Set 2

Subject Name: B ARCH

Creation Date: 2020-01-06 20:31:58

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Duration: 180

Total Marks: 400

Display Marks: Yes

B ARCH

Group Number : 1

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Group Id : 4050366

Group Maximum Duration : 0

Group Minimum Duration : 180

Show Attended Group? : No

Edit Attended Group? : No

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Break time: 0

Group Marks: 400

Is this Group for Examiner?: No

Mathematics

Section Id : 4056

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Section Number : 1

Section type : Online

Mandatory or Optional: Mandatory

Number of Questions: 25

Number of Questions to be attempted: 25

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Section Marks: 100

Sub-Section Number: 1

Sub-Section Id: 40503624

Question Shuffling Allowed : Yes

Question Number : 1 Question Type : MCQ Option Shuffling: Yes

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Correct Marks : 4 Wrong Marks : 1

If A = {1, 2, 3, 4}, then the number of functions on the set A, which are not one - one, is:

Options:

1. 232
2. 240

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3. 248
4. 256

Question Number : 1 Question Type : MCQ Option Shuffling: Yes

Correct Marks: 4 Wrong Marks : 1

? A = {1,2,3,4} ?, ? ? A ? ? ? ? ? ? ? ? ?, ? :

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Options:

1. 232
2. 240
3. 248
4. 256

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Question Number: 1 Question Type: MCQ Option Shuffling : Yes

Correct Marks: 4 Wrong Marks : 1

? A = {1, 2, 3, 4} ?, ? ?-? ? ? ? ? A ? ? ? ? ?

Options:

1. 232

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2. 240
3. 248
4. 256

Question Number: 2 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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The sum of the values of x satisfying the equation, vx (vx-4)-3vx-2+6=0 (x=0), is:

Options:

1. 26
2. 25
3. 10

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4. 8

Question Number: 2 Question Type: MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? vx (vx-4)-3vx-2+6=0 (x=0) ? ? ? ? x ? ? ? ? ? :

Options:

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1. 26
2. 25
3. 10
4. 8

Question Number: 2 Question Type : MCQ Option Shuffling: Yes

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Correct Marks : 4 Wrong Marks : 1

?vx (vx-4)-3vx-2+6=0 (x=0) ? ? ? x ? ? ? ? ?.

Options:

1. 26
2. 25

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3. 10
4. 8

Question Number: 3 Question Type: MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

If m be the least value of |z-3+i4|/2+|z-5-i2|/2, z?C attained at z = z0, then the ordered pair (z0, m) is equal to:

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Options:

1. (v13, 10)
2. (v17, 20)
3. (v17, 10)
4. (v13, 20)

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Question Number: 3 Question Type : MCQ Option Shuffling: Yes

Correct Marks: 4 Wrong Marks : 1

? z = z0 ? |z-3+i4|/2+|z-5-i2|/2, z?C ? ? ? ? ? m ?, ? ? ? (z0, m) ? ? :

Options:

1. (v13, 10)

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2. (v17, 20)
3. (v17, 10)
4. (v13, 20)

Question Number: 3 Question Type: MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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? z=zo ? |z - 3 + i4|/2 + |z - 5 - i2|/2, ze C ? ? ? m ? ? ?, ? ? ? ( zo, m) = _________.

Options:

1. (v13, 10)
2. (v17, 20)
3. (v17, 10)

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4. (v13, 20)

Question Number : 4 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

If for some c < 0, the quadratic equation, 2cx²-2(2c-1)x+3c²=0 has two distinct real roots, 1/a and 1/b, then the value of the determinant,

| 1+a 1 1 |

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| 1 1+b 1 | is:

| 1 1 1+c |

Options:

1. 2
2. 0

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3. 4/3
4. 1

Question Number: 4 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? ? c < 0 ? ? ? ? 2cx²-2(2c-1)x+3c² = 0 ? ? ? ? ? 1/a ? 1/b ?, ? ?

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| 1+a 1 1 |

| 1 1+b 1 | ? ? ? :

| 1 1 1+c |

Options:

1. 2

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2. 0
3. 4/3
4. 1

Question Number : 4 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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? ? c < 0 ? ? ? 2cx²-2(2c-1)x + 3c² = 0 ? ? ? ? 1/a ? 1/b ?, ? ?

| 1+a 1 1 |

| 1 1+b 1 | ? ? = _________

| 1 1 1+c |

Options:

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1. 2
2. 0
3. 4/3
4. 1

Question Number : 5 Question Type : MCQ Option Shuffling: Yes

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Correct Marks : 4 Wrong Marks : 1

Let A = | x 2y | ; x, y ? R.

| -1 y |

If AAT = | 1 0 | (a ? R), then a + y² is equal to :

| 0 a |

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Options:

1. 1
2. v2 - 1
3. 2
4. v2

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Question Number : 5 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? A = | x 2y | ; x, y ? R ? ?

| -1 y |

AAT = | 1 0 | (a ? R) ?, ? a + y² ? ? ? :

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| 0 a |

Options:

1. 1
2. v2 - 1
3. 2

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4. v2

Question Number: 5 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? A = | x 2y | ; x, y ? R. ?

| -1 y |

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AAT = | 1 0 | (a ? R) ?, ? a + y²= _________

| 0 a |

Options:

1. 1
2. v2 - 1

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3. 2
4. v2

Question Number : 6 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

Let S? denote the sum of the first n terms of an A.P., a1, a2, a3, ..., a?. If a5 + a9 = 1 and S9 = 6, then which one of the following is not true?

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Options:

1. S13 = 13/2
2. a13 = 0
3. a6 + a8 = 1
4. S6 = 19/2

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Question Number : 6 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? S?, ? ? a1, a2, a3, ..., a? ? ? n ? ? ? ? ? ? ? a5+a9 = 1 ? S9 = 6 ?, ? ? ? ? ? ? ? ? ? ?

Options:

1. S13 = 13/2

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2. a13 = 0
3. a6 + a8 = 1
4. S6 = 19/2

Question Number: 6 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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? S? ? ? ? (A.P.) a1, a2, a3, ..., a? ? ? n ? ? ? ?. ? a5 + a9 = 1 ? S9 = 6 ?, ? ? ? ? ?

Options:

1. S13 = 13/2
2. a13 = 0
3. a6 + a8 = 1

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4. S6 = 19/2

Question Number : 7 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

If S (r+3)/2? ?C? = a(3/2)? + ß, then a + ß is equal to :

r=1

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Options:

1. 2
2. 9
3. 3
4. 6

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Question Number : 7 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? S (r+3)/2? ?C? = a(3/2)? + ß ?, ? a + ß ? ? ? :

r=1

Options:

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1. 2
2. 9
3. 3
4. 6

Question Number : 7 Question Type : MCQ Option Shuffling: Yes

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Correct Marks : 4 Wrong Marks : 1

? S (r+3)/2? ?C? = a(3/2)? + ß ?, ? a+ß= _________

r=1

Options:

1. 2

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2. 9
3. 3
4. 6

Question Number : 8 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

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Let a function, f: (-1, 3) ? R be defined as f(x) = min{x[x], x[x]-2+2}, where [x] denotes the greatest integer=x. Then fis:

Options:

1. neither continuous nor differentiable at exactly 3 points.
2. neither continuous at two points and not differentiable at 3 points.
3. neither continuous nor differentiable at exactly two points.

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4. not continuous at only one point and not differentiable at three points.

Question Number: 8 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? ? ? f: (-1, 3) ? R, f(x) = min{x[x], x[x] - 2 +2} ? ? ?, ? [x], ? ? = x ? ? ?, ? f :

Options:

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1. ? ? ? ? ? ? ? ? ? ? ? ? ?
2. ? ? ? ? ? ? ? ? ? ? ? ? ?
3. ? ? ? ? ? ? ? ? ? ? ? ? ?
4. ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Question Number: 8 Question Type : MCQ Option Shuffling: Yes

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Correct Marks : 4 Wrong Marks : 1

f(x) = min{x[x], x[x] - 2 + 2} ? ? ?, ? [x] ? ? ? ? =x ?, ? f ? :

Options:

1. ? 3 ? ? ? ? ? ? ? ? ?.
2. ? ? ? ? ? ? 3 ? ? ? ?.

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3. ? ? ? ? ? ? ? ? ? ? ?.
4. ? ? ? ? ? ? ? ? ? ? ? ?.

Question Number : 9 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

lim {loge (e^(x(x-1)) - e^(x(1-x)))} / {loge (4x(x-1))} is equal to:

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x?1

Options:

1. 1
2. -loge 2
3. -2loge 2

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4. 1-loge 2

Question Number: 9 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

lim {loge (e^(x(x-1)) - e^(x(1-x)))} / {loge (4x(x-1))} ? ? :

x?1

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Options:

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

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Question Number : 9 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

lim {loge (e^(x(x-1)) - e^(x(1-x)))} / {loge (4x(x-1))} = _________

x?1

Options:

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

Question Number : 10 Question Type : MCQ Option Shuffling : Yes

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Correct Marks : 4 Wrong Marks : 1

The function f(x) = e^(x+1) (4x²-16x+11) is:

Options:

1. increasing in (-8, 1/2) ? (5/2, 8)
2. increasing in (-8, -2) ? (2, 8)

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3. decreasing in (-8, -5/2) ? (1/2, 8)
4. decreasing in (-8, 1/2) ? (5/2, 8)

Question Number : 10 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? f(x) = e^(x+1) (4x²-16x+11) :

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Options:

1. (-8, 1/2) ? (5/2, 8) ? ? ?
2. (-8, -2) ? (2, 8) ? ? ?
3. (-8, -5/2) ? (1/2, 8) ? ? ?
4. (-8, 1/2) ? (5/2, 8) ? ? ?

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Question Number : 10 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? f(x) = e^(x+1) (4x²-16x+11) ? :

Options:

1. (-8, 1/2) ? (5/2, 8) ? ? ?.

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2. (-8, -2) ? (2, 8) ? ? ?.
3. (-8, -5/2) ? (1/2, 8) ? ? ?.
4. (-8, 1/2) ? (5/2, 8) ? ? ?.

Question Number : 11 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

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The area (in sq. units) of the region {(x,y): 1/2 = y = sin x, 0 = x = p} is :

Options:

1. v3 - p/3
2. 3 - p/3
3. 3 - 2p/3

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4. v3 - p/6

Question Number : 11 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? {(x, y): 1/2 = y = sin x, 0 = x = p} ? ? (? ? ?) ? :

Options:

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1. v3 - p/3
2. 3 - p/3
3. 3 - 2p/3
4. v3 - p/6

Question Number : 11 Question Type : MCQ Option Shuffling : Yes

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Correct Marks : 4 Wrong Marks : 1

? {(x, y) : 1/2 = y = sin x, 0 = x = p} ? ? (?. ?) _________ ?.

Options:

1. v3 - p/3
2. 3 - p/3

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3. 3 - 2p/3
4. v3 - p/6

Question Number : 12 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

If x = x(y) is the solution of the differential equation, ydx - (x + 2y²) dy = 0, with x( - p) = p², then x is equal to :

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Options:

1. 2y² - p²
2. -2y² + 3py
3. -y² - 2py
4. 2y² + py

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Question Number : 12 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? x = x(y), ? ? ydx - (x + 2y²)dy=0, x( - p) = p², ? ? ?, ? x ? ? :

Options:

1. 2y² - p²

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2. -2y² + 3py
3. -y² - 2py
4. 2y² + py

Question Number : 12 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

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? x=x (y) ? ? ? ydx - (x + 2y²) dy = 0 ? ? ?, ? x(-p) = p², ? x= _________

Options:

1. 2y² - p²
2. -2y² + 3py
3. -y² - 2py

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4. 2y² + py

Question Number : 13 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

A ray of light is projected from the origin at angle of 60° with the positive direction of x-axis towards the line, y = 2, which gets reflected from the point (a, 2). Then the distance of the reflected ray of light from the point (2, 2) is:

Options:

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1. v3 - 1
2. 2(1 - 1/v3)
3. 3 - v3
4. 1 - 1/v3

Question Number : 13 Question Type : MCQ Option Shuffling : Yes

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Correct Marks : 4 Wrong Marks : 1

? ? ? ?, ? ? ? x-? ? ? ? ? 60° ? ? ? ? y = 2 ? ? ? ? ? ?, ? ? ? (a, 2) ? ? ? ? ? ? ? (2, 2) ? ? ? ? ? ? ? ? ? :

Options:

1. v3 - 1
2. 2(1 - 1/v3)

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3. 3 - v3
4. 1 - 1/v3

Question Number : 13 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

? ? ? ? ? ? y = 2 ? ? ? ?, ? ? (a, 2) ? ? ? ?. ? ? ? ? ? ? (2, 2) ? ? _________ ?.

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Options:

1. v3 - 1
2. 2(1 - 1/v3)
3. 3 - v3
4. 1 - 1/v3

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Question Number : 14 Question Type : MCQ Option Shuffling : Yes

Correct Marks : 4 Wrong Marks : 1

Let the ellipse, x²/a² + y²/b² = 1, a > b, pass through the point (2, 3) and have eccentricity equal to 1/2. Then equation of the normal to this ellipse at (2, 3) is :

Options:

1. 2y - x = 4

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2. 2x - y = 1
3. 3x - y = 3
4. 3x - 2y = 0

Question Number : 14 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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? ? x²/a² + y²/b² = 1, a > b, ? (2, 3) ? ? ? ? ? ? ? ? 1/2 ?, ? (2,3) ? ? ? ? ? ? ? :

Options:

1. 2y - x = 4
2. 2x - y = 1
3. 3x - y = 3

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4. 3x - 2y = 0

Question Number : 14 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? ? x²/a² + y²/b² = 1, a > b ? ? (2, 3) ? ? ? ? ? ? ? 1/2 ?. ? (2, 3) ? ? ? ? ? _________ ?.

Options:

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1. 2y - x = 4
2. 2x - y = 1
3. 3x - y = 3
4. 3x - 2y = 0

Question Number : 15 Question Type : MCQ Option Shuffling : Yes

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Correct Marks : 4 Wrong Marks : 1

If a variable plane in 3-dimensional space moves in such a way that the sum of the reciprocals of its intercepts on the x and y-axes exceeds the reciprocal of its intercept on the z-axis by 2, then all such planes will pass through the point :

Options:

1. (1/2, 1/2, 1/2)
2. (1/2, 1/2, -1/2)

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3. (1/2, -1/2, 1/2)
4. (1/2, 1/2, -1/2)

Question Number : 15 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

?, ? ? (3-dimensional) ? ? ? ? ? ? ? ? x- ? y- ? ? ? ? ? ? ? ? ? ? z-? ? ? ? ? ? ? ? 2 ? ?, ? ? ? ? ? ? ? ? ?, ? ? :

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Options:

1. (1/2, 1/2, 1/2)
2. (1/2, 1/2, -1/2)
3. (1/2, -1/2, 1/2)
4. (1/2, 1/2, -1/2)

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Question Number: 15 Question Type: MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

? ? ? ? ? ? ? ? ? ? ? ? x ? y-? ? ? ? ? ? ? z-? ? ? ? ? ? 2 ? ? ?, ? ? ? ? _________ ? ? ?.

Options:

1. (1/2, 1/2, 1/2)

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2. (1/2, 1/2, -1/2)
3. (1/2, -1/2, 1/2)
4. (1/2, 1/2, -1/2)

Question Number : 16 Question Type : MCQ Option Shuffling: Yes

Correct Marks : 4 Wrong Marks : 1

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If the volume of a parallelopiped whose coterminous edges are a= i + j + 2k, b=2i + ?j + k and c=2i + 2j + ?k is 35 cu.m, then a value of a·b + b·c - c·a is:

Options:

1. 2
2. -14
3. -10

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4. 22
   

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