Recently Active Question Of The Day Questions

In any arbitrary string, can we take the tension along the direction of the string? Justify... Also, Can you give a similar analysis for a rod? ...

Got this idea after one of sinchan's posts... Not worth a QOD.. but still a nice variation of Seating arrangement. What is the number of ways to seat people at each of the vertices in both the images below. *Image* Aside: I w ...

*Image* There is a chain of length L and mass per unit length lambda... on a sphere of radius R. The sphere is fixed... What is the force on the nail by the chain.. what is the total force on the nail .. :Keep in mind that th ...

Express (x^2+a^2)(y^2+b^2)(z^2+c^2) as a sum of two squares ...

Find the integral \int_{0}^{\pi/4}{\sin x \times \log(\sin x)dx} ...

*Image* A Long bus has to be passed from the top to the wider road on the side horizontally. The width of the road at the top= a The width of the road at the side= b Find the longest bus that can be made so that it ca ...

Draw the graph of the EMF vs Time for the coil given here.. The arrangement starts from rest and has a constant angular acceleration. The half part has a radius r, the magnetic field on the right side is B and α = constant = ...

find the value of [(3- 5 )100+(3- 6 )100+(3- 7 )100+(3- 8 )100] where [.] stands for greatest integer function.... I gave a variant of this one in an exam thinking that this would be easily cracked.. but no one seems to have ...

Equal volumes of acid, 1M HA and acid 1M HB are mixed. Ka for acids are respectively, 10-4 and 4*10-4. Find the pH of the resultant solution. ...

Given : Ag(NH3)2+→ Ag+ + 2NH3, Kc = 6.2 × 10–8 and Ksp of AgCl =1.8 × 10–10 at 298 K. If ammonia is added to a water solution containing excess of AgCI(s) only,. Calculate the concentration of the complex in 1.0 M aqu ...

What is the number of ways to tile a 9x3 floor using 3x1 tiles ? (This requires recursion) I am explaining the question a bit more elaborately with some examples.. because you may not have understood tiling... :) The example ...

A frictionless tube lies in the vertical plane and is in the shape of a function that has its endpoints at the same height but is otherwise arbitrary. A chain with uniform mass per unit length lies in the tube from end to end ...

N people are there in a group. It is known that the probability that atleast two of them having common birthday is "P". find the smallest N such that P is greater than 1/2 (This is an easy problem. Do not get intimida ...

*Image* This is an infinite grid... Find the resistance between two consecutive nodes... PS: This is a very old question which has appeared in a lot of places including IE Irodov..(If I remember correctly) This problem uses a ...

Find the remainder on division of the following expressions.... 1) 502008 by 7 2) 2008 by 7 3) 20082008 by 13 4) (1!+2!+3!+..........2008!) by 2008 5) Last 3 digits of (1!+2!+3!+..........2008!) 6) (1!+2!+3!+..........2008!) ...

Q.1 A ball B1 with mass(very small) m1 sits on the top of another ball B2 of mass m2. The bottom of B2 is at a height H above the ground and the bottom of B1 is at ht H+D above ground. Both ball are dropped from rest. All col ...

A fair coin is tossed n times. What is the probability that heads do not appear on consecutive tosses? I am giving this question as a continuation of the Tiling of the floor.. (to see how many of you understood the idea) ...

Assume that the day began 10-12 hrs late.. i forgot to post the question today! here it is in a hurrry.. i modified a question of irodov.. Dont have a final solution .. but the fearless and the conceptful should give it a sho ...

ex=x2+1 Solve this one rigorously. I dont want any short cuts or half attempts. Ideally this could fit into Graph of the day section.. But I thought that this is not a bad place either. ...

A small object loops a vertical loop in which a symmetrical section of angle 2a has been removed. Find the maximum and minimum heights from which the object, after loosing contact with the loop at point A and flying through t ...

If α,β and γ are the real roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with vertices (α,1/α) , (β,1/β) and (γ,1/γ) is: I guess one of the easier QOD's ...

p, q, r are the roots of ax^3+bx^2+cx+d=0 find the cubic equation whose roots are p^3+\frac{b}{a}\times p^2, q^3+\frac{b}{a}\times q^2 \text{ and } r^3+\frac{b}{a}\times r^2 This one is from FIITJEE AITS.. ...

Express the Determinant below as a polynomial in alpha's \begin{bmatrix} 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^{n-1}\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^{n-1}\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^{ ...

A large number of sticks (with mass density per unit length ρ) and circles (with radius R) lean on each other, as shown in the figure . Each stick makes an angle θ with the horizontal and is tangent to the next circle at it ...

\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}} = 1 Hint: Observe before you jump to solve ;) Src: Mathematics and Problem Solving : Soifer ...

Suppose that a bubble has the shape of a long cylinder, rather than that of a sphere. Determine an expression for the difference between the inside and outside pressures; express your answer in terms of the surface tension γ ...

Find the sum of the given expression here: \sum_{0\leq i\neq j\leq n}{\left( ^nC_i\times ^nC_j\right)} ...

Find the sum of this infinite series \sum_{0\leq i\neq j\leq \infty}{\left(3^{-i}\times 3^{-j})} ...

1) f(x)=max{1+x, 1-x} find the number of solutions of f(x)=tanx in [0,2Ï€] 2) The number of solutions of the equations 3y=[sinx+[sinx+[sinx]]] & [y+[y]]=2cosx is ...

What is the number of points of intersection of sin x and sin (sin x) in the interval [0, 2 pi] ...