Questions asked by Sasha Wills

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• What is the acceleration of a meteor at a distance #8xx10^6"m"# from the centre of the Earth? Take the mass of the Earth to be #6xx10^(24)"kg"#
  
• A spring is hung vertically. It is loaded with 50 g mass and allowed to oscillate. Calculate the frequency of oscillation when the spring is loaded with 150 g which exceeds 100m?
  
• A truck starts from rest at the top a slope which is 1 m high and 49 m long. What is the acceleration and it's speed at the bottom of the slope assuming friction is negligible?
  
• If A= A1i + A2j + A3k and B= B1i + B2j + B3k. Prove that A.B= A1B1+A2B2+A3B3?
  
• A car weighing 9800N is moving at 25 m/s. If the frictional force acting on it is 2000 N, how fast is the car moving when it has travelled 60m?
  
• A stone is dropped from the peak of a hill. It covers a distance of 30m in last second of its motion. What is height of the peak?
  
• If w is a complex cube roots of unity then w^17: 1. 0 2. 1 3. w 4. w^2 Pleas explain?
  
• In the binomial expansion of (a+b)^n the coefficients of the terms equidistant from the beginning and the ending are always..? I know the answer is EQUAL. But how?
  
• Is #(R,**)# a commutative group if #**# is defined in #R# by #a**b= 3ab #?
  
• Find the condition that one root of px^2-qx-r=0, (p is not equal to 0) maybe double of the other?
  
• Using mathematical induction prove that: 1+5+9+..+(4n-3)=n(2n-1), also verify the position for n=3. I know how to get the mathematical induction , how do I verify for n=3?
  
• Show that point (2,1),(5,1),(6,1) are vertices of right angled triangle?
  
• T is the set of real numbers of the form a+b√2, where a,b € Q and a,b are not simultaneously zero. Show that (T,•) is a group where "•" is an ordinary multiplication?
  
• N!/(n+1)! is equal to: 1) n+1 2) 1/(n+1) Please explain?
  
• If α,β are the roots of y^2-2y+3=0 then find the equation whose roots are 1/α^2 and 1/β^2 ?
  
• Let #"*"# defined in #ZZ# by #p"*"q=p+q+3# for all #p,q in ZZ# Show that a) #"*"# is commutative in #ZZ#. b) identity element w.r.t #"*"# exists in #ZZ#?
  
• Let * be defined in Z by: m*n=m+n+2 a) show that every element of Z has an inverse under *. ?
  
• Equal volumes of 0.02M CaCl2 0.0004M Na2SO4 are mixed. Will precipitate of CaSO4 form?
  
• Tan x/2= (1-cosx)sinx. Prove?
  
• Prove cos(a+b)cos(a-b)=cos^2b-sin^2a ?
  
• Which one is more concentrated 1 molar NaOH or 1 molal NaOH aqueous solution? Explain?
  
• A voltaic cell which is constructed with Sn+2/Sn (Ereduction=-0.14V) and Zn+2/Zn (Eoxidation=-0.76V) is represented by Zn|Zn+2(1M)||Sn+2|Sn(1M). What is the emf of the cell?
  
• An ambulance has a siren producing sound waves of frequency 2000 Hz and moving towards a listener standing on a bus stop. If the frequency heard by him is 2150 Hz. Find speed of ambulance. (Speed of sound 340 m/s)?
  
• Hydrogen gas in 500cm^3 container at a pressure of 700 torr is transferred to a container of volume 700 cm^3. What will the new pressure be? a) if no temperature change occurs. b) if it's temperature changes from 25C to 35C?
  
• How to assign 4 quantum numbers to 2 electrons in 3p orbitals?
  
• Please explain the method of finding period of a function e.g tan3x ?
  
• For the reaction H2+I2----2HI Kc is 49. Calculate the concentration of HI at equilibrium when initially one mole of H2 is mixed with one mole of I2 in 2 litre flask.?
  
• If 1g sample of limestone was dissolved in acid to give 0.38 g of #"CO"_2#. If limestone contains no carbonate other than #"CaCO"_3#, find the percentage of #"CaCO"_3# in the limestone?
  
• If |A+B|=|A|+|B| then the angle between the vectors A and B is *0 *180 *90 ?
  
• A body weighs 900N on earth's surface. At a distance of twice earth radius above the earth's surface , the weight of the body is: *100N *200N *300N *450?
  
• When a listener moves towards a stationary source of sound , the change in the pitch of sound occurs due to change in: a) wavelength b)intensity c) speed of waves d) all of the them?
  
• A belt 12.25 meters long passes around a 3.5 cm diameter pulley while belt makes three complete revolutions in a minute. How many radian does the wheel turn in 5 seconds?
  
• What is period of: sin x/2 + cot x/2?
  
• 0.2 mole of A and 0.4 mile of B were reacted at a certain temperature and allowed to come to equilibrium . A+B---2AB The equilibrium mixture contained 0.1 mole of A, find Kc if volume of the container was 2 dm^3?
  
• What is the volume of 0.602 M H2SO4 necessary to neutralise completely the hydroxide in 47.5 mL of NaOH having pH 13.39?
  
• A belt 12.25 meters long passes around a 3.5 cm diameter pulley while belt makes three complete revolutions in a minute. How many radian does the wheel turn in 5 seconds?
  
• Calculate the molarity of 1.5% w/v solution of PbCl2?
  
• During an acid base titration hydrochloride acid is filled in burette up to zero mark and 20 ml of 0.085M Na2CO3 solution is pipette out into flask using indicator: a) if burette reading at end point was noted to be 13.7ml determine molarity of HCl?
  
• A mixture of 0.2 mole O2 and 0.4 mole N2 gas is enclosed in a vessel of certain volume at 27C and 800 torr. If volume of mixture is doubled at same temperature then determine pressure of mixture and individual gases?
  
• How to solve the trig equation: #sqrt(1+cos(x))-sqrt(1-sin(x))=1#?
  
• Let * be defined in Z by m*n=m+n+2 Show that (Z,*) is an abelian group?
  
• Prove: Sq.rt[(1+cosx)/(1-cosx)]= cot x/2?
  
• If alpha and beta are the roots of px^2+qx+r=0 Form the equation whose roots are (2alpha+1/alpha), (2beta+1/beta)?
  
• If a point on the rim of a 24 cm diameter flywheel travels 7000 metres in two minutes through how many radians does the wheel turn in two seconds?
  
• The general term of the binomial (a+b)^n?
  
• How to simplify (n+2)!/(n+1)! Please explain?
  
• Two hikers start from the same point; one walks 9km heading east, the other one 10 km heading 55degrees north east. How far apart are they at the end of their walks? *do I have to subtract 55 from 90 here?
  
• What are the factors of #(9m^2+t^2)# in the set of complex numbers?
  
• Sin^4x-cos^4x= -cos2x or cos2x??
  
• What are the values of n and l for the last subshell of Na (Z=11) and B (Z=5)? What are their shapes?
  
• What is the ionic concentrations of Ag+ and CrO4^-2 in a saturated solution of Ag2CrO4 at 25C? Ksp of Ag2CrO4 is 1.9x10^-12 mole^3/dm^9?
  
• How to explain formation of dative bond in CH3NO2 molecule?
  
• The reaction between marble chips and hydrochloride acid is given as: CaCO3+2HCl---> CaCl2+CO2+H2O (T=25C) What is effect on rate of reaction if: 1)Marble chips are replaced by grind marble 2) temperature is raised to 35C?
  
• The concentration of Ag+ ions is 1x10^-6 M in AgBr solution. Find minimum concentration of Br- ions necessary to cause precipitation of AgBr. ( Ksp of AgBr= 4x10^-13 M^2)?
  
• A stone is dropped from the peak of a hill. It covers a distance of 30 m in last second of its motion. What is height of peak?
  
• A sound wave of frequency 500 Hz in air enters from a region of temperature 25C to a region of temperature 5C. Calculate the percent fractional change in wavelength?
  
• A pendulum with a period of 1.8 s on earth is moved to another planet, on the new planet it's period is2.5 s. What is the gravitational acceleration of this planet?
  
• A bullet is fired horizontally with 20 m/s from top of a building 20 m high. When the bullet is 10 m above the ground incidentally it hits a bird. Find time taken to hit the bird?
  
• A wooden ball of mass 10 g is suspended by a thread. The horizontal current of air blows it from one side so that so that thread makes an angle of 60 degrees with vertical. What is tension in thread and force of air current?
  
• How to find the value of ‘a’ and ‘b’ for which the lines given by ax-2y-1=0 , 6x-4y-b=0. a) are parallel b) have no common point ?
  
• A hydrocarbon, C4H6 absorbs two moles of hydrogen in the presence of platinum as catalyst. The reduction product is inert towards bromine and potassium permanganate. a) what possible structures of C4H6 can be drawn?
  
• How to find limit of (3e^x - e^-x -2)/x if x approaches 0?