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BUET admission questions 2001-02 (Bangladesh University of Engineering & Technology)

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  1. 1.For what value of a, the straight lines 3x+2y−5=0,ax+4y−9=03x + 2y - 5 = 0, ax + 4y - 9 = 0 and x+2y−7=0x + 2y - 7 = 0 will be concurrent?

    1. A.−7-7
    2. B.55
    3. C.33
    4. D.77

  2. 2.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
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