Bank Math

PrepBank · পাতা ৩৯ / ১৬১ · ৩,৮০১–৩,৯০০ / ১৬,১২৪

৩,৮০১.

A car go 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles ?

ক
ক) $10
খ
খ) $31
গ
গ) $40
ঘ
ঘ) $50

সঠিক উত্তর: খ

খ) $31

উত্তর

সঠিক উত্তর: খ

খ) $31

খ

ব্যাখ্যা

Question: A car go 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles ?

Solution:
গাড়িটির 33 মাইল যেতে খরচ হয় = $ 2.95
গাড়িটির 1 মাইল যেতে খরচ হয় = $ 2.95/33
গাড়িটির 1 মাইল যেতে খরচ হয় = $ (2.95 × 350)/33 = $31.287 ≈ $31

৩,৮০২.

A shopkeeper makes an item at Tk 1,200 and gives a 10% discount. If he still makes a 20% profit, what was the cost price?

ক
Tk. 900
খ
Tk. 840
গ
Tk. 790
ঘ
Tk. 950
ঙ
None of these

সঠিক উত্তর: ক

Tk. 900

উত্তর

সঠিক উত্তর: ক

Tk. 900

ক

ব্যাখ্যা

Question: A shopkeeper makes an item at Tk 1,200 and gives a 10% discount. If he still makes a 20% profit, what was the cost price?

Solution:
Selling price after 10% discount
= 1200 - 10% of 1200
= 1200 - {(10/100) × 1200}
= 1200 - 120
= 1080

Let the cost price = x
Profit = 20%

Now,
⇒ x + 20% of x = 1080
⇒ x + (20/100)x = 1080
⇒ x + (x/5) = 1080
⇒ 6x = 5400
⇒ x = 5400/6
∴ x = 900

So, the cost price of that item is Tk. 900

৩,৮০৩.

What is the sine of 45 degrees?

ক
0
খ
1/2
গ
√3/2
ঘ
√2/2

সঠিক উত্তর: ঘ

√2/2

উত্তর

সঠিক উত্তর: ঘ

√2/2

ঘ

ব্যাখ্যা

Question: What is the sine of 45 degrees?

Solution:
sin45 = 1/√2
= √2/2

৩,৮০৪.

If the radius of a sphere is increased by 10%, how much will the surface area be increased in percentage?

ক
ক) 21%
খ
খ) 10%
গ
গ) 18%
ঘ
ঘ) 20%

সঠিক উত্তর: ক

ক) 21%

উত্তর

সঠিক উত্তর: ক

ক) 21%

ক

ব্যাখ্যা

Surface area of sphere = 4πr²
Is the new radius is 10% increased, then new surface area will be = 4π(1.1)² = 4.84πr²

Surface area Increased in percentage = (4.84πr²/4πr² × 100) - 100 = 121 - 100 = 21%

৩,৮০৫.

What is the H.C.F. of 4/9, 8/12, and 16/18?

ক
2/75
খ
1/9
গ
84
ঘ
3/52
ঙ
4/9

সঠিক উত্তর: খ

1/9

উত্তর

সঠিক উত্তর: খ

1/9

খ

ব্যাখ্যা

Question: What is the H.C.F. of 4/9, 8/12, and 16/18?

Solution:
We know,
H.C.F. of fractions = (H.C.F. of numerators)/(L.C.M. of denominators)

H.C.F. of numerators:
H.C.F.(4, 8, 16) = 4

L.C.M. of denominators:
9 = 3²
12 = 2² × 3
18 = 2 × 3²∴ L.C.M. = 2² × 3² = 4 × 9 = 36

∴ Required H.C.F. = 4/36 = 1/9

৩,৮০৬.

The smallest 3-digit prime number is:

ক
101
খ
102
গ
103
ঘ
None of these

সঠিক উত্তর: ক

101

উত্তর

সঠিক উত্তর: ক

101

ক

ব্যাখ্যা

Question: The smallest 3-digit prime number is:

Solution:
১ এর চেয়ে বড় যে সকল সংখ্যাকে শুধু ১ এবং ঐ সংখ্যা ছাড়া আর কোনো সংখ্যা দ্বারা ভাগ করা যায় না, তাদেরকে মৌলিক সংখ্যা বলে।
অর্থাৎ মৌলিক সংখ্যার উৎপাদক হবে দুইটি: ১ এবং শুধুমাত্র সেই সংখ্যাটি।
তিন অঙ্ক বিশিষ্ট সবচেয়ে ছোট মৌলিক সংখ্যা = ১০১।

৩,৮০৭.

In a city, the fare of a cab consists of fixed charge plus the charge for the distance covered. For a journey of 8 km, the charge paid is Tk. 300 and for 15 km, the charge paid is Tk. 335. Determine the charge a person will have to pay for 24 km?

ক
ক) Tk. 236
খ
খ) Tk. 248
গ
গ) Tk. 346
ঘ
ঘ) Tk. 380

সঠিক উত্তর: ঘ

ঘ) Tk. 380

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 380

ঘ

ব্যাখ্যা

Question: In a city, the fare of a cab consists of fixed charge plus the charge for the distance covered. For a journey of 8 km, the charge paid is Tk. 300 and for 15 km, the charge paid is Tk. 335. Determine the charge a person will have to pay for 24 km?

A private taxi company charges a fixed charge along with a per kilometre charge based on the distance covered. For a journey of 24 km, the charges paid are Rs. 368 and for a journey of 32 km, the charges paid Rs. 464.

Let, the fixed charge be ‘a’ and charge per km be ‘b’.
According to question: a + 8b = 300 ---- (I)
a + 15b = 335 ---- (II)

(II) - (I),
15b - 8b = 35
7b = 34
b = 5

If we put the value of ‘b’ in equation (I), we get:
a + 8 × 5 = 300
a = 260

For travelling a distance of 24 km, a person will have to pay Rs. (a + 24b)
= 260 + 24 × 5
= 260 + 120
= 380

৩,৮০৮.

A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 30 km/hr and the second half at the rate of 50 km/hr. Find the total journey in km.

ক
375 km
খ
384 km
গ
405 km
ঘ
280 km

সঠিক উত্তর: ক

375 km

উত্তর

সঠিক উত্তর: ক

375 km

ক

ব্যাখ্যা

Question: A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 30 km/hr and the second half at the rate of 50 km/hr. Find the total journey in km.

Solution:
ধরা যাক, মোট যাত্রার দূরত্ব হলো d কিমি।
তাহলে, যাত্রার প্রথম অর্ধেকের দূরত্ব হবে d/2 কিমি
এবং দ্বিতীয় অর্ধেকের দূরত্বও হবে d/2 কিমি।

প্রথম অর্ধেক যাত্রায়,
সময় = দূরত্ব/গতিবেগ
= (d/2)/30 ঘন্টা
= d/60 ঘন্টা

দ্বিতীয় অর্ধেক যাত্রায়,
সময় = দূরত্ব/গতিবেগ
= (d/2)/50 ঘন্টা
= d/100 ঘন্টা

প্রশ্নমতে,
(d/60) + (d/100) = 10
⇒ (5d + 3d)/300 = 10
⇒ 8d/300 = 10
⇒ 8d = 10 × 300
⇒ 8d = 3000
⇒ d = 3000/8
⇒ d = 375 কিমি

∴ মোট যাত্রার দূরত্ব 375 কিলোমিটার।

৩,৮০৯.

θ is the positive acute angle and sinθ - cosθ = 0, then the value of secθ + cosecθ is?

ক
3/√2
খ
1
গ
2√2
ঘ
0

সঠিক উত্তর: গ

2√2

উত্তর

সঠিক উত্তর: গ

2√2

গ

ব্যাখ্যা

Question: θ is the positive acute angle and sinθ - cosθ = 0, then the value of secθ + cosecθ is?

Solution:

৩,৮১০.

A zip wire runs between two posts, 30m apart. The zip wire is at an angle of 60° to the horizontal. Calculate the length of the zip wire.

ক
80 m
খ
60 m
গ
45 m
ঘ
90 m

সঠিক উত্তর: খ

60 m

উত্তর

সঠিক উত্তর: খ

60 m

খ

ব্যাখ্যা

Question: A zip wire runs between two posts, 30m apart. The zip wire is at an angle of 60° to the horizontal. Calculate the length of the zip wire.

Solution:

Given,
Horizontal distance between posts is 30 meters
Angle of elevation, θ = 60°
Then, we find the Length of the zip wire (hypotenuse) = L
Since we know the adjacent side and the angle, and we need to find the hypotenuse, we use the cosine function.

⇒ cos(θ) = Adjacent/Hypotenuse
⇒ cos(60°) = 30/L
⇒ L = 30/(1/2)
= 30 × 2
= 60 m

So, Length of zip wire is = 60 m

৩,৮১১.

What is the average from 1 to 59?

ক
28.5
খ
29
গ
29.5
ঘ
30

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: What is the average from 1 to 59?

Solution:
We know,
Average of n natural numbers = (n + 1)/2
Here, n = 59

∴ Average = (59 + 1)/2
= 60/2
= 30

৩,৮১২.

If 3x + (3/x) = 5, then x³ + (1/x³) = ?

ক
260/27
খ
85/27
গ
-(10/27)
ঘ
-(90/27)

সঠিক উত্তর: গ

-(10/27)

উত্তর

সঠিক উত্তর: গ

-(10/27)

গ

ব্যাখ্যা

Question: If 3x + (3/x) = 5, then x³ + (1/x)³ = ?

Solution:
Given,
3x + (3/x) = 5
x + (1/x) = 5/3

∴ x³ + (1/x)³
{x + (1/x)}3 - 3.x.(1/x){x + (1/x)}
= (5/3)³ - 3 × (5/3)
= (125/27) - 5
= (125 - 135)/27
= - (10/27)

৩,৮১৩.

Two trains 150 m and 180 m long run at the speed of 72 km/hr and 36 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is:

ক
8 sec
খ
9.8 sec
গ
10 sec
ঘ
11 sec

সঠিক উত্তর: ঘ

11 sec

উত্তর

সঠিক উত্তর: ঘ

11 sec

ঘ

ব্যাখ্যা

Question: Two trains 150 m and 180 m long run at the speed of 72 km/hr and 36 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is:

Solution:
Relative speed = (72 + 36) km/hr
= 108 × (5/18) m/sec
= 30 m/sec

Distance covered in crossing each other = (150 + 180) m
= 330 m.

Required time = 330/30 sec
= 11 sec

৩,৮১৪.

In how many ways can the letters of 'PARALLEL' be arranged if the first letter is always P?

ক
420
খ
580
গ
360
ঘ
144

সঠিক উত্তর: ক

420

উত্তর

সঠিক উত্তর: ক

420

ক

ব্যাখ্যা

Question: In how many ways can the letters of 'PARALLEL' be arranged if the first letter is always P?

Solution:
The word 'PARALLEL' has a total of 8 letters.

Condition, The first letter is fixed as 'P'.
Now, the remaining 8 - 1 = 7 positions need to be filled with the remaining letters.

Among these 7 letters, there are repeated letters:
A (2 times) and L (3 times)

∴ Number of arrangements for the remaining 7 letters= 7!/(3! × 2!)
= 5040/12
= 420

৩,৮১৫.

If then a/b = ?

ক
0.16
খ
0.018
গ
0.016
ঘ
0.044

সঠিক উত্তর: গ

0.016

উত্তর

সঠিক উত্তর: গ

0.016

গ

ব্যাখ্যা

Question: If then a/b = ?

Solution:
√(0.04 × 0.4 × a) = 0.4 × 0.04 × √b
Or, {√(0.04 × 0.4 × a)}² = (0.4 × 0.04 × √b)²
Or, 0.04 × 0.4 × a = (0.4 × 0.04)² × b
Or, a = {(0.4 × 0.04)² × b}/(0.4 × 0.04)
Or, a = (0.4 × 0.04) × b
Or, a/b = 0.4 × 0.04
∴ a/b = 0.016

৩,৮১৬.

For which of the following values of x is (x + 78)/x an integer?

ক
9
খ
10
গ
11
ঘ
13
ঙ
None of these

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

প্রশ্ন: For which of the following values of x is (x + 78)/x an integer?

সমাধান:
x এর মান হবে 78 এর উৎপাদক।
অপশন গুলোর মধ্যে 78 এর উৎপাদক হলো 13
অতএব সঠিক উত্তর 13.

অপশন টেস্ট:
ক) x = 9 , (x + 78)/x = (9 + 78)/9 = 9.66 [পূর্ণসংখ্যা নয়]
খ) x = 10 , (x + 78)/x = (10 + 78)/10 = 8.8[পূর্ণসংখ্যা নয়]
গ) x = 11 , (x + 78)/x = (11 + 78)/11 = 8.09 [পূর্ণসংখ্যা নয়]
ঘ) x = 13 , (x + 78)/x = (13 + 78)/13 = 7; যা পূর্ণসংখ্যা

৩,৮১৭.

Which of the following is greater than 1?

ক
0.00004/0.005
খ
0.01/0.003
গ
0.003/0.006
ঘ
0.001/0.01

সঠিক উত্তর: খ

0.01/0.003

উত্তর

সঠিক উত্তর: খ

0.01/0.003

খ

ব্যাখ্যা

Question: Which of the following is greater than 1?

Solution:
0.00004/0.005 = 0.008
0.01/0.003 = 3.333
0.003/0.006 = 0.5
0.001/0.01 = 0.1

৩,৮১৮.

The average weight of 3 friends is 66 kg. None of the friends weights less than 62 kg. What can be the maximum weight of any three friends?

ক
70 kg
খ
65 kg
গ
72 kg
ঘ
74 kg

সঠিক উত্তর: ঘ

74 kg

উত্তর

সঠিক উত্তর: ঘ

74 kg

ঘ

ব্যাখ্যা

Question: The average weight of 3 friends is 66 kg. None of the friends weights less than 62 kg. What can be the maximum weight of any three friends?

Solution:
তিনজনের গড় ওজন ৬৬ কেজি
মোট ওজন ৬৬ × ৩ কেজি
= ১৯৮ কেজি

প্রতিজনের ওজন সর্বনিম্ন ৬২ কেজি
দুজনের সর্বনিম্ন ওজন ৬২ × ২ কেজি
= ১২৪ কেজি

একজনের সর্বোচ্চ ওজন হতে পারে = ১৯৮ - ১২৪ কেজি
= ৭৪ কেজি

৩,৮১৯.

A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

ক
ক) 40 km
খ
খ) 50 km
গ
গ) 55 km
ঘ
ঘ) 60 km

সঠিক উত্তর: ঘ

ঘ) 60 km

উত্তর

সঠিক উত্তর: ঘ

ঘ) 60 km

ঘ

ব্যাখ্যা

Question: A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

Solution:
Let
the distance between the stations A and B be x km
Time taken = 45 min = 45/60 = 3/4 hour

∴ Original speed =(x × 4/3)km/hr = 4x/3 km/hr

New speed = {(4x/3) - 5} km/hr.
= (4x - 15)/3 km/hr.

Now
x/{(4x - 15/3} =48/60
3x/(4x - 15) = 4/5
16x - 60 = 15x
16x - 15x = 60
x = 60 km

৩,৮২০.

In what ratio must rice at Tk 10 per kg be mixed with rice at Tk 16 per kg so that the mixture be worth Tk 12 per kg?

ক
ক) 2 : 5
খ
খ) 5 : 1
গ
গ) 3 : 1
ঘ
ঘ) 2 : 1

সঠিক উত্তর: ঘ

ঘ) 2 : 1

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2 : 1

ঘ

ব্যাখ্যা

Question: In what ratio must rice at Tk 10 per kg be mixed with rice at Tk 16 per kg so that the mixture be worth Tk 12 per kg?

Solution:
ধরি, প্রতি কেজি ১০ টাকায় বিক্রি করে x কেজি
প্রতি কেজি ১৬ টাকায় বিক্রি করে y কেজি

10x + 16y = 12(x + y)
⇒ 10x + 16y = 12x + 12y
⇒ 12x - 10x = 16y - 12y
⇒ 2x = 4y
∴ x/y = 2 = 2 : 1

৩,৮২১.

Successive discount of 20% and 15% are equal to a single discount of-

ক
30%
খ
32%
গ
34%
ঘ
35%

সঠিক উত্তর: খ

32%

উত্তর

সঠিক উত্তর: খ

32%

খ

ব্যাখ্যা

Question: Successive discount of 20% and 15% are equal to a single discount of-

Solution:
Let, The original price be 100 tk

After a 20% discount, the price is = 100 - 20 = 80 tk
Again, after a 15% discount, the new price is = 80 - {80 × (15/100)}
= 80 - 12
= 68

∴ Total discount= (100 - 68) = 32%

৩,৮২২.

The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is 16, then the other number is = ?

ক
24
খ
12
গ
36
ঘ
54

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is 16, then the other number is = ?

Solution:
Here,
HCF = 8
LCM = 48

One number = 16

Let the other number be = p
∴ 16p = 48 × 8
⇒ p = 24

Hence, the other number is = 24

৩,৮২৩.

Average of 60 numbers are 42. When 5 more numbers are included, the average of 65 numbers become 45. Find the average of 5 numbers.

ক
70
খ
78
গ
81
ঘ
90

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Average of 60 numbers are 42. When 5 more numbers are included, the average of 65 numbers become 45. Find the average of 5 numbers.

Solution:
Total of 60 numbers = 60 × 42 = 2520
Now, total of 65 numbers = 65 × 45 = 2925

Hence, sum of 5 numbers = 2925 - 2520 = 405

∴ Average of five numbers = 405/5
= 81

৩,৮২৪.

The difference in taka between simple and compound interest at 5% annually on a sum of Tk. 5000 after 2 years is –

ক
ক) 12.5
খ
খ) 25
গ
গ) 50
ঘ
ঘ) 500

সঠিক উত্তর: ক

ক) 12.5

উত্তর

সঠিক উত্তর: ক

ক) 12.5

ক

ব্যাখ্যা

SI = 500 × 2 × 5/100 = 500
CI = 5000(1 + 5/100)² – 5000= 512.5
Difference = 512.5 - 500 = 12.5

৩,৮২৫.

(0.04)^{- 1.5} = ?

ক
40
খ
125
গ
400
ঘ
250

সঠিক উত্তর: খ

125

উত্তর

সঠিক উত্তর: খ

125

খ

ব্যাখ্যা

Question: (0.04)^{- 1.5} = ?

Solution:
(0.04)^{- 1.5}
= (4/100)^{- 1.5}
= (1/25)^{- 1.5}
= (1/25)^{- (3/2)}
= (25)^3/2
= (5²)^3/2
= 5^{2 × (3/2)}
= 5³
= 125

৩,৮২৬.

Find the value of (3log2 + 2log3)/(log36 + log2)

ক
1
খ
2
গ
4
ঘ
6

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Find the value of (3log2 + 2log3)/(log36 + log2)

Solution:
3log2 + 2log3
= log2³ + log3²
= log8 + log9
= log(8×9)
= log72

log36+log2
= log(36 × 2)
= log72

(3log2 + 2log3) / (log36 + log2)
=log72 / log72
= 1

৩,৮২৭.

A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence?

ক
17 years
খ
23 years
গ
18 years
ঘ
13 years

সঠিক উত্তর: ঘ

13 years

উত্তর

সঠিক উত্তর: ঘ

13 years

ঘ

ব্যাখ্যা

Question: A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence?

Solution:
Let A’s present age be ‘x’ years.

According to the question,
x + 15 = 5 (x - 5)
⇒ x + 15 = 5 x - 25
⇒ 4x = 40
⇒ x = 10
⇒ A’s present age = 10 years

Therefore, A’s age 3 years hence = 10 + 3 = 13 years.

৩,৮২৮.

The average age of 50 students in a class is 18 years. When 10 new students are admitted, the average is increased by 0.5 years. The average age of new students is?

ক
15 years
খ
18 years
গ
20 years
ঘ
21 years
ঙ
22.5 years

সঠিক উত্তর: ঘ

21 years

উত্তর

সঠিক উত্তর: ঘ

21 years

ঘ

ব্যাখ্যা

Question: The average age of 50 students in a class is 18 years. When 10 new students are admitted, the average is increased by 0.5 years. The average age of new students is?

Solution:
50 জন শিক্ষার্থীর মোট বয়স = 50 × 18 = 900 বছর
10 জন নতুন শিক্ষার্থী ভর্তি হওয়ায় মোট শিক্ষার্থীর সংখ্যা = 50 + 10 = 60 জন

এখন, গড় বয়স বৃদ্ধি পাওয়ায় নতুন গড় বয়স = 18 + 0.5 = 18.5 বছর
সুতরাং, 60 জন শিক্ষার্থীর মোট বয়স = 60 × 18.5 = 1110 বছর

নতুন 10 জন শিক্ষার্থীর মোট বয়স = 1110 - 900 = 210 বছর
সুতরাং, নতুন 10 জন শিক্ষার্থীর গড় বয়স = 210/10 = 21 বছর।

৩,৮২৯.

If 283M456 is divisible by 3, what is the value of M?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 6

সঠিক উত্তর: ক

ক) 2

উত্তর

সঠিক উত্তর: ক

ক) 2

ক

ব্যাখ্যা

Question: If 283M456 is divisible by 3, what is the value of M?

Solution:
একটি সংখ্যা ৩ দ্বারা বিভাজ্য হবে যদি সংখ্যাটির অঙ্কগুলোর সমষ্টি ৩ দ্বারা বিভাজ্য হয়।

২ + ৮ + ৩ + ৪ + ৫ + ৬ = ২৮; এর সাথে ২ যোগ করলে ৩০ হয়, যা ৩ দ্বারা বিভাজ্য।
∴ M = ২

৩,৮৩০.

In a school, 30 students study Mathematics, 20 students study Science, and 12 students study both subjects. If 8 students study neither Mathematics nor Science, find the total number of students in the school.

ক
38
খ
46
গ
50
ঘ
62
ঙ
None of these

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In a school, 30 students study Mathematics, 20 students study Science, and 12 students study both subjects. If 8 students study neither Mathematics nor Science, find the total number of students in the school.

Solution:
Given that,
Students studying Mathematics, ∣M∣ = 30
Students studying Science, ∣S∣ = 20
Students studying both, ∣M ∩ S∣ = 12
Students studying neither = 8

We know,
∣M ∪ S∣ = ∣M∣ + ∣S∣ - ∣M ∩ S∣
= 30 + 20 - 12
= 38

∴ Total students in the class = students who study Mathematics or Science + students who play neither
= ∣M ∪ S∣ + Neither
= 38 + 8
= 46

৩,৮৩১.

sec²A + tan²A = 7, find, sec⁴A - tan⁴A =?

ক
5
খ
6
গ
7
ঘ
8

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: sec²A + tan²A = 7, find, sec⁴A - tan⁴A =?

Solution:
Given, sec²A + tan²A = 7

sec⁴A - tan⁴A
= (sec²A)² - (tan²A)²
= (sec²A + tan²A) (sec²A - tan²A)
= 7 × 1
= 7

৩,৮৩২.

Priom's income is 40% less than Ratul's income, Qader's income is 20% less than Priom's income, and Shahin's income is 40% less than Priom's income. If Ratul gave 60% of his income to Shahin and 40% of his income to Qader, Qader's new income would be what fraction of Shahin's new income?

ক
11/12
খ
13/17
গ
12/19
ঘ
None of these

সঠিক উত্তর: ক

11/12

উত্তর

সঠিক উত্তর: ক

11/12

ক

ব্যাখ্যা

Question: Priom's income is 40% less than Ratul's income, Qader's income is 20% less than Priom's income, and Shahin's income is 40% less than Priom's income. If Ratul gave 60% of his income to Shahin and 40% of his income to Qader, Qader's new income would be what fraction of Shahin's new income?

Solution:
let, priom's income = 0.6 × ratul's income
ratul's income = priom's income/0.6

Qader's income = 0.8 × prioms income
Shahins income = 0.6 × prioms income

Qader's new income = (0.8 × prioms income) + (0.4/0.6) × prioms income
= (22/15) × prioms income

Shahins new income = (0.6 × proms income) + (.6/.6) × prioms income
= (8/5) × prioms income

fraction = {(22/15) × prioms income} / (8/5) × prioms income
= 11/12

৩,৮৩৩.

5 ÷ √5 = ?

ক
√5
খ
5
গ
1/√5
ঘ
0.05

সঠিক উত্তর: ক

√5

উত্তর

সঠিক উত্তর: ক

√5

ক

ব্যাখ্যা

Question: 5 ÷ √5 = ?

Solution:
5 ÷ √5
= 5/√5
= √5

৩,৮৩৪.

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

ক
ক) 45 km/hr
খ
খ) 50 km/hr
গ
গ) 54 km/hr
ঘ
ঘ) 55 km/hr

সঠিক উত্তর: খ

খ) 50 km/hr

উত্তর

সঠিক উত্তর: খ

খ) 50 km/hr

খ

ব্যাখ্যা

Speed of the train relative to man
= 125/10 m/sec
= 25/2 m/sec
= (25/2)×(18/5) km/hr
= 45km/hr
Let the speed of the train be x km/hr. Then, relative speed=(x−5)km/hr
∴x−5= 45
⇒x = 50km/hr

৩,৮৩৫.

What is the angle between the hour and minute hands of a clock when it is 10 minutes past 3?

ক
25°
খ
45°
গ
35°
ঘ
30°

সঠিক উত্তর: গ

35°

উত্তর

সঠিক উত্তর: গ

35°

গ

ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 10 minutes past 3?

Solution:
10 minutes past 3 অর্থাৎ, 3 টা 10 মিনিট।
= 3 + (10/60) ঘন্টা
= 3 + 1/6
= 19/6 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 19/6 ঘন্টায় ঘোরে = 30 × (19/6) = 570/6 = 95°

মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 10 মিনিটে ঘোরে = 10 × 6 = 60°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |95° - 60°| = 35°

৩,৮৩৬.

On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5?

ক
2
খ
3
গ
5
ঘ
none of these

সঠিক উত্তর: ঘ

none of these

উত্তর

সঠিক উত্তর: ঘ

none of these

ঘ

ব্যাখ্যা

Question: On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5?

Solution:
Let the number be x and on dividing x by 5, we get m as quotient and 3 as remainder.
∴ x = 5m + 3
⇒ x²= (5m + 3)²
= (25m² + 30m + 9)
= 5(5m² + 6m + 1) + 4

∴ On dividing x² by 5, we get 4 as remainder.

৩,৮৩৭.

Find the diagonal and trace of the matrix

ক
1, 3, 6 and trace 10
খ
1, 2, 4 and trace 7
গ
1, - 5, 9 and trace 5
ঘ
4, - 5, 6 and trace 5

সঠিক উত্তর: গ

1, - 5, 9 and trace 5

উত্তর

সঠিক উত্তর: গ

1, - 5, 9 and trace 5

গ

ব্যাখ্যা

Question: Find the diagonal and trace of the matrix

Solution: The diagonal of a matrix consists of the elements from the upper left corner of the matrix to the lower right corner.

Or in other words, if a matrix is A, then the diagonal elements are a₁₁, a₂₂, and a₃₃.
Thus, the diagonal of A consists of the numbers 1, -5, and 9.
The trace of a matrix is the sum of the diagonal elements.

Thus,
Trace, tr = 1-5+9 = 5.

৩,৮৩৮.

A motorboat in still water travels at speed of 26 kmph. It goes 42 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

ক
1 hr
খ
1 hr 30 min
গ
1 hr 45 min
ঘ
2 hr

সঠিক উত্তর: খ

1 hr 30 min

উত্তর

সঠিক উত্তর: খ

1 hr 30 min

খ

ব্যাখ্যা

Question: A motorboat in still water travels at speed of 26 kmph. It goes 42 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

Solution:
মোটরযানের বেগ ২৬ কিমি/ঘণ্টা

স্রোতের বিপরীতে ১ঘণ্টা ৪৫ মিনিট বা ৭/৪ ঘণ্টায় যায় ৪২ কিমি
১ ঘণ্টায় যায় ৪২/৭/৪ কিমি
= ২৪ কিমি
স্রোতের বেগ = ২৬ - ২৪ কিমি/ঘণ্টা
= ২ কিমি/ঘণ্টা

স্রোতের অনুকূলে বেগ = ২৬ +২
= ২৮ কিমি/ঘণ্টা

৪২ কিমি যেতে সময় লাগে ৪২/২৮
= ৩/২
= ১.৫ ঘণ্টা
= ১ ঘণ্টা ৩০ মিনিট

৩,৮৩৯.

In number 235749, what is the face value of the numeral 5?

ক
50000
খ
5
গ
5000
ঘ
500

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In number 235749, what is the face value of the numeral 5?

Solution:
: In number 235749, the face value of 5 is 5.

৩,৮৪০.

a : b = 3 : 4 and b : c = 9 : 7. What is a : b : c?

ক
ক) 3 : 13 : 7
খ
খ) 3 : 36 : 28
গ
গ) 27 : 16 : 28
ঘ
ঘ) 27 : 36 : 28

সঠিক উত্তর: ঘ

ঘ) 27 : 36 : 28

উত্তর

সঠিক উত্তর: ঘ

ঘ) 27 : 36 : 28

ঘ

ব্যাখ্যা

B is common to both the ratios.
Values of b = 4 and 9 (That means they are not the same)
Make the values of 'b' the same as follows -
Multiply 3 : 4 up and down with 9 as shown
∴ (3 × 9)/(4 × 9) = 27/36 = a/b
Multiply 9 : 7 up and down with 4 as shown
∴ (9 × 4)/(7 × 4) = 36/28 = b/c
Since values of b are the same = 36
a : b : c = 27 : 36 : 28

৩,৮৪১.

B is twice the age of C, and A is 2 years older than B. With their ages adding up to 42, what is A's age?

ক
12 years
খ
18 years
গ
20 years
ঘ
22 years

সঠিক উত্তর: খ

18 years

উত্তর

সঠিক উত্তর: খ

18 years

খ

ব্যাখ্যা

Question: B is twice the age of C, and A is 2 years older than B. With their ages adding up to 42, what is A's age?

Solution:
Let,
C is = x years old
B is 2x years old
A is (2x + 2) years old

Now,
2x + 2x + 2 + x = 42
⇒ 5x + 2 = 42
⇒ 5x = 40
∴ x = 8
A is (2 × 8) + 2 years old
= 16 + 2 years old
= 18 years old

৩,৮৪২.

Which number will complete the series:
1, 3, 7, 15, 31, 63, 127, __?

ক
235
খ
253
গ
257
ঘ
255

সঠিক উত্তর: ঘ

255

উত্তর

সঠিক উত্তর: ঘ

255

ঘ

ব্যাখ্যা

Question: Which number will complete the series:
1, 3, 7, 15, 31, 63, 127, __?

Solution:
3 - 1 = 2
7 - 3 = 4 = 2 × 2
15 - 7 = 8 = 4 × 2
31 - 15 = 16 = 8 × 2
63 - 31 = 32 = 16 × 2
127 - 63 = 64 = 32 × 2

∴ The next number of 127 will be 127 + 64 × 2
= 127 + 128
= 255

৩,৮৪৩.

Simplify

ক
121
খ
241/38
গ
341/13
ঘ
97/17
ঙ
145/19

সঠিক উত্তর: গ

341/13

উত্তর

সঠিক উত্তর: গ

341/13

গ

ব্যাখ্যা

Question: Simplify
Solution:

৩,৮৪৪.

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

ক
13 : 33 : 60
খ
23 : 43 : 6
গ
23 : 33 : 60
ঘ
3 : 3 : 10

সঠিক উত্তর: গ

23 : 33 : 60

উত্তর

সঠিক উত্তর: গ

23 : 33 : 60

গ

ব্যাখ্যা

Let, A = 2y
B = 3y
C = 5y
New salary of A = 115/100 of 2y = 23y/10
New salary of B = 110/100 of 2y = 33y/10
New salary of C = 120/100 of 5y = 6Y
Required ratio = 23y/10 : 33y/10 : 6Y = 23 : 33 : 60

৩,৮৪৫.

In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Tk 157300 was their profit, how much amount did B receive?

ক
ক) 48000
খ
খ) 47000
গ
গ) 47400
ঘ
ঘ) 48400

সঠিক উত্তর: ঘ

ঘ) 48400

উত্তর

সঠিক উত্তর: ঘ

ঘ) 48400

ঘ

ব্যাখ্যা

A:B = 3:2 = 6:4
=> A:C = 2:1 = 6:3
=> A:B:C = 6:4:3
B share = (4/13)×157300
= 48400

৩,৮৪৬.

1 card is drawn at random from the pack of 52 cards. Find the Probability that it is an honor card.

ক
3/13
খ
1/2
গ
4/13
ঘ
35/52
ঙ
None of these

সঠিক উত্তর: গ

4/13

উত্তর

সঠিক উত্তর: গ

4/13

গ

ব্যাখ্যা

Question: 1 card is drawn at random from the pack of 52 cards. Find the Probability that it is an honor card.

Solution:
honor cards = (A, J, Q, K) 4 cards from each suits = 4 × 4 = 16

∴ P(honor card) = 16/52 = 4/13

৩,৮৪৭.

How many words can be formed by using the letters from the word 'DRIVER' such that all the vowels are never together?

ক
520
খ
280
গ
320
ঘ
240

সঠিক উত্তর: ঘ

240

উত্তর

সঠিক উত্তর: ঘ

240

ঘ

ব্যাখ্যা

Question: How many words can be formed by using the letters from the word 'DRIVER' such that all the vowels are never together?

Solution:
We assume all the vowels to be a single character, i.e., 'IE' is a single character.
So, now we have 5 characters in the word, namely, D, R, V, R, and IE.

But, R occurs 2 times.
Number of possible arrangements = 5!/2! = 60

Now,
the two vowels can be arranged in 2! = 2 ways.

Total number of possible words such that the vowels are always together = 60 × 2 = 120

Total number of possible words = 6!/2! = 720/2 = 360

Therefore, the total number of possible words such that the vowels are never together = 360 - 120 = 240

৩,৮৪৮.

In an election, 2 candidates participate in which the winner gets 60% of the total votes, and he wins the election by 2000 votes. Find the total number of votes in the election.

ক
3200
খ
6400
গ
10000
ঘ
13250

সঠিক উত্তর: গ

10000

উত্তর

সঠিক উত্তর: গ

10000

গ

ব্যাখ্যা

Question: In an election, 2 candidates participate in which the winner gets 60% of the total votes, and he wins the election by 2000 votes. Find the total number of votes in the election.

Solution:
Let total votes = 100
So, as per question, the winner gets 60 votes and the loser gets 40 votes.
Now, the difference between votes = 20, but ATQ, it is 2000.
So, we have to multiply 20 by 100 to make it equal to 2000.
So, 100 (the assumed total votes) are also required to be multiplied with 100.
Therefore, the total votes= 100 × 100= 10000.

৩,৮৪৯.

In a mixture of 100 litres, milk and water are in the ratio 4:1. 40 litres of mixture drawn off. Find the ratio of water and milk in the remaining mixture?

ক
ক) 2 :3
খ
খ) 1 : 4
গ
গ) 3 : 2
ঘ
ঘ) 4 : 1

সঠিক উত্তর: খ

খ) 1 : 4

উত্তর

সঠিক উত্তর: খ

খ) 1 : 4

খ

ব্যাখ্যা

Mixture = 100 litres

M : W = 4 : 1

Milk = 4/5 x100 = 80 litres

Water = 100 - 80 = 20 litres

In 40 litres of mixture, ratio will be same.

Milk = 4/5 x 40 = 32 litres
Water = 40 - 32 = 8 litres

Remaining Milk = 80 - 32 = 48 litres

Remaining Water = 20 - 8 = 12 litres

Water : Milk = 12 : 48 = 1 : 4

৩,৮৫০.

The average weight of A, B and C is 45kg. If the average weight of A and B is 40 kg and that of B and C is 43 kg, then the weight of B is-

ক
31 kg
খ
20 kg
গ
17 kg
ঘ
None of these

সঠিক উত্তর: ক

31 kg

উত্তর

সঠিক উত্তর: ক

31 kg

ক

ব্যাখ্যা

Question: The average weight of A, B and C is 45kg. If the average weight of A and B is 40 kg and that of B and C is 43 kg, then the weight of B is-

Solution:
Let A, B, C represent their respective weights.

Then, we have:
A + B + C =(45 × 3) = 135..............(i)
A + B = (40 × 2) = 80.................(ii)
B + C=(43 × 2) = 86.................(iii)

Adding (ii) and (iii),
we get: A + 2B + C =80 + 86
A + 2B + C =166 .....(iv)

Subtracting (i) from (iv),
we get:
A + 2B + C - (A + B + C) = 166 - 135
B = 31

∴ B's weight =31 kg.

৩,৮৫১.

An employee may claim Tk. 7.00 for each km when he travels by taxi and Tk. 6.00 for each km if he drives his own car. If in one week he claimed Tk. 595 for traveling 90 km. How many kms did he travel by taxi?

ক
55 kms
খ
35 kms
গ
25 kms
ঘ
65 kms

সঠিক উত্তর: ক

55 kms

উত্তর

সঠিক উত্তর: ক

55 kms

ক

ব্যাখ্যা

Question: An employee may claim Tk. 7.00 for each km when he travels by taxi and Tk. 6.00 for each km if he drives his own car. If in one week he claimed Tk. 595 for traveling 90 km. How many kms did he travel by taxi?

Solution:
Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90
⇒ x = 90 - y
But according to the question,
7x + 6y = 595
⇒ 7(90 - y) + 6y = 595
⇒ 630 - 7y + 6y = 595
⇒ y = 630 - 595
∴ y = 35

∴ x = 90 - 35 = 55

Therefore, the distance travelled by taxi is 55 kms.

৩,৮৫২.

Sakil purchased 120 exercise books at the rate of Tk. 3 each and sold 1/3 of them at the of Tk. 4 each, 1/2 of them at the rate of Tk.5 each and the rest at the cost price. His profit percentage is-

ক
ক) (100/9)%
খ
খ) (200/9)%
গ
গ) (400/9)%
ঘ
ঘ) (500/9)%

সঠিক উত্তর: গ

গ) (400/9)%

উত্তর

সঠিক উত্তর: গ

গ) (400/9)%

গ

ব্যাখ্যা

Total Cost price = Tk. (120 × 3) = Tk. 360
Total Sell Price = Tk. (40 × 4) + (60 × 5) + (20 × 3) = Tk. 520
Profit = Tk.(520 - 360) = Tk. 160
Profit% = {(160/360) × 100}% = (400/9)%

৩,৮৫৩.

2 + 2² + 2³ + ... + 2⁹ = ?

ক
ক) 2044
খ
খ) 1022
গ
গ) 1056
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) 1022

উত্তর

সঠিক উত্তর: খ

খ) 1022

খ

ব্যাখ্যা

This is a G.P.(general process) in which a = 2, r = 2^2/2= 2 and n = 9
S_n = a(rⁿ - 1)/(r - 1)
= 2 x (2⁹ - 1)/(2 - 1)
= 2 x (512 - 1)
= 2 x 511
= 1022.

৩,৮৫৪.

In the figure, AOC is the diameter of the circle and arc AXB = (1/2)arc BYC. Find ∠BOC = ?

ক
75º
খ
60º
গ
90º
ঘ
120º

সঠিক উত্তর: ঘ

120º

উত্তর

সঠিক উত্তর: ঘ

120º

ঘ

ব্যাখ্যা

Question: In the figure, AOC is the diameter of the circle and arc AXB = (1/2)arc BYC. Find ∠BOC = ?

Solution:
Given that,
arc AXB = (1/2) arc BYC
∴ ∠AOB = (1/2) ∠BOC

We know that,
∠AOB + ∠BOC = 180º

Therefore,
(1/2) ∠BOC + ∠BOC = 180º {linear pair since AOC is the diameter}
⇒ (3/2) ∠BOC 180º
⇒ ∠BOC = (2/3) × 180º = 120º
∴ ∠BOC = 120º

৩,৮৫৫.

The sides of a rectangular field are in the ratio 3 : 4 and its area is 7500 m². What is the cost of fencing it at Tk. 25 per meter?

ক
Tk. 8750
খ
Tk. 7750
গ
Tk. 6750
ঘ
Tk. 5750

সঠিক উত্তর: ক

Tk. 8750

উত্তর

সঠিক উত্তর: ক

Tk. 8750

ক

ব্যাখ্যা

Question: The sides of a rectangular field are in the ratio 3 : 4 and its area is 7500 m². What is the cost of fencing it at Tk. 25 per meter?

Solution:
Ratio between the sides of rectangle = 3 : 4
Let the ratio constant be x then,
Length = 4x and breadth = 3x

ATQ,
7500 = 3x × 4x =12x²
⇒ x² = 625
∴ x = 25

Perimeter = 2(75 + 100) = 2 × 175 = 350 m
Cost of fencing 1 meter = Tk. 25
Cost of fencing 350 m = 350 × 25 = 8750

৩,৮৫৬.

If 4y - 5x = 5, what is the smallest integer value of x for which y > 100?

ক
79
খ
80
গ
81
ঘ
82

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: If 4y - 5x = 5, what is the smallest integer value of x for which y > 100?

Solution:
Given,
4y - 5x = 5
⇒ 4y = 5x + 5
⇒ y = (5x + 5)/4

Now,
(5x + 5)/4 > 100
⇒ 5x + 5 > 400
⇒ 5x > 395
⇒ x > 395/5
⇒ x > 79

The smallest integer value for x is 80

৩,৮৫৭.

If log(2a/b) + log(3b/a) = log(a + b), then:

ক
ক) a + b = 1
খ
খ) a + b = 6
গ
গ) a + b = - 1
ঘ
ঘ) a + b = 0

সঠিক উত্তর: খ

খ) a + b = 6

উত্তর

সঠিক উত্তর: খ

খ) a + b = 6

খ

ব্যাখ্যা

log (2a/b) + log(3b/a) = log (a + b)
log{(2a/b) × (3b/a)} = log (a + b)
log6 = log (a + b)
a + b = 6

৩,৮৫৮.

A student loses 1 mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks, how many of them were correct?

ক
ক) 33
খ
খ) 31
গ
গ) 27
ঘ
ঘ) 37

সঠিক উত্তর: ক

ক) 33

উত্তর

সঠিক উত্তর: ক

ক) 33

ক

ব্যাখ্যা

Question: A student loses 1 mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks, how many of them were correct?

Solution:
ধরি,
মোট ভুল উত্তর = ক টি
প্রতিটি সঠিক উত্তরের জন্য প্রকৃতপক্ষে কাঁটা যায় = (২ + ১) = ৩ নম্বর।

প্রশ্নমতে,
(২ × ৬০) - ৩ক = ৩৯
৩ক = ১২০ - ৩৯
৩ক = ৮১
ক = ২৭

∴ সঠিক উত্তর = (৬০ - ২৭) = ৩৩ টি

৩,৮৫৯.

ক
5
খ
7
গ
123
ঘ
125

সঠিক উত্তর: ঘ

125

উত্তর

সঠিক উত্তর: ঘ

125

ঘ

ব্যাখ্যা

Question:

Solution:

৩,৮৬০.

A train 150m long, takes 30 seconds to cross a bridge 500m long. How much time will the train to cross a platform 370 m long?

ক
ক) 28 sec
খ
খ) 27 sec
গ
গ) 24 sec
ঘ
ঘ) 25 sec

সঠিক উত্তর: গ

গ) 24 sec

উত্তর

সঠিক উত্তর: গ

গ) 24 sec

গ

ব্যাখ্যা

Length of the train = 150 m
Length of the bridge = 500 m
∴ Total length = (500 + 150)m
= 650m

∴ Speed of the train =650/30 m/sec
= 65/3 m/sec

Now total length of the train and new bridge = (370 + 150)m
= 520m

∴ Time taken = (520 × 3)/65 sec
= 24 sec

৩,৮৬১.

A man, a woman, and a child together receive 84 Taka for 6 days' work. A woman's daily wage is twice a child's wage, and a man earns twice as much as a woman's. How much does a woman earn per day?

ক
3 Taka
খ
4 Taka
গ
5 Taka
ঘ
6 Taka

সঠিক উত্তর: খ

4 Taka

উত্তর

সঠিক উত্তর: খ

4 Taka

খ

ব্যাখ্যা

Question: A man, a woman, and a child together receive 84 Taka for 6 days' work. A woman's daily wage is twice a child's wage, and a man earns twice as much as a woman's. How much does a woman earn per day?

Solution:
Let,
C = Daily wage of the child (in Taka).
W = Daily wage of the woman (in Taka).
M = Daily wage of the man (in Taka).

A.T.Q,
W = 2C
M = 2(2C) = 4C

Total payment of 6 days = 6 (C + W + M)
84 = 6(C + 2C + 4C)
42C = 84
∴ C = 2

So, the woman earns = 2 × 2 = 4 taka

৩,৮৬২.

What will come at the place of the question mark?
5, 6, 8, 12, 20, ?

ক
28
খ
30
গ
32
ঘ
36

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: What will come at the place of the question mark?
5, 6, 8, 12, 20, ?

Solution:
5 + 1 =6
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20
20 + 16 = 36

৩,৮৬৩.

What is the average of the sum of the first 10 logical terms of the Fibonacci series if the series starts with zero?

ক
ক) 6
খ
খ) 7.5
গ
গ) 8
ঘ
ঘ) 8.8

সঠিক উত্তর: ঘ

ঘ) 8.8

উত্তর

সঠিক উত্তর: ঘ

ঘ) 8.8

ঘ

ব্যাখ্যা

Question: What is the average of the sum of the first 10 logical terms of the Fibonacci series if the series starts with zero?

Solution:
The first 10 logical terms of the Fibonacci series if the series starts with zero = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
So, the average = (0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34)/10
= 88/10
= 8.8

৩,৮৬৪.

The perimeter of an equilateral triangle is 84√3 cm. Find its height.

ক
40 cm
খ
39 cm
গ
36 cm
ঘ
44 cm
ঙ
None

সঠিক উত্তর: ঙ

None

উত্তর

সঠিক উত্তর: ঙ

None

ঙ

ব্যাখ্যা

Question: The perimeter of an equilateral triangle is 84√3 cm. Find its height.

Solution:
Given,
The perimeter of the equilateral triangle = 84√3 cm.
∴ Each side of the equilateral triangle = (84√3/3) = 28√3 cm.

We know,
The height of the equilateral triangle will be = (√3/2) × (28√3) = 42 cm

৩,৮৬৫.

By mixing two qualities of pulse in the ratio 2 : 3 and selling the mixture at the rate of Tk. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost of the smaller quantity be Tk. 14 per kg, the cos in Tk per kg of the larger quantity is :

ক
23
খ
24
গ
25
ঘ
26

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: By mixing two qualities of pulse in the ratio 2 : 3 and selling the mixture at the rate of Tk. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost of the smaller quantity be Tk. 14 per kg, the cos in Tk per kg of the larger quantity is :

Solution:
মনেকরি,
বেশি পরিমাণের ডাল এর মূল্য = x টাকা

দেওয়া আছে,
কম পরিমাণ : বেশি পরিমাণ = 2 : 3
অনুপাতদ্বয়ের যোগফল = 2 + 3 = 5

5 কেজি এর ক্রয়মূল্য = 14 × 2 + x × 3
= 28 + 3x

5 কেজি এর বিক্রয়মূল্য = 22 × 5 = 110

.: লাভ = 110 - (28 + 3x)
= 110 - 28 - 3x
= 82 - 3x

প্রশ্নমতে,
{(82 - 3x)/(28 + 3x)}× 100 % = 10%
(82 - 3x)/(28 + 3x) = 1/10
820 - 30x = 28 + 3x
3x + 30x = 820 - 28
33x = 792
x = 792/33
x = 24

৩,৮৬৬.

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Tk.1600 after 2 years at the same rate?

ক
ক) Tk. 363
খ
খ) Tk. 366
গ
গ) Tk. 336
ঘ
ঘ) Tk. 636

সঠিক উত্তর: গ

গ) Tk. 336

উত্তর

সঠিক উত্তর: গ

গ) Tk. 336

গ

ব্যাখ্যা

Let P = Tk. 100.
Then, S.I. Tk. 50 and T = 5 years
Rate =(100 × 50)/(100 × 5) = 10%

Now, P = Tk.. 1600.
T = 2 years and R = 10% p.a.

C.I. =1600(1 + 10/100)² - 1600
= 1600(1.1)² - 1600
= 1936 - 1600
= 336

৩,৮৬৭.

A started a business with Tk. 4000 and is joined afterwards by B with Tk. 6000. After how many months did B join if the profits at the end of the year are divided equally?

ক
3 months
খ
4 months
গ
5 months
ঘ
6 months

সঠিক উত্তর: খ

4 months

উত্তর

সঠিক উত্তর: খ

4 months

খ

ব্যাখ্যা

Question: A started a business with Tk. 4000 and is joined afterwards by B with Tk. 6000. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Let,
B joined after = x months

Then,
4000 × 12 = 6000 × (12 - x)
⇒ 48000 = 72000 - 6000x
⇒ 480 = 720 - 60x
⇒ 60x = 240
∴ x = 4

∴ B joined after 4 months.

৩,৮৬৮.

A man distributes Tk.16500 among his daughter, wife and son in such a manner that the daughter's share and the wife's share are of 1 : 2 ratio, and the son gets half of the total amount. Find the daughter's share?

ক
3040 Tk
খ
3300 Tk
গ
2000 Tk
ঘ
2750 Tk

সঠিক উত্তর: ঘ

2750 Tk

উত্তর

সঠিক উত্তর: ঘ

2750 Tk

ঘ

ব্যাখ্যা

Question: A man distributes Tk.16500 among his daughter, wife and son in such a manner that the daughter's share and the wife's share are of 1 : 2 ratio, and the son gets half of the total amount. Find the daughter's share?

Solution:
The daughter's share and the wife's share are of 1 : 2 ratio
daughter's share = x
wife's share = 2x

As the son gets half of the total amount
∴ son's share = 16500/2
= 8250 Tk

→ Rest of the share = 3x
According to the question,
→ 3x= 8250
→ x= 2750

→ daughter's share = x = 2750 Tk

৩,৮৬৯.

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

ক
ক) 215
খ
খ) 315
গ
গ) 415
ঘ
ঘ) 115
ঙ
ঙ) None of these

সঠিক উত্তর: খ

খ) 315

উত্তর

সঠিক উত্তর: খ

খ) 315

খ

ব্যাখ্যা

Parallelograms are formed when any two pairs of parallel lines (where each pair is not parallel to the other pair) intersect.
Hence, the given problem can be considered as selecting pairs of lines from the given 2 sets of parallel lines.
Therefore, the total number of parallelograms formed = ⁷C₂ x ⁶C₂ = 315

৩,৮৭০.

A Parking lot Contains 160 Vehicles. Each Vehicle is either a car or a motorcycle, and each vehicle is either red or green. 70 vehicles are red, and 120 vehicles are cars. If there are 18 green motorcycles, how many red cars are there?

ক
45
খ
48
গ
50
ঘ
54

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A Parking lot Contains 160 Vehicles. Each Vehicle is either a car or a motorcycle, and each vehicle is either red or green. 70 vehicles are red, and 120 vehicles are cars. If there are 18 green motorcycles, how many red cars are there?

Solution:
গাড়ি আছে ১২০ টি
মোটরসাইকেল = ১৬০ - ১২০ = ৪০ টি

লাল মোটরসাইকেল = ৪০ - ১৮ = ২২ টি
লাল গাড়ি = ৭০ - ২২ = ৪৮ টি

৩,৮৭১.

Since A is three times as efficient as B, he completes a task 40 days sooner. Find the time required for both to complete it working together.

ক
15 days
খ
24 days
গ
14 days
ঘ
30 days

সঠিক উত্তর: ক

15 days

উত্তর

সঠিক উত্তর: ক

15 days

ক

ব্যাখ্যা

Question: Since A is three times as efficient as B, he completes a task 40 days sooner. Find the time required for both to complete it working together.

Solution:
Let A alone takes x days
and B alone takes 3x days to complete the job.

ATQ,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A alone takes 20 days and B alone takes 3 × 20 = 60 days to complete the job.

(A + B)'s 1 days work = (1/20 + 1/60) = 1/15 part

∴ A and B together can do the work in 15 days.

৩,৮৭২.

A canvas costs Tk. 500 and the marked price is printed as Tk. 800. What is the profit % for the seller if he sells and offers a discount of 10% on the marked price?

ক
ক) 52%
খ
খ) 44%
গ
গ) 28%
ঘ
ঘ) 38%

সঠিক উত্তর: খ

খ) 44%

উত্তর

সঠিক উত্তর: খ

খ) 44%

খ

ব্যাখ্যা

Question: A canvas costs Tk. 500 and the marked price is printed as Tk. 800. What is the profit % for the seller if he sells and offers a discount of 10% on the marked price?

Solution:

After allowing a discount of 10% we get,
⇒ 90% of 800
⇒ (90 / 100) × 800
⇒ 720

∴ S.P = Tk. 720

Profit = S.P - C.P
⇒ 720 - 500
⇒ 220

Profit% = (Profit / C.P) × 100
⇒ (220 / 500) × 100
⇒ 44%

The profit% for the seller is 44%.

৩,৮৭৩.

Tap B is 5 times slower than Tap A in filling the same tank. Also tap B takes 32 minutes more than Tap A to fill the same tank completely. How long will the tank take to get full, if both the taps are opened simultaneously?

ক
ক) 20/3 hours
খ
খ) 22/3 hours
গ
গ) 25/3 hours
ঘ
ঘ) 29/3 hours

সঠিক উত্তর: ক

ক) 20/3 hours

উত্তর

সঠিক উত্তর: ক

ক) 20/3 hours

ক

ব্যাখ্যা

Let Tap A take T minutes to fill the tank alone.
Since Tap A is 5 times faster than Tap B, Tap B takes 5 times more time.
So time taken by Tap B = 5T minutes
Also, 5T-T = 32 ----------- Given
∴ T = 8 minutes = Time taken by A
Time taken by B = 5 x 8 = 40 minutes.

In 1 min, A + B fills = 1/8 + 1/40 = 3/20 parts
So entire tank is filled in = 20/3 hours.

৩,৮৭৪.

To gain 12% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 60 kg. of pure milk is-

ক
7 kg
খ
8.5 kg
গ
12 kg
ঘ
7.2 kg
ঙ
None of these

সঠিক উত্তর: ঘ

7.2 kg

উত্তর

সঠিক উত্তর: ঘ

7.2 kg

ঘ

ব্যাখ্যা

Question: To gain 12% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 60 kg. of pure milk is-

Solution:
দেওয়া আছে,
বিশুদ্ধ দুধের পরিমাণ = ৬০কেজি
বিক্রয়মূল্য বৃদ্ধি না করে অতিরিক্ত লাভ করতে হবে = ১২%
এখন,
বিক্রয়মূল্য বৃদ্ধি না করে আরো ১২% লাভ করতে হলে দুধের সাথে এর মোট পরিমাণের ১২% পানি যোগ করতে হবে।

∴ মিশ্রনে পানি পরিমাণ = ৬০ এর ১২% = ৬০ × (১২/১০০) = ৭.২ কেজি

সুতরাং, বিশুদ্ধ ৬০ কেজি দুধের সাথে ৭.২ কেজি পানি মিশ্রিত করলে বিক্রয়মূল্য বৃদ্ধি না করেও আরো ১২% লাভ করা যাবে।

৩,৮৭৫.

In 4 years the simple interest on certain sum of money is 9/25 of the principal. The annual rate of interest is-

ক
6%
খ
9%
গ
12%
ঘ
8.5%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In 4 years the simple interest on certain sum of money is 9/25 of the principal. The annual rate of interest is-

Solution:
Given that,
In 4 years, Simple Interest (SI) = 9/25 of Principal (P)

We know,
SI = (P × r × n)/100
⇒ 9P/25 = (P × r × 4)/100
⇒ 9/25 = r/25
∴ r = 9

∴ Annual rate of interest = 9%

৩,৮৭৬.

A pipe can fill up an empty tank in 12 minutes, Another pipe flows out 8 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 84 minute. How much water does the tank contain?

ক
ক) 92 liter
খ
খ) 105 liter
গ
গ) 112 liter
ঘ
ঘ) 120 liter

সঠিক উত্তর: গ

গ) 112 liter

উত্তর

সঠিক উত্তর: গ

গ) 112 liter

গ

ব্যাখ্যা

Question: A pipe can fill up an empty tank in 12 minutes, Another pipe flows out 8 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 84 minutes. How much water does the tank contain?

Solution:
Let the tank empty in x minute

According to the question,
(1/12) - (1/x) = 1/84
⇒ (1/12) - (1/84) = 1/x
⇒ 6/84 = 1/x
⇒ x = 84/6
⇒ x = 14

The tank emptied by the other pipe in 14 minute

∴ The tank contain = 14 × 8 = 112 liter

৩,৮৭৭.

How much water should be mixed with 100 kg of pure milk to achieve a 10% profit when selling the milk at its cost price?

ক
10 kg
খ
8 kg
গ
6 kg
ঘ
12 kg
ঙ
None of the above

সঠিক উত্তর: ক

10 kg

উত্তর

সঠিক উত্তর: ক

10 kg

ক

ব্যাখ্যা

Question: How much water should be mixed with 100 kg of pure milk to achieve a 10% profit when selling the milk at its cost price?

Solution:
Let the cost price of 100 kg pure milk be C.

If we add x kg of water, the total mixture will be (100 + x) kg.

The cost of this mixture remains C (since water is free).
When we sell this mixture at the pure milk's cost price, we sell (100 + x) kg at the price of 100 kg.

Our selling price will be C per 100 kg × (100 + x) kg = C × (100 + x)/100
For a 10% profit, this selling price must equal 1.1 × C

Setting up the equation:
C × (100 + x)/100 = 1.1 × C

Simplifying the equation,
⇒ (100 + x)/100 = 1.1
⇒ 100 + x = 110
⇒ x = 10

৩,৮৭৮.

A person has two acid solutions — one containing 40% acid and the other 60% acid. In what quantities should he mix each to obtain 10 liters of a 50% acid solution?

ক
1 liters
খ
2 liters
গ
3 liters
ঘ
5 liters

সঠিক উত্তর: ঘ

5 liters

উত্তর

সঠিক উত্তর: ঘ

5 liters

ঘ

ব্যাখ্যা

Question: A person has two acid solutions — one containing 40% acid and the other 60% acid. In what quantities should he mix each to obtain 10 liters of a 50% acid solution?

Solution:
ধরি,
প্রথম দ্রবণটি মেশাতে হবে = x লিটার
দ্বিতীয় দ্রবণটি মেশাতে হবে = (10 - x) লিটার

প্রশ্নমতে,
x লিটার 40% এসিডের দ্রবণ + (10 - x) লিটার 60% এসিডের দ্রবণ = 10 লিটার 50% এসিডের দ্রবণ
⇒ x × (40/100) + (10 - x) × (60/100) = 10 × (50/100)
⇒ (2x/5) + {3(10 - x)/5} = 5
⇒ (2x/5) + {(30 - 3x)/5} = 5
⇒ (2x + 30 - 3x)/5 = 5
⇒ (30 - x)/5 = 5
⇒ 30 - x = 25
⇒ x = 30 - 25
⇒ x = 5

40% এসিডের প্রথম দ্রবণটি মেশাতে হবে = 5 লিটার
60% এসিডের দ্বিতীয় দ্রবণটি মেশাতে হবে = (10 - 5) লিটার = 5 লিটার

অর্থাৎ 40% ও 60% এসিডের প্রতিটি দ্রবণ 5 লিটার করে মিশ্রিত করলে 50% এসিডের দ্রবণ পাওয়া যাবে।

৩,৮৭৯.

Rahul bought a bicycle and sold it at a loss of 15%. If he had bought it for 25% less and sold it for tk 80 more, he would have made a profit of 30%. What was the cost of the bicycle?

ক
640 tk
খ
780 tk
গ
820 tk
ঘ
810 tk

সঠিক উত্তর: ক

640 tk

উত্তর

সঠিক উত্তর: ক

640 tk

ক

ব্যাখ্যা

Question: Rahul bought a bicycle and sold it at a loss of 15%. If he had bought it for 25% less and sold it for tk 80 more, he would have made a profit of 30%. What was the cost of the bicycle?

Solution:
Let the cost price of the bicycle be x tk.
The selling price of the bicycle when sold at a 15% loss is 0.85x tk.
If the bicycle had been bought for 25% less, the cost price would be 0.75x tk.
If the selling price had been 80 tk more, the selling price would be 0.85x + 80 tk.
According to the problem, in this case, Rahul would have made a profit of 30%, so the selling price would be 1.3 × 0.75x = 0.975x tk.

ATQ,
0.85x + 80 = 0.975x
⇒ 0.975x - 0.85x = 80
⇒ 0.125x = 80
⇒ x = 80/0.125
⇒ x = 8000/125
∴ x = 640 tk

৩,৮৮০.

The number of trees in each row of a garden is equal to the total number of rows in the garden. If 59 trees have been uprooted in a storm, there are 841 trees in the garden. The number of rows of trees in the garden is -

ক
ক) 29
খ
খ) 30
গ
গ) 25
ঘ
ঘ) 27

সঠিক উত্তর: খ

খ) 30

উত্তর

সঠিক উত্তর: খ

খ) 30

খ

ব্যাখ্যা

Question: The number of trees in each row of a garden is equal to the total number of rows in the garden. If 59 trees have been uprooted in a storm, there are 841 trees in the garden. The number of rows of trees in the garden is -

Solution:
So, number of trees before storm = 841 + 59 = 900
So, the number of in the garden = √900 = 30

৩,৮৮১.

If the average of 'm' numbers is √2n² and the average of 'n' numbers is √2m², what is the average of the combined (m + n) numbers?

ক
2√2mn
খ
√2mn
গ
m²n²
ঘ
4mn

সঠিক উত্তর: খ

√2mn

উত্তর

সঠিক উত্তর: খ

√2mn

খ

ব্যাখ্যা

Question: If the average of 'm' numbers is √2n² and the average of 'n' numbers is √2m², what is the average of the combined (m + n) numbers?

Solution:
দেওয়া আছে,
m সংখ্যার গড় = √2n²
∴ m সংখ্যার সমষ্টি = m × √2n²

n সংখ্যার গড় = √2m²
∴ n সংখ্যার সমষ্টি = n × √2m²

∴ মোট সমষ্টি = m + n = (m × √2n²) + (n × √2m²)
= √2mn² + √2m²n
= √2mn(m + n)

∴ তাদের গড় = মোট সমষ্টি/(m + n)
= √2mn(m + n)/(m + n)
= √2mn

৩,৮৮২.

What is the interest for 2 years on 600 tk at a simple interest rate of 9.5%?

ক
108 tk
খ
114 tk
গ
118 tk
ঘ
122 tk

সঠিক উত্তর: খ

114 tk

উত্তর

সঠিক উত্তর: খ

114 tk

খ

ব্যাখ্যা

Question: What is the interest for 2 years on 600 tk at a simple interest rate of 9.5%?

Solution:
Interest rate, r = 9.5% = 9.5/100 = 95/1000
Principal amount, p = 600 tk
Time, n = 2 years

We know,
Simple Interest, I = Pnr
= 600 × 2 × (95/1000)
= 114 tk

৩,৮৮৩.

If 5 workers can collect 60 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

ক
160 kg
খ
140 kg
গ
120 kg
ঘ
200 kg

সঠিক উত্তর: ক

160 kg

উত্তর

সঠিক উত্তর: ক

160 kg

ক

ব্যাখ্যা

Question: If 5 workers can collect 60 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

Solution:
5 workers 3 days collection = 60 kg
1 worker 1 day collection = (60/15) kg
8 workers 5 days collection = ( 60 × 40 ) / 15 kg
= 160 kg

৩,৮৮৪.

Average age of 15 students of a class is 15 years. Out of these the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is-

ক
15 years
খ
11 years
গ
9 years
ঘ
18 years

সঠিক উত্তর: খ

11 years

উত্তর

সঠিক উত্তর: খ

11 years

খ

ব্যাখ্যা

Question: Average age of 15 students of a class is 15 years. Out of these the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is-

Solution:
Given that
Average age of 15 students = 15 years
Average age of 5 students = 14 years
Average age of 9 students = 16 years

Now,
Total age of all 15 students = 15 × 15 = 225 years
Total age of 5 students = 5 × 14 = 70 years
Total age of 9 students = 9 × 16 = 144 years

∴ Age of the 15th student = 225 - (70 + 144) = 225 - 214 = 11 years

৩,৮৮৫.

Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?

ক
14
খ
18
গ
1
ঘ
23

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?

Solution:
Given that, the series is: 53, 53, 40, 40, 27, 27, ...

Pattern - Each number is repeated twice, and the values themselves decrease by 13 each time.
1^st = 53
2^nd = 53 - 13 = 40 ⇒ 40
3^rd = 40 - 13 = 27 ⇒ 27
4^th = 27 - 13 = 14 ⇒ 14

So the next two numbers should be 14, 14.

So the number that should come next is 14.

৩,৮৮৬.

Tk. 325 has been divided among A, B, C in such a way that A had Tk. 20 more than B and C had Tk.15 more than A. How much was C’s share?

ক
Tk. 135
খ
Tk. 110
গ
Tk. 125
ঘ
Tk. 155
ঙ
Tk. 90

সঠিক উত্তর: গ

Tk. 125

উত্তর

সঠিক উত্তর: গ

Tk. 125

গ

ব্যাখ্যা

Question: Tk. 325 has been divided among A, B, C in such a way that A had Tk. 20 more than B and C had Tk.15 more than A. How much was C’s share?

Solution:
Let the share of A was x
A has 20 more than B.
So, Share of B was (x - 20)
And C had 15 more than A So, Share of C was (x + 15)
ATQ,
A + B + C = 325
⇒ x + x - 20 + x + 15 = 325
⇒ 3x - 5 = 325
⇒ 3x = 330
⇒ x = 110
So, Share of C = x + 15 = 110 + 15 = 125

৩,৮৮৭.

The difference between two positive numbers is 4 and the difference of their squares is 96. The largest number is -

ক
10
খ
12
গ
14
ঘ
16

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: The difference between two positive numbers is 4 and the difference of their squares is 96. The largest number is -

Solution:
Let the numbers be X and (X + 4)

then,
(X + 4)² - X² = 96
⇒ X² + 8X + 16 - X² = 96
⇒ 8X + 16 = 96
⇒ 8X = 80
⇒ X = 10

hence, the largest number is = (10 + 4) = 14

৩,৮৮৮.

To the nearest degree, what is in the measure of the second smallest angle in a right triangle with sides 5,12 and 13?

ক
ক) 23
খ
খ) 45
গ
গ) 47
ঘ
ঘ) 67

সঠিক উত্তর: ঘ

ঘ) 67

উত্তর

সঠিক উত্তর: ঘ

ঘ) 67

ঘ

ব্যাখ্যা

We know that, sinθ = AB/BC
⇒ sinθ = 12/13
⇒ Θ = sin^-112/13
∴ θ = 67.4°
We choose the closest number in value as answer which is 67

৩,৮৮৯.

If one-sixth of one-third of a number is 10, then what is one-fifth of the number?

ক
36
খ
42
গ
28
ঘ
56

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If one-sixth of one-third of a number is 10, then what is one-fifth of the number?

Solution:
Let, the number is x,

ATQ,
⇒ (1/6) × (1/3) × x = 10
⇒ x /18 = 10
⇒ x = 10 × 18
∴ x = 180

Now, find one-fifth of the number is,
x/5 = 180/5 = 36

So, one-fifth of the number is 36.

৩,৮৯০.

The present age of son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the son?

ক
ক) 25 years
খ
খ) 20 years
গ
গ) 30 years
ঘ
ঘ) 40 years

সঠিক উত্তর: খ

খ) 20 years

উত্তর

সঠিক উত্তর: খ

খ) 20 years

খ

ব্যাখ্যা

Question: The present age of son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the son?

Solution:
Let the mother's age be 2x years
Then, Son's age = x years

ATQ,
2x - 10 = 3(x - 10)
⇒ 2x - 10 = 3x - 30
⇒ x = 20

৩,৮৯১.

The ratio of the angles of a triangle is 2 : 3 : 4. What is the largest angle in digress?

ক
90°
খ
80°
গ
75°
ঘ
60°
ঙ
None of these

সঠিক উত্তর: খ

80°

উত্তর

সঠিক উত্তর: খ

80°

খ

ব্যাখ্যা

Question: The ratio of the angles of a triangle is 2 : 3 : 4. What is the largest angle in digress?

Solution:
Given that,
The ratio of the angles of a triangle is 2 : 3 : 4
Let the three angles be 2x, 3x, and 4x.
The sum of all angles in a triangle is always 180°
So,
⇒ 2x + 3x + 4x = 180°
⇒ 9x = 180°
⇒ x = 180°/9
⇒ x = 20°

So,The largest angle is = 4x = 4 × 20° = 80°

৩,৮৯২.

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

ক
ক) 15
খ
খ) 16
গ
গ) 17
ঘ
ঘ) 14

সঠিক উত্তর: খ

খ) 16

উত্তর

সঠিক উত্তর: খ

খ) 16

খ

ব্যাখ্যা

L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together
30/2 + 1 = 16 times
-------------------------------------------------
৬ টি বেল যথাক্রমে ২, ৪, ৬, ৮, ১০ ও ১২ সেকেন্ড পরপর বাজলে, ৩০ মিনিটে কতবার একত্রে বাজবে?
২, ৪, ৬, ৮, ১০ ও ১২ এর লসাগু ১২০ সেকেন্ড বা ২ মিনিট
২ মিনিটে একত্রে বাজে ১ বার
৩০ মিনিটে একত্রে বাজে ৩০/২ বার বা ১৫ বার
নির্ণেয় সংখ্যা (১৫ + ১) বার = ১৬ বার [ শুরুতে ১ বার বাজে তাই ১ যোগ হয়েছে ]

৩,৮৯৩.

How many leap years are there in 100 years?

ক
24
খ
25
গ
23
ঘ
26

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: How many leap years are there in 100 years?

Solution:
Given year is divided by 4, the quotient gives the number of leap years.
Here, 100 ÷ 4 = 25

But, as 100 is not a leap year
⇒ 25 - 1 = 24 leap years.

৩,৮৯৪.

Jamal is considering buying a cylindrical can that has a 5-inch radius and holds 1 gallon of oil. Determine the height of the cylinder.

ক
3.12 inches
খ
4.42 inches
গ
3.94 inches
ঘ
2.94 inches

সঠিক উত্তর: ঘ

2.94 inches

উত্তর

সঠিক উত্তর: ঘ

2.94 inches

ঘ

ব্যাখ্যা

Question: Jamal is considering buying a cylindrical can that has a 5-inch radius and holds 1 gallon of oil. Determine the height of the cylinder.

Solution:
Volume V is given by = 1 gallon
1 gallon= 231 cubic inches
Radius r = 5 inches

The volume of the cylinder is given by,
V = πr²h
⇒ 231 = (22/7) × (5)²× h
⇒ (231 × 7)/(22 × 25) = h
∴ h = 2.94 inches.

Therefore, the height is equivalent to 2.94 inches.

৩,৮৯৫.

Choose the equation of a circle with radius 6 and center (3, -5).

ক
(x - 3)² + (y + 5)²= 6
খ
(x + 3)² + (y - 5)² = 36
গ
(x + 3)² + (y - 5)² = 6
ঘ
(x - 3)² + (y + 5)² = 36

সঠিক উত্তর: ঘ

(x - 3)² + (y + 5)² = 36

উত্তর

সঠিক উত্তর: ঘ

(x - 3)² + (y + 5)² = 36

ঘ

ব্যাখ্যা

Question: Choose the equation of a circle with radius 6 and center (3, -5).

Solution:
দেওয়া আছে,
বৃত্তের কেন্দ্র = (3, -5)
ব্যাসার্ধ = 6

আমরা জানি,
বৃত্তের আদর্শ সমীকরণ,
(x - h)² +(y - k)² = r²
⇒ (x - 3)² + {y - (- 5)}² = 6² ; [এখানে h = 3, k = - 5 এবং r = 6]
∴ (x - 3)² + (y + 5)² = 36

সুতরাং, বৃত্তের সমীকরণ (x - 3)² + (y + 5)² = 36

৩,৮৯৬.

Once card drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?

ক
1/52
খ
4/13
গ
7/13
ঘ
1/26

সঠিক উত্তর: গ

7/13

উত্তর

সঠিক উত্তর: গ

7/13

গ

ব্যাখ্যা

Question: Once card drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?

Solution:
Total card = 52
Total red card 26 and total king card = 4
but 26 red cards have also 2 king card, so other 2 black king card.

So, Red card or king = 26 + 2 = 28

∴ Probability = 28/52 = 7/13

৩,৮৯৭.

Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is 7?

ক
ক) 1/6
খ
খ) 1/7
গ
গ) 1/36
ঘ
ঘ) 1/12

সঠিক উত্তর: ক

ক) 1/6

উত্তর

সঠিক উত্তর: ক

ক) 1/6

ক

ব্যাখ্যা

Number of possible outcomes when two dice are thrown simultaneously: 6 × 6 = 36
(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2),
(4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

The possible outcomes =(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
Hence, number of possible outcomes = 6

Required probability =6/36
= 1/6

৩,৮৯৮.

What is the slope of a line perpendicular to the line whose equation is 6x + 4y = 18?

ক
- 3/4
খ
2/3
গ
- 1/4
ঘ
3/5

সঠিক উত্তর: খ

2/3

উত্তর

সঠিক উত্তর: খ

2/3

খ

ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 6x + 4y = 18?

Solution:
সরল রেখার সাধারণ সমীকরণ,
y = mx + c ...... (1) (এখানে m = ঢাল)

যদি কোনো রেখার ঢাল হয় m, তবে তার লম্ব (perpendicular) রেখার ঢাল হবে,
m' = - (1/m)

এখন, 6x + 4y = 18
⇒ 4y = - 6x + 18
⇒ y = - (6/4) × x + 18/4
⇒ y = - (3/2) × x + 9/2

(1) নং এর সাথে তুলনা করে পাই, m = - (3/2)

∴ লম্ব (perpendicular) রেখার ঢাল হবে, m' = - {1/- (3/2)}
= 2/3

∴ লম্ব রেখার ঢাল = 2/3

৩,৮৯৯.

A telegraph post gets broken at a point against a storm and its top touches the ground at a distance 20 m from the base of the post making an angle 30° with the ground. What is the height of the post?

ক
ক) 40/√3
খ
খ) 20√3
গ
গ) 40√3
ঘ
ঘ) 30 m

সঠিক উত্তর: খ

খ) 20√3

উত্তর

সঠিক উত্তর: খ

খ) 20√3

খ

ব্যাখ্যা

Given, BC = 20 m
∠ACB = 30°

The total height of the telegraph post is (AB + CA) = ?
In ABC, tan 30° = AB/BC
1/√3 = AB 20

∴ AB = 20/√3m

Now, cos 30° = BC/AC
√3/2 = 20/AC
∴ AC = 40/√3 m

So, AB + CA
= (20/√3) + (40/√3)
= (60/√3)
= 20√3 m

৩,৯০০.

Determine the value of the 4^th term of the sequence: sin⁡(nπ/6)

ক
√2/2
খ
1/2
গ
1
ঘ
√3/2

সঠিক উত্তর: ঘ

√3/2

উত্তর

সঠিক উত্তর: ঘ

√3/2

ঘ

ব্যাখ্যা

Question: Determine the value of the 4^th term of the sequence: sin⁡(nπ/6)

Solution:
এখানে,
sin(nπ/6) এর চতুর্থ পদ = {sin(4 × π)/6}
= {sin(4 × 180°)/6}
= sin120°
= sin(90° + 30°)
= cos30°
= √3/2