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CUET admission questions 2014-15 (Chittagong University of Engineering & Technology)

All 10 questions of this paper are below. Subjects: Physics 1st Paper (2), Higher Math 1st Paper (6), Higher Math 2nd Paper (2).

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Physics 1st Paper

  1. 1.একটি ভর সিস্টেমের তিনটি ভর যথাক্রমে m1=1kgm_1 = 1\text{kg}, m2=2kgm_2 = 2\text{kg} এবং m3=3kgm_3 = 3\text{kg} একটি সমবাহু ত্রিভুজ (প্রতিটি বাহুর দৈর্ঘ্য 1m1\text{m}) এর তিনটি কর্ণারে অবস্থিত। ইহার ভরকেন্দ্র নির্ণয় কর।

    1. A.(3.53,36)(\frac{3.5}{\sqrt{3}}, \frac{\sqrt{3}}{6}) or (34,3.56)(\frac{\sqrt{3}}{4}, \frac{3.5}{6})
    2. B.(63.5,43)(\frac{6}{3.5}, \frac{4}{\sqrt{3}}) or (64,3.53)(\frac{6}{4}, \frac{3.5}{\sqrt{3}})
    3. C.(3.54,64)(\frac{3.5}{4}, \frac{6}{4}) or (64,3.54)(\frac{6}{4}, \frac{3.5}{4})
    4. D.(33.5,23)(\frac{3}{3.5}, \frac{2}{\sqrt{3}}) or (23,33.5)(\frac{2}{\sqrt{3}}, \frac{3}{3.5})

  2. 2.এক ব্যক্তি সিঁড়ি দিয়ে তিন তলায় উঠতে এক মিনিট সময় নেয়। সিঁড়িতে 4040 টি ধাপ রয়েছে এবং প্রতিটি ধাপের উচ্চতা 12 cm12\text{ cm}। ঐ ব্যক্তির ভর 80 kg80\text{ kg} হলে তার অশ্বক্ষমতা কত?

    1. A.0.094 HP0.094\text{ HP}
    2. B.0.480 HP0.480\text{ HP}
    3. C.0.048 HP0.048\text{ HP}
    4. D.0.840 HP0.840\text{ HP}
    5. E.0.084 HP0.084\text{ HP}

Higher Math 1st Paper

  1. 3.A perpendicular is drawn on the line x−3y+4=0x - \sqrt{3}y + 4 = 0 from the point (1,2)(1, 2). What is the distance of that perpendicular from the origin?

    1. A.−2−32\frac{-2 - \sqrt{3}}{2}
    2. B.2+32\frac{2 + \sqrt{3}}{2}
    3. C.2±22\frac{2 \pm \sqrt{2}}{2}
    4. D.None of them

  2. 4.If sin⁡α+sin⁡β=a\sin \alpha + \sin \beta = a and cos⁡α+cos⁡β=b\cos \alpha + \cos \beta = b, what is the value of cos⁡(α−β)\cos(\alpha - \beta)?

    1. A.a2+b2+22\frac{a^2 + b^2 + 2}{2}
    2. B.a2+b2−22\frac{a^2 + b^2 - 2}{2}
    3. C.a2−b2−22\frac{a^2 - b^2 - 2}{2}
    4. D.a2−b2+22\frac{a^2 - b^2 + 2}{2}

  3. 5.If in case of triangle ABC, a4+b4+c4=2c2(a2+b2)a^4 + b^4 + c^4 = 2c^2(a^2 + b^2), then the value of cos⁡C\cos C will be-

    1. A.12\frac{1}{\sqrt{2}}
    2. B.±12\pm \frac{1}{\sqrt{2}}
    3. C.±32\pm \frac{\sqrt{3}}{2}
    4. D.None of them

  4. 6.The value of lim⁡x→π(1+cos⁡xsin⁡x)\lim_{x \to \pi} \left(\frac{1+\cos x}{\sin x}\right) is-

    1. A.0
    2. B.1
    3. C.−1-1
    4. D.None of them

  5. 7.If x=tan⁡−11−cos⁡θ1+cos⁡θx = \tan^{-1} \sqrt{\frac{1-\cos \theta}{1+\cos \theta}} and y=tan⁡−1cos⁡θ1+sin⁡θy = \tan^{-1} \frac{\cos \theta}{1+\sin \theta}, what is the value of dydx\frac{dy}{dx}?

    1. A.−1-1
    2. B.11
    3. C.±1\pm 1
    4. D.00

  6. 8.Evaluate: ∫012x3e−x2dx\int_{0}^{1} 2x^3 e^{-x^2} dx.

    1. A.−2e+1-\frac{2}{e} + 1
    2. B.−2e-\frac{2}{e}
    3. C.−1e+1-\frac{1}{e} + 1
    4. D.None of these

Higher Math 2nd Paper

  1. 9.If the root 'a' of equation x3−2x2−x+2=0x^3 - 2x^2 - x + 2 = 0 lies in the range −2<x<0-2 < x < 0, the value of 3a3+2a2+13a^3 + 2a^2 + 1 is-

    1. A.-1
    2. B.0
    3. C.1
    4. D.None of them

  2. 10.A body of mass 4kg falls from a height of 150 meters and comes to rest after penetrating 2 meters in mud. The average thrust of mud on the object will be-

    1. A.2979.2N
    2. B.2879.2N
    3. C.2880.2N
    4. D.None of them
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