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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

  1. 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]

    --- Content provided by​ FirstRanker.com ---

    1. 0

      [Option ID = 42062]

    2. 1

      [Option ID = 42063]

      --- Content provided by​ FirstRanker.com ---

    3. 2

      [Option ID = 42064]

    4. 3

      --- Content provided by‌ FirstRanker.com ---

      [Option ID = 42065]

    Correct Answer :-

    • 1 [Option ID = 42063]

    2. --- Content provided by‌ FirstRanker.com ---

  2. The domain of the function f(x) = 16-xC2x-1+20-3xC4x-5, where the symbols have their usual meanings, is the set

    [Question ID = 10518]

    1. {2, 3}

      [Option ID = 42066]

      2. --- Content provided by‍ FirstRanker.com ---

    2. {2, 3, 4}

      [Option ID = 42067]

    3. {1, 2, 3, 4}

      [Option ID = 42068]

      --- Content provided by‌ FirstRanker.com ---

    4. {1, 2, 3}

      [Option ID = 42069]

    Correct Answer :-

    --- Content provided by‍ FirstRanker.com ---

    • {2, 3} [Option ID = 42066]

  3. If the function f(x) = ax+a-x/2, where a > 2, then f(x + y) + f(x - y) is equal to

    [Question ID = 10519]

    1. f(x) + f(y)

      --- Content provided by⁠ FirstRanker.com ---

      [Option ID = 42070]

    2. f(x) - f(y)

      [Option ID = 42071]

      3. --- Content provided by‌ FirstRanker.com ---

    3. f(y)

      [Option ID = 42072]

    4. 2f(x)f(y)

      [Option ID = 42073]

      --- Content provided by FirstRanker.com ---

    Correct Answer :-

    • 2f(x)f(y) [Option ID = 42073]

  4. Let Xn = {z = x + i y: |z|² = 1/n} for all integers n = 1. Then Xn is

    --- Content provided by FirstRanker.com ---

    1. A finite set

      [Option ID = 42074]

    2. Not a finite set

      [Option ID = 42075]

      --- Content provided by FirstRanker.com ---

    3. An empty set

      [Option ID = 42076]

    4. A finite set with more than one element

      --- Content provided by FirstRanker.com ---

      [Option ID = 42077]

    Correct Answer :-

    • A singleton set [Option ID = 42074]

    5. --- Content provided by‌ FirstRanker.com ---

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

    [Question ID = 10521]

    1. 7n/2

      [Option ID = 42078]

      2. --- Content provided by FirstRanker.com ---

    2. 7(n+1)/2

      [Option ID = 42079]

    3. 7n(n+1)/2

      [Option ID = 42080]

      --- Content provided by‍ FirstRanker.com ---

    4. 7n(n+1)/2

      [Option ID = 42081]

    Correct Answer :-

    --- Content provided by⁠ FirstRanker.com ---

    • 7n(n+1)/2 [Option ID = 42081]

  6. 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

      --- Content provided by⁠ FirstRanker.com ---

      [Option ID = 42082]

    2. 11

      [Option ID = 42083]

      3. --- Content provided by‌ FirstRanker.com ---

    3. 44

      [Option ID = 42084]

    4. cannot be determined

      [Option ID = 42085]

      --- Content provided by​ FirstRanker.com ---

    Correct Answer :-

    • 11 [Option ID = 42083]

  7. A die is thrown (2n+1) times, n ? N. The probability that faces with even numbers show odd number of times, is

    --- Content provided by‍ FirstRanker.com ---

    [Question ID = 10523]

    1. 2n+1/4n+3

      [Option ID = 42086]

    2. Less than 1/2

      --- Content provided by FirstRanker.com ---

      [Option ID = 42087]

    3. Greater than 1/2

    8. --- Content provided by‌ FirstRanker.com ---

  8. Correct Answer :-

    • 1/2 [Option ID = 42089]

  9. 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]

    --- Content provided by​ FirstRanker.com ---

    1. 3/4

      [Option ID = 42090]

    2. 4/5

      [Option ID = 42091]

      --- Content provided by⁠ FirstRanker.com ---

    3. 1/2

    4. 1/6

      [Option ID = 42093]

      --- Content provided by​ FirstRanker.com ---

    Correct Answer :-

    • 4/5 [Option ID = 42091]

  10. 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

    --- Content provided by FirstRanker.com ---

    [Question ID = 10525]

    1. 0.2

      [Option ID = 42094]

    2. 0.25

      --- Content provided by⁠ FirstRanker.com ---

      [Option ID = 42095]

    3. 0.6

      [Option ID = 42096]

      4. --- Content provided by⁠ FirstRanker.com ---

    4. 0.4

      [Option ID = 42097]

    Correct Answer :-

    • 0.2 [Option ID = 42094]

      • --- Content provided by‌ FirstRanker.com ---

  11. 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]

      --- Content provided by⁠ FirstRanker.com ---

    2. 1/3

      [Option ID = 42099]

    3. 1/2

      --- Content provided by‍ FirstRanker.com ---

      [Option ID = 42100]

    4. 1

      [Option ID = 42101]

      5. --- Content provided by⁠ FirstRanker.com ---

    Correct Answer :-

    • 1/2 [Option ID = 42100]

  12. If a randomly chosen point of the circle lies within the square, then outside the square, then

    [Question ID = 10527]

    --- Content provided by‍ FirstRanker.com ---

    1. p1 = p2

      [Option ID = 42102]

    2. p1 < p2

      [Option ID = 42103]

      --- Content provided by⁠ FirstRanker.com ---

    3. p1 > p2

      [Option ID = 42104]

    4. p1 - p2 = 1/3

      --- Content provided by​ FirstRanker.com ---

      [Option ID = 42105]

    Correct Answer :-

    • p1 > p2 [Option ID = 42104]

    13. --- Content provided by‍ FirstRanker.com ---

  13. 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. --- Content provided by‍ FirstRanker.com ---

    2. A, B are exclusive

      [Option ID = 42107]

    3. P(A) < P(B)

      [Option ID = 42108]

      --- Content provided by⁠ FirstRanker.com ---

    4. P(B) < P(A)

      [Option ID = 42109]

    Correct Answer :-

    --- Content provided by FirstRanker.com ---

    • P(A n B) = 1/3 [Option ID = 42106]

  14. 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)

      --- Content provided by‌ FirstRanker.com ---

      [Option ID = 42110]

    2. 6(n-3)/(n-1)(n-2)

      [Option ID = 42111]

      3. --- Content provided by‌ FirstRanker.com ---

    3. 6(n-4)/(n-1)(n-2)

      [Option ID = 42112]

    4. 6(n-2)/(n-1)(n-3)

      [Option ID = 42113]

      --- Content provided by‌ FirstRanker.com ---

    Correct Answer :-

    • 6(n-4)/(n-1)(n-2) [Option ID = 42112]

  15. If f(x) = 1/1-x, then the points of discontinuity of the function f3n(x), where, fn = fofo... of, n-times, is/are

    --- Content provided by‍ FirstRanker.com ---

    [Question ID = 10530]

    1. x = 2

    2. x = -1

      [Option ID = 42116]

      --- Content provided by⁠ FirstRanker.com ---

    3. continuous everywhere

      [Option ID = 42117]

    Correct Answer :-

    --- Content provided by FirstRanker.com ---

    • x = {0, 1} [Option ID = 42115]

  16. 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

      --- Content provided by‍ FirstRanker.com ---

      [Option ID = 42118]

    2. 2

    3. 5

      --- Content provided by⁠ FirstRanker.com ---

      [Option ID = 42120]

    4. 4

      [Option ID = 42121]

      5. --- Content provided by​ FirstRanker.com ---

    Correct Answer :-

    • 5 [Option ID = 42120]

  17. 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]

    --- Content provided by‍ FirstRanker.com ---

    1. 0

      [Option ID = 42122]

    2. 8

      3. --- Content provided by⁠ FirstRanker.com ---

    3. -1

      [Option ID = 42124]

    4. 2

      [Option ID = 42125]

      --- Content provided by FirstRanker.com ---

    Correct Answer :-

    • 8 [Option ID = 42123]

  18. 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

    --- Content provided by‌ FirstRanker.com ---

    [Question ID = 10533]

    1. v6-v2 unit

      [Option ID = 42126]

    2. v6+ v2 unit

      --- Content provided by FirstRanker.com ---

      [Option ID = 42127]

    3. -v6-v2 unit

    19. --- Content provided by‌ FirstRanker.com ---

  19. Correct Answer :-

    • v6-v2 unit [Option ID = 42126]

  20. ?p/20xsin x/1+ cos2x dx =

    [Question ID = 10534]

    --- Content provided by​ FirstRanker.com ---

    1. p/4

      [Option ID = 42130]

    2. p²/2

      [Option ID = 42131]

      --- Content provided by⁠ FirstRanker.com ---

    3. p²/4

      [Option ID = 42132]

    4. p/2

      --- Content provided by‍ FirstRanker.com ---

      [Option ID = 42133]

    Correct Answer :-

    • p²/4 [Option ID = 42132]

    21. --- Content provided by FirstRanker.com ---

  21. lim t?8 ?t11/x(x²+1) dx =

    [Question ID = 10535]

    1. ln v2

      [Option ID = 42134]

      2. --- Content provided by‍ FirstRanker.com ---

    2. 1 + ln 2

      [Option ID = 42135]

    3. ln 2

      [Option ID = 42136]

      --- Content provided by⁠ FirstRanker.com ---

    4. 1

      [Option ID = 42137]

    Correct Answer :-

    --- Content provided by⁠ FirstRanker.com ---

    • ln v2 [Option ID = 42134]

  22. 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

      --- Content provided by FirstRanker.com ---

      [Option ID = 42138]

    2. 38

      [Option ID = 42139]

      3. --- Content provided by⁠ FirstRanker.com ---

    3. 41

      [Option ID = 42140]

    4. 36

      [Option ID = 42141]

      --- Content provided by FirstRanker.com ---

    Correct Answer :-

    • 41

  23. Consider the two integrals for a > 0

    --- Content provided by‍ FirstRanker.com ---

    I1 = ?p/201/1 + tanax dx

    I2 = ?p/201/1+ cotax 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.

    --- Content provided by FirstRanker.com ---

    Statement III: I1 = I2 for all values of a.

    [Question ID = 10537]

    1. Only statements II and III are correct.

      [Option ID = 42142]

      2. --- Content provided by‌ FirstRanker.com ---

    2. Only statements I and III are correct.

      [Option ID = 42143]

    3. Only statement II is correct.

      [Option ID = 42144]

      --- Content provided by​ FirstRanker.com ---

    4. Only statement I is correct.

      [Option ID = 42145]

    Correct Answer :-

    --- Content provided by​ FirstRanker.com ---

    • Only statements II and III are correct. [Option ID = 42142]

  24. The minimum value of the function sin4x +1.5 cos4x is

    [Question ID = 10538]

    1. 0.6

      --- Content provided by​ FirstRanker.com ---

      [Option ID = 42146]

    2. 0.5

      [Option ID = 42147]

      3. --- Content provided by‌ FirstRanker.com ---

    3. 1.5

      [Option ID = 42148]

    4. 1

      5. --- Content provided by FirstRanker.com ---

  25. Correct Answer :-

    • 0.6 [Option ID = 42146]

  26. 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

    --- Content provided by⁠ FirstRanker.com ---

    [Question ID = 10539]

    1. 56

      [Option ID = 42150]

    2. 76

      --- Content provided by‌ FirstRanker.com ---

      [Option ID = 42151]

    3. 64

    27. --- Content provided by‍ FirstRanker.com ---

  27. Correct Answer :-

    • 76 [Option ID = 42151]

  28. p (x) is a polynomial with real coefficients. The remainder term of P(x)/(x + 3)3 is

    [Question ID = 10540]

    --- Content provided by‌ FirstRanker.com ---

    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]

      --- Content provided by‌ FirstRanker.com ---

    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

      --- Content provided by​ FirstRanker.com ---

      [Option ID = 42157]

    Correct Answer :-

    • P(-3) + P'(-3)(x+3) + 1/2P"(-3)(x + 3)2 [Option ID = 42154]

    29. --- Content provided by‌ FirstRanker.com ---

  29. 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

--- Content provided by​ FirstRanker.com ---

This post was last modified on 27 December 2020