Que 11: Calculate the number of squares in an 8×8 chessboard.
Ans 11: To calculate the number of squares in an 8×8 chessboard, we will calculate first with smaller numbers like 2×2 and 3×3.
In 2×2 there will be 4+1 = 5 squares.
In 3×3 there will be 9+4+1 = 14 squares.
In 4×4 there will be 16+9+4+1 = 30 squares.
Following the pattern we can calculate for 8×8 chessboard will be 64+49+36+25+16+9+4+1 = 204

Que 12: you have a 3 liter and a 5 liters buckets (Assume unlimited water source available). How will you measure 4 liters of water.
Ans 12:
We can follow the below sequence to get 4 liters of water. We can make the combination of 5 + 5 – 3 – 3 = 4 ltr. Refer to Table 6 for the sequence of activity.

Que 13: Find the angle between the minute and hour hands of the clock at 4:20 PM.
Ans 13:
First calculate the position of the minute hand w.r.t. 12 o’clock at 20 min. = (20*360o/60) = 120o. Then we can calculate the position of hour hand w.r.t 12 o’clock at 4:20 PM, we can write it as 420/60 = 41/3 = 13/3. To convert into the angle (13/3×360o / 12 ) = 130o. The Angle formed by the hour and minute hand will be 10o.

Que 14: You have two sand timers, which can show 4 minutes and 7 minutes respectively. Use both the sand timers(at one time or one after another or any other combination) and measure a time of 9 minutes.
Ans 14: Start the 7-minute sand timer and the 4-minute sand timer.
Once the 4-minute sand timer ends turn it upside down instantly.
Once the 7-minute sand timer ends turn it upside down instantly.
After the 4-minute sand timer ends turn the 7-minute sand timer upside down(it has now a minute of sand in it) So effectively 8 + 1 = 9.

Que 15: You have 9 balls, 8 of which have the same weight. The remaining one is defective and heavier than the rest. You can use a balance scale to compare weights to find which is the defective ball. How many measurements do you need so that you will be surely able to do it?
Ans 15:
We can split the balls into 3 groups with 3 balls in each group. Then we can compare any 2 groups if they are equal then defective ball is in the 3rd group or it will be in the heavier group. Then we will get 3 balls in which 1 is heavier, again we can compare 2 balls if they are equal 3rd ball is defective else heavier ball. So, in total, we need to measure 2 times to find out heavier balls.

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