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The number of flights leaving a certain airport doubles during every one-hour period between its 9 am opening and noon; afternoon, the number of flights leaving from the airport doubles during every two-hour period. If 4 flights left from the airport between 9 am and 10 am, how many flights left the airport between 2 pm and 4 pm?

Correct Answer: 64
9 টা থেকে noon অর্থাৎ 12টা পর্যন্ত flight সংখ্যা double হয় প্রতি 1 ঘণ্টায় । 9 টা থেকে 10 টায় ছুটি flight হলে 10 - 11 টায় 2x, 11 - 12 টায় 4x / Noori - এর পর প্রতি দুই ঘণ্টায় হয় দ্বিগুণ। 12 - 2 টায় ৪r 2টা থেকে 4টায় হয় 16x, তাহলে x = 4 দেওয়া আছে। সুতরাং ফ্লাইট সংখ্যা = 16x = 16 × 4 = 64

The admission ticket for an exhibition bears a password which is changed after every clock hour based on set of words chosen for each day. The following is an illustration of the code and steps of rearrangement for subsequent clock hours. The time is 9 a.m. to 3 p.m. Day's first password : First Batch ----- 9 a.m. to 10 a.m. is not ready cloth simple harmony burning Second Batch ----- 10 a.m. to 11 a.m. ready not is cloth burning harmony simple Third Batch ----- 11 a.m. to 12 noon cloth is not ready simple harmony burning Fourth Batch ----- 12 noon to 1 p.m. not is cloth ready burning harmony simple Fifth Batch ----- 1 p.m. to 2 p.m. ready cloth is not simple harmony burning and so on. If the password for 11 a.m. to 12 noon was --- "soap shy miss pen yet the she", what was the password for the first batch ?

Statement : The vehicular traffic has increased so much in the recent past that it takes at least two hours to travel between the city and the airport during peak hours.

Courses of Action :
I. Non-airport bound vehicles should not be allowed to ply on the road connecting the city and the airport.
II. The load of vehicular traffic should be diverted through various link roads during peak hours.
III. The departure and arrival of flights should be regulated so as to avoid congestion during peak hours.

If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?

If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?

A bakery opened with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon and 60% of the remaining rolls were sold between noon and closing time. How many dozen rolls were left unsold ?

A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80% of the remaining rolls were sold between noon and closing time. How many dozen rolls had been sold when the bakery closed yesterday?

Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let 'X' be the smallest initial number that results in a win for Amitabh. The sum of the digit of 'X' is:

The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$        where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$  are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$   is the angular momentum. The Hamiltonian does not commute with

The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$   $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$    $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$   = ?

$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$     $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$     $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$     is simplified to :