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BUET admission questions 2013-14 (Bangladesh University of Engineering & Technology)

All 13 questions of this paper are below. Subjects: Physics 1st Paper (1), Higher Math 1st Paper (8), Higher Math 2nd Paper (1).

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Physics 1st Paper

  1. 1.A force F⃗=(40i^+30j^) N\vec{F} = (40\hat{i} + 30\hat{j})\text{ N} is acting on an object of mass 10 kg10\text{ kg}. What is the magnitude of the acceleration of the object? Assume other forces are involved. (10 kg10\text{ kg} ভরের একটি বস্তুর উপর একটি বল, F⃗=(40i^+30j^) N\vec{F} = (40\hat{i} + 30\hat{j})\text{ N} ক্রিয়া করছে। বস্তুটির ত্বরণের মান কত? ধরে নাও অন্যান্য বল জড়িত নয়।)

    1. A.6 ms−26\text{ ms}^{-2}
    2. B.5 ms−25\text{ ms}^{-2}
    3. C.7 ms−27\text{ ms}^{-2}
    4. D.4 ms−24\text{ ms}^{-2}

Higher Math 1st Paper

  1. 2.For what value of a, the straight lines 3x+2y−5=0,ax+4y−9=03x + 2y - 5 = 0, ax + 4y - 9 = 0 and x+2y−7=0x + 2y - 7 = 0 will be concurrent?

    1. A.−7-7
    2. B.55
    3. C.33
    4. D.77

  2. 3.How many triangles can be formed by straight lines of length 1, 2, 3 and 4 units?

    1. A.1
    2. B.2
    3. C.3
    4. D.4

  3. 4.If y=(sin⁡−1x)2y = (\sin^{-1} x)^2, the value of (1−x2)y2−xy1(1 - x^2)y_2 - xy_1 will be-

    1. A.00
    2. B.22
    3. C.44
    4. D.11

  4. 5.For what value of k, will the tangent at the point x=1x = 1 of the curve y=k(x−1)(x+2)y = k(x - 1)(x + 2) make an angle of 60∘60^{\circ} with x-axis?

    1. A.13\frac{1}{\sqrt{3}}
    2. B.23\frac{2}{\sqrt{3}}
    3. C.32\frac{\sqrt{3}}{2}
    4. D.3\sqrt{3}

  5. 6.For the function f(x)=x+1xf(x) = x + \frac{1}{x}, the points at which tangents are parallel to x-axis are-

    1. A.(1,2),(−1,−2)(1, 2), (-1, -2)
    2. B.(−1,2),(1,0)(-1, 2), (1, 0)
    3. C.(2,−1),(0,1)(2, -1), (0, 1)
    4. D.(−1,2),(1,−2)(-1, 2), (1, -2)

  6. 7.If the rate of increase of the radius of a sphere is equal in magnitude to the rate of increase of its surface area, what will be the radius of the sphere?

    1. A.\frac{1}{4π}
    2. B.8π
    3. C.4π
    4. D.\frac{1}{8π}

  7. 8.What will be the value of sin⁡θ\sin \theta for which 7sec⁡θ−3tan⁡θ7 \sec \theta - 3 \tan \theta is minimum?

    1. A.73\frac{7}{3}
    2. B.710\frac{7}{10}
    3. C.−710\frac{-7}{10}
    4. D.37\frac{3}{7}

  8. 9.The value of 2∫sin⁡(2ex2)xex2dx2 \int \sin(2e^{x^2}) x e^{x^2} dx is:

    1. A.sin⁡(2ex2)+c\sin(2e^{x^2}) + c
    2. B.2sin⁡(2ex2)+c2 \sin(2e^{x^2}) + c
    3. C.cos⁡2(ex2)+c\cos^2(e^{x^2}) + c
    4. D.sin⁡2(ex2)+c\sin^2(e^{x^2}) + c

Higher Math 2nd Paper

  1. 10.The value of i+−i\sqrt{i} + \sqrt{-i} is-

    1. A.22
    2. B.11
    3. C.00
    4. D.2\sqrt{2}
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