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IUT admission questions 2010-11 (Islamic University of Technology)

All 10 questions of this paper are below. Subjects: Physics 1st Paper (2), Higher Math 1st Paper (5), Higher Math 2nd Paper (3).

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Physics 1st Paper

  1. 1.The larger and smaller resultants of two vectors are 28 units and 4 units, respectively. They acted on a particle with an angle of 90° with each other. What is the value of resultant?

    1. A.None of them
    2. B.28 unit
    3. C.24 unit
    4. D.20 unit

  2. 2.দুটি ভেক্টর রাশির বৃহত্তর ও ক্ষুদ্রতর লব্ধিদ্বয় যথাক্রমে 28 একক ও 4 একক। রাশি দুটি পরস্পরের সাথে 90° কোণে কোন একটি কণার উপর ক্রিয়া করল। লব্ধির মান কত?

    1. A.None of them
    2. B.28 unit
    3. C.24 unit
    4. D.20 unit

Higher Math 1st Paper

  1. 3.∣1ωω2ωω21ω21ω∣=?\begin{vmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{vmatrix} =?

    1. A.1
    2. B.ω\omega
    3. C.ω2\omega^2
    4. D.0

  2. 4.If the points (2,2−2x)(2, 2 - 2x), (1,2)(1, 2) and (2,b−2x)(2, b - 2x) are collinear, the value of b is—

    1. A.−1-1
    2. B.11
    3. C.22
    4. D.−2-2

  3. 5.If y=x2log⁡xy = x^2 \log x, then d3ydx3\frac{d^3y}{dx^3} is-

    1. A.−x2-\frac{x}{2}
    2. B.2x\frac{2}{x}
    3. C.−2x-\frac{2}{x}
    4. D.x2\frac{x}{2}

  4. 6.The radius of a circular plate increases at the rate of 0.25 cm/sec when heat is applied. If the radius of the plate is 7 cm, the area increase rate is-

    1. A.10 cm2^2/sec
    2. B.11 cm2^2/sec
    3. C.0.5 cm2^2/sec
    4. D.12 cm2^2/sec

  5. 7.Find the value of ∫exsec⁡x(1+tan⁡x)dx\int e^x \sec x (1 + \tan x) dx

    1. A.exsec⁡x+ce^x \sec x + c
    2. B.excos⁡ecx+ce^x \cos e cx + c
    3. C.extan⁡x+ce^x \tan x + c
    4. D.None of these

Higher Math 2nd Paper

  1. 8.If a moving point is P≡(asin⁡θ,bcos⁡θ)P \equiv (a \sin\theta, b \cos\theta), then the locus of PP will be a-

    1. A.Parabola
    2. B.Circle
    3. C.Ellipse
    4. D.Straight line

  2. 9.Evaluate: tan⁡−1mn−tan⁡−1m−nm+n\tan^{-1} \frac{m}{n} - \tan^{-1} \frac{m-n}{m+n}

    1. A.π3\frac{\pi}{3}
    2. B.π2\frac{\pi}{2}
    3. C.π9\frac{\pi}{9}
    4. D.π4\frac{\pi}{4}

  3. 10.How many solutions are there for sec⁡4θ−sec⁡2θ=2\sec 4\theta - \sec 2\theta = 2 [0∘<θ<180∘][0^\circ < \theta < 180^\circ]?

    1. A.3
    2. B.5
    3. C.6
    4. D.9
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