SmartPrep BD

IUT admission questions 2020-21 (Islamic University of Technology)

All 13 questions of this paper are below. Subjects: Physics 1st Paper (3), Higher Math 1st Paper (7).

Practise with answers

Not every question of this paper is in the bank yet ("partial"), so it is offered for practice only. Practise this paper to see the correct answers and explanations: every answer is checked instantly (free account needed).

Physics 1st Paper

  1. 1.Length of a simple pendulum, l=100.0±0.5l = 100.0 \pm 0.5 cm, and time period, T=(2.00±0.01)T = (2.00 \pm 0.01) s. Determine the percentage of error in acceleration due to gravity 'g'. (একটি সরল দোলকের দৈর্ঘ্য, l=100.0±0.5l = 100.0 \pm 0.5 cm এবং পর্যায়কাল, T=(2.00±0.01)T = (2.00 \pm 0.01) s। অভিকর্ষজ ত্বরণ g নির্ণয়ে শতকরা ত্রুটির পরিমাণ নির্ণয় কর।)

    1. A.±1.5%\pm 1.5\%
    2. B.±2.0%\pm 2.0\%
    3. C.±1.05%\pm 1.05\%
    4. D.±1.75%\pm 1.75\%

  2. 2.A 0.25 kg0.25\text{ kg} ball hits a brick wall with a velocity of 30 ms−130\text{ ms}^{-1} and bounces back at the same speed. If the ball is in contact with the wall for 0.1 s0.1\text{ s}, what is the value of the force exerted by the wall on the ball? (একটি 0.25 kg0.25\text{ kg} ভরের বল 30 ms−130\text{ ms}^{-1} বেগে একটি ইটের দেয়ালে আঘাত করে এবং একই গতিতে ফিরে আসে। যদি বলটি 0.10.1 সেকেন্ডের জন্য দেয়ালের সংস্পর্শে থাকে, তবে বলের উপর দেয়ালের দ্বারা প্রয়োগ করা বলের মান কত?)

    1. A.100 N100\text{ N}
    2. B.−150 N-150\text{ N}
    3. C.−300 N-300\text{ N}
    4. D.0 N0\text{ N}

  3. 3.The recoil velocity of a gun of mass of 8 kg8\text{ kg} is 10 ms−110\text{ ms}^{-1} when a bullet of mass of 10 g10\text{ g} leaves from the gun. After penetrating 0.3 m0.3\text{ m} inside the target the bullet stops. Calculate the applied resistance of the bullet? (একটি 8 kg8\text{ kg} ভরের বন্দুক থেকে একটি 10 g10\text{ g} ভরের বুলেট নির্গত হলে বন্দুকের পশ্চাৎ বেগ হয় 10 ms−110\text{ ms}^{-1}। লক্ষ্যবস্তুতে 0.3 m0.3\text{ m} প্রবেশ করার পর বুলেটটি থেমে যায়। বুলেটটির উপর প্রযুক্ত বাধানকারী বল কত?)

    1. A.1.067×105 N1.067 \times 10^5\text{ N}
    2. B.1.067×106 N1.067 \times 10^6\text{ N}
    3. C.1.067×107 N1.067 \times 10^7\text{ N}
    4. D.1.067×108 N1.067 \times 10^8\text{ N}

Higher Math 1st Paper

  1. 4.If 2[345x]+[1y01]=[70105]2 \begin{bmatrix} 3 & 4 \\ 5 & x \end{bmatrix} + \begin{bmatrix} 1 & y \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 7 & 0 \\ 10 & 5 \end{bmatrix}, then what is the value of (x−y)(x - y)?

    1. A.−8-8
    2. B.22
    3. C.1010
    4. D.−6-6

  2. 5.If A\text{A} is a 3×33 \times 3 invertible matrix and det⁡(A−1)=(det⁡A)k+2\det(\text{A}^{-1}) = (\det\text{A})^{k+2}, then the value of k is-

    1. A.1
    2. B.0
    3. C.-1
    4. D.-3

  3. 6.The locus of the center of the circles such that the point (2,3)(2, 3) is the midpoint of the chord 5x+2y=165x + 2y = 16 is-

    1. A.2x−5y=112x - 5y = 11
    2. B.2x+5y−11=02x + 5y - 11 = 0
    3. C.2x+5y+11=02x + 5y + 11 = 0
    4. D.None of these

  4. 7.α\alpha and β\beta are two positive acute angles and cos⁡2α=3cos⁡2β−13−cos⁡2β\cos 2\alpha = \frac{3 \cos 2\beta - 1}{3 - \cos 2\beta}. Which of the following relation is correct?

    1. A.tan⁡α=±tan⁡2β\tan \alpha = \pm \tan 2\beta
    2. B.tan⁡α=3tan⁡β\tan \alpha = \sqrt{3} \tan \beta
    3. C.tan⁡α=±3cot⁡β\tan \alpha = \pm \sqrt{3} \cot \beta
    4. D.tan⁡α=±2tan⁡β\tan \alpha = \pm \sqrt{2} \tan \beta

  5. 8.If in a triangle, (1−r1r2)(1−r1r3)=2(1 - \frac{r_1}{r_2})(1 - \frac{r_1}{r_3}) = 2 (r1,r2,r3r_1, r_2, r_3 denote the radii of the described circles opposite to the angles A, B and C respectively), then the triangle is-

    1. A.Right angled
    2. B.Isosceles
    3. C.Equilateral
    4. D.None of these

  6. 9.What is the value of lim⁡x→∞xx2+1\lim_{x \to \infty} \frac{x}{x^2+1}?

    1. A.22
    2. B.00
    3. C.33
    4. D.0.50.5

  7. 10.If tan⁡x=ntan⁡y,n∈R+\tan x = n \tan y, n \in R^+, then the maximum value of sec⁡2(x−y)\sec^2(x - y) is equal to-

    1. A.(n+1)22n\frac{(n+1)^2}{2n}
    2. B.(n+1)2n\frac{(n+1)^2}{n}
    3. C.(n+1)22\frac{(n+1)^2}{2}
    4. D.(n+1)24n\frac{(n+1)^2}{4n}
Practise with answers

Other papers

All Islamic University of Technology admission test papers →