BUTEX admission questions 2015-16 (Bangladesh University of Textiles)

Physics 1st Paper

1. 1.দুটি সমান মানের ভেক্টরের লব্ধির মান কোন অবস্থায় ওদের প্রত্যেকের মানের সমান হতে পারে?

   1. A.0°
   2. B.30°
   3. C.60°
   4. D.90°
   5. E.120°

   Tap an answer — the first 3 questions need no account

2. 2.$5\text{ kg}$ ভরের বস্তুর উপর কত বল প্রয়োগ করলে বস্তুটির নিম্নমুখী ত্বরণ $4\text{ ms}^{-2}$ হবে?

   1. A.$96\text{ N}$ downwards
   2. B.$96\text{ N}$ upwards
   3. C.$29\text{ N}$ upwards
   4. D.$29\text{ N}$ downwards

Higher Math 1st Paper

1. 3.If A, B and C are matrices of order $4 \times 5$, $5 \times 4$ and $4 \times 2$ respectively, then the order of $(A^T + B)C$ matrix is-

   1. A.$5 \times 4$
   2. B.$4 \times 2$
   3. C.$5 \times 2$
   4. D.$2 \times 5$

2. 4.What is the value of the determinant $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$?

   1. A.$a + b + c$
   2. B.0
   3. C.1
   4. D.abc
   See the answer

3. 5.For what value of k, the three straight lines $x - y + 5 = 0, x + y - 1 = 0, kx - y + 13 = 0$ will be concurrent?

   1. A.$1$
   2. B.$5$
   3. C.$7$
   4. D.$3$
   See the answer

4. 6.A circle whose center is at $(1, 2)$ touches x-axis. What is the length of intercept made on y-axis by the given circle?

   1. A.$\sqrt{3}$
   2. B.$2\sqrt{2}$
   3. C.$2\sqrt{3}$
   4. D.$3$
   See the answer

5. 7.If the line $3x + ky - 1 = 0$ touches the circle $x^2 + y^2 - 8x - 2y + 4 = 0$, then what are the values of $k$?

   1. A.$2, \frac{1}{6}$
   2. B.$-2, \frac{1}{6}$
   3. C.$2, -\frac{1}{6}$
   4. D.$-2, -\frac{1}{6}$
   See the answer

6. 8.If $x^p y^q = (x + y)^{p + q}$, then $\frac{dy}{dx} = ?$

   1. A.$\frac{x}{y}$
   2. B.$\frac{y}{x}$
   3. C.$\frac{y^2}{x}$
   4. D.$\frac{y}{x^2}$
   See the answer

7. 9.What is the maximum value of $x + \frac{1}{x}$?

   1. A.2
   2. B.1
   3. C.$-2$
   4. D.$-1$
   See the answer

8. 10.The value of $\int_0^{\pi/2} \sin^5 \theta \cos \theta d\theta$ will be:

   1. A.$\frac{1}{4}$
   2. B.$\frac{1}{5}$
   3. C.$\frac{1}{6}$
   4. D.None of these
   See the answer

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