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Bank Math

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

Bank Math

PrepBank · পাতা ৪৭ / ১৬১ · ৪,৬০১–৪,৭০০ / ১৬,১২৪

৪,৬০১.
tan15° + tan75° + tan105° + tan165° = ?
  1. ক
    6
  2. খ
    0
  3. গ
    13
  4. ঘ
    1
ব্যাখ্যা
Question: tan15° + tan75° + tan105° + tan165° = ?

Solution:
tan15° + tan75° + tan105° + tan165°
= tan15° + tan(90° - 15°) + tan(90° + 15°) + tan(2 × 90° - 15°)
= tan15° + cot15° - cot15° - tan15°
= 0
৪,৬০২.
Himel is two years older than rasel, who is twice as old as rajib. If the total of the ages of himel, rasel, and rajib is 72, how old is himel?
  1. ক
    38 years
  2. খ
    28 years
  3. গ
    30 years
  4. ঘ
    32 years
ব্যাখ্যা
প্রশ্ন: Himel is two years older than rasel, who is twice as old as rajib. If the total of the ages of himel, rasel, and rajib is 72, how old is himel?
 
সমাধান:
Let,
Rajib's age be = a years
Then, rasel's age = 2a years
Himel's age = (2a + 2) years
 
ATQ,
(2a + 2) + 2a + a = 72
⇒ 5a = 70
∴ a = 14
Hence, himel's age = (2 × 14) + 2 = 30 years.
৪,৬০৩.
a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?
  1. ক
    12
  2. খ
    10
  3. গ
    8
  4. ঘ
    6
  5. ঙ
    None of the above
ব্যাখ্যা
Question: a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?

Solution:
Let,
a = 2x
b = 3x
c = 4x

So,
2a - 3b + 4c = 4x - 9x + 16x = 33
⇒ 11x = 33
⇒ x = 3

∴ c = 4x = 4 × 3 = 12
৪,৬০৪.
If log(p/q) + log(q/p) = log(p + q), then-
  1. ক
    ক) p + q = 0
  2. খ
    খ) p - q = 1
  3. গ
    গ) p = q
  4. ঘ
    ঘ) p + q = 1
ব্যাখ্যা
Question: If log(p/q) + log(q/p) = log(p + q), then-

Solution: 
log(p/q) + log(q/p) = log(p + q)
⇒ log {(p/q) × (q/p)} = log(p + q)
⇒ log1 = log(p + q)
∴ p + q = 1
৪,৬০৫.
In a right triangle, the length of one of the legs is 3 and the length of the hypotenuse is 5. What is the perimeter of the triangle?
  1. ক
    10
  2. খ
    12
  3. গ
    14
  4. ঘ
    16
ব্যাখ্যা
Question: In a right triangle, the length of one of the legs is 3 and the length of the hypotenuse is 5. What is the perimeter of the triangle?

Solution:
সমকোণী ত্রিভুজের অতিভুজ = 5
সমকোণ সংলগ্ন এক বাহু = 3
সমকোণ সংলগ্ন অপর বাহু = a

প্রশ্নমতে
a2 + 32 = 52
⇒ a2 + 9 = 25
⇒ a2 = 25 - 9
⇒ a2 = 16
⇒ a2 = 42
∴ a = 4


∴ ত্রিভুজটির পরিসীমা = (3 + 4 + 5) = 12
৪,৬০৬.
What is the value of (2√3 - cot 30°) = ?
  1. ক
    0
  2. খ
    3√3
  3. গ
    √3
  4. ঘ
    3
ব্যাখ্যা
Question: What is the value of (2√3 - cot 30°) = ?

Solution:
Given that,
= (2√3 - cot 30°)
= (2√3 - √3)
= √3
৪,৬০৭.
Which of the following is a multiple of all three integers 2, 3 and 5?
  1. ক
    ক) 525
  2. খ
    খ) 660
  3. গ
    গ) 615
  4. ঘ
    ঘ) 620
  5. ঙ
    ঙ) None of the above
ব্যাখ্যা

Find LCM of 2, 3 and 5 is 30. So now divide all options.
Option that will have remainder 0 is the answer.

৪,৬০৮.
If X ∈ N and 31 < x < 37, and x is a prime number, then which of the following represents the list form of the set of such numbers?
  1. ক
    { }
  2. খ
    0
  3. গ
    {32, 33, 35}
  4. ঘ
    {31, 37}
  5. ঙ
    {33, 35, 37}
ব্যাখ্যা

Question: If X ∈ N and 31 < x < 37, and x is a prime number, then which of the following represents the list form of the set of such numbers?

Solution:
The natural numbers between 31 and 37 are:
32, 33, 34, 35, 36

Now, check which of these are prime:
32: divisible by 2 → not prime
33: divisible by 3 and 11 → not prime
34: divisible by 2 → not prime
35: divisible by 5 and 7 → not prime
36: divisible by 2, 3, etc. → not prime

So, there are no prime numbers between 31 and 37.

Therefore, the correct answer is the empty set: { }

৪,৬০৯.
A water bottle was brought for Tk. 75 and sold it again for 8%. What was its selling price in Tk.?
  1. ক
    Tk. 83
  2. খ
    Tk. 79
  3. গ
    Tk. 80
  4. ঘ
    Tk. 81
ব্যাখ্যা
Question: A water bottle was brought for Tk. 75 and sold it again for 8%. What was its selling price in Tk.?

Solution:
দেওয়া আছে, 
ক্রয়মূল্য = ৭৫ টাকা
৮% লাভে, বিক্রয়মূল্য = ১০০ + ৮ = ১০৮ টাকা

ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য = ১০৮ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য = ১০৮/১০০ টাকা
∴ ক্রয়মূল্য ৭৫ টাকা হলে বিক্রয়মূল্য = (১০৮ × ৭৫)/১০০ টাকা
= ৮১ টাকা
৪,৬১০.
There is an 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Tk. 14,000 after 3 years at the same rate?
  1. ক
    ক) Tk. 3794
  2. খ
    খ) Tk. 4612
  3. গ
    গ) Tk. 4634
  4. ঘ
    ঘ) Tk. 3714
ব্যাখ্যা
80% increase in 8 years at simple interest. That is 10% each year.
Therefore,
Rate of interest is 10%
10% (14000) = 1400
10% (1400) = 140
10% (140) = 14
Required compound interest = 3(1400 + 140) + 14
= Tk. 4634.
৪,৬১১.
If x - 2 = √3 then what is the value of x4 + (1/x)4?
  1. ক
    204
  2. খ
    198
  3. গ
    194
  4. ঘ
    144
ব্যাখ্যা
Question: If x - 2 = √3 then what is the value of x4 + (1/x)4?

Solution:
Given,
x - 2 = √3
⇒ x = 2 + √3

∴ (1/x) = 2 - √3

∴ x + (1/x) = 2 + √3 + 2 - √3 = 4

∴ x2 + (1/x2) = {x + (1/x)}2 - 2 . x . (1/x)
= (4)2 - 2
= 16 - 2
= 14

∴ x4 + (1/x)4 = {x2 + (1/x2)}2 - 2. x2. (1/x2)
= (14)2 - 2
= 196 - 2
= 194
৪,৬১২.
Out of 7 consonants and 4 vowels, how many 5-letter words can be formed using 3 consonants and 2 vowels, such that the word always starts with a vowel?
  1. ক
    11550
  2. খ
    10890
  3. গ
    10250
  4. ঘ
    10080
  5. ঙ
    None
ব্যাখ্যা
Question: Out of 7 consonants and 4 vowels, how many 5-letter words can be formed using 3 consonants and 2 vowels, such that the word always starts with a vowel?

Solution: 
Here,
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 × 4C2)
= 35 × 6
= 210

Number of groups, each having 3 consonants and 2 vowels = 210

We must arrange them into a 5-letter word starting with a vowel.
From the 2 vowels in each group, choose 1 to be in the first position = 2 ways

Remaining 4 letters can be arranged in 4! = 24 ways

Required number of ways = (210 × 2 × 24) = 10080
৪,৬১৩.
Today is Sunday. After 61 days, it will be -
  1. ক
    Friday
  2. খ
    Saturday
  3. গ
    Sunday
  4. ঘ
    Wednesday
ব্যাখ্যা
Question: Today is Sunday. After 61 days, it will be -

Solution: 
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Sunday.
∴ After 61 days, it will be Friday.
৪,৬১৪.
The diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. The curved surface area is:
  1. ক
    ক) 150 sq. cm
  2. খ
    খ) 165 sq. cm
  3. গ
    গ) 177 sq. cm
  4. ঘ
    ঘ) 10 sq.cm
ব্যাখ্যা

Given that.
Diameter of a right circular cone = 10.5 cm
Radius of a right circular cone = 10.5/2 = 5.25 cm
and slant height of a right circular cone (l) = 10 cm

∴ Lateral surface area of a cone = πrl
= 22/7 × 5.25 × 10
= 165 cm2

৪,৬১৫.
If the length of the face diagonal of a cube is 7√2 meters, what is the volume of the cube?
  1. ক
    256 m3
  2. খ
    343 m3
  3. গ
    294 m3
  4. ঘ
    392 m3
ব্যাখ্যা

Question: If the length of the face diagonal of a cube is 7√2 meters, what is the volume of the cube?

Solution:
Given that, 
The length of the face diagonal of the cube is 7√2 meters.

Let the edge length of the cube be a meters.
∴ The face diagonal of the cube = a√2 meters

According to the given condition:
a√2 = 7√2
∴ a = 7
Therefore, the volume of the cube = a3 = 73 = 343 cubic meters

∴ The volume of the cube is 343 m3.

৪,৬১৬.
If in a certain language PRIVATE is coded 1234567 and RISK is coded as 2398. How is KITE coded in the language?
  1. ক
    8567
  2. খ
    8367
  3. গ
    5678
  4. ঘ
    8357
ব্যাখ্যা
Question: If in a certain language PRIVATE is coded 1234567 and RISK is coded as 2398. How is KITE coded in the language?

Solution:
PRIVATE is coded 1234567
P = 1
R = 2
I = 3
V = 4
A = 5
T = 6
E = 7 
RISK is coded as 2398
R = 2
I = 3
S = 9
K = 8 

∴ KITE = 8367
৪,৬১৭.
If x =ya, y = zb and z = xc then what is the value of abc?
  1. ক
    1
  2. খ
    2
  3. গ
    0
  4. ঘ
    1/2
ব্যাখ্যা
Question: If x =ya, y = zb and z = xc then what is the value of abc?

Solution:
Given,
x =ya, y = zb and z = xc

Now,
xc = z
⇒ (ya)c = z
⇒ yac = z [ (am)n = am × n]
⇒ (zb)ac = z
⇒ zabc = z1
⇒ abc = 1
৪,৬১৮.
If the land of the isosceles triangle is 16cm and the other two sides are 10cm each, what is the area of the triangle?
  1. ক
    ক) 44 sq cm
  2. খ
    খ) 48 sq cm
  3. গ
    গ) 49 sq cm
  4. ঘ
    ঘ) 42 sq cm
ব্যাখ্যা
The area of the triangle
= (16/4)√(4 × 102 - 162)
= 4√(400 - 256)
= 4 × √144
= 4 × 12
= 48 sq cm
৪,৬১৯.
66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters will be-
  1. ক
    80 m
  2. খ
    84 m
  3. গ
    88 m
  4. ঘ
    92 m
ব্যাখ্যা
Question: 66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters will be-

Solution: 
ব্যাসার্ধ r = 1 mm/2 = 0.5 mm = 0.5/10 cm = 0.05 cm
তারের দৈর্ঘ্য h 

π r2h = 66
⇒ π (0.05)2 h = 66
⇒ h = 66/π (0.05)2 
= 8400 cm
= 8400/100 m
= 84 m
৪,৬২০.
If α, β are the roots of the equation x2 - 11x + 28 = 0 then αβ equals to:
  1. ক
    21
  2. খ
    28
  3. গ
    35
  4. ঘ
    49
ব্যাখ্যা

Question: If α, β are the roots of the equation x2 - 11x + 28 = 0, then αβ equals:

Solution:
x2 - 11x + 28 = 0
⇒ x2 - 7x - 4x + 28 = 0
⇒ x(x - 7) - 4(x - 7) = 0
⇒ (x - 7)(x - 4) = 0
⇒ x = 7, 4

Hence, α = 7, β = 4

Hence, The value of αβ = 7 × 4 = 28

∴ αβ = 28

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 = 28/1 = 28

৪,৬২১.
A television show was attended by 12 well known celebrities. Each one of them shook hands with each other once at the beginning of the show. Find the number of handshakes that took place on the show.
  1. ক
    ক) 24
  2. খ
    খ) 66
  3. গ
    গ) 120
  4. ঘ
    ঘ) 132
ব্যাখ্যা

There are 12 celebrities. A handshake needs 2 people.
This simply means in how many ways 2 people can be selected out of 12.

So the answer is 12C2

nCr = n!/r!(n - r)!

∴ 12C2 = 12!/2!(12 - 2)! = (12 × 11)/2
= 66 = number of handshakes. [If there are n people and they shake hands only once with each other, then, Number of handshakes = nc2 = n(n -1)/2]

৪,৬২২.
Tk 20 is the true discount on Tk 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
  1. ক
    ক) Tk. 10
  2. খ
    খ) Tk. 10.40
  3. গ
    গ) Tk. 15.20
  4. ঘ
    ঘ) Tk. 13
ব্যাখ্যা

Simple Interest on Tk. (260 - 20) for a given time = Tk. 20
Simple Interest on Tk. 240 for half the time = Tk. 10
True Discount On Tk. 250 = Tk. 10.
∴ True Discount On Tk. 260 = Tk. {(10/250) × 260}
= Tk. 10.40

৪,৬২৩.
The length of each side of square A is increased by 100 percent to make square B. Then each side of square B is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?
  1. ক
    40% 
  2. খ
    60% 
  3. গ
    80% 
  4. ঘ
    120% 
ব্যাখ্যা
Question: The length of each side of square A is increased by 100 percent to make square B. Then each side of square B is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?

Solution: 
let, length of square A is x m
area of A = x2 cm2

length of square B is x + x cm = 2x cm 
area of B = (2x)2 = 4x2 cm2 

length of square C = 2x + 2x × 0.5 = 3x
area of C = (3x)2
= 9x2 cm2 

 sum of the areas of square A and B = x2 + 4x2 = 5x2 

 percent increase of area of C = (9x2 - 5x2) × 100%/5x2 
= 80% 
৪,৬২৪.
A clothing store offers a dress initially at Tk. 1000. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?
  1. ক
    600
  2. খ
    680
  3. গ
    660
  4. ঘ
    690
ব্যাখ্যা
Question: A clothing store offers a dress initially at Tk. 1000. Then one week later, the store offers the dress at 15% off. The dress still doesn't sell, so after another week, the store reduces its new price by 20%. How much does the dress cost now?

Solution:
For the first discount,
we have 1000(1 - 0.15) = 1000(0.85) = 850
So the dress is worth Tk. 850

After the second discount,
we have 850(1 - 0.20) = 850(0.8) = 680

So the final dress price is Tk. 680
৪,৬২৫.
'Retard' is to 'Impel' as 'Obfuscate' is to -
  1. ক
    Hallucinate
  2. খ
    Confuse
  3. গ
    Irradiate
  4. ঘ
    Dampen
ব্যাখ্যা
Retard অর্থ ⇒ দমন করা; প্রতিহত করা; হ্রাস করা
Impel অর্থ ⇒ বাধ্য/প্রণোদিত/প্ররোচিত/প্রবত্ত/প্রবর্তিত করা
সুতরাং বিপরীত অর্থে ব্যবহৃত হয়েছে।

Obfuscate অর্থ ⇒ আচ্ছন্ন করা; বিভ্রান্ত বা হতবুদ্ধি করা।

Hallucinate অর্থ ⇒ যা চোখের সামনে নেই তা দেখা; কল্পিত বস্তু দেখা।
Confuse অর্থ ⇒  গুলিয়ে ফেলা; বিশৃঙ্খল করা; বিভ্রান্ত বা কিংকর্তব্যবিমূঢ় হওয়া বা করা।
Irradiate অর্থ ⇒  কিছুর উপর রশ্মিপাত/কিরণবর্ষণ করা;  সূর্যকিরণ, অতিবেগুনি রশ্মি বা তেজনিস্ক্রয়তার অধীন করা; কোনো বিষয়ের উপর আলোকপাত করা; দীপিত করা; উদ্ভাসিত করা।
Dampen অর্থ ⇒ নীরস করা

সকল অর্থ থেকে বুঝা যায় Obfuscate এবং Irradiate বিপরীত অর্থবিশিষ্ট।

উৎস: Accessible Dictionary.
৪,৬২৬.
A, B and C each working alone can complete a job in 8, 12 and 16 days respectively. If all three of them work together to complete the job and earn Tk. 3380, what will be C's share of the earnings?
  1. ক
    ক) Tk. 640
  2. খ
    খ) Tk. 780
  3. গ
    গ) Tk. 820
  4. ঘ
    ঘ) Tk. 830
ব্যাখ্যা
Question: A, B and C each working alone can complete a job in 8, 12 and 16 days respectively. If all three of them work together to complete the job and earn Tk. 3380, what will be C's share of the earnings?

Solution: 
A, B এবং C 1 দিনে করতে পারে কাজটির 1/8,1/12, এবং 1/16 অংশ 

A, B এবং C কাজের অনুপাত = 1/8 : 1/12 : 1/16
= (1/8) × 48  : (1/12) × 48 : (1/16) × 48
= 6 : 4 : 3
অনুপাতের রাশিগুলোর যোগফল = 6 + 4 + 3 = 13

C এর অংশ = 3380 এর 3/13 = 780
৪,৬২৭.
What will be the simple interest earned on an amount of Tk. 16,000 in 9 months at the rate of 25/4% p.a. ?
  1. ক
    850 Tk.
  2. খ
    810 Tk.
  3. গ
    790 Tk.
  4. ঘ
    750 Tk.
ব্যাখ্যা
Question: What will be the simple interest earned on an amount of Tk. 16,000 in 9 months at the rate of 25/4% p.a. ?

Solution:
here, 
P = 16000
n = 9/12 years = 3/4
r = 25/4%

we know,
I = Pnr
= 16000 × 3/4 × 25/4%
= 750
৪,৬২৮.
  1. ক
    11
  2. খ
    9
  3. গ
    13
  4. ঘ
    17
ব্যাখ্যা
Question:
 

Solution:
৪,৬২৯.
The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.
  1. ক
    3 : 2
  2. খ
    2 : 3
  3. গ
    1 : 2
  4. ঘ
    3 : 1
ব্যাখ্যা

Question: The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.

Solution: Average age of children = 12 years
Average age of adults = 32 years
Average age of the entire group = 20 years

Let, the number of adults = A
and, the number of children = C

Then, the total number of people in the group is (C + A)

ATQ,
12C + 32A = 20(C + A)
Or, 12C + 32A = 20C + 20A
Or, 32A - 20A = 20C - 12C
Or, 12A = 8C
Or, C : A = 12 : 8
Or, C : A = 3 : 2

∴ The ratio of children to adults in the group is 3 : 2.

৪,৬৩০.
Income of a company doubles after every one year. If the initial income was Tk. 4 lakhs, what would be the income after 5 years?
  1. ক
    Tk. 1.28 crores
  2. খ
    Tk. 1.24 crores
  3. গ
    Tk. 2.52 crores
  4. ঘ
    Tk. 2.56 crores
ব্যাখ্যা
Question: Income of a company doubles after every one year. If the initial income was Tk. 4 lakhs, what would be the income after 5 years?
 
Solution:
Initial income is 4 lakhs.
Income after 1 year = 4 × 2 = 8 lakhs.
Income after 2 years = 8 × 2 = 16 lakhs.
Income after 3 years = 16 × 2 = 32 lakhs.
Income after 4 years = 32 × 2 = 64 lakhs.
Income after 5 years = 64 × 2 = 128 lakhs = 1.28 crores.
৪,৬৩১.
If secθ + tanθ = x, then cotθ is - 
  1. ক
    ক) (x2 - 1)/2x
  2. খ
    খ) 2x/(x2 - 1)
  3. গ
    গ) x/(x2 - 1)
  4. ঘ
    ঘ) 2x/(x2 + 1)
ব্যাখ্যা
Question: If secθ + tanθ = x, then cotθ is - 

Solution:
দেওয়া আছে,
secθ + tanθ = x ................. (1)

আমরা জানি,
sec2θ - tan2θ = 1
বা, (secθ + tanθ)(secθ - tanθ) = 1
বা, x(secθ - tanθ) = 1
বা, secθ - tanθ = 1/x ................ (2)

(1) - (2) হতে পাই,
(secθ + tanθ) - (secθ - tanθ) = x - (1/x)
বা, 2tanθ = (x2 - 1)/x
বা, tanθ = (x2 - 1)/2x
∴ cotθ = 2x/(x2 - 1)
৪,৬৩২.
The average of the first five multiples of 11 is-
  1. ক
    ক) 165
  2. খ
    খ) 87.5
  3. গ
    গ) 66
  4. ঘ
    ঘ) 33
ব্যাখ্যা
Question: The average of the first five multiples of 11 is-

Solution: 
The  first five multiples of 11: (11 × 1), (11 × 2), (11 × 3), (11 × 4), (11 × 5)
their sum = (11 × 1) + (11 × 2) + (11 × 3) + (11 × 4) + (11 × 5)
= 11 (1 + 2 + 3 + 4 + 5)
= 11 × 15

∴ average = (11 × 15)/5
= 33
৪,৬৩৩.
A work can be finished in 16 days by 20 women. The same work can be finished in 15 days by 16 men. The ratio between the efficiency of a man and a woman is -
  1. ক
    4 : 3
  2. খ
    2 : 1
  3. গ
    2 : 3
  4. ঘ
    1 : 3
  5. ঙ
    5 : 4
ব্যাখ্যা

Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16 × 20)

Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15 × 16)
Efficiency of a man : efficiency of a woman
= 1/(15 × 16) : 1/(16 × 20)
= 1/15 : 1/20
= 1/3 : 1/4
= 4 : 3

৪,৬৩৪.
  1. ক
    - 2
  2. খ
    0
  3. গ
    2
  4. ঘ
    4
ব্যাখ্যা
Question:

Solution:
৪,৬৩৫.
If x2b4 = ab- 1, what is a in terms of b and x ?
  1. ক
    x2b3
  2. খ
    x2b- 3
  3. গ
    x2b5
  4. ঘ
    x2b- 5
  5. ঙ
    x2b6
ব্যাখ্যা

Question: If x2b4 = ab- 1, what is a in terms of b and x ?

Solution:
x2b4 = ab- 1
⇒ a/b = x2b4 
⇒ a = x2b4.b
⇒ a = x2b4 + 1
⇒ a = x2b5

৪,৬৩৬.
A train 240m long passed a pole in 24 seconds. How long will it take to pass a platform 650m long?
  1. ক
    ক) 65s
  2. খ
    খ) 89s
  3. গ
    গ) 100s
  4. ঘ
    ঘ) 130s
ব্যাখ্যা
প্রশ্ন: A train 240m long passed a pole in 24 seconds. How long will it take to pass a platform 650m long?

সমাধান:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার 

ট্রেনটি 240 মিটার অতিক্রম করতে সময় নেয় = 24 সেকেন্ড 
ট্রেনটি1 মিটার অতিক্রম করতে সময় নেয় = 24/240 সেকেন্ড 
ট্রেনটি 890 মিটার অতিক্রম করতে সময় নেয় = (24 × 890)/240 সেকেন্ড 
                                                                      = 89 সেকেন্ড
৪,৬৩৭.
Solve the inequality 2 ≤ - 4 - 3x < 17
  1. ক
    - 7 > x ≥ - 2
  2. খ
    - 7 < x ≤ 2
  3. গ
    7 < x ≤ - 2
  4. ঘ
    - 7 < x ≤ - 2
ব্যাখ্যা

Question: Solve the inequality 2 ≤ - 4 - 3x < 17

Solution:
2 ≤ - 4 - 3x < 17
⇒ 2 + 4 ≤ - 4 - 3x + 4 < 17 + 4
⇒ 6 ≤ - 3x < 21
⇒ - 6 ≥ 3x > - 21
⇒ - 6/3 ≥ 3x/3 > - 21/3
⇒ - 2 ≥ x > - 7
∴ - 7 < x ≤ - 2

৪,৬৩৮.
The value of (x - y)3 + (x + y)3 + 6x(x2 - y2)
  1. ক
    ক) 4x3
  2. খ
    খ) 8x3
  3. গ
    গ) 6x3
  4. ঘ
    ঘ) 9x3
ব্যাখ্যা
Question: The value of (x - y)3 + (x + y)3 + 6x(x2 - y2)

Solution: 
(x - y)3 + (x + y)3 + 6x(x2 - y2)
= (x - y)3 + (x + y)3 + 3.2x(x - y)(x + y)
Let
a = x - y
b = x + y
a + b = x - y + x + y = 2x

Given expression 
= (x - y)3 + (x + y)3 + 3.2x(x - y)(x + y)
= a3 +b3 + 3(a + b)ab
= a3 + b3 + 3ab(a + b)
= (a + b)3
= (2x)3
= 8x3
৪,৬৩৯.
Two persons Choton and Billal started a business in which Choton invested Tk. 50000, Billal invested Tk. 80000, after 4 months Robiul joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Robiul's share in the profit was Tk. 15000, then find Robiul's investment in the business.
  1. ক
    Tk. 113000
  2. খ
    Tk. 117000
  3. গ
    Tk. 120000
  4. ঘ
    Tk. 121000
ব্যাখ্যা
Question: Two persons Choton and Billal started a business in which Choton invested Tk. 50000, Billal invested Tk. 80000, after 4 months Robiul joined them with a certain amount. At the end of the year, a total profit of Tk. 40000 was recorded. Robiul's share in the profit was Tk. 15000, then find Robiul's investment in the business.

Solution:
Let,
Robiul's investment in the business be Tk. 1000x
Profit ratio of Choton, Billal and Robiul = (50000 × 12) : (80000 × 12) : {1000x × (12 - 4)}
= 75 : 120 : x

Total profit = 75 + 120 + x = 195 + x

Robiul's share in profit = x
ATQ,
(195 + x)/x = 40000/15000
⇒ (195 + x)/x = 8/3
⇒ 3(195 + x) = 8x
⇒ 585 + 3x = 8x
⇒ 5x = 585
⇒ x = 117

Investment by Robiul = 1000 × 117 = Tk. 117000
৪,৬৪০.
A family has two kids, and at least one is a boy. Find the probability that both children are boys.
  1. ক
    1/2
  2. খ
    1/4
  3. গ
    2/3
  4. ঘ
    1/3
ব্যাখ্যা
Question: A family has two kids, and at least one is a boy. Find the probability that both children are boys.

Solution:
Let B represent a boy and G a girl.

For 2 children, the total possible combinations are 4:
GG (both girls)
GB (girl then boy)
BG (boy then girl)
BB (both boys)

If at least one child is a boy, we exclude GG.
So, the valid outcomes are: GB, BG, BB — a total of 3 outcomes.

Out of these, only BB has both children as boys.

So, the probability that both kids are boys given that at least one is a boy = 1/3.
৪,৬৪১.
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
  1. ক
    10 liters
  2. খ
    20 liters
  3. গ
    30 liters
  4. ঘ
    40 liters
ব্যাখ্যা
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

Solution:
Number of liters of water in 150 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters

Let us Assume that another 'P' liters of water are added to the mixture to make water 25% of the new mixture.
So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P)
Thus, (30 + P) = 25% of (150 + P)
⇒ (30 + P) = (1/4)(150 + P)
⇒ 120 + 4P = 150 + P
⇒ 3P = 30
∴ P = 10 liters
৪,৬৪২.
The percentage profit earned by selling an article for TK 1730 is equal to the percentage loss incurred by selling the same article for TK 1270. At what price should the article be sold to make 20% profit?
  1. ক
    1800 TK
  2. খ
    2000 TK
  3. গ
    2400 TK
  4. ঘ
    2800 TK
  5. ঙ
    3000 TK
ব্যাখ্যা

Question: The percentage profit earned by selling an article for TK 1730 is equal to the percentage loss incurred by selling the same article for TK 1270. At what price should the article be sold to make 20% profit?

Solution:
Let C.P. = x TK
Profit = (1730 - x) TK
Loss = (x - 1270) TK

ATQ,
{(1730 - x)/x}100 = {(x - 1270)/x}100
⇒ 1730 - x = x - 1270
⇒ 2x = 3000
⇒ x = 1500

Required selling price for 20% profit = (1500 × 120%) TK
= 1500 × (120/100)
= 1500 × (6/5)
= 1800 TK

৪,৬৪৩.
From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 200 m high, the distance of point P from the foot of the tower is:
  1. ক
    298 meters
  2. খ
    312 meters
  3. গ
    346 meters
  4. ঘ
    450 meters
ব্যাখ্যা
tan30° = height/base
1/√3 = 200/base
or, base = 200√3 = 346m(approx.)
Therefore, the distance of point P from the foot of the tower = 346m
৪,৬৪৪.
A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
  1. ক
    ক) 16 km
  2. খ
    খ) 14 km
  3. গ
    গ) 12 km
  4. ঘ
    ঘ) 10 km
ব্যাখ্যা

Let the time in which he traveled on foot = x hour
Time for travelling on bicycle = (9-x) hr
Distance = Speed×Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4x4 = 16 km

৪,৬৪৫.
Adnan can do 1/5 of a work in 8 days. In how many days will he complete the work? 
  1. ক
    20 days
  2. খ
    30 days
  3. গ
    40 days
  4. ঘ
    15 days
  5. ঙ
    25 days
ব্যাখ্যা

Question: Adnan can do 1/5 of a work in 8 days. In how many days will he complete the work?

Solution:
Adnan can do 1/5 of a work in 8 days.
∴ He will complete the work in = 8 × 5 = 40 days

∴ Adnan will complete the work in 40 days.

৪,৬৪৬.
Observe the following diagram and answer the question. Find the number of students who play any two of the three sports.
  1. ক
    9
  2. খ
    5
  3. গ
    11
  4. ঘ
    13
  5. ঙ
    None of the above
ব্যাখ্যা
Question: Observe the following diagram and answer the question. Find the number of students who play any two of the three sports.

Solution:
The shaded part represents the students who play any two of the three sports which is shown below:

Hence, the students who play any two of the three sports are 6 + 5 = 11.
৪,৬৪৭.
What is the weight of 1 cubic meter of water?
  1. ক
    ক) 10kg
  2. খ
    খ) 100kg
  3. গ
    গ) 500kg
  4. ঘ
    ঘ) 1000kg
ব্যাখ্যা
A cubic meter is 1000 liters
1 liter of water weight 1 kg
so, 1 cubic meter of water weight 1000 kg
৪,৬৪৮.
Sumon bought 2 varieties of rice, costing taka 8 per kg and taka 12 per kg each, and mixed them in some ratio, then he sold the mixture at taka 12 Per kg. Making a profit of 20%. what was the ratio of the mixture?
  1. ক
    ক) 2 : 1
  2. খ
    খ) 1 : 2
  3. গ
    গ) 1 : 1
  4. ঘ
    ঘ) 3 : 1
  5. ঙ
    ঙ) None
ব্যাখ্যা

Let, the rice of two verities be in amount x and y
ATQ, 
(8x + 12y)120/100 = 12(x + y)
⇒ 8x + 12y = (12×100)/120(x + y) = 10x + 10y
⇒ 2x = 2y
∴ x : y = 1 : 1

৪,৬৪৯.
A ladder 17 feet long leans against a wall. The base is 8 feet from the wall. How high up the wall does the ladder reach?
  1. ক
    23 feet
  2. খ
    18 feet
  3. গ
    12 feet
  4. ঘ
    15 feet
ব্যাখ্যা
Question: A ladder 17 feet long leans against a wall. The base is 8 feet from the wall. How high up the wall does the ladder reach?

Solution:
Length of the ladder (hypotenuse) = 17 feet
Distance from base of ladder to the wall (one leg) = 8 feet

Using the Pythagorean theorem,
(Base)2 + (Height)2 = (Hypotenuse)2
⇒ 82 + h2 = 172
⇒ 64 + h2 = 289
⇒ h2 = 289 - 64
⇒ h2 = 225
⇒ h = √225 = 15
∴ h = 15

So the ladder reaches 15 feet up the wall.
৪,৬৫০.
The surface area of a cube is 96 square units. What is the length of the longest stick that can be placed inside the cube?
  1. ক
    8
  2. খ
    4√3
  3. গ
    4√2
  4. ঘ
    6√2
ব্যাখ্যা

Question: The surface area of a cube is 96 square units. What is the length of the longest stick that can be placed inside the cube?

Solution: 
Given that, 
Surface area of a cube = 96 square units

We know, 
Surface area of a cube, S = 6a2
⇒ 6a2 = 96
⇒ a2 = 96/6
⇒ a2 = 16 = 42
∴ a = 4

The longest stick that can fit inside the cube runs along the space diagonal.
So the space diagonal of a cube, d = a√3
= 4√3  ; [a = 4]

So the length of the longest stick that can be placed inside the cube is 4√3 units. 

৪,৬৫১.
A boat takes 10 hours to cover a distance while traveling upstream, whereas while travelling downstream it takes 9 hours. If the speed of the current is 4 kmph, what is the speed of the boat in still water?
  1. ক
    ক) 74 kmph
  2. খ
    খ) 76 kmph
  3. গ
    গ) 78 kmph
  4. ঘ
    ঘ) 79 kmph
ব্যাখ্যা
Let the speed of the boat in still water be x kmph
Then, Speed downstream = (x+4) kmph.
Speed upstream = (x-4) kmph.
∴ (x+4)× 9 = (x-4)×10
⇒ 9x+36 = 10x-40 ⇒ x = 76 ⇒ x = 76 kmph.
৪,৬৫২.
Novera bought a ticket to a cricket match for Tk. 25 and later sold the ticket to Nahid for Tk 75. What was the percent increase in the price of the ticket?
  1. ক
    ক) 50%
  2. খ
    খ) 100%
  3. গ
    গ) 200%
  4. ঘ
    ঘ) 300%
ব্যাখ্যা
প্রশ্ন: Novera bought a ticket to a cricket match for Tk. 25 and later sold the ticket to Nahid for Tk 75. What was the percent increase in the price of the ticket?

সমাধান: 
নভেরা একটি টিকিট ২৫ টাকায় কিনে। সে  ৭৫ টাকায় টিকিটটি নাহিদের কাছে বিক্রি করে। 

টিকিটের মূল্য শতকরা বৃদ্ধি পায় = (৭৫ - ২৫)/২৫ × ১০০%
= (৫০/২৫) × ১০০%
= ২০০% 
৪,৬৫৩.
A train travelling at the speed of x km/h crossed a 300 m long platform in 30 seconds, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?
  1. ক
    96 km/h
  2. খ
    112 km/h
  3. গ
    144 km/h
  4. ঘ
    210 km/h
  5. ঙ
    228 km/h
ব্যাখ্যা

Question: A train travelling at the speed of x km/h crossed a 300 m long platform in 30 seconds, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?

Solution: 
Train speed = x km/h
Length of train = L
Length of platform = 300m
Man's speed = 6 km/h

∴ (x - 6) × (5/18) = L/20
⇒ (5x - 30)/18 = L/20
⇒ 100x - 600 =18L . . . . . . (i)

And, x × (5/18) = (L+ 300)/30
⇒ 150x = 18L + 5400
⇒ v150x - 5400 = 18L . . . . . . (ii)

From equations (i) & (ii)
⇒ 100x - 600 = 150x - 5400
⇒ 50x = 4800
∴ x = 96 

৪,৬৫৪.
A hall, 20m long and 15m broad, is surrounded by a verandah of uniform width of 3.5m. The cost of flooring the verandah at Tk.2.50 per square meter is-
  1. ক
    ক) Tk. 600
  2. খ
    খ) Tk. 594
  3. গ
    গ) Tk. 735
  4. ঘ
    ঘ) Tk. 800
ব্যাখ্যা
বারান্দাসহ হল ঘরের দৈর্ঘ্য = {20 + (2 × 3.5)} মিটার 
                                         = 27 মিটার 

বারান্দাসহ হল ঘরের প্রস্থ = {15 + (2 × 3.5)} মিটার 
                                    = (15 + 7) মিটার 
                                      = 22 মিটার 
বারান্দাসহ হল ঘরের ক্ষেত্রফল = (27 × 22) বর্গমিটার 
                                               = 594 বর্গমিটার 


বারান্দাবাদে হল ঘরের ক্ষেত্রফল = (20 × 15) বর্গমিটার 
                                                 = 300 বর্গমিটার 
বারান্দার ক্ষেত্রফল = (594- 300) বর্গমিটার 
                             = 294 বর্গমিটার
মোট খরচ =(294 × 2.50) টাকা 
                  = 735 টাকা
৪,৬৫৫.

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
  1. ক
    |x| ≤ 5
  2. খ
    |x - 2| ≤ 3
  3. গ
    |x - 1| ≤ 4
  4. ঘ
    |x + 1| ≤ 4
  5. ঙ
    None of these
ব্যাখ্যা
Question:

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

Solution:
From the number line it follows that - 5 ≤x ≤ 3
(A) |x| ≤ 5 ⇒ - 5 ≤ x ≤ 5. Discard.

(B) |x - 2| ≤ 3 ⇒ - 3 ≤ x - 2 ≤ 3 ⇒ add 2 to all parts: - 1 ≤ x ≤ 5. Discard.

(C) |x - 1| ≤ 4 ⇒ - 4 ≤ x - 1≤ 4 ⇒ add 1 to all parts: - 3 ≤ x ≤ 5. Discard.

(D) |x +1| ≤ 4 ⇒ - 4 ≤ x + 1 ≤ 4 ⇒ subtract 1 from all parts: - 5 ≤ x ≤ 3. OK.
৪,৬৫৬.
An inline pipe takes half the time to fill a tank than an outline pipe. When both the pipes are opened, they take 9 hours to fill a tank. The outline pipe can empty the tank in -
  1. ক
    ক) 4.5 hours
  2. খ
    খ) 9 hours
  3. গ
    গ) 18 hours
  4. ঘ
    ঘ) 15 hours
ব্যাখ্যা
Question: An inline pipe takes half the time to fill a tank than an outline pipe. When both the pipes are opened, they take 9 hours to fill a tank. The outline pipe can empty the tank in - 

Solution: 
let, the inline pipe takes X hours to fill the tank.
so, the outline pipe takes 2X hours to empty it.

in one hour, 
inline pipe fills = 1/X 
outline pipe pumps out = 1/2X

total fill up = 1/X - 1/2X
= 1/2X

ATQ,
2X = 9
X = 4.5 hours

so, the outline pipe can empty the tank in = 2 × 4.5 = 9 hours
৪,৬৫৭.
L.C.M of two prime numbers x and y (x > y) is 161.The value of 3y - x is:
  1. ক
    ক) -2
  2. খ
    খ) -1
  3. গ
    গ) 1
  4. ঘ
    ঘ) 2
ব্যাখ্যা

H.C.F of two prime numbers is 1.
Product of numbers = (1 × 161) = 161.
Let the numbers be a and b.
Then, ab = 161.
Now, co - primes with product 161 are (1, 161) and (7, 23).
Since x and y are prime numbers and x > y, we have x = 23 and y = 7
∴ 3y -x = (3 × 7) - 23 = -2
Answer is : -2

৪,৬৫৮.
The sum of four consecutive even integers is 76. What is the product of the middle two numbers?
  1. ক
    360
  2. খ
    280
  3. গ
    320
  4. ঘ
    210
ব্যাখ্যা
Question: The sum of four consecutive even integers is 76. What is the product of the middle two numbers?

Solution:
Let the four consecutive even integers are n, n + 2, n + 4, and n + 6. Their sum is 76.

ATQ,
⇒ n + (n + 2) + (n + 4) + (n + 6) = 76
⇒ 4n + 12 = 76
⇒ 4n = 76 - 12
⇒ 4n = 64
⇒ n = 64/4
∴ n = 16

The numbers are 16, 18, 20, and 22. The middle two numbers are 18 and 20. Their product is = 18 × 20 = 360
৪,৬৫৯.
Find the side of a square whose area is equal to the area of a rectangle with sides 10 m. and 6.4m .
  1. ক
    ক) 4 m.
  2. খ
    খ) 6 m.
  3. গ
    গ) 8 m.
  4. ঘ
    ঘ) 10 m.
ব্যাখ্যা
Given that 
Length of a rectangle = 10 m 
Breadth of a rectangle = 6.4 m 
Area of a rectangle = 6.4 × 10 = 64m2
According to the question 
Area of square = Area of rectangle 
Suppose the side of square be x m. 
64 = (x)2
(8)2=(x)2 

Thus, the side is 8 m.
৪,৬৬০.
50 persons can do a work in 12 day's by working 8 hours a day. Working how many hours per day can 60 persons finish the work in 16 days?
  1. ক
    ক) 8 hours
  2. খ
    খ) 6 hours
  3. গ
    গ) 5 hours
  4. ঘ
    ঘ) 4 hours
ব্যাখ্যা
50 persons can do a work in 12 day's by working 8 hours a day
1 person can do a work in 1 day's by working 8 × 50 × 12 hours a day
60 persons can do a work in 16 day's by working (8 × 50 × 12)/(60 × 12) hours a day = 5 hours a day
৪,৬৬১.
  1. ক
    12
  2. খ
    9/4
  3. গ
    15
  4. ঘ
    8
ব্যাখ্যা

Question:

Solution:

৪,৬৬২.
কোনটি ত্রিভুজের ক্ষেত্রফল?
  1. ক
    (1/2) × ভূমি × উচ্চতা
  2. খ
    ভূমি × উচ্চতা
  3. গ
    লম্ব × ভূমি
  4. ঘ
    (1/2) × লম্ব × উচ্চতা
ব্যাখ্যা

প্রশ্ন: কোনটি ত্রিভুজের ক্ষেত্রফল?

সমাধান:
• ত্রিভুজের ক্ষেত্রফল = (1/2) × ভূমি × উচ্চতা

• সামন্তরিকের ক্ষেত্রফল = ভূমি × উচ্চতা

৪,৬৬৩.
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is-
  1. ক
    9
  2. খ
    11
  3. গ
    13
  4. ঘ
    15
ব্যাখ্যা
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is-

Solution:
Let the three odd integers be x, x + 2 and x + 4.
Then,
3x = 2(x + 4) + 3
⇒ 3x = 2x + 8 + 3
∴ x = 11.

∴ Third integer = x + 4 = 11 + 4 = 15.
৪,৬৬৪.
If a + b + c = 5 and a2 + b2 + c2 = 35, find the value of a3 + b3 + c3 - 3abc.
  1. ক
    255
  2. খ
    200
  3. গ
    352
  4. ঘ
    220
ব্যাখ্যা

Question: If a + b + c = 5 and a2 + b2 + c2 = 35, find the value of a3 + b3 + c3 - 3abc.

Solution:
Given, a + b + c = 5 and a2 + b2 + c2 = 35

We know,
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
⇒ (5)2 = 35 + 2(ab + bc + ca)
⇒ 25 = 35 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 25 - 35 
⇒ 2(ab + bc + ca) = - 10
∴ ab + bc + ca = - 5

Now,
a3 + b3 + c3 - 3abc
= (a + b + c){a2 + b2 + c2 - (ab + bc + ca)}
= 5 × {35 - (- 5)}
= 5 × 40
= 200

Therefore, the value is 200.

৪,৬৬৫.
Three runners P, Q and R run a race, with runner P finishing 15 metres ahead of runner Q and 24 metres ahead of runner R, in another race of same type runner Q finished 10 metres ahead of runner R. Each runner travels the entire distance at a constant speed. The length of the race is?
  1. ক
    140 metres
  2. খ
    150 metres
  3. গ
    160 metres
  4. ঘ
    180 metres
ব্যাখ্যা
Question: Three runners P, Q and R run a race, with runner P finishing 15 metres ahead of runner Q and 24 metres ahead of runner R, in another race of same type runner Q finished 10 metres ahead of runner R. Each runner travels the entire distance at a constant speed. The length of the race is?

Solution:
Let P finish the race of = x metres
Q finish the race of = (x - 15) meters.
R finish the race of = (x - 24) ............. (1)

In another race of Q & R
Q finish race of = x meters.
R finish race of = (x - 10) .............. (2)

Ratio of speeds of Q & R,
(x - 15)/(x - 24) = x/(x - 10)
⇒ (x - 15)(x - 10) = x(x - 24)
⇒ x2 - 15x - 10x + 150 = x2 - 24x
⇒ x2 - 25x + 150 = x2 - 24x
⇒ 150 = x
∴ x = 150 metres
৪,৬৬৬.
If x + (1/x) = 3, then x - (1/x) = ?
  1. ক
    √3
  2. খ
    3
  3. গ
    √5
  4. ঘ
    2
ব্যাখ্যা

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

solution: 
Given,
x + (1/x) = 3

We know,
{x - (1/x)}2 = {x + (1/x)}2 - 4 . x . 1/x
⇒ {x - (1/x)}2 =  32 - 4
⇒ {x - (1/x)}2 = 9 - 4
⇒ {x - (1/x)}2 = 5
∴ x - (1/x) = √5

৪,৬৬৭.
A bucket is 2/7 full. If 18 liters of water are added, it becomes exactly full. What is the capacity of the bucket?
  1. ক
    32 liters
  2. খ
    25.2 liters
  3. গ
    18.5 liters
  4. ঘ
    27 liters
ব্যাখ্যা

Question: A bucket is 2/7 full. If 18 liters of water are added, it becomes exactly full. What is the capacity of the bucket?

Solution:
Let the capacity of the bucket 'x' liters.
Initially the bucket has (2/7) of x = 2x/7 liters of water
After adding 18 liters then the bucket becomes full. 

So we can form the equation,
(2x/7) + 18 = x
⇒ x - (2x/7) = 18 
⇒ (7x - 2x)/7 = 18
⇒ 5x/7 = 18
⇒ x = (18 × 7)/5
⇒ x = 126/5
∴ x = 25.2 liters

So the capacity of the bucket is 25.2 liters.

৪,৬৬৮.
Halim purchased brand A pen for Taka 200 each and brand B pen for Taka 100 each. If he purchased a total of 8 of these pens for Taka 1,200 how many pens of brand A did he purchased?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 5
  4. ঘ
    ঘ) 6
ব্যাখ্যা

ধরি, A brand এর কলম সংখ্যা x টি
B brand এর কলম সংখ্যা (8 - x) টি
ATQ,
200x + (8 - x)×100 = 1200
⇒ 200x + 800 - 100x = 1200
⇒ 100x = 1200 - 800
⇒ x = 400/100
⇒ x = 4

৪,৬৬৯.
How many positive integers less than 500 can be formed using the number 1, 2, 3 and 5 for the digit?
  1. ক
    ক) 48
  2. খ
    খ) 24
  3. গ
    গ) 60
  4. ঘ
    ঘ) 68
ব্যাখ্যা
১ম ক্ষেত্রেঃ
3 অংক বিশিষ্ট 500 থেকে ছোট সংখ্যার ক্ষেত্রে যার প্রথমে 5 কে বসানো যাবে না। 500 এর থেকে ছোট 3 অংক বিশিষ্ট সংখ্যার প্রথম ঘরে 5 ভিন্ন বাকি 3 টি সংখ্যার যেকোনোটি নিতে পারি। আবার ২য় ও ৩য় ঘরে 1, 2, 3,5 এই 4টি অংকের যে কোনটিই নেওয়া যায়।
এক্ষেত্রে  3× 4 × 4 = 48 উপায়ে

২য় ক্ষেত্রেঃ
2 অংক বিশিষ্ট 500 থেকে ছোট সংখ্যার ক্ষেত্রে 1, 2, 3, 5 এর যেকোনো ২টি অংক নিয়েই 500 থেকে ছোট সংখ্যা গঠন করা যাবে।
= 4 × 4 = 16 উপায়ে

৩য় ক্ষেত্রেঃ 1 অংক বিশিষ্ট 500 থেকে ছোট সংখ্যার ক্ষেত্রে 1, 2, 3, 5 এই 4টি অংকের যে কোনটি নিয়েই 500 থেকে ছোট। অংকবিশিষ্ট সংখ্যা গঠন করা যায়।
= 4 উপায়ে

1, 2, 3, 5 এই 4টি অংক নিয়ে 500 থেকে ছোট মোট সংখ্যা গঠন করা যাবে 48 + 16 + 4 = 68 উপায়ে।
৪,৬৭০.
A train 150 metres long is travelling at 72 km/h. How much time will it take to completely cross a railway platform that is 250 metres long?
  1. ক
    18 sec
  2. খ
    22 sec
  3. গ
    16.5 sec
  4. ঘ
    20 sec
ব্যাখ্যা

Question: A train 150 metres long is travelling at 72 km/h. How much time will it take to completely cross a railway platform that is 250 metres long?

Solution:
Here,
Speed of the running train = 72 km/hr
= {72 × (5/18)} m/sec
= 20 m/sec

And length of the train is = 150 metres
Length of platform = 250 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (150 + 250)/30
= 400/20 
= 20 sec

৪,৬৭১.
If ÷ means ×, × means +, + means - and - means +, find the value of 16 × 3 + 5 - 2 ÷ 4.
  1. ক
    7
  2. খ
    12
  3. গ
    16
  4. ঘ
    22
ব্যাখ্যা
Question: If ÷ means ×, × means +, + means - and - means +, find the value of 16 × 3 + 5 - 2 ÷ 4.

Solution: 
16 × 3 + 5 - 2 ÷ 4
=16 + 3 - 5 + 2 × 4
= 27 - 5
= 22
৪,৬৭২.
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
  1. ক
    3 km/hr
  2. খ
    4 km/hr
  3. গ
    5 km/hr
  4. ঘ
    8 km/hr
ব্যাখ্যা
Question: A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Solution: 
Let
The speed of the stream is x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.

Now,
{30/(15 + x)} + {30/(15 - x)} = 9/2
⇒ 30(15 - x) + 30(15 + x)/(15 + x)(15 - x) = 9/2
⇒ (450 - 30x + 450 + 30x)/(225 - x2) = 9/2
⇒ 900/(225 - x2) = 9/2
⇒ 100/(225 - x2) = 1/2
⇒ 200 = 225 - x2
⇒ x2 = 225 - 200
⇒ x2 = 25 
⇒ x2 = 52 
⇒ x = 5

the speed of the stream is 5 km/hr.
৪,৬৭৩.
3/4th of square were taken to form shape A and the rest was made to form shape B. Shape A was divided into four equal squares (Shape C), what will be the ratio of the one shape C to one shape B.
  1. ক
    ক) 1 : 4
  2. খ
    খ) 3 : 16
  3. গ
    গ) 1 : 2
  4. ঘ
    ঘ) 3 : 4
ব্যাখ্যা

Let, A = 3x/4
and, B = x/4
So, C = (3x/4) / 4 = 3x/16
∴ C:B = 3x/16 : x/4 = 3:4

৪,৬৭৪.
The sum of the interior angles of a regular polygon is 1260°. How many sides does the polygon have? 
  1. ক
    10 sides
  2. খ
    8 sides
  3. গ
    9 sides
  4. ঘ
    6 sides
ব্যাখ্যা

Question: The sum of the interior angles of a regular polygon is 1260°. How many sides does the polygon have?

Solution:
We know, the sum of the interior angles of a polygon = (n - 2) × 180°

Given,
(n - 2) × 180 = 1260
⇒ n - 2 = 1260/180
⇒ n - 2 = 7
⇒ n = 7 + 2
n = 9

∴ The polygon has 9 sides.

৪,৬৭৫.
75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?
  1. ক
    45
  2. খ
    47
  3. গ
    49
  4. ঘ
    50
  5. ঙ
    51
ব্যাখ্যা
Remaining work = 1 - (1/3) = 2/3
Let number of more employees needed be E
Thus (75+E) employees complete 2/3 works in 50 hours.
∴ 75 employes × 40 hours × (2/3) = (75 + E) × 50 hours × (1/3)
∴ E = 45 = these many more employees are needed.
৪,৬৭৬.
Jim is a car salesman who gets a base monthly salary and a commission for each car he sells. Jim's monthly earnings are given by the function f(x) = c(4+ x), where x represents the number of cars he sold for the month. If Jim sells 6 cars in a month he earns $2,000. How much is Jim's base salary ?
  1. ক
    ক) $500
  2. খ
    খ) $600
  3. গ
    গ) $700
  4. ঘ
    ঘ) $800
ব্যাখ্যা
Question: Jim is a car salesman who gets a base monthly salary and a commission for each car he sells. Jim's monthly earnings are given by the function f(x) = c(4 + x), where x represents the number of cars he sold for the month. If Jim sells 6 cars in a month he earns $2,000. How much is Jim's base salary ?

Solution: 
দেয়া আছে,
f(x) = c(4 + x)
f(6) = c(4 + 6)
c× 10 = 2000
c = 2000/10
  = 200

x = 0 হলে তখন আমরা মূল বেতন বের করতে পারবো 
f(0) = c(4 + 0)
       = c × 4
        = $200 × 4
        = $800
৪,৬৭৭.
A car wheel rotates 12 times per minute. How many degrees does the wheel rotate in 5 seconds? 
  1. ক
    720°
  2. খ
    360°
  3. গ
    90°
  4. ঘ
    180°
ব্যাখ্যা

Question: A car wheel rotates 12 times per minute. How many degrees does the wheel rotate in 5 seconds?

Solution:
We know that  
1 minute = 60 seconds  

The wheel rotates 12 times in 60 seconds.  
∴ In 1 second the wheel rotates 12/60 = 1/5 of a full rotation.  
∴ In 5 seconds the wheel rotates 12 × (5/60) = 60/60 = 1 full rotation.

∴ A full rotation = 360°

Therefore, the wheel rotates 360° in 5 seconds.

৪,৬৭৮.
In a race, Amir finished ahead of Sara but behind Rehan. Sara finished ahead of Nabil but behind Ali. Nabil finished ahead of Zain and Ail finished behind Amir. Who came first in the race?
  1. ক
    Ali
  2. খ
    Amir
  3. গ
    Rehan
  4. ঘ
    Sara
  5. ঙ
    Nabil
ব্যাখ্যা
Question: In a race, Amir finished ahead of Sara but behind Rehan. Sara finished ahead of Nabil but behind Ali. Nabil finished ahead of Zain and Ail finished behind Amir. Who came first in the race?

Solution:
Amir finished ahead of Sara but behind Rehan
⇒ Rehan > Amir > Sara

Sara finished ahead of Nabil but behind Ali
⇒ Ali > Sara > Nabil

Nabil finished ahead of Zain
⇒ Nabil > Zain
Ail finished behind Amir
⇒ Amir > Ali

Rehan > Amir > Ali > Sara > Nabil > Zain

∴ Rehan came first in the race.
৪,৬৭৯.
The difference between the numerator and the denominator of a fraction is 5. If 5 is added to the denominator the fraction is decreased by 5/4 then the value of the fraction will be equal to:
  1. ক
    13/4
  2. খ
    9/4
  3. গ
    5/3
  4. ঘ
    4/5
ব্যাখ্যা
Question: The difference between the numerator and the denominator of a fraction is 5. If 5 is added to the denominator the fraction is decreased by 5/4 then the value of the fraction will be equal to:

Solution:
ধরি,
ভগ্নাংশটির হর = x
ভগ্নাংশটির লব = x + 5

∴ ভগ্নাংশটি = (x + 5)/x

প্রশ্নমতে,
{(x + 5)/x} - {(x + 5)/(x + 5)} = 5/4
⇒ {(x + 5)/x} - 1 = 5/4
⇒ {(x + 5)/x} = (5/4) + 1
∴ {(x + 5)/x} = 9/4

∴ ভগ্নাংশটি = 9/4
৪,৬৮০.
What is the sum of the series:
112 + 122 + 132 + ........ + 202
  1. ক
    2465
  2. খ
    2845
  3. গ
    2485
  4. ঘ
    2495
ব্যাখ্যা
Question: What is the sum of the series:
112 + 122 + 132 + ........ + 202

Solution: 
112 + 122 + 132 + ........ + 202
= (12 + 22 + 32 + .... + 202) - (12 + 22 + 32 + .... + 102)
= [{20(20 + 1)(2 × 20 + 1}/6] - [{10(10 + 1)(2 × 10 + 1)}/6]
= {(20 × 21 × 41)/6} - {(10 × 11 × 21)/6}
= 2870 - 385
= 2485
৪,৬৮১.
Rajib is walking on a foggy road at a speed of x km/hr. Due to low visibility, he sees only up to 600 meters. If a car overtakes him from behind with the speed of 15 km/hr then he can see the car for 216 seconds. Find the speed of Rajib.
  1. ক
    4 km/hr 
  2. খ
    5 km/hr 
  3. গ
    6 km/hr 
  4. ঘ
    8 km/hr 
ব্যাখ্যা
Question: Rajib is walking on a foggy road at a speed of x km/hr. Due to low visibility, he sees only up to 600 meters. If a car overtakes him from behind with the speed of 15 km/hr then he can see the car for 216 seconds. Find the speed of Rajib.

Solution: 
216 seconds = 216/60 min 
= 3.6 min 
= 3.6/60  hr
=0.06 hr

ATQ,
(15 × 0.06) - 0.06x = 600/1000
⇒ 0.06x = 0.9 - 0.6
⇒ 0.06x = 0.3
⇒ x = 0.3/0.06 = 5 km/hr
৪,৬৮২.
A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is
  1. ক
    4.5 km/hr
  2. খ
    5.5 km/hr
  3. গ
    4 km/hr
  4. ঘ
    6.5 km/hr
  5. ঙ
    None of these
ব্যাখ্যা
Question: A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is

Solution:
Speed of upstream = 24/6 = 4 km/hr.
Speed of downstream = 35/7 = 5km/hr.

∴ Speed of man in still water = (4 + 5)/2 = 4.5 km/hr.
৪,৬৮৩.
Karim can do a job in 15 minutes and his brother takes twice as long to do the same job. If they work together, how long it takes to complete the job?
  1. ক
    5
  2. খ
    7.5
  3. গ
    10
  4. ঘ
    12.5
ব্যাখ্যা
Question: Karim can do a job in 15 minutes and his brother takes twice as long to do the same job. If they work together, how long it takes to complete the job?

Solution: 
করিমের সময় লাগে ১৫ মিনিট 
তার ভাইয়ের সময় লাগে ৩০ মিনিট 

১ মিনিটে তারা কাজ সম্পন্ন করে = (১/১৫) + (১/৩০)
= (২ + ১)/৩০ 
= ৩/৩০ 
= ১/১০ অংশ 

∴ সম্পূর্ণ কাজ করতে সময় লাগে = ১০ মিনিট 
৪,৬৮৪.
Rahim purchased items worth Tk. 40, including a sales tax of 60 paisa on taxable purchases. If the tax rate was 8%, what was the cost of the tax-free items?
  1. ক
    Tk. 29.3
  2. খ
    Tk. 31.9
  3. গ
    Tk. 29.1
  4. ঘ
    Tk. 33.1
ব্যাখ্যা
Question: Rahim purchased items worth Tk. 40, including a sales tax of 60 paisa on taxable purchases. If the tax rate was 8%, what was the cost of the tax-free items?

Solution:
Let the cost of taxable purchases be x taka.

According to the question,
0.08x = 60/100
⇒ x = 60/(100 × 0.08)
= 7.5 taka

∴ The cost of the tax-free items was = 40 - 7.5 - 0.6
= Tk. 31.9
৪,৬৮৫.
The area of a rectangle that has length = 2a2b and breadth = 3ab2 is:
  1. ক
    6a3b3
  2. খ
    a3b3
  3. গ
    2a3b3
  4. ঘ
    4a3b3
ব্যাখ্যা
Question: The area of a rectangle that has length = 2a2b and breadth = 3ab2 is:

Solution:
দেওয়া আছে,
আয়তক্ষেত্রের দৈর্ঘ্য = 2a2b
এবং আয়তক্ষেত্রের প্রস্থ = 3ab2
আয়তক্ষেত্রের ক্ষেত্রফল = দৈর্ঘ্য × প্রস্থ
= 2a2b × 3ab2
= 6a3b3
৪,৬৮৬.
The simple interest received on a sum of money at the end of 10 years is two times of the principal. At the same rate of interest, what would be the ratio of principal and compound interest received at the end of two years?
  1. ক
    ক) 25 : 11
  2. খ
    খ) 20 : 11
  3. গ
    গ) 20 : 9
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Let, Principal = x and interest 2x
ATQ, 2x = (x × 10 × r)/100
Or, r = 20%
Again, Let, Principal = 100
So, C = 100(1 + 20/100)2
         = 100(1 + 1/5)2 = 144
∴ Interest = 144 – 100 = 44
∴ Required ratio = 100 : 44 = 25 : 11

৪,৬৮৭.
A tower 17.5 m high casts a shadow of 40.25 m. What is the height of the building which casts a shadow 28.75 m long under similar conditions?
  1. ক
    10 m
  2. খ
    12.5 m
  3. গ
    17.2 m
  4. ঘ
    21.25 m
ব্যাখ্যা
Question: A tower 17.5 m high casts a shadow of 40.25 m. What is the height of the building which casts a shadow 28.75 m long under similar conditions?

Solution:
Let the height of the building is x
Now, the shadow ratio = building ratio
Height is directly proportional to shadow, so:
40.25 : 28.75 = 17.5 : x
Now, x = (28.75 × 17.5)/ 40.25 = 12.5 m
৪,৬৮৮.
If, 4 × nP3 = 3 × (n + 1)P3, what is the value of n?
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 14
ব্যাখ্যা
Question: If, 4 × nP3 = 3 × (n + 1)P3, what is the value of n?

Solution:
4n!/(n - 3)! = 3(n +1)!/(n + 1 - 3)!
⇒ 4 n(n - 1)(n - 2)(n - 3)!/(n - 3)! = 3 (n + 1) n (n - 1) (n - 2)!/(n - 2)!
⇒ 4 n(n - 1)(n - 2) =  3 (n + 1) n (n - 1)
⇒ 4 (n - 2) = 3 (n + 1)
⇒ 4n - 8 = 3n + 3
⇒ 4n - 3n = 3 + 8
∴ n = 11
৪,৬৮৯.
If x2 - 45x + 324 = 0, then what is the values of x?
  1. ক
    36, 9
  2. খ
    35, 9
  3. গ
    - 36, 9
  4. ঘ
    - 36, - 9
ব্যাখ্যা
Question: If x2 - 45x + 324 = 0, then what is the values of x?

Solution:
x2 - 45x + 324 = 0
⇒ x2- 36x - 9x + 324 = 0
⇒ x(x - 36) - 9(x - 36) = 0
⇒ (x - 36)(x - 9) = 0
Either x - 36 = 0 or x - 9 = 0
∴ x = 36, 9
৪,৬৯০.
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk. 1140, the total profit is:
  1. ক
    ক) Tk. 1000
  2. খ
    খ) Tk. 1200
  3. গ
    গ) Tk. 1440
  4. ঘ
    ঘ) Tk. 2000
ব্যাখ্যা
Let total profit be Tk. 100
After paying 5% to charity, A's share = 95 × 3/5 = 57
Total profit = 100/57 × 1140 = 2000
৪,৬৯১.
The perimeter of a circle measures 16π cm. What is the area of the circle in sq. cm?
  1. ক
    128π
  2. খ
    64π
  3. গ
    32
  4. ঘ
    256π
ব্যাখ্যা

Question: The perimeter of a circle measures 16π cm. What is the area of the circle in sq. cm?

Solution:
ধরি, বৃত্তের ব্যাসার্ধ = r
বৃত্তের পরিধি = 2πr
বৃত্তের ক্ষেত্রফল = πr2

প্রশ্ন অনুসারে,
2πr = 16π
⇒ 2r = 16
⇒ r = 8

বৃত্তের ক্ষেত্রফল = πr2
= π × (8)2
= 64π

৪,৬৯২.
If 5(3a - 7) = 20, then what is the value of (3a - 8)?
  1. ক
    11/3
  2. খ
    14
  3. গ
    0
  4. ঘ
    3
  5. ঙ
    None
ব্যাখ্যা
প্রশ্ন: If 5(3a - 7) = 20, then what is the value of (3a - 8)?

সমাধান:
5(3a - 7) = 20
⇒ 3a - 7 = 4
⇒ 3a - 7 - 1 = 4  - 1 [উভয় পক্ষ থেকে 1 বিয়োগ করে]
∴ 3a - 8 = 3
৪,৬৯৩.
100 taka is doubled in 5 years when compounded annually. How many more years will it take to get another 200 taka compound interest-
  1. ক
    ক) 3 years
  2. খ
    খ) 5 years
  3. গ
    গ) 10 years
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Question: 100 taka is doubled in 5 years when compounded annually. How many more years will it take to get another 200 taka compound interest-

Solution:
100 taka invested in compound interest becomes 200 taka in 5 years.
The amount will double again in another 5 years.

i.e., the amount will become 400 taka in another 5 years.
So, to earn another 200 taka interest, it will take another 5 years.
৪,৬৯৪.
What is the geometric average of 4 and 16?
  1. ক
    ক) 8
  2. খ
    খ) 10
  3. গ
    গ) 12
  4. ঘ
    ঘ) 14
ব্যাখ্যা
Queston: What is the geometric average of 4 and 16? 

Solution: 
geometric average of 4 and 16 = √(4 × 16)
= √64
= 8
৪,৬৯৫.
The average of 8 numbers is 28. If 4 more numbers , with an average 24 are added to the numbers, what will be the average of the combined 12 numbers?
  1. ক
    18
  2. খ
    24.5
  3. গ
    28.75
  4. ঘ
    26.67
ব্যাখ্যা
Question: The average of 8 numbers is 28. If 4 more numbers , with an average 24 are added to the numbers, what will be the average of the combined 12 numbers?

Solution:
Sum of the first 8 numbers is,
Total sum = Average × Number 
= 28 × 8 = 224
And the sum of the next 4 numbers is,
= 24 × 4 = 96
∴ The total sum of all 12 numbers is,
224 + 96 = 320

∴ New Average = Total Sum/Total Numbers​
= 320/12
= 26.67
৪,৬৯৬.
Calculate the surface area of a cylinder with radius 6 cm and height 15 cm.
  1. ক
    252π square cm
  2. খ
    792π square cm
  3. গ
    540π square cm
  4. ঘ
    None of these
ব্যাখ্যা
Question: Calculate the surface area of a cylinder with radius 6 cm and height 15 cm.

Solution:
Here,
radius r = 6 cm
height h = 15 cm
Surface Area = (2πrh + 2πr2)
Surface Area = 2 × π × 6 × 15 + 2 × π × 62 = 252π square cm
৪,৬৯৭.
If x = √3 + √2, then find the value of x3 - (1/x)3 = ?
  1. ক
    18√2
  2. খ
    36
  3. গ
    22√2
  4. ঘ
    54
  5. ঙ
    36√3
ব্যাখ্যা

Question: If x = √3 + √2, then find the value of x3 - (1/x)3 = ?

Solution:
দেওয়া আছে, x = √3 + √2
সুতরাং, 1/x = 1/(√3 + √2)
= (√3 - √2)/{(√3 + √2)(√3 - √2)}
= (√3 - √2)/{(√3)2 - (√2)2}
= (√3 - √2)/(3 - 2)
= √3 - √2

অতএব, x - (1/x) = (√3 + √2) - (√3 - √2)
= √3 + √2 - √3 + √2
= 2√2

আমরা জানি,
x3 - (1/x)3 = {x - (1/x)}3 + 3 . x . 1/x . {x - (1/x)}
= (2√2)3 + 3(2√2)
= (8 × 2√2) + 6√2
= 16√2 + 6√2
= 22√2

∴ নির্ণেয় মান হলো 22√2

৪,৬৯৮.
Nazir walks 10 km towards the north. From there, he walks 6 km towards the south. Then he walks 3 km towards the east. How far and in which direction is he with reference to his starting point?
  1. ক
    ক) 5 km, West
  2. খ
    খ) 5 km, North-East
  3. গ
    গ) 7 km, East
  4. ঘ
    ঘ) 7 km, South-East
ব্যাখ্যা
Question: Nazir walks 10 km towards the north. From there, he walks 6 km towards the south. Then he walks 3 km towards the east. How far and in which direction is he with reference to his starting point?

Solution

From the figure, we get OC which is the required distance,

OC = √(OB2 + BC2)
OC = √(42 + 32)
OC = 5 km (North-East)
৪,৬৯৯.
P, Q, R, S, T and U were sitting around a circular table, facing the centre. They were sitting at equal distances from one another. T and R were sitting exactly next to each other. P was at the immediate right of U. Q was at the immediate left of T. R is third to the left of S. Who is sitting to the immediate left of Q?
  1. ক
    P
  2. খ
    S
  3. গ
    Q
  4. ঘ
    T
ব্যাখ্যা
Question: P, Q, R, S, T and U were sitting around a circular table, facing the centre. They were sitting at equal distances from one another. T and R were sitting exactly next to each other. P was at the immediate right of U. Q was at the immediate left of T. R is third to the left of S. Who is sitting to the immediate left of Q?

Solution:

- Q was at the immediate left of T.
- T and R were sitting exactly next to each other.
- R is third to the left of S.
- P was at the immediate right of U.
- S is sitting to the immediate left of Q.

Hence, the correct answer is S.
৪,৭০০.
The difference between simple and compound interest(compounded annually) on a certain sum of money for 2 years at 4% per annum is Tk. 1.What is the sum?
  1. ক
    ক) Tk. 645
  2. খ
    খ) Tk. 625
  3. গ
    গ) Tk. 500
  4. ঘ
    ঘ) Tk. 645
ব্যাখ্যা

P(4/100)2 =1
⇒ P(1/25)2 = 1
⇒ P/252 = 1
⇒ P = 625
Hence The sum is Tk. 625.