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  1. U

    Lagrange's mean value theorem problem

    Homework Statement Homework Equations Lagrange's mean value theorem The Attempt at a Solution Applying LMVT, There exists c belonging to (0,1) which satisfies f'(c) = f(1)-f(0)/1 = -f(0) But this gets me nowhere close to the options... :(
  2. U

    Definite integration problem

    Homework Statement ∫dt/(t^2 +2tcos a + 1) (Limits of the integral are from 0 to 1) (0<a<π) Homework Equations The Attempt at a Solution Put t=sin a dt=cosa da ∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2] = ((cosec a)/2) ∫sin 2a...
  3. U

    Does the colour of light change with a change in medium

    Homework Statement This is just my doubt and not really a question. We know that speed of light changes upon change in medium of propagation. Its wavelength also changes. But its frequency doesn't change. So, does the colour of light change upon change in the medium of propagation...
  4. U

    Lewis acids and bases

    hi all! I am not able to understand what's a Lewis acid and a Lewis base. tell me if these are Lewis acids or Lewis bases and tell me the reason. HCl, H2SO4, H3PO4, CO2, HCN. my approach: first 3 I'm not able to decide. 4th one I thought to be Lewis base as 2lone pairs of electrons left in...
  5. U

    Change in velocity of light with change in optical density

    hey guys! we know that velocity of a wave = wavelength x frequency. and speed of light changes with change in optical density. so there must be change in either frequency or wavelength or both. which of these quantities change with change in optical density? and why?
  6. U

    Propagation of light as wave

    huy there! everyone says that light has wave particle duality. it means light is a wave and also consists of a particle. now, wave is a disturbance in a medium. but, we know that light can travel without a medium. then why do we say it is a wave? (i know that it is a non mechanical wave then why...
  7. U

    A simple problem on linear equation in two variables

    Homework Statement if a+11b is completely divisible by 13 and a+13b is completely divisible by 11 then find the the smallest possible value of a+b. a and b are positive integers. the answer is 28 Homework Equations a+11b= 13x a+13b= 11y The Attempt at a Solution i have equated...
  8. U

    Is universe expanding or contracting?

    gravity pulls two galaxies. Andromeda and Milky Way are going to collide in few billion years. this seems to show that everything in the universe is moving close to each other i.e. contracting. but, since the universe was formed, it has been expanding due to dark energy. how do you explain this...
  9. U

    Life and death of stars

    can anyone tell me about various stages of life of a star? when does a neutron star, supernova, pulsar form?
  10. U

    What does light emitted by quasar convey?

    people say that light emitted by quasar states that it is moving away from us? why? is it related to doppler effect? if so please explain.
  11. U

    Difference between pseudo force and centrifugal force

    what is pseudo force and centrifugal force? can anyone differentiate between them? is one a special case of the other?
  12. U

    A simple projectile question

    Homework Statement in a soccer practice session the football is kept at the centre of the field 40 yards from the 10 feet high goalpost. a goal is attempted by kicking the football at a speed of 64 feet/second at an angle of 450(45 degree) to the horizontal. will the ball reach the goalpost...
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