Questions asked by Ananya G.

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• The displacement of a body is given by r=√(a^2-t^2)+tcos t^2, where a is constant. Find velocity?
  
• Differentiate: tcos(t^2) ?
  
• Please show the integration of #(x^3)/((x^4+7)^8)dx# step by step?
  
• Find the value of #x^3-6x^2+6x # when # x=2+2^(2/3)+2^(1/3)?#
  
• A particle is projected at an angle A and after t seconds, it appears to have an angle of B with the horizontal. The initial velocity is:- A)gt/(2 sin(A-B)) B)gt cos B/(sin (A-B)) C)sin(A-B)/2gt D)2 sin(A-B)/(gt cos B)?
  
• Find the values of '#k#' if equation #x^3-3x^2+2=k# has:- (i)3 real roots (ii)1 real root?
  
• A light source of wavelength λ illuminates a metal and ejects photo-electrons with (K.E)max=1eV. Another light source of wavelength λ/3 ejects photo-electrons from the same metal with (K.E)max=4eV. Find the value of Work Function?
  
• Prove that sin(20°)cos(40°)+cos(20°)sin(40°)=√3/2 ?
  
• If tan A and tan B are the roots of the quadratic equation x^2-ax+b=0 then find the value of sin^2(A+B)?
  
• Find the value of tan 203°+tan 22°+tan 203° tan 22°?
  
• If A+B=225°, then find the value of #(cot A/(1+cot A))(cot B/(1+cot B))#?
  
• Find the value of (sin 24° cos 6°-sin 6° sin 66°)/(sin 21° cos 39°- cos 51° sin 69°)?
  
• Eliminate θ from the relations: sec θ=1-b tan θ and a²sec²θ=5+b²tan²θ?
  
• In a sample of H-atom electrons make transition from 5th excited state upto ground state, producing all possible types of photons, then find out the number of lines in Infrared region?
  
• A boat, which has a speed of 5km/h in still water, crosses a river of width 1km along the shortest path possible in 15 minutes. Find the velocity of the river?
  
• Prove that: #(sin²A-sin²B)/((sin A cos A)-(sin B cos B))=tan(A+B)#?
  
• If x+y+z=π/2, then prove that: sin 2x + sin 2y + sin 2z= 4 cos x cos y cos z?
  
• Solve cos θ+sin θ=cos 2θ+sin 2θ?
  
• Solve: tan²θ-(1+√3)tanθ+√3=0?
  
• If 2cos²(π+x)+3sin(π+x) vanishes then the values of x lying in the interval from 0 to 2π is x=π/6 or 5π/6. Explain how?
  
• Solve 5sinθ+2cosθ=5?
  
• Find the number of solutions of equation: (1-tan θ)(1+tan θ) sec²θ+2^(tan²θ)=0 when θ∈(-π/2,π/2)?
  
• What is the complete solution set of the equation 1+2cosec x=(-sec²x/2)/2?
  
• Two springs are in a series combination and are attached to a block of mass 'm' which is in equilibrium. Spring constants:k and k’ Extensions:x and x’ respectively. Find the force exerted by spring on the block?
  
• If the percentage yield of the given reaction is #30%#, how many total moles of the gases will be produced if #8# moles of #"NaNO"_3# are initially taken?