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Delhi University Entrance Test (DUET) 2020 Previous Year Question Paper With Answer Key

This post was last modified on 27 December 2020

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DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

Topic:- ME MSC S2

If 2 < x² <3, then the number of positive roots of {x²} = ¹/₂ (where {x} denotes the fractional part of x) is

[Question ID = 10517]
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1. 0
  
  [Option ID = 42062]
2. 1
  
  [Option ID = 42063]
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3. 2
  
  [Option ID = 42064]
4. 3
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  [Option ID = 42065]
Correct Answer :-
- 1 [Option ID = 42063]

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The domain of the function f(x) = ^16-xC_2x-1+^20-3xC_4x-5, where the symbols have their usual meanings, is the set

[Question ID = 10518]
1. {2, 3}
  
  [Option ID = 42066]
2. {2, 3, 4}
  
  [Option ID = 42067]
3. {1, 2, 3, 4}
  
  [Option ID = 42068]
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4. {1, 2, 3}
  
  [Option ID = 42069]
Correct Answer :-
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- {2, 3} [Option ID = 42066]
If the function f(x) = ^{a^x+a^-x}/₂, where a > 2, then f(x + y) + f(x - y) is equal to

[Question ID = 10519]
1. f(x) + f(y)
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  [Option ID = 42070]
2. f(x) - f(y)
  
  [Option ID = 42071]
3. f(y)
  
  [Option ID = 42072]
4. 2f(x)f(y)
  
  [Option ID = 42073]
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Correct Answer :-
- 2f(x)f(y) [Option ID = 42073]
Let X_n = {z = x + i y: |z|² = ¹/_n} for all integers n = 1. Then X_n is
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1. A finite set
  
  [Option ID = 42074]
2. Not a finite set
  
  [Option ID = 42075]
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3. An empty set
  
  [Option ID = 42076]
4. A finite set with more than one element
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  [Option ID = 42077]
Correct Answer :-
- A singleton set [Option ID = 42074]

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If f: R ? R satisfies f(x + y) = f(x) + f (y), ?x, y ? R and f(1) = 7, then ?ⁿ_r=1f(r) is

[Question ID = 10521]
1. ⁷ⁿ/₂
  
  [Option ID = 42078]
2. ⁷⁽ⁿ⁺¹⁾/₂
  
  [Option ID = 42079]
3. ^7n(n+1)/₂
  
  [Option ID = 42080]
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4. ^7n(n+1)/₂
  
  [Option ID = 42081]
Correct Answer :-
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- ^7n(n+1)/₂ [Option ID = 42081]
64 numbers that are not necessarily distinct, are placed on the squares of a chessboard such that the sum of the numbers in every 2x2 square is 11. The sum of the four numbers in the corners of the board is

[Question ID = 10522]
1. 22
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  [Option ID = 42082]
2. 11
  
  [Option ID = 42083]
3. 44
  
  [Option ID = 42084]
4. cannot be determined
  
  [Option ID = 42085]
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Correct Answer :-
- 11 [Option ID = 42083]
A die is thrown (2n+1) times, n ? N. The probability that faces with even numbers show odd number of times, is
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[Question ID = 10523]
1. ^2ⁿ⁺¹/_4ⁿ⁺³
  
  [Option ID = 42086]
2. Less than 1/2
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  [Option ID = 42087]
3. Greater than 1/2

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Correct Answer :-
- 1/2 [Option ID = 42089]
The outcomes of an experiment are represented by points in the square bounded by x = 0, y = 0, x = 2 and y = 2 in XY plane. If the probability is distributed uniformly, then the probability that x² + y² > 1 is closest to

[Question ID = 10524]
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1. 3/4
  
  [Option ID = 42090]
2. 4/5
  
  [Option ID = 42091]
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3. 1/2
4. 1/6
  
  [Option ID = 42093]
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Correct Answer :-
- 4/5 [Option ID = 42091]
A number x is chosen from the set {1, 2, 3, ..., 99, 100}. If A is the event that the chosen number x satisfies ^x-40/₁₀ = 2, then the probability of the event A is
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[Question ID = 10525]
1. 0.2
  
  [Option ID = 42094]
2. 0.25
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  [Option ID = 42095]
3. 0.6
  
  [Option ID = 42096]
4. 0.4
  
  [Option ID = 42097]
Correct Answer :-
- 0.2 [Option ID = 42094]
Let x₁,x₂, x₃ be uncorrelated variables each having the same standard deviation. The coefficient of correlation between (x₁+x₂) and (x₂ + x₃) is

[Question ID = 10526]
1. 1/4
  
  [Option ID = 42098]
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2. 1/3
  
  [Option ID = 42099]
3. 1/2
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  [Option ID = 42100]
4. 1
  
  [Option ID = 42101]
Correct Answer :-
- 1/2 [Option ID = 42100]
If a randomly chosen point of the circle lies within the square, then outside the square, then

[Question ID = 10527]
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1. p₁ = p₂
  
  [Option ID = 42102]
2. p₁ < p₂
  
  [Option ID = 42103]
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3. p₁ > p₂
  
  [Option ID = 42104]
4. p₁ - p₂ = 1/3
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  [Option ID = 42105]
Correct Answer :-
- p₁ > p₂ [Option ID = 42104]

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Given that x ? [0,1] and y ? [0,1]. Let A be the event of (x, y) satisfying y² = x and B be the event of satisfying x² = y, then

[Question ID = 10528]
1. P(A n B) = 1/3
  
  [Option ID = 42106]
2. A, B are exclusive
  
  [Option ID = 42107]
3. P(A) < P(B)
  
  [Option ID = 42108]
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4. P(B) < P(A)
  
  [Option ID = 42109]
Correct Answer :-
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- P(A n B) = 1/3 [Option ID = 42106]
A triangle is formed with the vertices of n sided regular polygon. Then the probability that the triangle have exactly one side common with the side of the polygon is

[Question ID = 10529]
1. ^6(n-2)(n-3)/_n(n-1)
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  [Option ID = 42110]
2. ^6(n-3)/_(n-1)(n-2)
  
  [Option ID = 42111]
3. ^6(n-4)/_(n-1)(n-2)
  
  [Option ID = 42112]
4. ^6(n-2)/_(n-1)(n-3)
  
  [Option ID = 42113]
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Correct Answer :-
- ^6(n-4)/_(n-1)(n-2) [Option ID = 42112]
If f(x) = ¹/_1-x, then the points of discontinuity of the function f³ⁿ(x), where, fⁿ = fofo... of, n-times, is/are
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[Question ID = 10530]
1. x = 2
2. x = -1
  
  [Option ID = 42116]
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3. continuous everywhere
  
  [Option ID = 42117]
Correct Answer :-
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- x = {0, 1} [Option ID = 42115]
The signum function is defined as sgn(x) = ^{-1, x < 0 0, x = 0 1, x > 0} .The number of points, where f(x) = sgn(x²-3x + 2) + [x-3], x ? [0,4] is discontinuous, where [.] denotes the greatest integers, is

[Question ID = 10531]
1. 3
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  [Option ID = 42118]
2. 2
3. 5
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  [Option ID = 42120]
4. 4
  
  [Option ID = 42121]
Correct Answer :-
- 5 [Option ID = 42120]
Let f be a function defined and continuous on [2,5]. If f(x) takes rational values for all x and f(4) = 8, then the value of f(3.7) is

[Question ID = 10532]
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1. 0
  
  [Option ID = 42122]
2. 8
3. -1
  
  [Option ID = 42124]
4. 2
  
  [Option ID = 42125]
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Correct Answer :-
- 8 [Option ID = 42123]
Two adjacent side of a cyclic quadrilateral measure 2 unit each and the angle between them is 30°. If the angle bisector of the angle between these sides passes through the opposite vertex and the centre of the circumscribed circle, then the radius of this circle is
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[Question ID = 10533]
1. v6-v2 unit
  
  [Option ID = 42126]
2. v6+ v2 unit
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  [Option ID = 42127]
3. -v6-v2 unit

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Correct Answer :-
- v6-v2 unit [Option ID = 42126]
?^p/2₀^{xsin x}/_{1+ cos²x} dx =

[Question ID = 10534]
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1. p/4
  
  [Option ID = 42130]
2. p²/2
  
  [Option ID = 42131]
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3. p²/4
  
  [Option ID = 42132]
4. p/2
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  [Option ID = 42133]
Correct Answer :-
- p²/4 [Option ID = 42132]

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lim _t?8 ?^t₁¹/_x(x²+1) dx =

[Question ID = 10535]
1. ln v2
  
  [Option ID = 42134]
2. 1 + ln 2
  
  [Option ID = 42135]
3. ln 2
  
  [Option ID = 42136]
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4. 1
  
  [Option ID = 42137]
Correct Answer :-
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- ln v2 [Option ID = 42134]
f (x) is a polynomial that satisfies f (x + y) = f (x) + f (y) +3xy for real numbers x and y. If f'(0) = 35, then the value f'(2) is

[Question ID = 10536]
1. 76
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  [Option ID = 42138]
2. 38
  
  [Option ID = 42139]
3. 41
  
  [Option ID = 42140]
4. 36
  
  [Option ID = 42141]
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Correct Answer :-
- 41
Consider the two integrals for a > 0
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I₁ = ?^p/2₀¹/_{1 + tan^ax} dx

I₂ = ?^p/2₀¹/_{1+ cot^ax} dx

and the statements

Statement I: The value of I₁ depends on the value of a.

Statement II: The value of I₂ does not depend on the value of a.
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Statement III: I₁ = I₂ for all values of a.

[Question ID = 10537]
1. Only statements II and III are correct.
  
  [Option ID = 42142]
2. Only statements I and III are correct.
  
  [Option ID = 42143]
3. Only statement II is correct.
  
  [Option ID = 42144]
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4. Only statement I is correct.
  
  [Option ID = 42145]
Correct Answer :-
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- Only statements II and III are correct. [Option ID = 42142]
The minimum value of the function sin⁴x +1.5 cos⁴x is

[Question ID = 10538]
1. 0.6
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  [Option ID = 42146]
2. 0.5
  
  [Option ID = 42147]
3. 1.5
  
  [Option ID = 42148]
4. 1
Correct Answer :-
- 0.6 [Option ID = 42146]
The number of ways in which three integers can be selected from the numbers 1 to 12 so that their sum is exactly divisible by 3 is
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[Question ID = 10539]
1. 56
  
  [Option ID = 42150]
2. 76
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  [Option ID = 42151]
3. 64

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Correct Answer :-
- 76 [Option ID = 42151]
p (x) is a polynomial with real coefficients. The remainder term of ^P(x)/_{(x + 3)³} is

[Question ID = 10540]
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1. P(-3) + P'(-3)(x+3) + ¹/₂P"(-3)(x + 3)²
  
  [Option ID = 42154]
2. P(3) + P'(3)(x + 3) + P"(3)(x+3)²
  
  [Option ID = 42155]
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3. P(-3) + P'(-3)(x + 3) + P(-3)(x + 3)²
  
  [Option ID = 42156]
4. P(3) - P'(3)(x + 3) + ¹/₂P" (3)(x + 3)²
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  [Option ID = 42157]
Correct Answer :-
- P(-3) + P'(-3)(x+3) + ¹/₂P"(-3)(x + 3)² [Option ID = 42154]

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The graph of x - y against x + y is given below

This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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This post was last modified on 27 December 2020

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