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Bangladesh Bank Recruitment Test for Officer (General) Examination Held On: 25.05.2018 || 2018

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Solve the following mathematical problems:

A place of stone fell from a balloon when it was flying in the upward direction with a velocity 20 m/sec. What will be the height of the balloon when the stone hit the ground in 10 seconds?

প্রশ্নে বলা হচ্ছে যে, 20ms^-1 সেকেন্ডে ঊর্ধ্বমূখী কোন বেলুন হতে একটি পাথর 10 সেকেন্ডে ভূমিকে স্পর্শ করলে তখন ভূমি হতে বেলুনের উচ্চতা কত হবে?

এটি পদার্থবিজ্ঞানের অঙ্ক । অঙ্কটির সমাধান করতে হলে বেশ কয়েকটি বিষয়ের উপর সম্যক ধারণা থাকতে হবে।

অভিকর্ষজত্বরণ (g) হলো প্রতি সেকেন্ডে পড়ন্ত বস্তুর বেগ যার মান ঊর্ধ্বমুখী হলে হবে g = -9.8ms^-2এবং বেগ (Velocity) কে u দ্বারা সূচিত করা হবে। আর সময়কে t দ্বারা সূচিত করে, উচ্চতাকে h দ্বারা সূচিত করতে হবে। এখন আসুন অঙ্কের সমাধানে চলে যাইঃ

পাথরের ক্ষেত্রে, $h = u t t + \frac{1}{2} g t^{2}$

= $= (20 \times 10) + \frac{1}{2} \times 9.8 \times 10^{2} = 200 + 490 = 690 m$

বেলুনের ক্ষেত্রে, $h = u t - \frac{1}{2} g t^{2} = (20 \times 10) - \frac{1}{2} \times 9.8 \times 10^{2} = 200 - 490 = 290 m u = 20 m s^{- 1}, g = 9.8 m s^{- 2}; t = 10 s e c o n d$

The total hight of ballon is = (690 +290)m = 980m (answer)

Solve the following mathematical problems:

Find the maximum value of z=6x+2y, subject to the conditions $x \geq 0, y \geq 0, x + y = 5, x \leq 2, y \leq 4.$

We get the following conditions, $x \geq 0, y \geq 0, x + y = 5, x \leq 2, y \leq 4$
As the maximum value of x is 2,
So the values of x may be x = 0, 1, 2.
And as the maximum value of y is 4,
So the values of y may be y = 0, 1, 2, 3, 4.
And according to another condition x + y = 5.
This also approves the first condition because here x+y=2+3 = 5.

That mean's if we take x = 2 and y = 3,
Then x+y=5 equation will be true.
From here, we get the maximum value of x = 2 and
The maximum value of y = 3.
The maximum value of z= 6x+2y

$\Rightarrow z = (6 \times 2) (2 \times 3) \Rightarrow z = 12 + 6 ∴ z = 18$

Solve the following mathematical problems:

The sum of the digits of a two-digit number is subtracted from the number. How two-digit numbers can be formed so that the digit in the unit place of the resulting number many such 6?

Let the number be 10X + Y, (Y is in unit place and X is in the tenth place)

So the sum of the digits will be X + Y if the sum of the digits subtracted from the number than the result will be 10X + Y - (X + Y) = 9X

So the number resulting will be always the product of 9 so if its need to have 6 in unit place

So the value of X must be 4 as e result it will be $9 \times 4 = 36$ here 6 in the unit place so all the two digit number which has 4 in tenth places will be the number

So total such number will be 10 (40, 41, 42, 43, 44, 45, 46, 47, 48, 49) (ans.)

Solve the following mathematical problems:

How many ways are there to divide 50 people into 3 groups so that each group contains members equal to a prime number?

50 people will be kept in 3 groups where all group are consisted of the number of people equivalent to prime number.

So, 1^st way is = 2 +5+43 = 50

2^nd way is = 2 +7+41 = 50

3^rdway is = 2 +11 + 37 = 50

4^th way is = 2 +17 +31 = 50

5^th way is = 2 +19 +29 = 50

(ans.) 5 ways.

Solve the following mathematical problems:

A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.

Radius of semi circular sheet, $r = \frac{28}{2} 14 m$

Circumference of the sheet = $πr = (\frac{22}{7} \times 14) = 44 cm$

Here, circumference of semi circle will be equal to the circumference of the base of cone.

Now, let the radius of the base of cone = R

According to question = $= 2 πR = 44 = R = \frac{44}{2 π} = \frac{44}{\frac{22 \times 2}{7}} = 44 \times \frac{7}{22 \times 2} = 7 cm$

Here, radius of semi circle equals to the height of cone.

That mean's l = r = 14 cm

Now, we know $^{2} = h^{2} + R^{2} \Rightarrow h^{2} = l^{2} - R^{2} \Rightarrow h^{2} = {(14)}^{2} - {(7)}^{2} = 196 - 49 = 147 \Rightarrow h = \sqrt{49 \times 3} = \sqrt{7^{2} \times 3} = 7 \sqrt{3} ∴ h = 7 \sqrt{3}$

So, the depth is $7 \sqrt{3}$ cm and

The capacity will be = $(\frac{1}{3} {πr}^{2} h) = (\frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 7 \sqrt{3}) = 622.37 c m^{3}$ (ans)

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Bangladesh Bank Recruitment Test for Officer (General) Examination Held On: 25.05.2018 || 2018

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