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IUT admission questions 2023-24 (Islamic University of Technology)

All 18 questions of this paper are below. Subjects: Chemistry 1st Paper (1), Higher Math 1st Paper (8), Higher Math 2nd Paper (1).

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Chemistry 1st Paper

  1. 1.What is the principle underlying HPLC (High- Performance Liquid Chromatography)?

    1. A.Separation based on differences in boiling points.
    2. B.Separation based on differences in solubility.
    3. C.Separation based on differences in affinity for the stationary phase.
    4. D.Separation based on differences in vapor pressure.

Higher Math 1st Paper

  1. 2.If the matrix [a+482a−2]\begin{bmatrix} a+4 & 8 \\ 2 & a-2 \end{bmatrix} is singular, find the values of a.

    1. A.3,83, 8
    2. B.4,84, 8
    3. C.8,38, 3
    4. D.−6,4-6, 4

  2. 3.The equation of a circle is x2+y2+4x+6y−12=0x^2 + y^2 + 4x + 6y - 12 = 0. The co-ordinate of one end of a diameter on this circle is (1,1)(1, 1). Find the co-ordinate of the other end point of the diameter.

    1. A.(−5,−7)(-5, -7)
    2. B.(−3,−5)(-3, -5)
    3. C.(−5,−6)(-5, -6)
    4. D.(−3,−6)(-3, -6)

  3. 4.The center of the circle x=2−3cos⁡2θ,y=1+3sin⁡2θx = 2 - 3 \cos 2\theta, y = 1 + 3 \sin 2\theta is-

    1. A.(−2,−1)(-2, -1)
    2. B.(2,1)(2, 1)
    3. C.(2,−1)(2, -1)
    4. D.None

  4. 5.lim⁡x→0ex−e−x−2xx−sin⁡x=?\lim_{x \to 0} \frac{e^x-e^{-x}-2x}{x-\sin x} = ?

    1. A.12\frac{1}{2}
    2. B.22
    3. C.11
    4. D.None

  5. 6.ddxtan⁡−1(cos⁡x1+sin⁡x)=\frac{d}{dx}\tan^{-1}\left(\frac{\cos x}{1+\sin x}\right)=?

    1. A.00
    2. B.12\frac{1}{2}
    3. C.−1-1
    4. D.−12-\frac{1}{2}

  6. 7.If xy+x2y2−5=0xy + x^2y^2 - 5 = 0, find dydx\frac{dy}{dx}.

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

  7. 8.Consider a curve C given by the equation, y=2x2−x+3y = 2x^2 - x + 3 Assume C crosses the y-axis at the point P and the straight-line L is normal to C at point P. Find the equation of the line L.

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

  8. 9.The minimum value of 'm' for which the function f(x)=x2+mx+1\text{f(x)} = \text{x}^2 + \text{mx} + 1 becomes an increasing function in the interval 3<x<53 < \text{x} < 5 is:

    1. A.33
    2. B.43\frac{4}{3}
    3. C.−6-6
    4. D.22

Higher Math 2nd Paper

  1. 10.3−4i=?\sqrt{3 - 4i} =?

    1. A.±(2−i)\pm(2 - i)
    2. B.±(2+i)\pm(2 + i)
    3. C.±(4−i)\pm(4 - i)
    4. D.±(4+i)\pm(4 + i)
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