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Please help me with these problems

  1. Dec 10, 2005 #1
    Please help me i am in 11th grade. These were the questions asked to me in a test and after the test was over the teacher asked to sumbmit the complete set of solutions for the test in four days time. There were total thirty questions I was able to do seventeen. I need help plz or i will be mincemeat...

    I need the step-by-step solutions of the following problems and theorums, axioms used if any.

    although i have the correct answers...I want the Working.

    well.... here goes.....:

    1] If the expression mx - 1 + 1/x is non negative for all positive real x, then the minimum value of m must be:
    (a) -1/2 (b) 0 (c) 1/4 (d) 1/2

    2] If a,b,c are the pth,qth,rth terms of an Harmonic Progression, then
    ab(p-q) + bc(q-r) +ca(r-p) equals
    (a) 1 (b) -1 (c) 0 (d) None

    3] Given p Arithmatic Progressions, each of which consists of n terms. If their 1st terms are 1,2,3,...,p and common differences are 1,3,5,...,(2p-1)
    respectively, then the sum of the terms of all the progressions is:
    (a) np(np+1)/2 (b) n(p+1)/2 (c) np(n+1) (d)None

    4] the straight line y = x + 2 rotates about a point where it cuts the x axis and becomes perpendicular to ax + by + c = 0 then its eqn is
    (a) ax + by + 2a =0 (b) ax - by - 2a = 0
    (c) bx + ay - 2b =0 (d) ay - bx + 2b = 0

    5] Points on the line x + y = 4 that lie at a unit distanance from 4x+3y-10=0 are
    (a) (3,1)&(7,11) (b) (-3,7)&(2,2) (c) (-3,7)&(-7,11) (d)none of these

    6] two lines are given by (x-2y)2 + c(x-2y) = 0 the value of c such that the distance between them is 3 is
    (a) c=0 (b) c=±v3

    7] drawn from the origin are two mutually perpendicular lines forming an isoceles triangle together with the st. line 2x+y=a then the area of the triangle is
    a) (a^2)/2 b) (a^2)/3 c) (a^2)/5

    8] The minimum value of (sin a)^2 + (cos a)^4 is
    a) 3/8 b) 1 c) 3/4

    9]Value of sin 10° + sin 50° + sin 70° =
    a) 1/16 b) 1/8

    10] If
    cos² A + cos² B + cos² C = 1 then triangle ABC is
    a) equilateral triangle b)right triangle c)isoseles triangle

    11]in a triangle ABC, tan(A/2), tan(B/2), tan(C/2) are in harmonic progression. then cot(A/2)*cot(C/2) is
    a)1 b) 2 c) 3

    12] If a lies in the third quadrant, then v4(sin a)^4 + (sin a)^2 + 4 [cos{45°+(a/2)}]^2 equals
    a)1 b)2 c)-2

    13] If a and ß are two distinct roots of a(tan x)+b(sec x)=c, then tan(a+ß) equals
    (a) (a^2 - c^2)/(a^2 + c^2) (b) (a^2 + c^2)/(a^2 - c^2)
    (c) 2ac/(a^2 + c^2) (d) 2ac//(a^2 - c^2)

    correct answers
    1] c
    2] c
    3] a
    4] d
    5] a
    6] b
    7] c
    8] c
    9] a or b(not sure)
    10] b or c(not sure)
    11] c
    12] b
    13] d

    List of Symbols used by me
    + alt+3544
    a alt+3552
    ß alt+3553
    p alt+3555
    S alt+3556
    s alt+3557
    F alt+3560
    O alt+3562
    8 alt+3564
    f alt+3565
    e alt+3566
    n alt+3567
    ± alt+3569
    = alt+3570
    = alt+3571

    ˜ alt+3575
    ° alt+3576
    v alt+3579
    n alt+3580
    ² alt+3581
    ♂ alt+3595
    ♀ alt+3596
    ↕ alt+3602
    ¶ alt+3604
    § alt+3605
    T alt+1257
    Last edited: Dec 10, 2005
  2. jcsd
  3. Dec 10, 2005 #2


    User Avatar
    Homework Helper

    IMHO, it's time for you to do some reading:
    Click here or here
    Now, what have you done? Post your work, and where you get stuck, so that we can help (we do not show you step-by-step solution) you.
  4. Dec 10, 2005 #3


    User Avatar
    Science Advisor

    Surely, you know better than to begin asking for help by insulting the people you are asking? Perhaps you don't realize that that is exactly what you are doing when you say: "I need the step-by-step solutions of the following problems and theorums, axioms used if any."

    Your teacher expects you to to do these problems. They were given as a test- which indicates that your teacher thinks you ought to be able to do them without using your textbook in a limited time. Now you are being given a chance to do them over 4 days using your text book. You surely ought to be able to do them yourself.

    Perhaps you need hints or corrections where you have gone wrong. Fine, show us what you have done, what you do understand about these problems, where you have difficulty and we will be happy to help you. However, none of us here dislikes either you or your teacher enough to try to tricky your teacher into thinking you have learned something when you have not. It is insulting for you to suggest that we would.
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