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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes২৩ বৈধ · ১ অসম্পূর্ণ
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Area, Volumes & Surface Area, Height & Distance (Trigonometry) [ব্যাংকের সকল পরীক্ষা যেকোনো প্যাকেজের জন্য ফ্রি]
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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৪ প্রশ্ন

১.
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is ____ metre square.
  1. ক
    ক) 1520
  2. খ
    খ) 2420
  3. গ
    গ) 2480
  4. ঘ
    ঘ) 2520
ব্যাখ্যা

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103
Solving the two equations, we get:
l = 63 and b = 40
∴ Area = (l x b) = (63 x 40) m2 = 2520 m2

২.
A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :
  1. ক
    ক) 16000
  2. খ
    খ) 18000
  3. গ
    গ) 20000
  4. ঘ
    ঘ) 22000
ব্যাখ্যা

Number of bricks
=Courtyard area/1 brick area
=(2500×1600 / 20×10)=20000

৩.
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
  1. ক
    ক) 75 cu. m
  2. খ
    খ) 750 cu. m
  3. গ
    গ) 7500 cu. m
  4. ঘ
    ঘ) 75000 cu. m
ব্যাখ্যা

1 hectare = 10,000 m2
So, Area = (1.5 x 10000) m2 = 15000 m2.
Depth =5/100 m=1/20m.
Volume = (Area x Depth) =15000 x1/20m3= 750 m3.

৪.
What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Tk. 10 per square meter?
  1. ক
    ক) Tk. 3430
  2. খ
    খ) Tk. 3440
  3. গ
    গ) Tk. 3450
  4. ঘ
    ঘ) Tk. 3460
ব্যাখ্যা

In this question, we are having perimeter.
We know Perimeter = 2(l+b), right
So, 2(l+b) = 340
As we have to make 1 meter boundary around this,
so Area of boundary = ((l+2)+(b+2)-lb)
= 2(l+b)+4 = 340+4 = 344
So required cost will be = 344 × 10 = 3440

৫.
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
  1. ক
    ক) 4120 m cube
  2. খ
    খ) 4140 m cube
  3. গ
    গ) 5140 m cube
  4. ঘ
    ঘ) 5120 m cube
ব্যাখ্যা

l = (48 - 16)m = 32 m, [because 8+8 = 16]
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m cube
= 5120 m cube.

৬.
The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.
  1. ক
    ক) 9 cm
  2. খ
    খ) 8 cm
  3. গ
    গ) 7 cm
  4. ঘ
    ঘ) 6 cm
ব্যাখ্যা

Let the lengths of the line segments be x and x+2 cm
then,
(x+2)2−x2=32
x2+4x+4−x2=32
4x=28
x=7cm

Hence, the greater line should be, x + 2 = 9
৭.
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m³, then the rise in the water level in the tank will be:
  1. ক
    ক) 20 cm
  2. খ
    খ) 25 cm
  3. গ
    গ) 35 cm
  4. ঘ
    ঘ) 50 cm
ব্যাখ্যা

Total volume of water displaced = (4 x 50) m3 = 200 m3.
Rise in water level =200/(40 x 20)m 0.25 m = 25 cm.

৮.
The area of rhombus is 150 cm square. The length of one of the its diagonals is 10 cm. The length of the other diagonal is:
  1. ক
    ক) 15 cm
  2. খ
    খ) 20 cm
  3. গ
    গ) 25 cm
  4. ঘ
    ঘ) 30 cm
ব্যাখ্যা

We know the product of diagonals is 1/2×(product of diagonals)
Let one diagonal be d1 and d2
So as per question
1/2×d1×d2=150
1/2×10×d2=150
d2=150/5 = 30

৯.
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
  1. ক
    ক) 90 cm
  2. খ
    খ) 1 dm
  3. গ
    গ) 1.1 cm
  4. ঘ
    ঘ) 2 m
ব্যাখ্যা

Let the thickness of the bottom be x cm.
Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000
320 x 250 x (110 - x) = 8000 x 1000
(110 - x) =8000 x 1000/320 x 250= 100
 x = 10 cm = 1 dm.

১০.
The area of incircle of an equilateral triangle of side 42 cm is ___ cm2
  1. ক
    ক) 462
  2. খ
    খ) 452
  3. গ
    গ) 442
  4. ঘ
    ঘ) 432
ব্যাখ্যা

Radius of incircle
=a/2√3
=42/ 2√3
=7√3
Area of incircle
=22/7×49×3
=462 cm2

১১.
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
  1. ক
    ক) 814
  2. খ
    খ) 820
  3. গ
    গ) 840
  4. ঘ
    ঘ) 844
ব্যাখ্যা

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles 
= (1517 x 902) / (41 x 41)= 814.

১২.
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
  1. ক
    ক) 5600
  2. খ
    খ) 6000
  3. গ
    গ) 6400
  4. ঘ
    ঘ) 7200
ব্যাখ্যা

Number of bricks =Volume of the wall/ Volume of 1 brick
=800 x 600 x 22.5/25 x 11.25 x 6
= 6400.

১৩.
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
  1. ক
    ক) 2.91 m
  2. খ
    খ) 3 m
  3. গ
    গ) 5.82 m
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.

১৪.
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
  1. ক
    ক) 34
  2. খ
    খ) 40
  3. গ
    গ) 68
  4. ঘ
    ঘ) 88
ব্যাখ্যা

We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.

১৫.
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is
  1. ক
    ক) 456
  2. খ
    খ) 458
  3. গ
    গ) 558
  4. ঘ
    ঘ) 568
ব্যাখ্যা

Area to be plastered= [2(l + b) x h] + (l x b)
= {[2(25 + 12) x 6] + (25 x 12)} m2
= (444 + 300) m2
= 744 m2.
Cost of plastering = Rs.744 x (75/100)
= Rs. 558

১৬.
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m³) is:
  1. ক
    ক) 4830
  2. খ
    খ) 5120
  3. গ
    গ) 6420
  4. ঘ
    ঘ) 8960
ব্যাখ্যা

Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.

১৭.
If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is:
  1. ক
    ক) 10.52 sq.cm
  2. খ
    খ) 11.52 sq.cm
  3. গ
    গ) 12.52 sq.cm
  4. ঘ
    ঘ) 13.52 sq.cm
ব্যাখ্যা
p>Area of the square :
=[1/2×(5.2)2] sq.cm
= (1/2×27.04) sq.cm
=13.52 sq.cm

১৮.
The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:
  1. ক
    ক) 30°
  2. খ
    খ) 45°
  3. গ
    গ) 60°
  4. ঘ
    ঘ) 90°
অনির্ধারিত
ব্যাখ্যা

√3 এর বদলে 3 দেয়া আছে। উত্তর বাতিল করা হয়েছে।
√3 এর ক্ষেত্রে সমাধান এরকম হবে -

Let AB be the tree and AC be its shadow.
Let Angle ACB =θ
Then,AC/AB = √3
cot θ = √3
θ = 30°.

১৯.
From a point C on a level ground, the angle of elevation of the top of a tower is 30 degree. If the tower is 100 meter high, find the distance from point C to the foot of the tower.
  1. ক
    ক) 170 meter
  2. খ
    খ) 172 meter
  3. গ
    গ) 173 meter
  4. ঘ
    ঘ) 167 meter
ব্যাখ্যা
.


Let AB be the tower
then∠ACB=30º
AB=100 meter
AB/AC= tan30º
=>100/AC= 1/√3
=>AC= √3/100
=>AC= 1.73×100
=>AC= 173meter

২০.
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
  1. ক
    ক) 2.5 m
  2. খ
    খ) 4.9 m
  3. গ
    গ) 5.7 m
  4. ঘ
    ঘ) 9.2 m
ব্যাখ্যা


Let AB be the wall and BC be the ladder.
Then, ∠ACB = 60° = AC = 4.6m
AC/BC=cos⁡60∘=1/2
⇒ BC = 2 × AC = 2 × 4.6 = 9.2m

২১.
The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:
  1. ক
    ক) 14.8 m
  2. খ
    খ) 68.2m
  3. গ
    গ) 12.5 m
  4. ঘ
    ঘ) 24.8 m
ব্যাখ্যা


Consider the diagram shown above where PR represents the ladder and RQ represents the wall.
cos⁡60∘=PQ/PR
1/2=12.4/PR
PR=2×12.4=24.8m

২২.
Ramesh and Suresh’s mud forts have heights 8cm and 15 cm. They are 24 cm apart. How far are the fort tops from each other?
  1. ক
    ক) 22 cm
  2. খ
    খ) 23 cm
  3. গ
    গ) 25 cm
  4. ঘ
    ঘ) 24.5 cm
২৩.
Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
  1. ক
    ক) 23 ft
  2. খ
    খ) 42 ft
  3. গ
    গ) 54 ft
  4. ঘ
    ঘ) 68 ft
২৪.
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
  1. ক
    ক) 2%
  2. খ
    খ) 2.02%
  3. গ
    গ) 4%
  4. ঘ
    ঘ) 4.04%
ব্যাখ্যা

100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error =404/(100 x 100) x 100%= 4.04%