বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Let
there are x number of marbles and capacity of the bowl is y marbles
3x/4 = y/2
⇒ y = 3x/2
x + 100 = y
⇒ x + 100 = 3x/2
⇒ (3x/2) - x = 100
⇒ x/2 = 100
∴ x = 200
Solution:
Let the required numbers be x and y.
Now, according to the given conditions:
x + y = 22 (1)
Five times one number is equal to six times the other:
5x = 6y (2)
From equation (2), we get:
x = (6y) / 5
Substitute this value into equation (1):
6y / 5 + y = 22
(6y + 5y) / 5 = 22
11y / 5 = 22
y = 10
Now, substitute y = 10 into equation (2):
x = (6 × 10) / 5
x = 12
Therefore, the required numbers are x = 12 and y = 10.
Solution:
The square root of (7 + 3√5)(7 - 3√5) is:
√{(7 + 3√5)(7 - 3√5)} = √{7² - (3√5)²}
= √{49 - 45}
= √4
= 2
Solution:
Let the cost of a table be Tk. x and the cost of a chair be Tk. y.
Then, the following equations are given:
2x + 3y = 3500 (i)
3x + 2y = 4000 (ii)
Multiply equation (ii) by 3 and equation (i) by 2:
3 × (3x + 2y) = 12000
2 × (2x + 3y) = 7000
⇒ 9x + 6y - 4x - 6y = 12000 - 7000
⇒ 5x = 5000
⇒ x = 1000
The cost of a table is Tk. 1000
Solution:
100 × 10 - 100 + 2000 ÷ 100
= 100 × 10 - 100 + 20
= 1000 - 100 + 20
= 1020 - 100
= 920
Solution:
0.014 × 0.014 = 0.000196