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CUET admission questions 2011-12 (Chittagong University of Engineering & 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.নিম্নলিখিত ভেক্টর প্রোডাক্টের মান বাহির কর: (2i^−3j^)⋅[(i^+j^−k^)×(3i^−k^)](2\hat{i} - 3\hat{j}) \cdot [(\hat{i} + \hat{j} - \hat{k}) \times (3\hat{i} - \hat{k})]

    1. A.44
    2. B.88
    3. C.−4-4
    4. D.None of these

  2. 2.একটি লিফট 1ms−21\text{ms}^{-2} ত্বরণে নিচে নামছে। লিফটের মধ্যে দাঁড়ানো একজন ব্যক্তির ভর 65 kg65\text{ kg} হলে তিনি যে বল অনুভব করবেন

    1. A.350 N350\text{ N}
    2. B.572 N572\text{ N}
    3. C.250 N250\text{ N}
    4. D.None of these

Higher Math 1st Paper

  1. 3.If y=10log⁡(sin⁡x)y=10^{\log(\sin x)}, what is the value of dydx\frac{dy}{dx}?

    1. A.10log⁡(sin⁡x)log⁡e10(cot⁡x)10^{\log(\sin x)}\log_e^{10(\cot x)}
    2. B.10log⁡(sin⁡x)log⁡e10/sin⁡x10^{\log(\sin x)}\log_e^{10/\sin x}
    3. C.10log⁡(sin⁡x)log⁡e1010^{\log(\sin x)}\log_e^{10}
    4. D.None of these

  2. 4.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}

  3. 5.For what value of C, will the tangent of the curve y=Cx(1+x)y = Cx(1 + x) at the origin make an angle 30∘30^{\circ} with x-axis?

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

  4. 6.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

  5. 7.What is the area bounded by the curves y=xy = x and y2=16xy^2 = 16x?

    1. A.5123\frac{512}{3} sq. unit
    2. B.128 sq. unit
    3. C.1283\frac{128}{3} sq. unit
    4. D.None of these

Higher Math 2nd Paper

  1. 8.What is the distance between the foci of the hyperbola x2−y2=18x^2 - y^2 = 18?

    1. A.222\sqrt{2} unit
    2. B.12 unit
    3. C.3 unit
    4. D.None of these

  2. 9.Forces 2N, 4N and 6N are acting simultaneously on a particle along the sides AB, BC and CA of an equilateral triangle ABC respectively. Find the magnitude of the resultant.

    1. A.232\sqrt{3}N
    2. B.12N
    3. C.2N
    4. D.None of these

  3. 10.If a particle is projected with velocity u and 45∘45^{\circ} inclined with the horizontal direction, then the horizontal range is-

    1. A.u22g\frac{u^2}{2g}
    2. B.u22g\frac{u^2}{\sqrt{2}g}
    3. C.(ug)2\left(\frac{u}{\sqrt{g}}\right)^2
    4. D.None of these
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