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  1. kshitij

    What is the best shape for a soccer goal post?

    disclaimer: this is a made up question, so I don't know if theres a valid solution possible here First lets talk about the square post, it is clear that the shot will go in only if the ball hits the side AB of the square shown below, so the probability of a shot going in is simply ##\frac 1 3##...
  2. kshitij

    What is the ideal number of guesses to maximize your marks in MCQs?

    To approach this, I first assumed the case when the students attempts all the remaining questions. Probability that they gain 4 marks for a guess = ##\frac 1 4## Probability that they lose 1 for a guess = ##\frac 3 4## Now let us say the number of correct guesses = ##r## Now we should have at...
  3. kshitij

    Quadratic equation and its roots

    On simplifying the given equation we get, x^2-x-1=0 and using the quadratic formula we get x=(1+√5)/2 and x=(1-√5)/2 Now, as the formula suggests, there are two possible values for x which satisfies the given equation. But now, if we follow a process in any general calculator by entering...
  4. kshitij

    Number of choosing r non-consecutive numbers out of N natural numbers

    I have seen a solution for this question which was as follows, first out of 15 elements, take away 5, thus there are 11 gaps created for the remaining 10 numbers (say N) as, _N_N_N_N_N_N_N_N_N_N_ now, now we can insert back the 5 to comply with the non-consecutive stipulation for which, number...
  5. kshitij

    Elastic collision between two balls with different masses

    Since in an elastic collision, both momentum and energy is conserved, P(initial)=P(final) m1(3v)=m1v+m2v m2/m1=2 Which was the given answer but if we use conservation of energy, K.E(initial)=K.E(final) 1/2*m1*(3v)^2=1/2*m2*v^2+1/2*m1*v^2 m2/m1=8 Why do we get two different answers and why...
  6. kshitij

    Projectile motion in 2D

    I know the conventional method for solving this question using the formula for maximum range of a projectile in an inclined plane, but since it is an objective problem, if we consider a non general case where α=0, then clearly we can see that (see attachment) only one option matches which...
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