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  1. Krushnaraj Pandya

    The Double-Slit Experiment

    I have always seen YouTube videos saying how an electron 'knows' when we are observing it but I always put that down to youtubers creating popular science (verging on science fiction) hype for more views. I suppose there is more science behind an electron behaving like a particle when we put a...
  2. Krushnaraj Pandya

    Programs CS vs CE for AI

    Hello, I'm an Indian student just graduating from high school and am about to begin studies in Memorial University of Newfoundland. I'm not sure whether to pursue a computer science degree or a computer engineering degree- I'm fascinated by AI and have learned a bit of coding myself, any...
  3. Krushnaraj Pandya

    Admissions Applying with high percentile/low scores

    Good day everyone, I'm an Indian student about to complete high school and I've applied for computer engineering in Memorial University of Newfoundland, Canada. My class 10th GPA is 9.6 and I am expecting at least 85% in class 12th boards. This year the JEE (Indian SATs for engineering) was also...
  4. Krushnaraj Pandya

    Admissions Undergraduate programs in Canada

    Good day everyone, I'm an Indian student about to pass out from high school- The competition here is intense for the few truly good engineering colleges here so I'm looking for some guidance to studying in Canadian universities. I'd really appreciate your help- Thank you. a) I am expecting a...
  5. Krushnaraj Pandya

    Denominator=0 in a 3d line

    Homework Statement I noticed that for a line parallel to z axis the equation is (x-a)/0 = (y-b)/0 = (z-c)/k = t. Homework Equations Any 3d geometry equations The Attempt at a Solution I can't quite grasp how to visualize this, also I can't see any constant like a 2d line parallel to x axis...
  6. Krushnaraj Pandya

    Apparent wavelength in Doppler's effect

    Homework Statement a source of sound of frequency f emits sound with speed v, is at rest. If an observer is moving at towards source with speed u, then wavelength of sound waves observed by the observer will be? Homework Equations f' = f(u+v)/u...(i) f' is apparent frequency, f is the real...
  7. Krushnaraj Pandya

    Angle between a plane and a line

    Homework Statement If the plane 3x+y+2z+6=0 is parallel to the line (3x-1)/2b = 3-y = (z-1)/a then 3a+3b is? Homework Equations angle between two lines=90 degree when l1l2+m1m2+n1n2=0 where l,m,n are direction ratios...(i) The Attempt at a Solution First I divided x/3 and 3-y by -1 to get the...
  8. Krushnaraj Pandya

    Vector equation of a plane in normal form

    Homework Statement A vector n of magnitude 8 units is inclined to x,y and z axis at 45, 60 and 60 degrees resoectively.If the plane passes through (root2, -1, 1) and is normal to n then find its equation. Homework Equations (r-a).n=0 where r is position vector of a point on plane, a is a point...
  9. Krushnaraj Pandya

    Line of intersection of two planes

    Homework Statement Find equation of line of intersection of planes r.(3i-j+k)=1 and r.((i+4j-2k)=2 Homework Equations a x b gives a perpendicular vector to a and b...(i) The Attempt at a Solution to write equation of a line r=a+tb we need a point a on the line and a parallel vector b. Taking...
  10. Krushnaraj Pandya

    Fastest way to find consistency/solutions of equations

    Homework Statement Consider three equations in three variables, To check their consistency usually the adjoint of the matrix (from coefficients of x,y and z are found) and the inverse is found for the solution. I have heard of cramer's rule but it has a similar complexity. These same kind of...
  11. Krushnaraj Pandya

    Dependence of Coulomb's law on the medium

    Homework Statement I read in my textbook that the force exerted by a charged particle q1 on another charged particle q2 does not depend on the medium between them. Yet we multiply ε by ε(r) in coulomb's law when there is a medium present between the particles. Can someone please explain this...
  12. Krushnaraj Pandya

    Identifying the equation of a parabola

    Homework Statement Find the value of z for which (10x-5)^2 + (10y-7)^2 = z^2((5x+12y+7)^2 is a parabola Homework Equations eccentricity of parabola=1 The Attempt at a Solution I can solve this by expanding everything and writing h^2-ab=0 but this equation looks suspiciously similar to...
  13. Krushnaraj Pandya

    The minimum of a function in a given domain

    Homework Statement The operating cost of a truck is 12+(x/6) per km, when the truck travels x km/hr. If the driver earns 6 rupees (*or whatever currency your country has) per hour, what is the most economic speed to operate the truck on a 400 km road? Also, due to weather, the truck can travel...
  14. Krushnaraj Pandya

    Limit problem

    Homework Statement ## \lim x-a \frac {{a^x-{x^a}}}{{x^x}-{a^a}} = -1## then a is? Homework Equations L'Hospital rule The Attempt at a Solution Using LHR we can write numerator as ##\frac{a^x ln{a}-ax^{a-1}}{x^xln(x+1)}## plugging x=a and equating to -1 gives 1-ln(a)=ln(a+1); so 1=ln(a(a+1))...
  15. Krushnaraj Pandya

    Rules to apply L'Hospital on a limit

    Homework Statement ## \lim x-0 \frac {xcosx-log(1+x)}{x^2}## Homework Equations ##\frac{log(1+x)}{x}=1## ...(i) The Attempt at a Solution Using (i) we can write numerator as xcosx-x, cancelling x from denominator we have cosx-1/x, this is 0/0 form so we can use LHR which gives us -sinx/1 but...
  16. Krushnaraj Pandya

    Limit of 0^0 form

    Homework Statement lim x--->0 |x|^sinx is? Homework Equations lim x-->0 f(x)^g(x), if both functions tend to 0, limit is equal to e^log[f(x).g(x)] with the same limit..(i) The Attempt at a Solution when x>0, it is x^sinx and x<0 it is -1/x^sinx. putting the first case in (i) we get...
  17. Krushnaraj Pandya

    Vector of shortest distance between two skew lines

    Homework Statement how to write the vector equation of the line of shortest distance between two skew lines in the shortest and most efficient way? (The exact lines given in a particular problem in my book can be referenced- L1=(3i+8j+3k)+λ(3i-j+k) and L2=(-3i-7j+6k)+μ(-3i+2j+4k) ) 2. Relevant...
  18. Krushnaraj Pandya

    Efficient solution to a 3D geometry distance problem

    Homework Statement Find the coordinates of those points on the lines (x+1)/2 = (y+2)/2 = (z-3)/6 which is at a distance of 3 units from the point (1,-2,3) 2. Relevant methods 1) assume a point, use distance formula- (very calculative) 2) write vector equation of line, find foot of...
  19. Krushnaraj Pandya

    Faster ways to calculate distance between a point and a line in 3D

    Homework Statement Suppose a line is given, say (x-3)=(y-2)=z in Cartesian form and we are supposed to find a point on it which is at a distance say, 6 units from a given arbitrary point (1,2,3). 2. Relevant tedious methods 1) write line in vector form then equate modulus of vector between...
  20. Krushnaraj Pandya

    Relation between vector length and direction ratios

    Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1....(2) The...
  21. Krushnaraj Pandya

    Can a direction cosine squared be negative?

    Homework Statement A line makes some angle T with each of x and z axis, and angle U with y axis so that sin^2(U)=3sin^2(T). Homework Equations 2cos^2(T)+cos^2(U)=1 .......(i) cos^2(x)+sin^2(x)=1 The Attempt at a Solution Using the above two eqns. give us the correct value for cos^2(T) which is...
  22. Krushnaraj Pandya

    A violation of the sine rule?

    Homework Statement If magnitudes of vector a,b and c are 1,2,3 respectively and vectors a+b+c=0 then it is obvious that a and b will be in the opposite direction to c therefore cancelling it out but let's assume for a moment that we don't know this and we want to figure this out using the sine...
  23. Krushnaraj Pandya

    Equation of a circle from given conditions

    Homework Statement Equation of the circle passing through the point (1,2) and (3,4) and touching the line 3x+y-3=0 is? Homework Equations x^2+y^2+2gx+2fy+c=0...(1) (-g,-f)=center of circle sqrt(g^2+f^2-c)=radius...(2) The Attempt at a Solution Putting (1,2) and (3,4) in equation 1 we get...
  24. Krushnaraj Pandya

    Splitting of a convex lens problem

    Homework Statement A thin convex lens of focal length 20 cm is split into two parts along the principal axis, now there is a 2mm gap between the top and bottom parts, an object O is placed at 10 cm from the lens, the distance between the two virtual images will be? Homework Equations 1/v - 1/u...
  25. Krushnaraj Pandya

    Can a real image be erect?

    Homework Statement My question is, are real images always inverted and virtual always erect? Homework Equations 1/v+1/u=1/f for mirrors and 1/v-1/u=1/f for lenses The Attempt at a Solution Consider a concave lens, with object at -x. the condition for a virtual image is v<0; i.e on the same...
  26. Krushnaraj Pandya

    Ratio of the length of resistive wires in a square

    Homework Statement In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED. Homework...
  27. Krushnaraj Pandya

    Voltmeter readings across a closed/open switch in circuits

    Homework Statement The following figure shows a circuit containing a bulb, switch and battery. Four voltmeters are connected in it to measure potential difference. Which voltmeters give non-zero readings and which ones read terminal potential difference when the switch is 1) open and 2) closed...
  28. Krushnaraj Pandya

    Current through capacitors in parallel

    Homework Statement In the given circuit at t=0 S is closed then at time t, i1/i2 a) is constant b) increases c) decreases d) first increases then decreases Homework Equations V=IR, Q=CV The Attempt at a Solution At t=0, capacitors act like closed switches, so I2=2I1, where I2 and I1 are the...
  29. Krushnaraj Pandya

    Energy in capacitor at steady state

    Homework Statement In the circuit shown, C1= 1 microfarad, C2=3 microfarad, in steady state, the energy stored in these capacitors are? Homework Equations Kirchoff's laws, E=0.5CV^2, V=IR The Attempt at a Solution At steady state, no current passes through the capacitors, so current is...
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