Download JEE-Main 2020 B.Arch E 1st Sep 2020 Shift 1 Question Paper

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National Testing Agency

B ARCH

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Mathematics

Question Number : 1 Question Id : 4050369074 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 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:

1. 40503632951. f is not invertible

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2. 40503632952. f^-1(x) = sgn (x-1)vx-1

3. 40503632953. f^-1(x) = vx-1

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4. 40503632954. f^-1(x) = sgn(x)vx-1

Question Number : 1 Question Id : 4050369074 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? ? f: R ? R, f(x)=1+x|x| ? ? ? ? ? sgn(x)= { 1, ? x = 0 -1, ? x < 0 } ?, ? :

Options:

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1. 40503632951. f ? ? ?

2. 40503632952. f^-1(x) = sgn (x-1)vx-1

3. 40503632953. f^-1(x) = vx-1

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4. 40503632954. f^-1(x) = sgn(x) vx-1

Question Number : 2 Question Id : 4050369075 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 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 root of the second equation, then the ordered pair (?, ß) is equal to :

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Options:

1. 40503632955. (-3, 1/3)

2. 40503632956. (-3, -1/3)

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3. 40503632957. (3, 1/3)

4. 40503632958. (3, -1/3)

Question Number : 2 Question Id : 4050369075 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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? ? x²-x-12=0 ? ?x²+10x + 3 = 0 (? ? ? ? ?) ? ? ? ? a ? ? ? ? ? ? ? ß ?, ? ? ? (?, ß) ? ? :

Options:

1. 40503632955. (-3, 1/3)

2. 40503632956. (-3, -1/3)

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3. 40503632957. (3, 1/3)

40503632958. (3, -1/3)

Question Number : 3 Question Id : 4050369076 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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If z = -1 + iv2, then which one of the following is not true ?

Options:

1. 40503632959. Re(z⁴) + Re(z³) = -2

2. 40503632960. Im(z⁴) + Im(z³) = 5v2

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3. 40503632961. Im(z⁴) - Re(z³) = 4v2-5

4. 40503632962. Re(z⁴) - Im(z³) = v2-7

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Question Number : 3 Question Id : 4050369076 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? z = -1 + iv2 ?, ? ? ? ? ? ? ? ? ?

Options:

1. 40503632959. Re(z⁴) + Re(z³) = -2

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2. 40503632960. Im(z⁴) + Im(z³) = 5v2

3. 40503632961. Im(z⁴) - Re(z³) = 4v2 - 5

4. 40503632962. Re(z⁴) - Im(z³) = v2 - 7

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Question Number : 4 Question Id : 4050369077 Question Type : MCQ Option Shuffling : Yes Display Ques 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? |

Options:

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1. 40503632963. is independent of a.

2. 40503632964. is independent of ß.

3. 40503632965. is independent of ?.

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4. 40503632966. depends on all a, ß and ?.

Question Number : 4 Question Id : 4050369077 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

?e(0, p/2), ?e(p, 2p) ? ß?R ? ? ?

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| cos²a cos(a + ?) -sin(a + ?) | | sina sin? cos? | ? ? : | ßcosa -cos? sin? |

Options:

1. 40503632963. a ? ? ?

2. 40503632964. ß ? ? ?

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3. 40503632965. ? ? ? ?

4. 40503632966. a, ß ? ? ? ? ? ? ?

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Question Number : 5 Question Id : 4050369078 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 |, a?R and B = [b_ij]_3x3 | 3 1 1 |

such that AB=rI, r? 0 in R. If b₃₂ = -3/2 r and |adjB| =r⁵, then |adj(AB)| equals :

Options:

1. 40503632967. 4¹²

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2. 40503632968. 2¹²

3. 40503632969. 2⁶

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4. 40503632970. 4⁸

Question Number : 5 Question Id : 4050369078 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 = | a 1 2 | | 1 2 3 |, a?R ? B = [b_ij]_3x3 ? | 3 1 1 |

? ? ? AB =rI, r? 0 (r?R)? ? b₃₂ = -3/2 r ? |adjB| = r⁵ ?, ? |adj(AB)| ? ? :

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Options:

1. 40503632967. 4¹²

2. 40503632968. 2¹²

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3. 40503632969. 2⁶

4. 40503632970. 4⁸

Question Number : 6 Question Id : 4050369079 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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Let a₁, a₂, a₃ a₄ and a₅ be in A.P. with the common difference greater than 2. If ?⁵_i=1 a_i = 30 and a₁a₂a₃a₄a₅=3840, then a₁a₅ is equal to:

Options:

1. 40503632971. 82

2. 40503632972. -128

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3. 40503632973. 128

4. 40503632974. -82

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Question Number : 6 Question Id : 4050369079 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? a₁, a₂, a₃, a₄ ? a₅ ? ? ? ? ?

? ? 2 ? ? ? ? ?⁵_i=1 a_i = 30 ? a₁a₂a₃a₄a₅ = 3840 ?, ? a₁a₅ ? ? :

Options:

1. 40503632971. 82

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2. 40503632972. -128

Question Number : 7 Question Id : 4050369080 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 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:

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Options:

1. 40503632975. {1}

2. 40503632976. {0}

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3. 40503632977. {0,1}

4. 40503632978. F (an empty set)

Question Number : 7 Question Id : 4050369080 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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? ? f ? g ? ? ? ? ? : f(x)=2cosx-2+3|x| sin|x| ? g(x) = x⁵ +x. ? ? ?, ? (fog) (x) ? ? ?, ? ? S ?, ? S ? ? :

Options:

1. 40503632975. {1}

2. 40503632976. {0}

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3. 40503632977. {0,1}

4. 40503632978. F (? ? ?)

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Question Number : 8 Question Id : 4050369081 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 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:

1. 40503632979. 2v3

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2. 40503632980. 3v2

3. 40503632981. 4

4. 40503632982. 2v2

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Question Number : 8 Question Id : 4050369081 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? R ? ? ? f ? ? ? ?, ? ? f(0) = 4 ? ? ? g(x) = 1/2 f²(x) + 3x³ - 5, R ? ? ? ? ? f(1) ? ? ? :

Options:

1. 40503632979. 2v3

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2. 40503632980. 3v2

3. 40503632981. 4

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4. 40503632982. 2v2

Question Number : 9 Question Id : 4050369082 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(x) = (2x²-9x+11)e^-x, -8 < x < 8. Then f has :

Options:

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1. 40503632983. a local maxima at x = 1/2 and a local minima at x=2.

2. 40503632984. a local minima at x = 1/2 and a local maxima at x=2.

3. 40503632985. neither a local maxima nor a local minima at x = 1/2

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4. 40503632986. neither a local maxima nor a local minima at x=2.

Question Number : 9 Question Id : 4050369082 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? f(x) = (2x²-9x+11)e^-x, - 8 < x < 8 ?, ? f ? :

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Options:

1. 40503632983. x = 1/2 ? ? ? ? ? x = 2 ? ? ? ?

2. 40503632984. x = 1/2 ? ? ? ? ? x = 2 ? ? ? ?

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3. 40503632985. x = 1/2 ? ? ? ? ? ? ? ? ? ?

4. 40503632986. x = 2 ? ? ? ? ? ? ? ? ? ?

Question Number : 10 Question Id : 4050369083 Question Type : MCQ Option Shuffling : Yes Display Que Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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If for x > 0,

? e^vx sin(p/4 + vx) / vx dx = e^vx. f(x) + C,

where C is a constant of integration, then f(x) is equal to:

Options:

1. 40503632987. 3/v2 cosvx

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2. 40503632988. 2v2/3 sinvx

3. 40503632989. v2 sinvx

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4. 40503632990. v2 cosvx

Question Number : 10 Question Id : 4050369083 Question Type : MCQ Option Shuffling : Yes Display Que Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? x > 0 ? ?

? e^vx sin(p/4 + vx) / vx dx = e^vx. f(x) + C,

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? C ? ? ? ?, ? f(x) ? ? :

Options:

1. 40503632987. 3/v2 cosvx

2. 40503632988. 2v2/3 sinvx

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3. 40503632989. v2 sinvx

4. 40503632990. v2 cosvx

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Question Number : 11 Question Id : 4050369084 Question Type : MCQ Option Shuffling : Yes Display Que Question Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

If y(x) = ?^x2_p²/16 sinx sinv? / 1 + cos²v? d?, then y(p/4) is equal to :

Options:

1. 40503632991. p/3v2

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2. 40503632992. p/12

3. 40503632993. p/6

4. 40503632994. p/3

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Question Number : 11 Question Id : 4050369084 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

? y(x) = ?^x2_p²/16 sinx sinv? / 1 + cos²v? d? ?, ? y(p/4) ? ? :

Options:

1. 40503632991. p/3v2

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2. 40503632992. p/12

3. 40503632993. p/6

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4. 40503632994. p/3

Question Number : 12 Question Id : 4050369085 Question Type : MCQ Option Shuffling : Yes Display Ques 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:

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1. 40503632995. 1/3

2. 40503632996. 2/3

3. 40503632997. 1/2

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4. 40503632998. 4/3

Question Number : 12 Question Id : 4050369085 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

? {(x, y)?R² : 2|x| + |y| =2 ? x + y =1} ? ? (? ? ?) ? :

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Options:

1. 40503632995. 1/3

2. 40503632996. 2/3

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3. 40503632997. 1/2

4. 40503632998. 4/3

Question Number : 13 Question Id : 4050369086 Question Type : MCQ Option Shuffling : Yes Display Ques Mandatory : No Single Line Question Option : No Option Orientation : Vertical Correct Marks : 4 Wrong Marks : 1

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Let ABC be a triangle such that the vertex A has coordinates (-3,

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