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IUT admission questions 2014-15 (Islamic University of Technology)

All 22 questions of this paper are below. Subjects: Physics 1st Paper (3), Higher Math 1st Paper (7).

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Physics 1st Paper

  1. 1.40 N40\text{ N} এর একটি বল 8 kg8\text{ kg} ভরের একটি স্থির বস্তুর উপরে ক্রিয়া করে। 4 sec4\text{ sec} পর যদি বলের ক্রিয়া বন্ধ হয়ে যায় তবে প্রথম থেকে 9 sec9\text{ sec} এ বস্তুটি কত দূরত্ব অতিক্রম করবে?

    1. A.120 m120\text{ m}
    2. B.110 m110\text{ m}
    3. C.130 m130\text{ m}
    4. D.140 m140\text{ m}
    5. E.150 m150\text{ m}

  2. 2.A 35.0g35.0 \text{g} bullet strikes a 5.0kg5.0 \text{kg} stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6ms−18.6\text{ms}^{-1}. What was the original speed of the bullet? (একটি 35.0g35.0\text{g} বুলেট একটি 5.0kg5.0\text{kg} স্থির কাঠের ব্লকে আঘাত করে এবং ব্লকের ভেতরে ঢুকে যায়। তারপর ব্লক এবং বুলেট একসাথে 8.6ms−18.6\text{ms}^{-1} বেগে উড়ে যায়। বুলেটটির প্রাথমিক বেগ কত ছিল?)

    1. A.1.2×103ms−11.2 \times 10^3\text{ms}^{-1}
    2. B.1.35×103ms−11.35 \times 10^3\text{ms}^{-1}
    3. C.1.35×102ms−11.35 \times 10^2\text{ms}^{-1}
    4. D.1.2×102ms−11.2 \times 10^2\text{ms}^{-1}

  3. 3.When the velocity of a moving object is increased by 4 ms−14\text{ ms}^{-1}, its kinetic energy is doubled. What is the initial velocity of the object? (যখন কোন গতিশীল বস্তুর বেগ 4 ms−14\text{ ms}^{-1} বৃদ্ধি করা হয়, তখন এর গতিশক্তি দ্বিগুণ হয়। বস্তুটির প্রাথমিক বেগ কত?)

    1. A.4.66ms−14.66\text{ms}^{-1}
    2. B.9.66ms−19.66\text{ms}^{-1}
    3. C.7.66ms−17.66\text{ms}^{-1}
    4. D.6.66ms−16.66\text{ms}^{-1}

Higher Math 1st Paper

  1. 4.If A=[1234]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and AB=[671617]AB = \begin{bmatrix} 6 & 7 \\ 16 & 17 \end{bmatrix}, then B = ?

    1. A.[4213]\begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}
    2. B.[4312]\begin{bmatrix} 4 & 3 \\ 1 & 2 \end{bmatrix}
    3. C.[4132]\begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}
    4. D.[4321]\begin{bmatrix} 4 & 3 \\ 2 & 1 \end{bmatrix}

  2. 5.∣x+yxyxx+zzyzy+z∣=?\begin{vmatrix} x+y & x & y \\ x & x+z & z \\ y & z & y+z \end{vmatrix} = ?

    1. A.4xyz4xyz
    2. B.00
    3. C.11
    4. D.xy+yz+zxxy + yz + zx

  3. 6.If ∣abcdefghi∣=−6\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -6, then ∣3a3b3c−d−e−f4g4h4i∣=?\begin{vmatrix} 3a & 3b & 3c \\ -d & -e & -f \\ 4g & 4h & 4i \end{vmatrix} =?

    1. A.72
    2. B.-72
    3. C.6
    4. D.24

  4. 7.Assume that the point A(5, 6) is a reflection of the point B(-1, 8) in a line, when a mirror is placed along the line. The equation of the line is-

    1. A.3x−y−23=03x - y - 23 = 0
    2. B.x+3y−23=0x + 3y - 23 = 0
    3. C.3x−y+1=03x - y + 1 = 0
    4. D.x+3y−1=0x + 3y - 1 = 0

  5. 8.If the circles x2+y2−16x−12y+75=0x^2 + y^2 - 16x - 12y + 75 = 0 and 5x2+5y2−32x−24y+75=05x^2 + 5y^2 - 32x - 24y + 75 = 0 touch each other, then the equation of the common tangent of their point of contact is-

    1. A.3y+5x=293y + 5x = 29
    2. B.3y+4x=253y + 4x = 25
    3. C.3y+4x=243y + 4x = 24
    4. D.3y+5x=253y + 5x = 25

  6. 9.The value of lim⁡x→∞(x2+1−x)\lim_{x \to \infty} (\sqrt{x^2+1}-x) is-

    1. A.00
    2. B.∞\infty
    3. C.−∞-\infty
    4. D.11

  7. 10.ddxln⁡sin⁡x1−cos⁡x=\frac{d}{dx}\ln\frac{\sin x}{1-\cos x}=?

    1. A.−1-1
    2. B.cot⁡x−tan⁡x+1\cot x-\tan x+1
    3. C.cosec⁡x\operatorname{cosec} x
    4. D.−cosec⁡x-\operatorname{cosec} x
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