লগ ইননিবন্ধন
বিষয়সমূহ

PrepBank · বিষয়ভিত্তিক প্রশ্ন

Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ১৪ / ১৬১ · ১,৩০১–১,৪০০ / ১৬,১২৪

১,৩০১.
The next number of the sequence is - 4 3 9 3 19 3 ....
  1. ক
    ক) 31
  2. খ
    খ) 32
  3. গ
    গ) 39
  4. ঘ
    ঘ) 49
ব্যাখ্যা

জোড় স্থানগুলোতে সর্বদা 3 স্থির রেখে প্রথম সংখ্যা থেকে তৃতীয়, পঞ্চম, সপ্তম সংখ্যায় যথাক্রমে
5; 5 × 2 = 10; 10 × 2 = 20 ......... এভাবে বাড়বে ।
তাই, 4 + 5 = 9
9 + (5 × 2)
= 9 + 10
= 19
19 + (10 × 2)
= 19 + 20
= 39 হবে ।
ANswer: 39.

১,৩০২.
  1. ক
    32/143
  2. খ
    16/81
  3. গ
    4/9
  4. ঘ
    3/2
ব্যাখ্যা

Question: 

Solution: 

১,৩০৩.
The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is-
  1. ক
    103
  2. খ
    85
  3. গ
    106
  4. ঘ
    115
ব্যাখ্যা

Question: The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is-

Solution: 
The required number = Number of numbers, which are (divisible by 3 + divisible by 7 - divisible by 21)

Now,
Number of number divisible by 3,
 = {(198 - 3)/3} + 1
= 65 + 1 = 66 

Number of number divisible by 7
= {(196 - 7)/7} + 1
= 27 + 1 = 28 

And,
Number of number divisible by 21,
= {(189 - 21)/21} + 1
= 8 + 1 =  9

Thus, the divisible value = 66 + 28 - 9 = 85 

Thus, number of numbers which are not divisible by 3 or 7
= 200 - 85 = 115

১,৩০৪.
If a team of 5 workers can assemble a motorcycle in 6 hours, how many hours would it take a team of 10 workers to assemble the same motorcycle, working at the same constant rate?
  1. ক
    180 minutes
  2. খ
    160 minutes
  3. গ
    150 minutes
  4. ঘ
    100 minutes
  5. ঙ
    90 minutes
ব্যাখ্যা

Question: If a team of 5 workers can assemble a motorcycle in 6 hours, how many hours would it take a team of 10 workers to assemble the same motorcycle, working at the same constant rate?

Solution:
Given,
5 workers can assemble a motorcycle in 6 hours
∴ 1 worker can assemble a motorcycle in (6 × 5) = 30 hours
∴ 10 workers can assemble a motorcycle in 30/10 = 3 hours
= 3 × 60 minutes
= 180 minutes

১,৩০৫.
Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6 ?
  1. ক
    5/12
  2. খ
    1/2
  3. গ
    2/3
  4. ঘ
    7/18
ব্যাখ্যা

Question: Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6 ?

Solution:
Two fair dice are thrown together.
So total possible outcomes = 6 × 6 = 36

And, 
Let E be the event that the sum of the numbers on the two faces is divisible by 4 or 6.
Then E = {(1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (5, 1), (5,  3), (6, 2), (6, 6)}
∴ n (E) = 14.

Hence, P(E) = n(E)/n(S) = 14/36
= 7/18

So the probability that the sum is divisible by 4 or 6 is 7/18.

১,৩০৬.
How much coffee, costing Tk. 100 per kg, should be mixed with 20 kg of cocoa priced at Tk. 300 per kg to get a blend worth Tk. 200 per kg? 
  1. ক
    14
  2. খ
    12
  3. গ
    20
  4. ঘ
    15
  5. ঙ
    None
ব্যাখ্যা

Question: How much coffee, costing Tk. 100 per kg, should be mixed with 20 kg of cocoa priced at Tk. 300 per kg to get a blend worth Tk. 200 per kg?

Solution:
Ratio in which cocoa and coffee should be mixed
= 300 - 200 : 200 - 100
= 100 : 100
= 1 : 1

Let x be the quantity of coffee at 100/kg.

∴ 1 : 1 = x : 20
⇒ x = 20

১,৩০৭.
Six years ago, the ratio of the ages of Ashraf and Rahat was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Rahat's age at present?
  1. ক
    16
  2. খ
    15
  3. গ
    17
  4. ঘ
    18
ব্যাখ্যা

Given that, six years ago, ratio of the ages of Ashraf and Rahat = 6:5
Hence we can assume that,
age of Ashraf six years ago = 6x
age of Rahat six years ago = 5x
After 4 years, the ratio of their ages = 11:10
⇒ (6x + 10):(5x + 10) = 11:10
⇒ 10(6x + 10) = 11(5x + 10)
⇒ 5x = 10
⇒ x = 10/5
⇒ x = 2
Rahat's present age
=(5x + 6) = 5 × 2 + 6
= 16.

১,৩০৮.
Mr. Jaman sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?
  1. ক
    Tk. 450
  2. খ
    Tk. 300
  3. গ
    Tk. 350
  4. ঘ
    Tk. 400
ব্যাখ্যা
Question: Mr. Jaman sold an article at 6% loss. Had he sold it for Tk. 64 more, he would have made a profit of 10%. Then the cost of the article is =?

Solution: 
Let, the cost of the article is x taka
Selling price = 0.94x 

ATQ, 
0.94x + 64 = 1.1x
⇒ 1.1x - 0.94x = 64 
⇒ 0.16x = 64 
⇒ x = 64/0.16
∴ x = 400 taka 
১,৩০৯.
A car manufacturer has 2,992 forklifts, which is approximately one forklift for every 48.9 employees. Which of the following is the closest approximation in thousands, of the number of employees employed by the manufacturer?
  1. ক
    ক) 60
  2. খ
    খ) 100
  3. গ
    গ) 150
  4. ঘ
    ঘ) 175
ব্যাখ্যা
Question :A car manufacturer has 2,992 forklifts, which is approximately one forklift for every 48.9 employees. Which of the following is the closest approximation in thousands, of the number of employees employed by the manufacturer?
Solution: 
একটি প্রতিষ্ঠানে ট্রলি রয়েছে 2,992। 
প্রতিষ্ঠানে একটি ট্রলির জন্য কর্মীসংখ্যা বরাদ্ধ রয়েছে 48.9 জন। 
Approx 2992 = 3000
and approx 48.9 = 50

সুতরাং, কর্মীসংখ্যা হতে পারে = 3,000 × 50 = 150,000 = 150 thousands
১,৩১০.
There are 3 doors to a lecture room. In how many ways can a lecturer enter the room from one door and leave from another door?
  1. ক
    1
  2. খ
    3
  3. গ
    6
  4. ঘ
    9
ব্যাখ্যা

Question: There are 3 doors to a lecture room. In how many ways can a lecturer enter the room from one door and leave from another door?

Solution: 
As the lecturer can't leave the hall by the door he/she enters.

So, number of ways can a student enter the hall through a door and leave the hall by a different door is = 3 × 2 = 6

১,৩১১.
On a certain sum of money, the simple interest for 2 years is Tk. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?
  1. ক
    Tk. 3.75
  2. খ
    Tk. 7
  3. গ
    Tk. 9
  4. ঘ
    Tk.35
ব্যাখ্যা
Question: On a certain sum of money, the simple interest for 2 years is Tk. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?

Solution: 
let, the sum be P 

350 = P × 2 × 4/100 
⇒ 350 = P × 2/25
⇒ P = 4375 

compounded interest = 4375 (1 + .04)2 - P 
= 4375 × (262/252) - 4375 
= 4732 - 4375 
= 357 taka 

difference = 357 - 350 tk 
= 7 tk.
১,৩১২.
Age of mother 10 years ago was 3 times the age of her son. After 10 years, mother’s age will be twice that of his son. Find the ratio of their present ages.
  1. ক
    11 : 7
  2. খ
    9 : 5
  3. গ
    7 : 4
  4. ঘ
    7 : 3
ব্যাখ্যা
Question: Age of mother 10 years ago was 3 times the age of her son. After 10 years, mother’s age will be twice that of his son. Find the ratio of their present ages.

Solution:
We are given that, age of mother 10 years ago was 3 times the age of her son
So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.
At present: Mother’s age will be (3x + 10) and son’s age will be (x + 10)
After 10 years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10

Mother’s age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20

We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3
১,৩১৩.
If 8826P is divisible by 9, what is the value of P?
  1. ক
    3
  2. খ
    4
  3. গ
    6
  4. ঘ
    7
ব্যাখ্যা
Question: If 8826P is divisible by 9, what is the value of P? 

Solution:
 একটি সংখ্যা ৯ দ্বারা বিভাজ্য হবে যদি সংখ্যাটির অঙ্কগুলোর সমষ্টি ৯ দ্বারা বিভাজ্য হয়। 

৮ + ৮ + ২ + ৬ = ২৪; এর সাথে ৩ যোগ করলে ২৭ হয়, যা ৯ দ্বারা বিভাজ্য।
∴ P = ৩
১,৩১৪.
Train A passes a lamp post in 9 seconds and 700 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long?
  1. ক
    ক) 32 seconds
  2. খ
    খ) 31 seconds
  3. গ
    গ) 33 seconds
  4. ঘ
    ঘ) 30 seconds
ব্যাখ্যা

Let the length of the train is x m. and its speed is v. m/s.

Distance = Speed × time [S = V × T]
x = v × 9 .........(i).
(x+700) = v × 30 ........(ii).

Dividing the eqn. (i) by (ii).

x/(x+700)= 3/10.
⇒ 10x=3x + 2100.
⇒ 7x=2100.
⇒ x= 2100/7.
⇒ x= 300. m.

putting x = 300 in eqn. (1).
300 = v × 9
⇒ v = 300/9
⇒ v = 100/3 m/s.

Let the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (300 + 800) = (100/3) × t. [putting x= 300. and v= 100/3.]
⇒ t = (1100×3)/100
⇒ t = 33 seconds.

১,৩১৫.
The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is:
  1. ক
    increased by 3%
  2. খ
    decreased by 5.3%
  3. গ
    increased by 5.3%
  4. ঘ
    decreased by 10%
ব্যাখ্যা

Question: The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately, the price of the article is:

Solution: 
let, the price be 100 taka 

after 30% raise = 100 + 30 = 130 taka

after first 10% discount = 130 - 13 = 117 taka

after second 10% discount = 117 - 117 × 0.1 
= 117 - 11.7
= 105.3

১,৩১৬.
log2√10 - log2√(5/2) = ?
  1. ক
    2/5
  2. খ
    0
  3. গ
    1
  4. ঘ
    √2/5
ব্যাখ্যা
Question: log2√10 - log2√(5/2) = ?

Solution:
log2√10 - log√(5/2)
= log2(10)(1/2) - log2(5/2)(1/2)
= (1/2)log2(10) - (1/2)log2(5/2)
= (1/2)[log2(5 × 2) - log2(5/2)]
= (1/2)[log25 + log22 - (log25 - log22)]
= (1/2)[log25 + 1 - log2(5) + 1]
= (1/2) × 2
= 1
১,৩১৭.
How long will it take a sum of money invested at 5% per annum simple interest to increase its value by 20%?
  1. ক
    ক) 4 years
  2. খ
    খ) 5 years
  3. গ
    গ) 8 years
  4. ঘ
    ঘ) 10 years
ব্যাখ্যা
Question: How long will it take a sum of money invested at 5% per annum simple interest to increase its value by 20%?

Solution:
Let the principal (p) be 100 Tk
So, Interest, I = 100 × 20% = 20 Tk
and Interest, r = 5% = 5/100 = 1/20
Time, n = ?

ATQ, 
I = pnr
⇒ n = I/pr
⇒ n = (20 × 20)/100 = 4
১,৩১৮.
A cricket team has won 35 games out of 60 played. It has 30 more games to play. How many of these must the team win to make a record 70% win for them?
  1. ক
    ক) 28
  2. খ
    খ) 27
  3. গ
    গ) 23
  4. ঘ
    ঘ) 21
ব্যাখ্যা
প্রশ্ন : A cricket team has won 35 games out of 60 played. It has 30 more games to play. How many of these must the team win to make a record 70% win for them?
 
সমাধান : 
মনেকরি,
অবশিষ্ট খেলারগুলোর মধ্যে x টিতে জিততে হবে। 

প্রশ্নমতে, 
35 + x = (60 + 30) এর 70%
35 + x = 90 এর 70/100
35 + x = 63
x = 63 - 35 
x = 28
১,৩১৯.
If x = -1, then - (x4 + x3 + x2 + x) =?
  1. ক
    ক) -10
  2. খ
    খ) -4
  3. গ
    গ) 0
  4. ঘ
    ঘ) 4
  5. ঙ
    ঙ) 10
ব্যাখ্যা
Question: If x = -1, then - (x4 + x3 + x2 + x) =?

Solution:
 - (x4 + x3 + x2 + x)
= -{(- 1)4 + (- 1)3 + (- 1)2 + (-1)}
= - (1 - 1 + 1 - 1)
= 0
১,৩২০.
The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is- 
  1. ক
    12 years 
  2. খ
    10 years 
  3. গ
    9 years 
  4. ঘ
    8 years 
ব্যাখ্যা
Question: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is- 

Solution: 
total age = 15 × 3 years = 45 years 

let their ages be 3x, 5x, 7x 

3x + 5x + 7x = 45 
⇒ 15x = 45 
⇒ x = 3 

youngest boy = 3 × 3 years 
= 9 years  
১,৩২১.
If A = 30°, find the value of sin2A/cosA?
  1. ক
    0
  2. খ
    √3/2
  3. গ
    √2
  4. ঘ
    1
ব্যাখ্যা
Question: If A = 30°, find the value of sin2A/cosA?

Solution: 
sin2A/cosA
= (2sinAcosA)/cosA
= 2sinA
= 2sin30°
= 1
১,৩২২.
Fourth propotional to (a2 - b2),(a2 - ab), (a3 + b3)
  1. ক
    ক) a(a2 + ab + b2)
  2. খ
    খ) a(a2 - ab + b2)
  3. গ
    গ) 2a(a2 - ab - b2)
  4. ঘ
    ঘ) a(a3 - 2ab + b3)
ব্যাখ্যা
Question: Fourth propotional to (a2 - b2),(a2 - ab), (a3 + b3)
Solution: 
Let the fourth proportional to (a2 - b2),(a2 - ab),(a3 + b3) be x

Then,
(a2 - b2) : (a2 - ab) :: (a3 + b3) : x
(a2 - b2)/(a2 - ab) = (a3 + b3)/x
(a + b)/a = (a + b)(a2 - ab + b2)/x
1/a = (a2 - ab + b2)/x
x = a(a2 - ab + b2)
১,৩২৩.
What is the value of (10P1 × 5P3).
  1. ক
    500
  2. খ
    600
  3. গ
    800
  4. ঘ
    1200
ব্যাখ্যা

Question: What is the value of (10P1 × 5P3).

Solution:
10P1 = 10!/(10 - 1)!
= 10!/9!
= (10 × 9!)/9! 
= 10

5P3 = 5!/(5 - 3)! 
= 5!/2!
= (5 × 4 × 3 × 2!)/2!
= 60

∴ 10P1 × 5P3 = 10 × 60 
= 600  

১,৩২৪.
A boy of height 1.3 m is walking away from the base of a lamp post at a speed of 0.9 m/sec. Find the height of the lamp post from the ground, if the shadow of the boy is 2.4 m after walking for 5 sec.
  1. ক
    7.9 m
  2. খ
    5.5 m
  3. গ
    3.6 m
  4. ঘ
    3.74 m
ব্যাখ্যা
Question: A boy of height 1.3 m is walking away from the base of a lamp post at a speed of 0.9 m/sec. Find the height of the lamp post from the ground, if the shadow of the boy is 2.4 m after walking for 5 sec.

Solution:
Given that,
Height of the boy = 1.3m
Speed of the boy = 0.9 m/s

∴ Distance travelled by boy in 5 sec = 0.9 × 5 = 4.5m

∴ Total distance of shadow of boy and distance from base of lamp post = 2.4 + 4.5 = 6.9 m
Let the height of lamp post be 'h' m

According to question,
⇒ 1.3/2.4 = h/6.9
⇒ h = (6.9 × 1.3)/2.4
⇒ h = 3.7375 = 3.74m

So, The height of the lamp post is 3.74 meters.

১,৩২৫.
The length of a rectangle is thrice its breath, and its perimeter is 104 meters. What is its area?
  1. ক
    507 sq. m.
  2. খ
    508 sq. m.
  3. গ
    509 sq. m.
  4. ঘ
    510 sq. m.
ব্যাখ্যা
Question: The length of a rectangle is thrice its breath, and its perimeter is 104 meters. What is its area?

Solution:
Let the breath = x
So, the Length = 3x

Perimeter of a rectangle = 2 (Length + Breadth)
So, 2(3x + x) = 104
⇒ 6x + 2x = 104
⇒ 8x = 104
∴ x = 104/8 = 13

Now, Breadth = 13, so, length = 13 × 3 = 39

So, its area = Length × Breadth
= 39 × 13 = 507 sq. m.
১,৩২৬.
Kalam earns Tk. 7.50 per hour on days other than Friday and twice the rate on Friday. Last week he worked a total of 60 hours, including 8 hours on Friday. What is his earnings for the week?
  1. ক
    Tk. 510
  2. খ
    Tk. 650
  3. গ
    Tk. 480
  4. ঘ
    Tk. 390
ব্যাখ্যা

Question: Kalam earns Tk. 7.50 per hour on days other than Friday and twice the rate on Friday. Last week he worked a total of 60 hours, including 8 hours on Friday. What is his earnings for the week?

Solution: 
During the week, Kalam worked a total of 60 - 8 = 52 hours at a rate of Tk. 7.50 per hour.
On Friday, he worked 8 hours at a rate of Tk. 7.50 × 2 = Tk. 15.00 per hour.

Therefore, his total earnings for the week were (52 × 7.50 + 8 × 15) = Tk. 510

১,৩২৭.
Three numbers are in the ratio 1 : 2 : 3, and the sum of their cubes is 4500. The smallest number will be -
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 10
ব্যাখ্যা

x:2x:3x
x3+8x3+27x3=4500
36x3=4500
x3= 4500/ 36 =125
x= 5
Smallest number is 5

১,৩২৮.
John purchased a machine for Tk. 80,000. After spending Tk. 5000 on repair and Tk. 1000 on transport he sold it with 25% profit. What price did he sell the machine?
  1. ক
    Tk. 107000
  2. খ
    Tk. 108500
  3. গ
    Tk. 107500
  4. ঘ
    Tk. 108000
ব্যাখ্যা

cost price = 80000 + 5000 + 1000
= 86000
profit = 25%
Selling price = 86000 + 86000 × (1/4)
= Tk. 107500

১,৩২৯.
If 2m + n = √2, 81m - n = 3 then what is the value of n?
  1. ক
    ক) 3/8
  2. খ
    খ) 1/4
  3. গ
    গ) 1/8
  4. ঘ
    ঘ) 5/8
ব্যাখ্যা
Question: If 2m + n = √2, 81m - n = 3 then what is the value of n?

Solution: 
 2 m + n = √2
⇒ (√2)2(m + n) =  √2
⇒ m + n = 1/2

81 m - n = 3
⇒ 3 4(m - n) = 3
⇒ m - n = 1/4

m + n -m + n = (1/2) - (1/4)
⇒ 2n = (2 - 1)/4
 ⇒ 2n = 1/4
∴ n = 1/8
১,৩৩০.
A and B two taps fill in a tank in 5 hours and 10 hours respectively. If both tapes are opened together, the tank will be full in:
  1. ক
    ক) 3 hours
  2. খ
    খ) 5 hours
  3. গ
    গ) 10/3 hours
  4. ঘ
    ঘ) 20/3 hours
ব্যাখ্যা
Question: A and B two taps fill in a tank in 5 hours and 10 hours respectively. If both tapes are opened together, the tank will be full in: 

Solution: 
A's 1 hour's work = 1/5
B's 1 hour's work = 1/10

(A+B)'s 1 hour's work = (1/5) + (1/10)
= (2 + 1)/10
= 3/10 

Now, 
3/10 parts both the taps can fill the tank in 1 hour
∴ 1 part both the taps can fill the tank in 10 × (1/3) hours
= 10/3 hours

 ∴ The tank will be full in 10/3 hours.
১,৩৩১.
Two cars start towards each other from points 200 km apart. One car travels at 40 km/hr and the other travels at 35 km/hr. How far apart will the two cars be after four hours of continuous travelling?
  1. ক
    ক) 100 km
  2. খ
    খ) 75 km
  3. গ
    গ) 40 km
  4. ঘ
    ঘ) 20 km
ব্যাখ্যা


AC = 40 × 4
= 160 km
BD = 35 × 4
= 140 km
BC = 200 - 160
= 40 km
AD = 200 - 140
= 60 km
∴ CD = 200 - BC - AD
= 200 - 40 - 60
= 100 km
Hence, 100 km apart will the two cars be after four hours of continuous travelling.

১,৩৩২.
If tan 53° = 4/3, then, what is the value of tan8°?
  1. ক
    1/7
  2. খ
    3
  3. গ
    7
  4. ঘ
    1/2
ব্যাখ্যা

Question: If tan 53° = 4/3, then, what is the value of tan8°?

Solution:
Given that,
tan 53° = 4/3

We know,
tan(A - B) = (tanA - tanB)/(1 + tanA tanB)

Now,
8° = 53° - 45°
tan8° = tan(53° - 45°)
⇒ tan8° = (tan53° - tan45°)/(1 + tan53° tan45°)
⇒ tan8° = {(4/3) - 1}/{1 + (4/3) × 1}
⇒ tan8° = (1/3)/(7/3)
⇒ tan8° = 1/7

১,৩৩৩.
In a certain code 'TIME' is written as 'WLPH'. How would 'PEN' be written in that code?
  1. ক
    ক) SHR
  2. খ
    খ) QHQ
  3. গ
    গ) SPQ
  4. ঘ
    ঘ) SHQ
ব্যাখ্যা
Question: In a certain code 'TIME' is written as 'WLPH'. How would 'PEN' be written in that code?

Solution: 
T এর পরের দুটি বর্ণ পরেরটি W
I এর পরের দুটি বর্ণ পরেরটি L
M এর পরের দুটি বর্ণ পরেরটি P
E এর পরের দুটি বর্ণ পরেরটি H 

অনুরুপভাবে, 
P এর পরের দুটি বর্ণ পরেরটি S
E এর পরের দুটি বর্ণ পরেরটি H
N এর পরের দুটি বর্ণ পরেরটি Q
১,৩৩৪.
In the figure below, AB is perpendicular to BC and DB = DC. If AD = √7 cm and AC = 5 cm, what is the value of BC?
  1. ক
    √6 cm
  2. খ
    2√3 cm
  3. গ
    4√2 cm
  4. ঘ
    2√6 cm
  5. ঙ
    4 cm
ব্যাখ্যা

Question: In the figure below, AB is perpendicular to BC and DB = DC. If AD = √7 cm and AC = 5 cm, what is the value of BC?

Solution:

ΔABD-এ, পিথাগোরাসের উপপাদ্য অনুযায়ী,
BD2 + AB2 = AD2
⇒ BD2 + AB2 = (√7)2
⇒ BD2 + AB2 = 7 ... (1)

আবার, ΔABC-এ,
BC2 + AB2 = AC2
⇒ (BD + DC)2 + AB2 = 52
⇒ (2DC)2 + AB2 = 25 [যেহেতু BD = DC, তাই BC = BD + DC = 2DC]
⇒ 4DC2 + AB2 = 25
⇒ 3DC2 + (DC2 + AB2) = 25 [যেহেতু BD = DC, তাই BD2 = DC2]
⇒ 3DC2 + 7 = 25 [সমীকরণ (1) থেকে মান বসিয়ে]
⇒ 3DC2 = 25 - 7
⇒ 3DC2 = 18
⇒ DC2 = 6
⇒ DC = √6

অতএব, BC = 2DC (যেহেতু BD = DC)
= 2√6 cm

∴ BC এর মান 2√6 cm

১,৩৩৫.
HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is:
  1. ক
    52
  2. খ
    56
  3. গ
    60
  4. ঘ
    63
  5. ঙ
    66
ব্যাখ্যা
Question: HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is:

Solution:
Let, the numbers be 7x and 7y
where x and y are co-prime.

Now, LCM of = 7x
and 7y = 7xy

∴ 7xy = 140
⇒ xy = 140/7
⇒ xy = 20

Now, required values of x and y whose product is 50 and are coprime, will be 4 and 5.
∴ Numbers are 28 and 35 which lie between 20 and 45.

∴ Required sum = (28 + 35)
= 63
১,৩৩৬.
(3x + 3x + 3x)/3x = ?
  1. ক
    ক) 3x
  2. খ
    খ) 3x + 1
  3. গ
    গ) 1
  4. ঘ
    ঘ) 3
ব্যাখ্যা
Question: (3x + 3x + 3x)/3x = ?

Solution:
(3x + 3x + 3x)3x 
= {3x (1 + 1 + 1)}/3x
= (3x . 3)/3x
= 3(x + 1)/3x
= 3x + 1 - x
= 31
= 3
১,৩৩৭.
If x = 7 - 4√3, then √x + (1/√x) is equal to?
  1. ক
    3
  2. খ
    1
  3. গ
    4
  4. ঘ
    2
ব্যাখ্যা
Question: If x = 7 - 4√3, then √x + (1/√x) is equal to?

Solution:
১,৩৩৮.
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
  1. ক
    9
  2. খ
    12
  3. গ
    8
  4. ঘ
    14
  5. ঙ
    10
ব্যাখ্যা
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x
or, 14 x x = 6 x 21
or, x = (6 x 21)/14
so, x = 9.
১,৩৩৯.
The ages of five people are as follows 36, 48, 52, 40, and 44 years. What should be the age of a sixth person so that the average age of all six becomes 45 years?
  1. ক
    30 years
  2. খ
    50 years
  3. গ
    52 years
  4. ঘ
    None
ব্যাখ্যা

Question: The ages of five people are as follows 36, 48, 52, 40, and 44 years. What should be the age of a sixth person so that the average age of all six becomes 45 years?

Solution:
Let the age of the sixth person be x.
The average of six persons = Total age of 6 persons ÷ 6.

ATQ, 
(36 + 48 + 52 + 40 + 44 + x)/6 = 45
⇒ (220 + x)/6 = 45
⇒ 220 + x = 270
⇒ x = 270 - 220
⇒ x = 50

∴ The age of the sixth person should be 50 years.

১,৩৪০.
In 6 years, Amir will be twice as old as Bablu was 12 years ago. If Amir is now 9 years older than Bablu, then the present age of Bablu is-
  1. ক
    37 years
  2. খ
    41 years
  3. গ
    39 years
  4. ঘ
    35 years
ব্যাখ্যা
Question: In 6 years, Amir will be twice as old as Bablu was 12 years ago. If Amir is now 9 years older than Bablu, then the present age of Bablu is-

Solution:
Let,
The present age of Bablu is x years. 
∴ The present age of Aamir is (x + 9) years.
After 6 years, the age of Amir would be (x + 9 + 6) = (x + 15) years
Before 12 years, the age of Bablu was (x - 12) years.

ATQ,
(x + 15) = 2(x - 12)
⇒ x + 15 = 2x - 24
⇒ x = 15 + 24 
∴ x = 39

∴ The present age of Bablu is 39 years.
১,৩৪১.
Which number should replace both the x in the following equation?
x /1776 = 111/ x
  1. ক
    ক) 354
  2. খ
    খ) 544
  3. গ
    গ) 644
  4. ঘ
    ঘ) 444
ব্যাখ্যা

Let x /1776 = 111/ x
Then,
⇔x2=111×1776
⇔x2=111×111×16
⇔x= √ {(111)2×(4)2}
⇔x=111×4
⇔x=444

১,৩৪২.
Two inline pipes are used to fill a tank in 6 hours. The first inline pipe has double efficiency than the second one. How much time will the second pipe take to fill the tank alone?
  1. ক
    ক) 12 hours
  2. খ
    খ) 18 hours
  3. গ
    গ) 9 hours
  4. ঘ
    ঘ) 24 hours
ব্যাখ্যা
Question: Two inline pipes are used to fill a tank in 6 hours. The first inline pipe has double efficiency than the second one. How much time will the second pipe take to fill the tank alone?

Solution: 
ধরি,
দ্বিতীয় পাইপ ক সময়ে সম্পূর্ণ চৌবাচ্চা একা পূর্ণ করতে পারে।
যেহেতু 
প্রথম পাইপের দক্ষতা দ্বিতীয় পাইপের চেয়ে বেশি সেহেতু প্রথম পাইপের সময় লাগবে ক/২।

১ ঘন্টায় ২য় পাইপ পূর্ণ করে ১/ক অংশ
১ম পাইপ পূর্ণ করে ২/ক অংশ

১ ঘন্টায় মোট পূর্ণ করে = (১/ক + ২/ক) অংশ
= ৩/ক অংশ

∴ সম্পূর্ণ অংশ পূর্ণ করতে মোট সময় লাগবে = ক/৩ সময়

প্রশ্নমতে,
ক/৩ = ৬
ক = ১৮ 

∴ ২য় পাইপের সম্পূর্ণ চৌবাচ্চা পূর্ণ করতে সময় লাগবে ১৮ ঘন্টা।
১,৩৪৩.
Find out the value of the term, (2x + 3)2.
  1. ক
    2x2 + 12x + 9
  2. খ
    4x2 + 12x + 9
  3. গ
    4x2 - 12x + 9
  4. ঘ
    4x2 + 6x + 9
ব্যাখ্যা
Question: Find out the value of the term, (2x + 3)2.

Solution:
Using algebraic formula,
(a + b)2 = a2 + 2ab + b2

∴ (2x + 3)2 = (2x)2 + 2 × 2x × 3 + 32 
⇒ (2x + 3)2 = 4x2 + 12x + 9
১,৩৪৪.
A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.
  1. ক
    34 m
  2. খ
    272 m
  3. গ
    1156 m
  4. ঘ
    136 m
ব্যাখ্যা
Question: A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.

Solution:
Let, one side of the park is x meter.
So, one side of the park with path = x + (2 + 2)
= x + 4

We know,
Area of the park = x2
Area of the path, (x + 4)2 - x2 = 288
⇒ x2 + 8x + 16 - x2 = 288 
⇒ 8x + 16 = 288
⇒ 8x = 288 - 16
⇒ 8x = 272
⇒ x = 272/8
∴ x = 34

One side of the square = 34 m.
So, perimeter of the square =4 × 34
= 136 m
১,৩৪৫.
For the function f(x) = x2 + 2x - 2, find x when f(x) = 6.
  1. ক
    46
  2. খ
    4
  3. গ
    3
  4. ঘ
    2
ব্যাখ্যা
Question: For the function f(x) = x2 + 2x - 2, find x when f(x) = 6.

Solution:
f(x) = x2 + 2x - 2
f(x) = 6

∴ x2 + 2x - 2 = 6
⇒ x2 + 2x - 2 - 6 = 0
⇒ x2 + 2x - 8 = 0
⇒ x2 + 4x - 2x - 8 = 0
⇒ x(x + 4) - 2(x + 4) = 0
⇒ (x + 4)(x - 2) = 0
∴ x + 4 = 0   or  x - 2 = 0
∴ x = - 4    or     x = 2
১,৩৪৬.
Which number is divisible by 2, 3, 4 and 6 but is not divisible by 5?
  1. ক
    ক) 138
  2. খ
    খ) 644
  3. গ
    গ) 1020
  4. ঘ
    ঘ) 1428
ব্যাখ্যা
Question: Which number is divisible by 2, 3, 4 and 6 but is not divisible by 5?

Solution: 
অপশন টেস্ট:
অপশন ক) 138 সংখ্যাটি 4 দ্বারা বিভাজ্য নয় 
অপশন খ) 644 সংখ্যাটি 3 দ্বারা বিভাজ্য নয়
অপশন গ) 1020সংখ্যাটি 5 দ্বারা বিভাজ্য 
অপশন ঘ) 1428 সংখ্যাটি  2, 3, 4 এবং 6 দ্বারা বিভাজ্য 5 দ্বারা বিভাজ্য নয়
১,৩৪৭.
A motorboat, whose speed in 18 km/h in still water goes 36 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is-
  1. ক
    8 km/h
  2. খ
    5 km/h
  3. গ
    5.5 km/h
  4. ঘ
    6 km/h
ব্যাখ্যা
Question: A motorboat, whose speed in 18 km/h in still water goes 36 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is-

Solution:
Let, the speed of the stream = x km/h
Then,
Speed downstream = (18 + x) km/h
Speed upstream = (18 - x) km/h

ATQ,
36/(18 + x) + 36/(18 - x) = 4.5
⇒ 36{(18 + x) + (18 - x)}/(18 + x)(18 - x) = 4.5
⇒ 1296/(324 - x2) = 9/2
⇒ 9(324 - x2) = 2 × 1296
⇒ 2916 - 2592 = 9x2
⇒ 9x2 = 324
⇒ x2 = 36 = 62
∴ x = 6

∴ The speed of the stream is 6 km/h
১,৩৪৮.
Shamim spends 40% of his income on education and 50% of the remaining on food. He gives Tk. 1000 as monthly rent and now has Tk. 2000 left with him. What is his monthly income?
  1. ক
    Tk. 8000
  2. খ
    Tk. 10000
  3. গ
    Tk. 12000
  4. ঘ
    Tk. 14000
ব্যাখ্যা
Question: Shamim spends 40% of his income on education and 50% of the remaining on food. He gives Tk. 1000 as monthly rent and now has Tk. 2000 left with him. What is his monthly income?

Solution:
Shamim's saving and rent = (1000 + 2000) = Tk. 3000
Let, his monthly income be = Tk. 100

40% of his income he spent on education = Tk. 40
Remaining = (100 - 40) = 60
50% of remaining on food = (60 × 50)/100 =Tk. 30

Now, that 30 must be equal to his saving and rent:
30 = 3000 then,
1 = 3000/30
∴ 100 = (3000 × 100)/30 =Tk. 10000

So, his income = Tk. 10000
১,৩৪৯.
What should be added to 2x2 + 3x - 5 to make x2 - x + 1?
  1. ক
    ক) -x2 - 4x + 6
  2. খ
    খ) x2 - 4x + 6
  3. গ
    গ) x2 - 4x + 6
  4. ঘ
    ঘ) x2 - 4x + 6
ব্যাখ্যা

Let A is to be added them 2x2 + 3x - 5 + A = x2 - x + 1
A = x2 - x + 1 - (2x2 + 3x - 5)
A = x2 - x + 1 - 2x2 - 3x + 5
A = -x2 - 4x + 6.

১,৩৫০.
Solve the following equation:
  1. ক
    - 2, - 2
  2. খ
    - 4, 4
  3. গ
    2, - 3
  4. ঘ
    None of the above
ব্যাখ্যা
Question: Solve the following equation:


Solution:
(x + 8)/x = (x + 2)/2
⇒ 2x + 16 = x2 + 2x
⇒ 16 = x2
⇒ x2 - 16 = 0
⇒ x2 - 42= 0
⇒ (x + 4)(x - 4) = 0
∴ x = - 4 or  x = 4
১,৩৫১.
How many diagonals can be drawn in a pentagon?
  1. ক
    9
  2. খ
    7
  3. গ
    5
  4. ঘ
    11
ব্যাখ্যা
Question: How many diagonals can be drawn in a pentagon?

Solution: 
A pentagon has 5 sides. We obtain the diagonals by joining the vertices in pairs.
Total number of sides and diagonals,
= 5C2
= 10
This includes its 5 sides also.

∴ Diagonals = 10 – 5 = 5
১,৩৫২.
The length and breadth of a square are increased by 30% and 20% respectively. The area of the resulting rectangle exceeds the area of the square by?
  1. ক
    56%
  2. খ
    82%
  3. গ
    65%
  4. ঘ
    42%
ব্যাখ্যা
Question: The length and breadth of a square are increased by 30% and 20% respectively. The area of the resulting rectangle exceeds the area of the square by?

Solution:
Let,
The length is = 100 
∴ Original Area of the Square is = 1002 = 10000

New Length = 100 + 30 = 130
New Breadth = 100 + 20 = 120

∴ New Area = (New Length) × (New Breadth)
= 130 × 120 = 15600

∴ Increase in Area = {(New Area−Original Area​)/Original Area} × 100
= {(15600 - 10000)/10000} × 100
= (5600/10000) × 100
= 56%

∴ The area of the resulting rectangle exceeds the area of the original square by 56%.
১,৩৫৩.
If sec(x − 30°) = 2/√3, tan x = ?
  1. ক
    ক) √3
  2. খ
    খ) 1/√2
  3. গ
    গ) 1/√3
  4. ঘ
    ঘ) 1
ব্যাখ্যা

sec (x − 30°) = 2/√3
Or, sec (x - 30°) = sec 30°
Or, x - 30° = 30°
Or, x = 60°
∴ tan 60° = √3

১,৩৫৪.
28√? + 1,426 = 3/4 of 2,872
  1. ক
    ক) 576
  2. খ
    খ) 1,296
  3. গ
    গ) 676
  4. ঘ
    ঘ) 1,444
ব্যাখ্যা
28√? + 1,426 = 3/4 of 2872
⇒ 28√?  = 3/4 × 2872 - 1,426 = 728
⇒ √?  = 728/28 = 26
⇒ ? = 262 = 676
১,৩৫৫.
If α, β are the roots of the equation x2 - 9x + 20 = 0, then αβ equals:
  1. ক
    11
  2. খ
    20
  3. গ
    28
  4. ঘ
    24
ব্যাখ্যা

Question: If α, β are the roots of the equation x2 - 9x + 20 = 0, then αβ equals:

Solution:
x2 - 9x + 20 = 0
⇒ x2 - 5x - 4x + 20 = 0
⇒ x(x - 5) - 4(x - 5) = 0
⇒ (x - 5)(x - 4) = 0
⇒ x = 5, 4

Hence, α = 5, β = 4

Hence, The value of α × β = 5 × 4 = 20
∴ αβ = 20

Shortcut:
দ্বিঘাত সমীকরণ ax2 + bx + c = 0 এর মূলদ্বয় α এবং β হলে,
αβ = c/a [যেখানে, a হলো x2 এর সহগ এবং c ধ্রুবক পদ]
∴ αβ = 20/1 = 20

১,৩৫৬.
যদি কখ <০ এবং খ > ০ হয়, তাহলে নিচের কোনটি সত্য নয়?
  1. ক
    (২খ + ৩) × (ক + ২) > ৬
  2. খ
    (২খ + ৩খ) × (২ - ক) > ৬
  3. গ
    (২ক + ১) × (২ - ক) < ৬
  4. ঘ
    (২ক - ১) × (২ + ক) < ৬
  5. ঙ
    খ ও গ উভয়ই
ব্যাখ্যা
প্রশ্ন: যদি কখ <০ এবং খ > ০ হয়, তাহলে নিচের কোনটি সত্য নয়?

সমাধান:
দেওয়া আছে,
কখ <০ এবং খ > ০ হলে, খ এর মান ০ অপেক্ষা বড় এবং ক এর মান ০ অপেক্ষা ছোট হবে।

ধরি,
ক = - ১
খ = ১

এখন,
(২খ + ৩খ) × (২ - ক) > ৬
⇒ (২ + ৩) × {২ - (- ১)} > ৬
⇒ ৫ × ৩ > ৬
∴ ১৫ > ৬, ইহা সত্য

(২খ + ৩) × (ক + ২) > ৬
⇒ (২ + ৩) × {(- ১) + ২} > ৬
⇒ ৫ × ১ > ৬
∴ ৫ > ৬, ইহা সত্য নয়

(২ক + ১) × (২ - ক) < ৬
⇒ {২ (- ১)} + ১} × {২ - (- ১)} < ৬
⇒ (- ২ + ১) × (২ + ১) < ৬
⇒ - ১ × ৩ < ৬
∴ - ৩ < ৬, ইহা সত্য

(২ক - ১) × (২ + ক) < ৬
⇒ {২ × (- ১) - ১} × (২ + (- ১)} < ৬
⇒ (- ২ - ১) × ১ < ৬
⇒ - ৪ < ৬, ইহা সত্য
১,৩৫৭.
Jubin's front lawn is 1/3 the size of his back lawn. If John mows 1/2 of his front lawn and 2/3 of his back lawn, what fraction of his lawn is left unmowed?
  1. ক
    1/6
  2. খ
    1/3
  3. গ
    3/8
  4. ঘ
    1/2
  5. ঙ
    5/8
ব্যাখ্যা
Question: Jubin's front lawn is 1/3 the size of his back lawn. If John mows 1/2 of his front lawn and 2/3 of his back lawn, what fraction of his lawn is left unmowed?

Solution:
Let say back lawn = 6
Therefore front lawn = (1/3) × 6 =2
Total = 6 + 2 = 8
Now moved lawn= {(1/2) × 2} + {(2/3) × 6} = 5
Therefore unmoved lawn = total - moved = 8 - 5 =3
∴ Fraction = unmoved/total = 3/8
১,৩৫৮.
If x2 + 4x + 2 is even, then which one of the following could be the value of x?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 9
  4. ঘ
    ঘ) 7
ব্যাখ্যা
x = 3 হলে x2 + 4x + 2 = 32 + 4 × 3 + 2 = 9 + 12 + 2 = 23 
x = 4 হলে x2 + 4x + 2 = 42 + 4 × 4 + 2 = 16 + 16 + 2 = 34
x = 9 হলে x2 + 4x + 2 = 92 + 4 × 9 + 2 = 81 + 36 + 2 = 119
x = 7 হলে x2 + 4x + 2 = 72 + 4 × 7+ 2 = 49 + 28 + 2 = 79
১,৩৫৯.
Rina bought 8 mangoes for Tk. 40. She sold 5 mangoes for Tk. 40. What is her profit percentage?
  1. ক
    66.66%
  2. খ
    60%
  3. গ
    33.33%
  4. ঘ
    66%
ব্যাখ্যা
Question: Rina bought 8 mangoes for Tk. 40. She sold 5 mangoes for Tk. 40. What is her profit percentage?

Solution:
৮ টি আমের ক্রয়মূল্য ৪০ টাকা
১ টি আমের ক্রয়মূল্য ৪০/৮ = ৫ টাকা

আবার,
৫ টি আমের বিক্রয়মূল্য ৪০ টাকা
১ টি আমের বিক্রয়মূল্য ৪০/৫ = ৮ টাকা

∴ লাভ = ৮ - ৫ = ৩ টাকা

∴ ৫ টাকায় লাভ হয় ৩ টাকা
১ টাকায় লাভ হয় ৩/৫ টাকা
১০০ টাকায় লাভ হয় ৩০০/৫ = ৬০ টাকা

∴ লাভ ৬০%
১,৩৬০.
A bus was supposed to travel 240 km at its normal speed. But because of heavy traffic, it had to slow down by 10 km/h and therefore reached the destination 2 hours later than the scheduled time. What was the bus’s original (normal) speed?
  1. ক
    50 km/hr
  2. খ
    55 km/hr
  3. গ
    40 km/hr
  4. ঘ
    30 km/hr
ব্যাখ্যা

Question: A bus was supposed to travel 240 km at its normal speed. But because of heavy traffic, it had to slow down by 10 km/h and therefore reached the destination 2 hours later than the scheduled time. What was the bus’s original (normal) speed?

Solution:
Let, the original speed = x km/hr
Distance = 240 km

Time taken at original speed = 240 / x
Time taken at reduced speed = 240 / (x - 10)

According to the question:
240 / (x - 10) - 240 / x = 2

LCM: x(x - 10)
Now,
240x - 240(x - 10) = 2x(x - 10)
⇒ 240x - 240x + 2400 = 2x2 - 20x
⇒ 2x2 - 20x - 2400 = 0
⇒ x2 - 10x - 1200 = 0

Solve quadratic: x2 - 10x - 1200 = 0

Factors: (x - 40)(x + 30) = 0
x = 40 or -30 (speed cannot be negative)
So the speed is 40 km/hr.

১,৩৬১.
Nipa is 25% more efficient than Tima. Tima alone can build a craft in 25 days. Find the number of days taken by Nipa to finish the same piece of work?
  1. ক
    25 days
  2. খ
    16 days
  3. গ
    20 days
  4. ঘ
    22 days
ব্যাখ্যা
The ratio of times taken by Tima and Nipa
= 125 : 100
= 5: 4
Suppose Nipa takes x days to do the work.
5 : 4 = 25 : x
so, 5x= (4 x 25)
or, 5x = 100
x = 20 days
১,৩৬২.
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
  1. ক
    ক) 256
  2. খ
    খ) 24
  3. গ
    গ) 12
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Let the 3 boys be B1, B2, B3 and 4 prizes be P1, P2, P3 and P4
Now B1 is eligible to receive any of the 4 available prizes (so 4 ways)
B2 will receive prize from rest 3 available prizes(so 3 ways)
B3 will receive his prize from the rest 2 prizes available(so 2 ways)
So total ways would be: 4 × 3 × 2 × 1 = 24 Ways
Hence, the 4 prizes can be distributed in 24 ways

১,৩৬৩.
The greatest number that can be subtracted from 10000 so that the remainder may be divisible by 32, 36, 48 and 54 is-
  1. ক
    9136
  2. খ
    9316
  3. গ
    9216
  4. ঘ
    9236
  5. ঙ
    None of these
ব্যাখ্যা
Question: The greatest number that can be subtracted from 10000 so that the remainder may be divisible by 32, 36, 48 and 54 is-

Solution:
LCM of 32, 36, 48 and 54 = 864
Required greatest number = 10000 - 864 = 9136
∴ Required greatest number = 9136
১,৩৬৪.
The average mark obtained by 15 students was 10 and the average mark obtained by 10 students was 15. What was the average mark obtained by all students?
  1. ক
    ক) 10
  2. খ
    খ) 12.5
  3. গ
    গ) 15
  4. ঘ
    ঘ) 12
ব্যাখ্যা
15 জনের মোট নম্বর 15 × 10 = 150
10 জনের মোট নম্বর = 10 × 15 = 150

25 জনের মোট নম্বর = 150 + 150 = 300
25 জনের গড় নম্বর = 300/25 = 12
১,৩৬৫.
The number of students who take both the subjects Mathematics and Chemistry is 30. This represents 10% of the enrollment in Mathematics and 12% of the enrollment in Chemistry. How many students take atleast one of these two subjects?
  1. ক
    480
  2. খ
    490
  3. গ
    520
  4. ঘ
    540
ব্যাখ্যা
Question: The number of students who take both the subjects Mathematics and Chemistry is 30. This represents 10% of the enrollment in Mathematics and 12% of the enrollment in Chemistry. How many students take atleast one of these two subjects?

Solution:
Let number of students taken Mathematics = m
number of students taken Chemistry = c

ATQ, 0.10m = 0.12c = 30
⇒ 0.10m = 30 and, 0.12c = 30
⇒ m = 300 and, c = 250

∴ Total number of students taken atleast one of these two subjects 
= 300 + 250 − 30 = 520
১,৩৬৬.
Two pipes can fill a tank in 18 and 27 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 12 minutes. The capacity of the tank is:
  1. ক
    352 gallons.
  2. খ
    385 gallons.
  3. গ
    432 gallons.
  4. ঘ
    472 gallons.
ব্যাখ্যা
Question: Two pipes can fill a tank in 18 and 27 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 12 minutes. The capacity of the tank is:

Solution:
Let
the capacity of the tank be x gallons.

Then,
First pipe fills = x/18​ gallons per minute
Second pipe fills = x/27 gallons per minute
Waste pipe empties = 4 gallons per minute

All three working together fill the tank in 12 minutes,

ATQ,
x/18 + x/27 - 4 = x/12
⇒ x/18 + x/27 - x/12 = 4
⇒ (6x + 4x - 9x)/108 = 4
⇒ x/108 = 4
∴ x = 432

∴ Capacity of the tank = 432 gallons.
১,৩৬৭.
Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to the profit on 5 oranges. What is the percentage point difference between the profit percentage and discount percentage?
  1. ক
    ক) 20%
  2. খ
    খ) 22.22%
  3. গ
    গ) 16.66%
  4. ঘ
    ঘ) 15%
ব্যাখ্যা

According to the question
The cost price of 12 oranges = The sale price of 9 oranges
So profit% = (12 C.P. - 9 C.P.)/9 C.P × 100 = 33.33%

Then it is said that,
5 S.P. - 5 C.P. = 10 M.P. -10 S.P.
From that
we get the relation between M.P. and S.P., that is,
27 S.P. = 24 M.P.(With help of 12 C.P. = 9 S.P.)
Then Discount%
= M.P. - S.P./M.P
= (27 M.P. - 24 M.P.)/27 M.P × 100
= 11.11%
So, % point discount
= 33.33% - 11.11%
= 22.22%

১,৩৬৮.
What is the net discount for successive discounts of 20% and 30%?
  1. ক
    ক) 44%
  2. খ
    খ) 36%
  3. গ
    গ) 48%
  4. ঘ
    ঘ) 24%
ব্যাখ্যা
Question: What is the net discount for successive discounts of 20% and 30%?
Solution: 
ধরি, লিখিত মূল্য  ‘x’.

20% ছাড়ের পর, 
⇒ বিক্রয়মূল্য  = x - 0.2x = 0.8x

30% ছাড়ের পর,
⇒ বিক্রয়মূল্য = 0.8x - 0.8 × 0.3x = 0.56x

∴ মোট ছাড় = [(x - 0.56x)/x] × 100 = 44%
১,৩৬৯.
If a sum of Tk. 9 is lent to be paid back in 10 equal monthly installments of Tk. 1 each, the rate of interest is -
  1. ক
    ক) 11%
  2. খ
    খ) 26.67%
  3. গ
    গ) 11.33%
  4. ঘ
    ঘ) 266.67%
ব্যাখ্যা

Let the rate of interest be R%
Amount due in 10 months
= 9 + simple interest on Tk. 9 for ten months
= 9 + {9 × R × (10/12)}/100
= 9 + (3R/40)
With the formula mentioned,
1 = 100{9 + 3R/40)}/[(100 × 10) + {R × 10(10 - 1)/(2 × 21)}]
900 + (15R/2) = 1000 + (15R/4)
15R/4 = 100
R = 26.67.
Hence the interest rate is 26.67%.

১,৩৭০.
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
  1. ক
    ক) 35 years
  2. খ
    খ) 40 years
  3. গ
    গ) 45 years
  4. ঘ
    ঘ) 50 years
  5. ঙ
    ঙ) 55 years
ব্যাখ্যা

Sum of the present ages of husband, wife and child
= (27 x 3 + 3 x 3) years
= 90 years
Sum of the present ages of wife and child
= (20 x 2 + 5 x 2) years
= 50 years
∴ Husband's present age
= (90 - 50) years
= 40 years

১,৩৭১.
The average of three numbers is X. If two numbers of them are Y and Z. What is the 3rd number?
  1. ক
    ক) - Z + 3X - Y
  2. খ
    খ) - Z + 3X + Y
  3. গ
    গ) Z + 3X - Y
  4. ঘ
    ঘ) - Z - 3X - Y
ব্যাখ্যা
Question: The average of three numbers is X. If two numbers of them are Y and Z. What is the 3rd number?

Solution: 
3টি সংখ্যার সমষ্টি = 3X
তৃতীয় সংখ্যাটি = 3X - (Y + Z)
= 3X - Y - Z
= - Z + 3X - Y
১,৩৭২.
Find out the wrong number in the series:
455, 445, 465, 435, 485, 415, 515, 455
  1. ক
    455
  2. খ
    465
  3. গ
    485
  4. ঘ
    415
ব্যাখ্যা
Question: Find out the wrong number in the series:
455, 445, 465, 435, 485, 415, 515, 455

Solution:
The given series is made of two different series:

First: 455, 465, 485, 515, and

Second: 445, 435, 415, 455

The sequence in first series is + 10, + 20, + 30, and
The sequence in second series is - 10, - 20. So, the number 455 is wrong as it should be 415 - 30 = 385
১,৩৭৩.
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is-
  1. ক
    ক) 50 days
  2. খ
    খ) 38 days
  3. গ
    গ) 48 days
  4. ঘ
    ঘ) 42 days
ব্যাখ্যা
প্রশ্ন: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is-

সমাধান: 
দিন বাকি আছে (৪৫ - ১০) দিন
= ৩৫ দিন

সৈন্য বাকি থাকে (১৫০ - ২৫) জন
= ১২৫ জন

১৫০ জনের চলবে ৩৫ দিন
∴ ১ জনের চলবে ৩৫ × ১৫০ দিন
∴ ১২৫ জনের চলবে (৩৫ × ১৫০)/১২৫ দিন
= ৪২ দিন
১,৩৭৪.
An acute angled triangle ABC, If sin2(A + B - C) = 1 and tan (B + C - A) = √3, then the value of angle ∠B is -
  1. ক
    ক) 30°
  2. খ
    খ) 52(1/2)°
  3. গ
    গ) 60°
  4. ঘ
    ঘ) 45°
ব্যাখ্যা

দেওয়া আছে,
sin2(A + B + C) = 1
⇒ sin 2(A + B + C) = sin 90°
⇒ 2(A + B + C) = 90°
∴ (A + B + C) = 45°............(i)
আবার, tan (B + C - A) = √3
⇒ tan (B + C - A) = tan60°(tan 60° = √3)
B + C - A = 60°............(ii)
এখন, (i) ও (ii) নং সমীকরণ যোগ করে পাই,
(A + B - C) + (B + C - A) = 45° + 60°
⇒2B = 105°
⇒ B = 52(1/2)°

১,৩৭৫.
An alloy of gold and copper weights 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?
  1. ক
    40 gm
  2. খ
    50 gm
  3. গ
    45 gm
  4. ঘ
    60 gm
ব্যাখ্যা
Question: An alloy of gold and copper weights 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?

Solution:
Gold in alloy =50 × 80% = 40gm
Copper in alloy =50 × 20% =10gm
Now,
(40 + x)/10 = 90/10
⇒ 40 + x = 90
⇒ x = 90 - 40
∴ x = 50gm
১,৩৭৬.
Three boys agree to divide a bag of marbles in the following manner. The first boy takes one more than half the marbles. The second takes a third of the number remaining. The third boy finds that he is left with twice as many marbles as the second boy. The original number of marbles is -
  1. ক
    38
  2. খ
    36
  3. গ
    32
  4. ঘ
    Cannot be determined
ব্যাখ্যা
Question: Three boys agree to divide a bag of marbles in the following manner. The first boy takes one more than half the marbles. The second takes a third of the number remaining. The third boy finds that he is left with twice as many marbles as the second boy. The original number of marbles is -

Solution: 
মোট মার্বেল সংখ্যা ৩৮ হলে, 
প্রথম জন পাবে = (৩৮/২) + ১ = ১৯ + ১ = ২০ 
দ্বিতীয় জন পাবে = (৩৮ - ২০)/৩ = ১৮/৩ = ৬ 
তৃতীয় জন পায় = ৩৮ - (২০ + ৬) = ৩৮ - ২৬ = ১২ ; যা দ্বিতীয় জনের দ্বিগুণ।  

মোট মার্বেল সংখ্যা ৩৬ হলে, 
প্রথম জন পাবে = (৩৬/২) + ১ = ১৮ + ১ = ১৯
দ্বিতীয় জন পাবে = (৩৬ - ১৯)/৩ = ১৭/৩  
তৃতীয় জন পায় = ৩৮ - (১৯ + ১৭/৩) = ৩৪/৩ ; যা দ্বিতীয় জনের দ্বিগুণ। 

মোট মার্বেল সংখ্যা ৩২ হলে, 
প্রথম জন পাবে = (৩২/২) + ১ = ১৬ + ১ = ১৭ 
দ্বিতীয় জন পাবে = (৩২ - ১৭)/৩ = ১৫/৩ = ৫ 
তৃতীয় জন পায় = ৩২ - (১৭ + ৫) = ৩২ - ২২ = ১০ ; যা দ্বিতীয় জনের দ্বিগুণ। 

অতএব, প্রশ্নের প্রদত্ত তথ্য অনুযায়ী তিনটিই উত্তর হিসেবে গ্রহণযোগ্য। মূলত কয়টি মার্বেল ছিল তা নির্ণয় করার জন্য পর্যাপ্ত তথ্য প্রশ্নে দেয়া নেই।
১,৩৭৭.
If m is the average of the first 10 positive multiples of 5 and M is the median of the first 10 positive multiples of 5, what is the value of M – m?
  1. ক
    0
  2. খ
    - 5.75
  3. গ
    5.75
  4. ঘ
    0.50
ব্যাখ্যা
Question: If m is the average of the first 10 positive multiples of 5 and M is the median of the first 10 positive multiples of 5, what is the value of M – m?

Solution: 
The first 10 multiples of 5 are = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
average of these numbers is, m = (5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50)/10
= 27.5

the median of these numbers, M = (25 + 30)/2 = 27.5

∴ M - n = 0
১,৩৭৮.
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?
  1. ক
    ক) 27
  2. খ
    খ) 31
  3. গ
    গ) 33
  4. ঘ
    ঘ) 37
ব্যাখ্যা

Let us assume that he answered x question correctly. Marks scored by him in x question = 2x
Then, wrong answer would be = 60 – x
Marks lost by him in (60 – x) questions = (60 – x)×1
ATQ,
2x – (60 – x) = 39
Or, 3x = 99
∴ x = 33

১,৩৭৯.
A man can row 9 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream?
  1. ক
    6 km/h
  2. খ
    5 km/h
  3. গ
    3 km/h
  4. ঘ
    2 km/h
ব্যাখ্যা
Question: A man can row 9 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream?

Solution: 
Let,
the rate of stream = x km/h

∴ Downstream speed = 9 + x
∴ Upstream speed = 9 - x

ATQ,
9 + x = 2(9 - x)
⇒ 9 + x = 18 - 2x
⇒ x + 2x = 18 - 9
⇒ 3x = 9
∴ x = 3

∴ the rate of stream 3 km/h
১,৩৮০.
Mr. Ronaldo can finish a Task in 20 days and Mr. Messi can do in 30 days. With help of Mr. Salah, they did the job in 10 days only. Then how many days are necessary to complete the task by Mr. Salah?
  1. ক
    ক) 80 days
  2. খ
    খ) 60 days
  3. গ
    গ) 50 days
  4. ঘ
    ঘ) 70 days
ব্যাখ্যা
মনে করি, মি সালেহ x দিনে করতে পারে।
প্রশ্নমতে,
1/20 + 1/30 + 1/x = 1/10
=> 1/x = 1/10 - 1/20 - 1/30
=> 1/x = 1/60
=> x = 60
১,৩৮১.
A number is as less than 480 as is (3/2)times greater than 320. What is the number?
  1. ক
    ক) 64
  2. খ
    খ) 66
  3. গ
    গ) 62
  4. ঘ
    ঘ) 60
ব্যাখ্যা
Question: A number is as less than 480 as is (3/2)times greater than 320. What is the number?

Solution: 
ধরি,
সংখ্যাটি x

প্রশ্নমতে,
480 - x = 320 + (3x/2)
বা, 960 - 2x = 640 + 3x
বা, 5x = 960 - 640
বা, 5x = 320
∴ x = 64

∴ সংখ্যাটি = 64
১,৩৮২.
If the simple interest on Tk. X at X% per annum for 5 years is Tk. X, what is the value of X?
  1. ক
    12.5
  2. খ
    10
  3. গ
    20
  4. ঘ
    25
  5. ঙ
    50
ব্যাখ্যা

Question: If the simple interest on Tk. X at X% per annum for 5 years is Tk. X, what is the value of X?

Solution:
Given,
P = X
r = X% = X/100
n = 5 years
I = X

We know,
I = Prn
⇒ X = X × (X/100) × 5
⇒ X = X × (X/20)
∴ X = 20

১,৩৮৩.
A rectangular floor of dimensions 18 m × 12 m is to be covered with a carpet 60 cm wide. Calculate how many metres of carpet are required.
  1. ক
    360 m
  2. খ
    216 m
  3. গ
    188 m
  4. ঘ
    320m
ব্যাখ্যা

Question: A rectangular floor of dimensions 18 m × 12 m is to be covered with a carpet 60 cm wide. Calculate how many metres of carpet are required.

Solution:
Given that,
Floor dimensions = 18 m × 12 m
Carpet width = 60 cm = 0.6 m [1m = 100cm]

Now, Area of floor = length × breadth = 18 × 12 = 216m2

And,
Width of carpet = 0.6m Length of carpet required = L m 
Area covered by L m of carpet = 0.6 × L  m2

This must equal the area of the floor, 0.6 × L = 216
L = 216/0.6 = 360 m

So 360 metres of carpet will be required.

১,৩৮৪.
In how many different ways can the letters of the word 'MACHINE' be arranged so that the vowels may occupy only the odd positions?
  1. ক
    ক) 256
  2. খ
    খ) 325
  3. গ
    গ) 450
  4. ঘ
    ঘ) 576
ব্যাখ্যা
Question: In how many different ways can the letters of the word 'MACHINE' be arranged so that the vowels may occupy only the odd positions? 

Solution: 
Vowel ৩টি ৪টি বিজোড় স্থানে রেখে, 4P3 = 24
Consonant ৪টির জন্য জায়গা আছে জোড় ৩টি + বিজোড় ১টি = ৪টি।
তাহলে সাজানো যাবে, 4P4 = 24 
মোট বিন্যাস = 24 × 24 = 576 
১,৩৮৫.
If X is an odd integer and Y is an even integer. Which of the following statements is (are) always true?
(I) (X + Y) is odd
(II) XY is odd
(III) (2X + Y) is even
  1. ক
    I only
  2. খ
    II and III only
  3. গ
    III only
  4. ঘ
    I and III only
  5. ঙ
    None of these
ব্যাখ্যা

odd + even = odd (4 + 5 = 9)
odd × even = even (4 × 5 = 20)
even × odd = even × even = even (2 × 5 + 4 = 14).

১,৩৮৬.
Mehedi pays 3 workers P, Q and R a total of Tk. 6000 a week. P is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P make in a week?
  1. ক
    ক) Tk. 1968.6
  2. খ
    খ) Tk. 1978.5
  3. গ
    গ) Tk. 1967.2
  4. ঘ
    ঘ) Tk. 1975.3
ব্যাখ্যা
Question: Mehedi pays 3 workers P, Q and R a total of Tk. 6000 a week. P is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P make in a week?

Solution:
Let,
P is paid Tk. x
Q is paid Tk. (100x)/125 = (4x)/5
R is paid Tk. (100x)/80 = (5x)/4

ATQ,
x + (4x)/5 + (5x)/4 = 6000
⇒ 20x + 16x + 25x = 6000 × 20 [multiply with 20]
⇒ 61x = 120000
⇒ x = 120000/61
∴ x = 1967.2

∴ P makes 1967.2 Tk. in a week. 
১,৩৮৭.
A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is - 
  1. ক
    ক) Tk 15,000
  2. খ
    খ) Tk 16,000
  3. গ
    গ) Tk 17,000
  4. ঘ
    ঘ) Tk 20,000
ব্যাখ্যা
Questoin: A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is - 

Solution: 
Let the sum be Tk x and original rate be R%
Then, ((x × (R +1) × 3)/100) - {(x × R × 3)/100} = 510
⇒ 3Rx + 3x - 3Rx = 51000
⇒ 3x = 51000
⇒ x = 17000

Hence, sum = Tk 17,000
১,৩৮৮.
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 5.5 m away from the wall. The length of the ladder is:
  1. ক
    ক) 5.5m
  2. খ
    খ) 2.75 m
  3. গ
    গ) 11 m
  4. ঘ
    ঘ) 12 m
ব্যাখ্যা
Let AB be the wall and AC be the ladder.
Then,
∠ACB =  60° and BC = 5.5 m.
⇒ cos 60° = BC/AC
⇒ 1/2 = BC/AC
⇒ AC = 2 × BC
⇒ AC = (2 × 5.5)m
 AC =11 m

১,৩৮৯.
An employee pays Tk.100 for each day a worker and forfeits Tk.20 for each day he idle. At the end of 50 days, if the worker got Tk.2600, for how many days did the worker remain idle?
  1. ক
    ক) 18 days
  2. খ
    খ) 20 days
  3. গ
    গ) 21 days
  4. ঘ
    ঘ) 23 days
ব্যাখ্যা
Question: An employee pays Tk.100 for each day a worker and forfeits Tk.20 for each day he idle. At the end of 50 days, if the worker got Tk.2600, for how many days did the worker remain idle?

Solution: 
প্রতিদিন উপস্থিত থাকার জন্য পায় ১০০ টাকা এবং একদিন অনুপস্থিত থাকলে জরিমানা হয় ২০ টাকা।

যদি ৫০ দিন উপস্থিত থাকত তাহলে মোট পেত = ৫০ × ১০০ = ৫০০০ টাকা
তাহলে, কম পায় = ৫০০০ - ২৬০০ = ২৪০০ টাকা

একদিন অনুপস্থিত থাকলে মোট ক্ষতি হয় = ১০০ + ২০ = ১২০ টাকা

∴ মোট অনুপস্থিত ছিল = ২৪০০/১২০ = ২০ দিন
১,৩৯০.
For which value of P will the square root of 4x2 - Px + 9 be an integer?
  1. ক
    20
  2. খ
    9
  3. গ
    12
  4. ঘ
    16
  5. ঙ
    None of these
ব্যাখ্যা
Question: For which value of P will the square root of 4x2 - Px + 9 be an integer?

Solution:
4x2 - px + 9
= (2x)2 - 2 ⋅ 2 ⋅ 3 + 32 - px + 2 ⋅ 2x ⋅ 3
= (2x - 3)2 + 12x - px

রাশিটি পূর্ণবর্গ হলে,
12x - px = 0 
⇒ px = 12x
∴ p = 12
১,৩৯১.
  1. ক
    6√10
  2. খ
    10√5
  3. গ
    5√10
  4. ঘ
    2√10
ব্যাখ্যা

Question:

Solution: 

১,৩৯২.
A batsman scored 104 runs which included 6 boundaries and 4 sixes. What percent of his total score did he make by running between the wickets?
  1. ক
    54%
  2. খ
    53.85%
  3. গ
    56%
  4. ঘ
    54.85%
ব্যাখ্যা
Question: A batsman scored 104 runs which included 6 boundaries and 4 sixes. What percent of his total score did he make by running between the wickets?

Solution:
Total score of batsman = 104 runs
runs from boundaries = 4 × 6 = 24
runs from sixes = 6 × 4 = 24

∴ Total runs from boundaries and sixes = 24 + 24
                                                                = 48 runs

Scores by running between the wickets = 104 - 48 = 56 runs
percentage of his score made by running between wickets = (56/104) × 100 % = 53.85%
১,৩৯৩.
Ibrahim has 20 ounces of a 20% flavoured solution. How much salt should he add to make it a 25% solution?
  1. ক
    ক) 10.3
  2. খ
    খ) 50
  3. গ
    গ) 1.33
  4. ঘ
    ঘ) 5
ব্যাখ্যা

Let y be the amount of flavour.
(0.2 × 20) + 1 × y = 0.25 (20 + y)
Or, 4 + y = 5 + 0.25y
Or, 0.75y = 1
So, y = 1.33

১,৩৯৪.
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investment?
  1. ক
    5 : 7 : 8
  2. খ
    20 : 49 : 64
  3. গ
    38 : 28 : 21
  4. ঘ
    10 : 13 : 20
ব্যাখ্যা

Question: Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months, and 7 months respectively. What was the ratio of their investment?

Solution:
Let their investments be
x Tk for 14 months,
y Tk for 8 months and
z Tk for 7 months respectively.

Then,
14x : 8y : 7z = 5 : 7 : 8

Now, 
14x/8y = 5/7
⇒ 98x = 40y
⇒ y = 49x/20

And,
14x/7z = 5/8
⇒ 112x = 35z
⇒ z = 16x/5

∴ x : y : z
= x : 49x/20 : 16x/5
= 20 : 49 : 64

১,৩৯৫.
The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 m toward the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:
  1. ক
    17.3 m
  2. খ
    21.9 m
  3. গ
    27.3 m
  4. ঘ
    30 m
ব্যাখ্যা
Question: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 m toward the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is:

Solution:

Let
PR = h meter, be the height of the tower.
The observer is standing at a point Q such that, the distance between the observer and the tower is QR = (20 + x) m, where
QR = QS + SR = (20 + x) m
∠PQR = 30°
∠PSR = 30° + 15° = 45°

In ΔPQR
tan(30°) = PR/QR
⇒ 1/√3 = h/(20 + x)
⇒ 20 + x = √3h
⇒ x = √3h - 20 .........(1)

In ΔPSR
tan(45°) = h/x
⇒ 1 = h/x
⇒ x = h

Substituting x = h in (1), we get
h = √3h - 20
⇒ (√3 - 1)h = 20
h = 20/(√3 - 1)
= {20(√3 + 1)}/{(√3 - 1)(√3 + 1)}
= {20(√3 + 1)}/2
= 10(√3 + 1)
= 10 (1.732 + 1)
= 10 × 2.732
= 27.32 m
১,৩৯৬.
If the average of three consecutive even numbers is 34, find the largest of these numbers.
  1. ক
    30
  2. খ
    32
  3. গ
    34
  4. ঘ
    36
ব্যাখ্যা
Question: If the average of three consecutive even numbers is 34, find the largest of these numbers.

Solution:
Let the first number is x, then the next two even numbers would be x + 2, x + 4

As per question;
(x + x + 2 + x + 4)/3 = 34
⇒ (3x + 6)/3 = 34
⇒ 3x + 6 = 102
⇒ 3x = 96
∴ x = 32

Largest number would be = 32 + 4 = 36
১,৩৯৭.
Mr. Shobuj was both the 14th highest and the 14th lowest in a tennis tournament. How many participants were in the tournament?
  1. ক
    ক) 27
  2. খ
    খ) 28
  3. গ
    গ) 29
  4. ঘ
    ঘ) 30
ব্যাখ্যা
Number of participants are = 14 + 14 - 1 = 27
১,৩৯৮.
A dice is thrown. What is the probability that the number shown on the dice is not divisible by 3?
  1. ক
    1/2
  2. খ
    2/3
  3. গ
    1/4
  4. ঘ
    3/5
ব্যাখ্যা
Question: A dice is thrown. What is the probability that the number shown on the dice is not divisible by 3?

Solution:
S = {1, 2, 3, 4, 5, 6}
n(S) = 6

Then,
E(not divisible by 3) = {1, 2, 4, 5}
n(E) = 4

∴ P(not divisible by 3) = 4/6
= 2/3
১,৩৯৯.
If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is
  1. ক
    4/8
  2. খ
    2/8
  3. গ
    1/8
  4. ঘ
    3/8
ব্যাখ্যা
Question: If three unbiased coins are tossed simultaneously, then the probability of exactly two heads is

Solution: 
n(S) = 23 = 8 
Let E = Event of getting exactly two heads,
= {(H, H, T), (H, T, H), (T, H, H)}
= n(E)
= 3
Required probability = 3/8
১,৪০০.
A sum of money is distributed equally among 15 persons, but if 5 more persons were included, each person would get Tk. 50 less. What was the total sum?
  1. ক
    Tk. 4000
  2. খ
    Tk. 3000
  3. গ
    Tk. 3500
  4. ঘ
    Tk. 5000
  5. ঙ
    None
ব্যাখ্যা

Question: A sum of money is distributed equally among 15 persons, but if 5 more persons were included, each person would get Tk. 50 less. What was the total sum?

Solution:
Let the total sum be Tk. x.

When the sum is distributed among 15 persons, each person gets x/15.
If 5 more persons are included, making it 20 persons, each person would get x/20.

According to the question,
(x/15) - (x/20) = 50

⇒ (4x - 3x)/60 = 50
⇒ x/60 = 50
⇒ x = 50 × 60
⇒ x = 3000

∴ The total sum of money is Tk. 3000.