বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Solution:
Given that, A right triangle with sides are 6 cm, 8 cm, and 10 cm.
We know, Area = (1/2) × base × height
= (1/2) × 6 × 8 = 24 cm2
So the area of the right triangle is 24cm2.
Solution:
Given that,
Blue marbles = 3
White marbles = 2
Red marbles = 4
∴ Total marbles = 3 + 2 + 4 = 9
And, number of non-white marbles = Blue + Red = 3 + 4 = 7
We know,
P(not white) = favorable outcomes/total outcomes
= 7/9
Solution:
Given that,
Total surface area of a cube, S = 150 square units.
We know,
Surface area of a cube, S = 6a2
⇒ 6a2 = 150
⇒ a2 = 150/6
⇒ a2 = 25
⇒ a2 = 52
∴ a = 5
And we know, Volume of a cube, V = a3
= 53
= 125
So the volume of the cube is 125 cubic units.
Solution:
Given that, Diagonal of rectangle, d = 13
Width, w = 5
We know,
Pythagorean theorem, l2 + w2 = d2
⇒ 132 = l2 + 52
⇒ 169 = l2 + 25
⇒ l2 = 169 - 25
⇒ l2 = 144 = 122
∴ l = 12
∴ length In a rectangle is, l = 12
Perimeter of a rectangle, P = 2(l + w)
= 2(12 + 5) = 2 × 17 = 34
So the perimeter of the rectangle is 34.
Solution:
Given that,
Surface area of a cube = 96 square units
We know,
Surface area of a cube, S = 6a2
⇒ 6a2 = 96
⇒ a2 = 96/6
⇒ a2 = 16 = 42
∴ a = 4
The longest stick that can fit inside the cube runs along the space diagonal.
So the space diagonal of a cube, d = a√3 = 4√3 ; [a = 4]
So the length of the longest stick that can be placed inside the cube is 4√3 units.