Bank Math

PrepBank · পাতা ১০৫ / ১৬১ · ১০,৪০১–১০,৫০০ / ১৬,১২৪

১০,৪০১.

Find the value of x, when x³ - x = 0

ক
0, 1, 2
খ
0, 1, - 1
গ
0, 1, - 2
ঘ
1, 2, - 3

ব্যাখ্যা

Question: Find the value of x, when x³ - x = 0

Solution:
Given,
x³ - x = 0
⇒ x(x² - 1) = 0
⇒ x(x + 1)(x - 1) = 0
∴ x = 0, 1, - 1

১০,৪০২.

The factors of x² - 7x + 12 are :

ক
(x + 3) and (x - 4)
খ
(x - 3) and (x + 4)
গ
(x - 3) and (x - 4)
ঘ
(x + 3) and (x + 4)

ব্যাখ্যা

x² - 7x + 12
= x² - 3x - 4x + 12
= x(x - 3) - 4(x - 3)
= (x - 3)(x - 4)
The factors of x² - 7x + 12 are (x - 3) and (x - 4)

১০,৪০৩.

A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the whole work alone?

ক
ক) 60 days
খ
খ) 70 days
গ
গ) 80 days
ঘ
ঘ) 90 days

ব্যাখ্যা

Let A's 1 day's work = x and B's 1 day's work = y
Then, x+y = 1/40 and 20x+60y = 1
Solving these two equations, we get, x = 1/80 and y = 1/80
Therefore B's 1 day work = 1/80
Hence, B alone shall finish the whole work in 80 days

১০,৪০৪.

An amount of Tk.10000 becomes Tk.14641 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest p. c. p. a?

ক
ক) 10%
খ
খ) 15%
গ
গ) 18%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: An amount of Tk. 10000 becomes Tk. 14641 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest p. c. p. a?

Solution:
Let
the rate be r% p. a

Now
10000 × {1 + r/(2 × 100)}^{2 ×2} = 14641
{1 + r/(2 × 100)}⁴ = 14641/10000
(1 + r/200)⁴ = (11/10)⁴
1 +r/200 = 11/10
r/200 = (11/10) - 1
r/200 = (11 - 10)/10
r/200 = 1/10
r = 200/10
r = 20

The rate be 20% p. a

১০,৪০৫.

In how many different ways can the letters of the word TOTAL be arranged?

ক
45
খ
60
গ
72
ঘ
120

ব্যাখ্যা

Question: In how many different ways can the letters of the word TOTAL be arranged?

Solution:
Number of letter in word = 5
Repeated letter T = 2, and rest of the letters are unique.

∴ The number of arrangement = 5!/2! = 120/2 = 60

১০,৪০৬.

ক
1/1000
খ
1/50
গ
100
ঘ
1/10
ঙ
None of these

ব্যাখ্যা

Question:

Solution:

১০,৪০৭.

If the average of 'p' numbers is 3q² and the average of 'q' numbers is 3p², what is the average of the combined (p + q) numbers?

ক
3pq
খ
6pq
গ
3(p² + q²)
ঘ
3p²q²

ব্যাখ্যা

Question: If the average of 'p' numbers is 3q² and the average of 'q' numbers is 3p², what is the average of the combined (p + q) numbers?

Solution:
দেওয়া আছে, 'p' সংখ্যার গড় = 3q²
∴ p সংখ্যার সমষ্টি = p × 3q²

'q' সংখ্যার গড় = 3p²
∴ 'q' সংখ্যার সমষ্টি = q × 3p²

∴ মোট সমষ্টি = (p × 3q²) + (q × 3p²)
= 3pq² + 3p²q
= 3pq(q + p)

∴ তাদের গড় = মোট সমষ্টি / (p + q)
= 3pq(p + q) / (p + q)
= 3pq

১০,৪০৮.

In the diagram, ABCD is a rectangle with AP = PQ = QB. What is the ratio of the areas of ΔCPQ and that of the rectangle?

ক
1 : 3
খ
5 : 6
গ
1 : 9
ঘ
1 : 6

ব্যাখ্যা

Question: In the diagram, ABCD is a rectangle with AP = PQ = QB. What is the ratio of the areas of ΔCPQ and that of the rectangle?

Solution:
let, length of rectangle is AB = x m and breadth BC = y m
area = xy m²

AP = PQ = BQ = x/3

area of ΔCPQ = (1/2) × (PQ) × BC
= (1/2) × (x/3) × y
= xy/6

ratio = (xy/6) : xy
= 1 : 6

১০,৪০৯.

The LCM of the two numbers is 360, and their HCF is 24. If one of the numbers is 120, find the other number.

ক
48
খ
72
গ
144
ঘ
36
ঙ
None of these

ব্যাখ্যা

Question: The LCM of the two numbers is 360, and their HCF is 24. If one of the numbers is 120, find the other number.

Solution:
We know that the product of the HCF and LCM of two numbers is equal to the product of the two numbers.
Let the number be a and b.

So, for two numbers a = 120 and b with HCF = 24 and LCM = 360:

HCF × LCM = a × b
⇒ 24 × 360 = 120 × b
⇒ (24 × 360)/120 = b
⇒ 24 × 3 = b
∴ b = 72.

১০,৪১০.

Himu can complete a piece of work in 30 days and Nazmul in 40 days. Find the remaining work left to complete, if they work together for 8 days -

ক
2/5
খ
1/12
গ
8/15
ঘ
4/19

ব্যাখ্যা

Himu's 1 day work = 1/30
Nazmul's 1 day work = 1/40
Then, (Himu + Nazmul)'s 1 day work = 1/30 + 1/40
= 7/120
And (Himu + Nazmul)'s 8 day's work = 8 x (7/120)
= 7/15
Therefore, Remaining work = (1 - 7/15)
= 8/15.

১০,৪১১.

The compound interest on Tk. 2500 for 2 years at 10% p. a is-

ক
ক) Tk. 395.5
খ
খ) Tk. 375.5
গ
গ) Tk. 378.5
ঘ
ঘ) Tk. 525.0

ব্যাখ্যা

Given,
Principal, P = Tk. 2500
Compound rate , R = 10%
Time n = 2 years

Compound Principal = [2500(1 + 10/100)²]
= [2500(1.1)²]
=3025

∴C.I. = Tk.(3025 - 2500)=Tk. 525

১০,৪১২.

If the sum of 15, 6, 14 and 15 is equal to the sum of 1, 17, x and x + 2, what is the value of x?

ক
ক) 10
খ
খ) 15
গ
গ) 18
ঘ
ঘ) 26

ব্যাখ্যা

The sum of 15, 6, 14 and 15 = 15 + 6 + 14 + 15 = 50
The sum of 1, 17, x and x + 2 = 1 + 17 + x + x + 2 = 20 + 2x
Therefore, 20 + 2x = 50
⇒ 2x = 50 - 20 = 30
⇒ x = 15

১০,৪১৩.

If X ∈ N and 17 < x < 23, and x is a prime number, then which of the following represents the list form of the set of such numbers?

ক
{18, 20, 21}
খ
{ }
গ
{19}
ঘ
{18, 19, 23}

ব্যাখ্যা

Question: If X ∈ N and 17 < x < 23, and x is a prime number, then which of the following represents the list form of the set of such numbers?

Solution:
দেয়া আছে:
X ∈ N and 17 < x < 23

List all natural numbers between 17 and 23
⇒ 18, 19, 20, 21, 22

∴ Identify the prime numbers among them
⇒ 18 → divisible by 2; not prime.
⇒ 19 → prime.
⇒ 20 → divisible by 2; not prime.
⇒ 21 → divisible by 3 and 7; not prime.
⇒ 22 → divisible by 2; not prime.

∴ List of prime numbers in this range
{19}.

১০,৪১৪.

A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

ক
8 Taka per kg
খ
10 Taka per kg
গ
12 Taka per kg
ঘ
6 Taka per kg

ব্যাখ্যা

Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for 240 Taka. What is the original price per kg of sugar?

Solution:
Reduction in the price of 20% amount of sugar will increase by 25%
It means, 25% = 6 Kg.

So, initially, total Sugar = 6 × 4 = 24 kg.

Thus, the original price of the sugar was = 240/24
= 10 Taka per kg.

১০,৪১৫.

In a set, there are 17 consecutive integers with a maximum value of 8. What is the average of the set?

ক
ক) -2
খ
খ) 0
গ
গ) 2
ঘ
ঘ) 5
ঙ
ঙ) None

ব্যাখ্যা

Let's go backward from 8 to the 17th digit: 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8
The average is = {8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 + (-1) + (-2) + (-3) + (-4) + (-5) + (-6) + (-7) + (-8)} / 17
= 0/17 = 0

১০,৪১৬.

A speed of 14 meters per second is the same as -

ক
ক) 50 km/hr
খ
খ) 46.6 km/hr
গ
গ) 28 km/hr
ঘ
ঘ) 70 km/hr

ব্যাখ্যা

Question: A speed of 14 meters per second is the same as

Solution:
1 second speed = 14 meters.
1 hour or 3600 seconds speed = (14 × 3600) meters
= 50400 meters
= 50400/100 km/hr.
= 50.4 km/hr.
≈ 50 km/hr.

[আসন্ন মান হিসেবে অপশন (ক) অধিকগ্রহণযোগ্য]

১০,৪১৭.

The values of p for equation 2x² - 4x + p = 0 to have real roots is:

ক
ক) P ≤ -2
খ
খ) P ≥ 2
গ
গ) P ≤ 2
ঘ
ঘ) P ≥ -7

ব্যাখ্যা

এখানে, 2x² - 4x + p = 0 সমীকরণকে ax^2 + bx + c = 0 সমীকরণের সাথে তুলনা করলে বাস্তব মূলের জন্য b² - 4ac ≥ 0 হবে
∴ (-4)² - 4(2)(p) ≥ 0
⇒ 16 - 8p ≥ 0
⇒ 16 ≥ 8p
⇒ 8p ≤ 16
∴ p ≤ 2

১০,৪১৮.

The ratio of green marbles to red marbles in a box 3:5. If there are 24 marbles in the box, how many additional green marbles will be required to make the ratio of green marbles to red marbles 1:1?

ক
12
খ
9
গ
6
ঘ
3
ঙ
2

ব্যাখ্যা

Number of green ball = 24 × (3/8) = 9
Number of red ball= 24 × (5/8) = 15
since the required ratio is 1:1
so, additional green ball = (15 - 9) = 6

১০,৪১৯.

If 40% of a number is 120, what is 75% of the number?

ক
220
খ
275
গ
350
ঘ
420
ঙ
225

ব্যাখ্যা

Question: If 40% of a number is 120, what is 75% of the number?

Solution:
Let the number is x
Given that,
⇒ 40% of x =120
⇒ (40/100) × x = 120
⇒ x = (120 × 10)/4
⇒ x = 300

Now, find 75% of x,
75% of x = (75/100) × 300
= 225

১০,৪২০.

In a class, there are 12 boys and 16 girls. One of them is called out by an enrollment number, what is the probability that the one called is a girl?

ক
ক) 1/4
খ
খ) 2/5
গ
গ) 5/12
ঘ
ঘ) 4/7

ব্যাখ্যা

Let S be the sample space.
Total number of students in the class=12 boys + 16 girls = 28
Then, n(S) = 28
Let E be the event of calling one of them by enrollment number.
Given that, the number of girls = 16.
Then, n(E) = 16.
The probability that the one called is a girl = n(S)/n(E) = 16/28 = 4/7.

১০,৪২১.

Raitul walked 25 metres towards South. Then he turned to his left and walked 20 metres. He then turned to his left and walked 25 metres. He again turned to his right and walked 15 metres. At what distance is he from the starting point and in which direction?

ক
35 metres North
খ
35 metres East
গ
40 metres East
ঘ
60 metres East

ব্যাখ্যা

Question: Raitul walked 25 metres towards South. Then he turned to his left and walked 20 metres. He then turned to his left and walked 25 metres. He again turned to his right and walked 15 metres. At what distance is he from the starting point and in which direction?

Solution:

The movements of Raitul are as shown in figure.
Raitul's distance from starting point A to end point E = AE = (AD + DE) = (BC + DE) = (20 + 15) m = 35 m.
Also, E is to the East of A.

১০,৪২২.

What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?

ক
- (1/8)
খ
12
গ
3/4
ঘ
- (1/10)

ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?

Solution:
The general equation of a straight line is
y = mx + c ......(1) (Where, m = slope)

If the slope of a line is m, then the slope of the line perpendicular to it is,
m' = - (1/m)

Now,
20x - 2y = 6
⇒ 2y = 20x - 6
∴ y = 10x - 3
Comparing with equation (1), we get,
∴ m = 10

∴ The slope of the perpendicular line is, m' = - (1/10)

১০,৪২৩.

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

ক
ক) 12 years
খ
খ) 14 years
গ
গ) 10 years
ঘ
ঘ) 8 years

ব্যাখ্যা

Let
C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.

Now
(2x + 2) + 2x + x = 27
5x = 25
x = 5

Hence, B's age = 2x = 10 years

১০,৪২৪.

A starts business with Tk. 3,500 and after 5 months, B joins A with some capital. After a year, if the profit is divided in the ratio 2 : 3. Then B’s contribution in the total capital is -

ক
ক) Tk 8000
খ
খ) Tk 7000
গ
গ) Tk 9000
ঘ
ঘ) Tk 1200

ব্যাখ্যা

Investment of A is Tk. 3,500 for 1 year
B invested for 7 months.
The ratio of profit of A and B = 2 : 3

Let B's capital be Tk. x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x
Then, (3500×12)/7x = 2/3

⇒14x = 126000

⇒x = 9000

১০,৪২৫.

How many revolutions per minute does a 140 cm diameter scooter wheel need to maintain a speed of 132 km/h?

ক
620
খ
575
গ
480
ঘ
720
ঙ
500

ব্যাখ্যা

Question: How many revolutions per minute does a 140 cm diameter scooter wheel need to maintain a speed of 132 km/h?

Solution:
Distance travelled by wheel in one revolution = circumference of wheel
= (22/7) × 140 = 440 cm.

And
Speed of scooter = 132 km/hr = (132 × 1000 × 100)/60 cm/min = 220000 cm/min.

∴ Revolutions per minute = Distance covered per minute/Distance per revolution
= 220000/440 = 500

So the answer is indeed 500 revolutions per minute.

১০,৪২৬.

In a room of 40 people, 22 players play cricket while 30 players play football. How many players play both?

ক
16
খ
12
গ
8
ঘ
10

ব্যাখ্যা

Question: In a room of 40 people, 22 players play cricket while 30 players play football. How many players play both?

Solution:
We know,
Total = n(C) + n(F) - both
⇒ 40 = 22 + 30 - both
⇒ both = 52 - 40
⇒ both = 12

∴ 12 players play both cricket and football.

১০,৪২৭.

Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

ক
Tk. 15
খ
Tk. 20
গ
Tk. 25
ঘ
Tk. 30

ব্যাখ্যা

Question: Find the difference of amount if 40% discount is given on Tk. 1000 and two consecutive discounts 30% and 10% are given on the same amount.

Solution:
40% discount on 1000 = 1000 × 40% = 400

Two consecutive discounts on 1000.
30% discount on 1000 = 30% of 1000
= 300

After 30% discount on 1000 = 1000 - 300
= 700

Again,
After 10% discount on 700 = 10% of 700
= 70

Total discount = 300 + 70
= Tk. 370
So, the difference = 400 - 370
= Tk. 30

১০,৪২৮.

In a school, there are 55% students play Cricket, 50% students play Hockey and 25% students play both games. The difference between the number of students who play both games and the number of students who do not play any games is 40. Find the number of students who play only one game.

ক
490
খ
400
গ
440
ঘ
390

ব্যাখ্যা

Question: In a school, there are 55% students play Cricket, 50% students play Hockey and 25% students play both games. The difference between the number of students who play both games and the number of students who do not play any games is 40. Find the number of students who play only one game.

Solution:
Total number of students in a school be N.
Total number of students who play only Cricket = (55/100 - 25/100)N
= 30N/100

Total number of students who play only Hockey = (50/100 - 25/100)N
= 25N/100

Total number of students who do not play any Game = N - 30N/100 - 25N/100 - 25N/100
= 20N/100

ATQ,
25N/100 - 20N/100 = 40
⇒ 5N/100 = 40
⇒ N = (40 × 100)/5
∴ N = 800

Total number of students who play only one game = 30N/100 + 25N/100
= 55N/100
= (55 × 800)/100
= 440

১০,৪২৯.

Provisions for a camp were planned for 120 men or 200 children. After 150 children have eaten, how many men can still be served?

ক
30
খ
20
গ
40
ঘ
35

ব্যাখ্যা

Question: Provisions for a camp were planned for 120 men or 200 children. After 150 children have eaten, how many men can still be served?

Solution:
Camp has = 200 children
Already have taken meal = 150 children

Remaining children to take meal = 200 - 150 = 50 children

the camp has meal for 200 children = 120 men
the camp has meal for 1 children = 120/200 men
the camp has meal for 50 children = (120 × 50)/200 men
= 30 men

১০,৪৩০.

A computer programmer needs to print 148 documents. The documents have an average (arithmetic mean) length of 10 pages and the printer takes 15 seconds to print each page. Approximately how many hours will it take to print all the documents if they are printed without interruptions?

ক
0.5 hr
খ
2 hr
গ
2.5 hr
ঘ
6 hr

ব্যাখ্যা

Question: A computer programmer needs to print 148 documents. The documents have an average (arithmetic mean) length of 10 pages and the printer takes 15 seconds to print each page. Approximately how many hours will it take to print all the documents if they are printed without interruptions?

Solution:
Number of Documents = 148.
Avg. Number of pages per document = 10.
Total Pages = 148 × 10 = 1480.

Speed of Printer = 15 Seconds Per Page.

1 Page = 15 Seconds.
1480 Pages = 15 × 1480 = 22200 Seconds.
Value in Hours = 22200/(60 × 60) = 6.16 hours ≈ 6 Hours.

১০,৪৩১.

If a/b = 3/4 and b/c = 5/6, then, (b + c)/(a + b) =?

ক
ক) 35/44
খ
খ) 44/35
গ
গ) 11/35
ঘ
ঘ) 35/11

ব্যাখ্যা

প্রশ্ন: If a/b = 3/4 and b/c = 5/6, then, (b + c)/(a + b) =?

সমাধান:
a/b = 3/4
⇒ (a/b) + 1 = (3/4) + 1
∴ (a + b)/b = 7/4

b/c = 5/6
⇒ c/b = 6/5
⇒ c/b + 1 = 6/5 + 1
∴ (b + c)/b = 11/5

{(a + b)/b}/{(b + c)/b} = (7/4)/(11/5)
⇒ (a + b)/(b + c) = (7 × 5)/(4 × 11)
⇒ (a + b)/(b + c) = 35/44
⇒ (b + c)/(a + b) = 44/35

১০,৪৩২.

If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is -

ক
√3
খ
1
গ
1/2
ঘ
3

ব্যাখ্যা

Question: If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is -

Solution:
Given,
sinA + sin²A = 1
⇒ sinA = 1 - sin²A
⇒ sinA = cos²A
⇒ sin²A = cos⁴A
⇒ 1 - cos²A = cos⁴A
∴ cos²A + cos⁴A = 1

১০,৪৩৩.

Find the value of x; 2^{x - 4} = 4a^{x - 6} [a > 0, a ≠ 2]

ক
ক) 0
খ
খ) 1
গ
গ) 3
ঘ
ঘ) 6

ব্যাখ্যা

Question: Find the value of x; 2^{x - 4} = 4a^{x - 6} [a > 0, a ≠ 2]

Solution:
2^{x - 4} = 4a^{x - 6}
⇒ (2^{x - 4})/4 = a^{x - 6}
⇒ (2^{x - 4})/2² = a^{x - 6}
⇒ 2^{x - 4 - 2} = a^{x - 6}
⇒ 2^{x - 6} = a^{x- 6}
⇒ (2/a)^{x - 6} = 1
⇒ (2/a)^{x - 6} = (2/a)⁰
⇒ x - 6 = 0
⇒ x = 6

১০,৪৩৪.

If the areas of a circle and a square are equal then the ratio of their perimeters is-

ক
√π : 1
খ
√π : 2
গ
√π : 3
ঘ
None of the above

ব্যাখ্যা

Question: If the areas of a circle and a square are equal then the ratio of their perimeters is-
(যদি একটি বৃত্ত এবং একটি বর্গের ক্ষেত্রফল সমান হয়, তবে তাদের পরিসরের অনুপাত হবে -)

Solution:
ধরা যাক, বর্গের প্রতিটি দিকের দৈর্ঘ্য = a cm এবং বৃত্তের ব্যাসার্ধ = r cm.

প্রশ্নানুসারে,
বৃত্তের ক্ষেত্রফল = বর্গের ক্ষেত্রফল
⇒ a² = πr²
⇒ a = r√π

∴ প্রয়োজনীয় অনুপাত = 2πr/4a
= 2πr/4r√π
= √π/2
= √π : 2

১০,৪৩৫.

If 2p/(p²- 2p + 1) = 1/4, then the value of p + (1/p) is?

ক
ক) 10
খ
খ) 8
গ
গ) 4
ঘ
ঘ) 2

ব্যাখ্যা

Question: If 2p/(p²- 2p + 1) = 1/4, then the value of p + (1/p) is?

Solution:

১০,৪৩৬.

A 20 m long, and 15 m broad hall is surrounded by a verandah with a uniform width of 2.5 m. Find the cost of flooring the verandah at Tk. 3.50 per square meter.

ক
Tk. 500
খ
Tk. 600
গ
Tk. 700
ঘ
Tk. 800

ব্যাখ্যা

Question: A 20 m long, and 15 m broad hall is surrounded by a verandah with a uniform width of 2.5 m. Find the cost of flooring the verandah at Tk. 3.50 per square meter.

Solution:
Length of the hall = 20 m,
Breadth of hall = 15 m,

Area of hall = L × B = 20 × 15 = 300 m²

Length of hall with verandah = 20 + 2.5 + 2.5 = 25 m,
Breadth of hall with verandah = 15 + 2.5 + 2.5 = 20 m,

Area of hall with verandah = 25 × 20 = 500 m²

Area of verandah = area of hall with verandah - area of hall
= 500 - 300 = 200 m²

Cost of flooring the verandah is Tk. 3.50 per square meter.
So, the cost of flooring the entire verandah = 3.50 × 200 = 700

১০,৪৩৭.

The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

ক
5
খ
8
গ
12
ঘ
18

ব্যাখ্যা

Question: The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

Solution:
total distance = 10 × 300 cm
= 3000 cm
= 30 m

speed = 30/6 ms^-1
= 5 ms^-1
= (5 × 3600)/(1000) kmh^-1
= 18 kmh^-1

১০,৪৩৮.

The areas of a square and a rhombus are equal. The diagonals of the rhombus are 6 meters and 8 meters, respectively. What is the length of one side of the square?

ক
5√6 meters
খ
3√6 meters
গ
2√6 meters
ঘ
7√6 meters

ব্যাখ্যা

Question: The areas of a square and a rhombus are equal. The diagonals of the rhombus are 6 meters and 8 meters, respectively. What is the length of one side of the square?

Solution:
The area of the rhombus = (1/2) × Product of the diagonals
= (1/2) × 6 × 8
= 24 square meters

The area of the square = 24 square meters.
∴ Length of one side of the square = √24 meters
= 2√6 meters

∴ the length of one side of the square is 2√6 meters.

১০,৪৩৯.

Which one of the following is a rational number?

ক
√3 × √5
খ
√11 × √2
গ
√3 × √27
ঘ
√6 × √16
ঙ
√7 × √13

ব্যাখ্যা

Question: Which one of the following is a rational number?

Solution:
ক) √3 × √5 = √15 ........ irrational
খ) √11 × √2 = √22 ........ irrational
গ) √3 × √27 = √81 = 9 ........ rational
ঘ) √6 × √16 = √96 ........ irrational
ঙ) √7 × √13 = √91 ........ irrational

Answer: গ) √3 × √27 = 9 is a rational number

১০,৪৪০.

The average of 3, 8, 7, and x is 6 and the average of 19, 2, 7, x and y is 9. What is the value of y?

ক
18
খ
16
গ
15
ঘ
11

ব্যাখ্যা

Question: The average of 3, 8, 7, and x is 6 and the average of 19, 2, 7, x and y is 9. What is the value of y?

Solution:
Given that
average of 3, 8, 7, x is 6

Therefore,
6 = (3 + 8 + 7 + x)/4
⇒ 24 = 18 + x
⇒ x = 24 - 18
∴ x = 6

Therefore,
9 = (19 + 2 + 7 + x + y)/5
⇒ 45 = 28 + 6 + y
⇒ y = 45 - 34
∴ y = 11

১০,৪৪১.

If the diameter of a circle is 4 cm, what is the area of the circle in square centimeters?

ক
ক) π cm²
খ
খ) 2π cm²
গ
গ) 4π cm²
ঘ
ঘ) 8π cm²

ব্যাখ্যা

Question: If the diameter of a circle is 4 cm, what is the area of the circle in square centimeters?

Solution:
বৃত্তের ব্যাস 4 সেন্টিমিটার
বৃত্তের ব্যাসার্ধ r = 4/2 = 2 সেন্টিমিটার
বৃত্তের ক্ষেত্রফল = πr² বর্গসেন্টিমিটার
= π(2)² বর্গসেন্টিমিটার
= 4π বর্গসেন্টিমিটার

১০,৪৪২.

If the interest of Tk. H of H% in 4 years is Tk.H, Then H = ?

ক
ক) 25
খ
খ) 20
গ
গ) 30
ঘ
ঘ) 32

ব্যাখ্যা

সরল মুনাফার ক্ষেত্রে,
I = Pnr
Or, H = H × 4 × H/100
Or, H = 100/4
Or, H = 25

১০,৪৪৩.

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is-

ক
Tk. 3500
খ
Tk. 3750
গ
Tk. 3840
ঘ
Tk. 3900

ব্যাখ্যা

Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is-

Solution:
Let the cost of a chair and a table are x and y respectively.
Then,
10x = 4y
⇒ y = (10/4)x = 5x/2
∴ y = 5x/2 .......(1)
And,
15x + 2y = 4000
⇒ 15x + 2(5x/2) = 4000
⇒ 20x = 4000
⇒ x = 4000/20
∴ x = 200

From (1),
y = 5x/2 = (5 × 200)/2 = 500
∴ y = 500

Hence, the cost of 12chairs and 3tables is,
= 12x + 3y
= (2400 + 1500)
= 3900

So the total price of 12 chairs and 3 tables is Tk. 3900.

১০,৪৪৪.

x, y are positive integers. When x is divided by y, the remainder is 5. If x/y = 5.20, what is the value of x?

ক
425
খ
330
গ
155
ঘ
130

ব্যাখ্যা

Question: x, y are positive integers. When x is divided by y, the remainder is 5. If x/y = 5.20, what is the value of x?

Solution:
দেওয়া আছে
x/y = 5.20
⇒ x/y = 520/100
∴ x/y = 26/5

এখানে 5 দিয়ে 26 ভাগ করলে ভাগশেষ 1 থাকে
কিন্তু বলা আছে ভাগশেষ 5 থাকবে
তাই
26/5 এর লব ও হরের সাথে 5 গুণ করতে হবে।
x/y = 26/5 = (26 × 5)/(5 × 5) = 130/25
130 কে 25 দ্বারা ভাগ করলে 5 ভাগশেষ থাকে।
∴ x এর মান = 130

১০,৪৪৫.

In a box, there are 7 red, 8 blue, and 5 green balls. One ball is picked randomly. What is the probability that it is neither red nor green?

ক
1/12
খ
2/5
গ
3/5
ঘ
5/8

ব্যাখ্যা

Question: In a box, there are 7 red, 8 blue, and 5 green balls. One ball is picked randomly. What is the probability that it is neither red nor green?

Solution:
মোট বলের সংখ্যা = 7 + 8 + 5 = 20 টি।

ধরি, E হলো এমন ঘটনা যেখানে বলটি লাল বা সবুজ কোনোটিই নয়, অর্থাৎ বলটি নীল।
∴ অনুকূল ফলাফলের সংখ্যা, n(E) = 8

সম্ভাব্যতা = (অনুকূল ফলাফলের সংখ্যা)/(মোট ফলাফলের সংখ্যা) = 8/20
= 2/5

অতএব, বলটি লাল বা সবুজ না হওয়ার সম্ভাব্যতা হলো 2/5

১০,৪৪৬.

If a + b + c = 6 and a² + b² + c²= 14 find the value of (ab + bc + ca).

ক
11
খ
14
গ
21
ঘ
26

ব্যাখ্যা

প্রশ্ন: If a + b + c = 6 and a² + b² + c²= 14 find the value of (ab + bc + ca).

সমাধান:
দেওয়া আছে,
a + b + c = 6 এবং a²+ b² + c² = 14

আমরা জানি,
(a + b + c)² = ( a² + b² + c²) + 2(ab + bc + ca)
বা, (6)² =14 + 2(ab + bc + ca)
বা, 36 = 14 + 2(ab + bc + ca)
বা, 36 - 14 = 2(ab + bc + ca)
বা, 22 = 2(ab + bc + ca)
বা, ab + bc + ca = 22/2
বা, ab + bc + ca = 11

১০,৪৪৭.

Three pipes A, B, and C can fill a tank in 5, 10, and 30 hours respectively. Pipe A was opened at 8 a.m., Pipe B at 9 a.m., and Pipe C at 10 a.m. When will the tank be completely full?

ক
11 : 00 a.m.
খ
11 : 30 a.m.
গ
12 : 00 p.m.
ঘ
12 : 45 p.m.

ব্যাখ্যা

Question: Three pipes A, B, and C can fill a tank in 5, 10, and 30 hours respectively. Pipe A was opened at 8 a.m., Pipe B at 9 a.m., and Pipe C at 10 a.m. When will the tank be completely full?

Solution:
ধরি, চৌবাচ্চাটি 8 a.m. এর x ঘন্টা পর পূর্ণ হবে।

তাহলে, পাইপগুলির কাজের সময়কাল নিম্নরূপ:
A কাজ করেছে x ঘন্টা
B কাজ করেছে (x - 1) ঘন্টা
C কাজ করেছে (x - 2) ঘন্টা

প্রশ্নমতে:
x/5 + (x - 1)/10 + (x - 2)/30 = 1
⇒ (6x + 3(x - 1) + 1(x - 2))/30 = 1
⇒ 6x + 3x - 3 + x - 2 = 30
⇒ (6x + 3x + x) - (3 + 2) = 30
⇒ 10x - 5 = 30
⇒ 10x = 30 + 5
⇒ 10x = 35
⇒ x = 35/10
⇒ x = 3.5 ঘন্টা।

অতএব, চৌবাচ্চাটি 8 a.m. এর 3.5 ঘন্টা পর পূর্ণ হবে।
8:00 a.m. + 3 ঘন্টা 30 মিনিট = 11 : 30 a.m.
∴ চৌবাচ্চাটি 11 : 30 a.m. এ পূর্ণ হবে।

১০,৪৪৮.

If P = {x : x is a factor of 12 } and Q = {x : x is a multiple of 3 and x ≤ 12} then determine P - Q:

ক
{1, 3, 4}
খ
{1, 2, 4}
গ
{1, 2, 3, 4}
ঘ
{ }

ব্যাখ্যা

Question: If P = {x : x is a factor of 12 } and Q = {x : x is a multiple of 3 and x ≤ 12} then determine P - Q:

Solution:
Given,
P = {x : x is a factor of 12 }
∴ P = {1, 2, 3, 4, 6, 12}

Q = {x : x is a multiple of 3 and x ≤ 12}
∴ Q = {3, 6, 9, 12}

∴ P - Q = {1, 2, 3, 4, 6, 12} - {3, 6, 9, 12}
= {1, 2, 4}

১০,৪৪৯.

If y < 2 and 2x - 3y = 0 which of the following must be true?

ক
x < 3
খ
x < 6
গ
x > 3
ঘ
x > 6
ঙ
None

ব্যাখ্যা

Question: If y < 2 and 2x - 3y = 0 which of the following must be true?

Solution:
Here, 2x - 3y = 0
⇒ 2x = 3y
⇒ x = (3/2)y ................(i)

And, y < 2
⇒ (3/2)y < (3/2) × 2
∴ x < 3 [From (i)]

১০,৪৫০.

If the 3rd term and 7th term of an arithmetic progression are 17 and 37 respectively. Find the first term of the progression.

ক
7
খ
5
গ
6
ঘ
8

ব্যাখ্যা

Question: If the 3rd term and 7th term of an arithmetic progression are 17 and 37 respectively. Find the first term of the progression.

Solution:
3rd term of an AP is 17
a₃=a + (n - 1)d
⇒ 17 = a + (3 - 1)d
∴ 17 = a + 2d .................(1)

a₇ = a + (n - 1)d
⇒ 37 = a + (7 - 1)d
⇒ 37 = a + 6d ..................(2)

Subtract (1) from (2), we get
37 - 17 = a + 6d - a - 2d
⇒ 20 = 4d
∴ d = 5

Put d = 5 in equation (1), we get
17 = a + 2(5)
⇒ a = 17 - 10
∴ a = 7

∴ The first term of the progression is 7

১০,৪৫১.

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

ক
9
খ
10
গ
12
ঘ
20
ঙ
25

ব্যাখ্যা

Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Solution:
Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = (9/54) × 60 min = 10 min.

১০,৪৫২.

A minibus takes 6 hour less to cover 1680 km distance, if its speed is increased by 14 kmph ? What is the usual time of the minibus ?

ক
20
খ
24
গ
30
ঘ
36
ঙ
42

ব্যাখ্যা

Let speed be y km/hour
1680/y - 1680/(y + 14) = 6 or, y = 56 but y ≠ - 76
The usual time of the minibus shall be 1680/56 = 30 hours

১০,৪৫৩.

If √32 +√128 = √x then find the value of x.

ক
ক) 828
খ
খ) 882
গ
গ) 288
ঘ
ঘ) 424

ব্যাখ্যা

Question: If √32 +√128 = √x then find the value of x.

Solution:
√32 +√128 =√x
⇒ 4√2 + 8√2 = √x
⇒ 12√2 = √x
⇒ x = (12√2)²
⇒ x = (144× 2)
⇒ x = 288

∴ The required value of x is 288

১০,৪৫৪.

A 40-meter long rope is cut into two unequal pieces. If one piece is 18 meter longer than the other, what is the length (in meter) of the shorter piece?

ক
ক) 10
খ
খ) 11
গ
গ) 18
ঘ
ঘ) None

ব্যাখ্যা

Question: A 40-meter long rope is cut into two unequal pieces. If one piece is 18 meter longer than the other, what is the length (in meter) of the shorter piece?

Solution:
ধরি, বড় টুকরোটির দৈর্ঘ্য x মিটার
ছোট টুকরোটির দৈর্ঘ্য x - 18 মিটার

x + x - 18 = 40
⇒ 2x = 58
∴ x = 29

ছোট টুকরোটির দৈর্ঘ্য = 29 - 18
= 11 মিটার

১০,৪৫৫.

In Rakib's opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Rakib, and he thinks that Rakib's weight is greater than 60 kg but less than 70 kg. His sister's view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Rakib?

ক
60
খ
65
গ
67
ঘ
54

ব্যাখ্যা

Question: In Rakib's opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Rakib, and he thinks that Rakib's weight is greater than 60 kg but less than 70 kg. His sister's view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Rakib?

Solution:
Let Rakib's weight by X kg.
According to Rakib: 65 < X < 72
According to Rakib's father: 60 < X < 70.
According to Rakib's sister: X <= 68

The different possible weights of Rakib or the values that satisfy all the above conditions are 66, 67 and 68.
So, the Average of different possible weights of Rakib = (66 + 67 + 68)/3
= 201/3
= 67 kg.

১০,৪৫৬.

The perimeter of a rectangle is 80 inches. The width is 8 inches less than 3 times the length. Find the width of the rectangle.

ক
ক) 28 inches
খ
খ) 30 inches
গ
গ) 25 inches
ঘ
ঘ) 16 inches

ব্যাখ্যা

Let, length = x and Width = 3x - 8
ATQ,
2(x + 3x - 8) = 80
Or, 4x - 8 = 80/2 = 40
Or, 4x = 48
Or, x = 12
So, width = 3 × 12 - 8 = 28

১০,৪৫৭.

In a mixture, the ratio of the milk and water is 6: 5. When 22 liter mixture is replaced by water, the ratio becomes 9: 13. What is the quantity of water after replacement?

ক
62 liter
খ
50 liter
গ
40 liter
ঘ
52 liter

ব্যাখ্যা

Question: In a mixture, the ratio of the milk and water is 6: 5. When 22 liter mixture is replaced by water, the ratio becomes 9 : 13. What is the quantity of water after replacement?

Solution:
Given that,
milk : water = 6 : 5
And 22 liter mixture are replaced by water

Now,
Let milk = 6x and water = 5x
In 22 liter mixture, milk removed = (6/11) × 22 = 12 liter
And water removed = (5/11) × 22 = 10 liter

According to question,
(6x - 12) : (5x - 10 + 22) = 9 : 13
⇒ 13(6x - 12) = 9(5x + 12)
⇒ 78x - 156 = 45x + 108
⇒ 78x - 45x = 108 + 156
⇒ 33x = 264
⇒ x = 8
∴ Initial water = 5x = 5 × 8 = 40 liters
Water removed in 22 L mixture = 10 liters
And water added back = 22 liters

∴ Water after replacement = Initial water - water removed + water added
= 40 - 10 + 22
= 52 liters

So the quantity of water after replacement is 52 liters.

১০,৪৫৮.

Two trains, one from Dhaka to Chittagong and one from Chittagong to Dhaka, started simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What is the ratio of their speed?

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

ব্যাখ্যা

Question: Two trains, one from Dhaka to Chittagong and one from Chittagong to Dhaka, started simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What is the ratio of their speed?

Solution:

ধরি,
প্রথম ট্রেনের বেগ S₁ এবং এটি ঢাকা থেকে চট্টগ্রাম যাচ্ছে।
দ্বিতীয় ট্রেনের বেগ S₂ এবং এটি চট্টগ্রাম থেকে ঢাকা যাচ্ছে।
তারা t সময় পর P বিন্দুতে মিলিত হবে।

ঢাকা থেকে P বিন্দুর জন্য
প্রথম ট্রেনের দূরত্ব = S₁t
দ্বিতীয় ট্রেনের দূরত্ব = 9S₂
∴ S₁t = 9S₂. . . . . .(1)

চট্টগ্রাম থেকে P বিন্দুর জন্য
প্রথম ট্রেনের দূরত্ব = 4S₁
দ্বিতীয় ট্রেনের দূরত্ব = S₂t
∴ S₂t = 4S₁. . . . . . (2)

(1) ÷ (2)
S₁t/S₂t = 9S₂/4S₁
S₁²/S₂² = 9/4
S₁/S₂ = 3/2
S₁ : S₂ = 3 : 2

১০,৪৫৯.

The average age of 8 children of a family is 12 yr. If the age of 7 children is 12, 8, 14, 11, 9, 13 and 15 yr, then the age of 8th child will be-

ক
12 yr
খ
14 yr
গ
13 yr
ঘ
15 yr
ঙ
None of above

ব্যাখ্যা

Total age of 8 children = 8 x 12 = 96 yr
Total age of 7 children = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82
The age of 8th child = 96 - 82 = 14 yr

১০,৪৬০.

A shopkeeper marks up his goods by 30% above the cost price. He then offers a discount of 10% on the marked price. What is the overall percentage profit?

ক
20%
খ
37%
গ
27%
ঘ
17%

ব্যাখ্যা

Question: A shopkeeper marks up his goods by 30% above the cost price. He then offers a discount of 10% on the marked price. What is the overall percentage profit?

Solution:
Let,
the cost price (CP) be Tk. 100

Marked Price = 30% more than cost price
= 100 + 30
= Tk. 130

Discount = 10% of 130
= (10/100) × 130
= Tk. 13

Selling Price (SP) = 130 - 13 = Tk. 117

∴ Profit = SP - CP = 117 - 100 = Tk. 17

∴ Overall percentage profit = (profit / cost price) × 100%
= (17 / 100) × 100%
= 17%

১০,৪৬১.

List price of an article at a showroom is 2000 taka and it is being sold at successive discount of 20% and 10%, what will be net selling price of it?

ক
1440 taka
খ
1240 taka
গ
1340 taka
ঘ
1140 taka
ঙ
1200 taka

ব্যাখ্যা

List price of an article = 2000 taka
After discount,
selling price = 2000 taka × 80% × 90% = 1440 taka

১০,৪৬২.

A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to mixture to raise the percentage of water to 25%

ক
ক) 2 kg
খ
খ) 4 kg
গ
গ) 5 kg
ঘ
ঘ) 6 kg

ব্যাখ্যা

In 1st mixture, water = 10/100 × 20 = 2 kg
So, Spirit = 20-2 = 18 kg
In 2nd mixture where the water is 25%,
75 kg of spirit is contained in 100 kg mixture
So, 18 kg spirit is contained in = (100×18)/75 = 24 kg
So, water to be added = 24-20 = 4 kg

১০,৪৬৩.

There are two inlets and one outlet to a tank. Inlet A and B take 1.5 hours and 2 hours respectively to fill the tank. While outlet C can empty the entire tank in 30 minutes. The gardener decides to open Inlet A at 8 am when he arrives on duty and Inlet B one hour later. Outlet C is opened at 10 am. What will be the time by his watch when the tank will be entirely empty again?

ক
ক) 1.25 pm
খ
খ) 12 pm
গ
গ) 12.12 pm
ঘ
ঘ) 12.18 pm

ব্যাখ্যা

Let the tank get empty in T hours counting from 8 am.
A is on for T hours and work is done by A = Work in 1-hour × T hours = T/1.5 = 2T/3

Similarly, B starts at 9 am i.e. it's on for (T-1) hours & work done is = (T - 1)/2

Similarly, C starts at 10 am i.e. it's on for (T-2) hours & work done is = (T - 2)/(1/2) = 2(T - 2)

Initially, the tank is empty and after T hours too, it is empty. So, the total work done is 0.

According to the question,
2T/3 + (T - 1)/2 - 2(T - 2) = 0
⇒ (4T + 3T - 3 - 12 T + 24)/6 = 0
⇒ -5T + 21 = 0
⇒ 5T = 21
⇒ T = 21/5
= 4.2 hours = 4 hours 12 minutes5
This time is needed for the tank to get empty.
The exact time will be 4 hours 12 min from 8 am = 12.12 pm

১০,৪৬৪.

ঘ
1

ব্যাখ্যা

Question:

Solution:
Given that,

১০,৪৬৫.

If the area of a square is 529 square meters, what is the perimeter of the square?

ক
96 meters.
খ
92 meters.
গ
94 meters.
ঘ
86 meters.

ব্যাখ্যা

Question: If the area of a square is 529 square meters, what is the perimeter of the square?

Solution:
Given,
The area of the square = 529 square meters.

Therefore,
The length of one side of the square = √529 meters = 23 meters.

We know,
The perimeter of a square = 4 × length of one side
= 23 × 4 meters
= 92 meters

Thus, the perimeter of the square is 92 meters.

১০,৪৬৬.

The ratio between the speeds of two trains is 5 : 6. If the second train runs 450 km in 5 hours, then the speed of the first train is:

ক
75 km/hr
খ
90 km/hr
গ
100 km/hr
ঘ
120 km/hr

ব্যাখ্যা

Question: The ratio between the speeds of two trains is 5 : 6. If the second train runs 450 km in 5 hours, then the speed of the first train is:

সমাধান:
দ্বিতীয় ট্রেনের গতিবেগ = দূরত্ব/সময়
= 450 কিমি/5 ঘন্টা
= 90 কিমি/ঘন্টা

এখন, দুটি ট্রেনের গতিবেগের অনুপাত হলো 5 : 6।

ধরি, প্রথম ট্রেনের গতিবেগ 5x এবং দ্বিতীয় ট্রেনের গতিবেগ 6x।
তাহলে, 6x = 90 কিমি/ঘন্টা
⇒ x = 90/6
∴ x = 15

সুতরাং, প্রথম ট্রেনের গতিবেগ = 5x = 5 × 15 = 75 কিমি/ঘন্টা

১০,৪৬৭.

What is the reflex angle between the hands of a clock at 10.30?

ক
- 135°
খ
135°
গ
- 225°
ঘ
225°

ব্যাখ্যা

Question: What is the reflex angle between the hands of a clock at 10.30?

Solution:
We Know,
The angle between the hands of the clock is |11M - 60H|/2
= |(11 × 30) - (60 × 10)|/2
= |330 - 600|/2
= |- 270|/2
= 135°

∴ Reflex angle = 360° - 135°
= 225°

১০,৪৬৮.

If a man were to sell his bike for Tk. 67500, he would lose 25%. To gain 25% at what price should he sell it?

ক
Tk. 108500
খ
Tk. 110000
গ
Tk. 111800
ঘ
Tk. 112500

ব্যাখ্যা

Question: If a man were to sell his bike for Tk. 67500, he would lose 25%. To gain 25% at what price should he sell it?

Solution:
Let,
the cost price of the bike be x
Selling at Tk. 67,500 causes a 25% loss,

ATQ,
75% of cost price = 67500
⇒ cost price = 67500 ÷ 75%
⇒ cost price = 67500 ÷ (75/100)
⇒ cost price = {67500 × (100/75)}
∴ cost price = Tk. 90000

∴ To gain 25% he should sell it = (125/100) × 90000
= Tk. 112500

১০,৪৬৯.

20 years ago, my age was 1/3 of what it is now. What is my present age?

ক
ক) 66 years
খ
খ) 36 years
গ
গ) 33 years
ঘ
ঘ) 35 years
ঙ
ঙ) 30 years

ব্যাখ্যা

Let the present age be x years.
20 years ago my age was x - 20.

According to given data,
x - 20 = x/3
=> 2x = 60
=> x = 30

১০,৪৭০.

ক
3
খ
5/9
গ
5
ঘ
8

ব্যাখ্যা

Question:

Solution:

১০,৪৭১.

If 2^{n - 1} + 2^{n + 1} = 320, then the value of n is = ?

ক
5
খ
6
গ
7
ঘ
8

ব্যাখ্যা

Question: If 2^{n - 1} + 2^{n + 1} = 320, then the value of n is = ?

Solution:

১০,৪৭২.

A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 5

ব্যাখ্যা

Question: A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

Solution:
ধরি
ভাগফল = x

সংখ্যাটি = 3x + 1 ................(1)
এবং x = 2q + 1

(1) ⇒
সংখ্যাটি = 3(2q + 1) + 1
= 6q + 3 + 1
= 6q + 4

সংখ্যাটিকে 6 দ্বারা ভাগ করলে ভাগশেষ 4 থাকবে।

১০,৪৭৩.

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

ক
ক) 50% increase
খ
খ) 25% increase
গ
গ) 50% decrease
ঘ
ঘ) 75% increase

ব্যাখ্যা

Let the original dimensions be x by y.
A₁ =xy
According to the question, new dimensions are x/2 and 3y
New area, A₂=3xy/2
A₁- A₂= xy/2
(A₁- A₂) / A₁= ( xy/2)/xy × 100% = 50% increase

১০,৪৭৪.

Two numbers are in the ratio 2 : 3. If 4 is subtracted from the first number, the ratio becomes 1 : 2. What are the numbers?

ক
12, 18
খ
10, 15
গ
14, 21
ঘ
16, 24

ব্যাখ্যা

Question: Two numbers are in the ratio 2 : 3. If 4 is subtracted from the first number, the ratio becomes 1 : 2. What are the numbers?

Solution:
Let the two numbers be: 2x and 3x

According to the question,
(2x - 4)/3x = 1/2
⇒ 2(2x - 4) = 3x
⇒ 4x - 8 = 3x
⇒ x = 8

∴ First number = 2 × 8 = 16
∴ Second number = 3 × 8 = 24

১০,৪৭৫.

A tank can be filled by a tap in 8 hours. After one-third of the tank is filled, two more identical taps are opened. How long will it take to fill the tank completely?

ক
5.66 hours
খ
3.88 hours
গ
4.44 hours
ঘ
7.48 hours
ঙ
6.44 hours

ব্যাখ্যা

Question: A tank can be filled by a tap in 8 hours. After one-third of the tank is filled, two more identical taps are opened. How long will it take to fill the tank completely?

Solution:
One tap fills the tank in 8 hours
rate of one tap = 1/8 tank/hour.

After one-third of the tank is filled, 2 more taps are opened.

∴ Time to fill one-third of the tank = (1/3)/(1/8) = 8/3 hours

∴ Remaining = 1 - (1/3)
= (3 - 1)/3
= 2/3 of the tank

Now 3 taps are working
∴ combined rate = 3× (1/8)=3/8 tank/hour

∴ Time to fill remaining tank = (2/3)/(3/8)
= (2/3) × (8/3)
= 16/9 hours

∴ Total time = (8/3) + (16/9) hours
= 40/9 hours
= 4.44 hours

১০,৪৭৬.

A guy bought 10 pencils for Tk. 50 and sold them for Tk. 60. What is his gain in terms of percentage?

ক
20%
খ
10%
গ
12%
ঘ
5%

ব্যাখ্যা

Question: A guy bought 10 pencils for Tk. 50 and sold them for Tk. 60. What is his gain in terms of percentage?

Solution:
Profit = SP - CP = 60 - 50 = 10

Gain % = (Profit/CP) × 100% = (10/50) × 100% = 20%

১০,৪৭৭.

A mixture of 150 liters of milk and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

ক
18 liters
খ
15 liters
গ
10 liters
ঘ
9 liters

ব্যাখ্যা

Question: A mixture of 150 liters of milk and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

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

Let,
P liters of water be added.
So, new amount of water = (30 + P)
and new total mixture = (150 + P)

ATQ,
(30 + P) = 25% of (150 + P)
⇒ 30 + P = (25/100) × (150 + P)
⇒ 30 + P = (1/4) × (150 + P)
⇒ 120 + 4P = 150 + P
⇒ 4P - P = 150 - 120
⇒ 3P = 30
∴ P = 10

∴ 10 liters more water should be added.

১০,৪৭৮.

A 50 g gold-copper alloy contains 80% gold. How much additional gold is needed to raise the gold percentage to 90%?

ক
30 gm
খ
50 gm
গ
60 gm
ঘ
55 gm
ঙ
None of the above

ব্যাখ্যা

Question: A 50 g gold-copper alloy contains 80% gold. How much additional gold is needed to raise the gold percentage 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

১০,৪৭৯.

A water filter can be filled with 11 jugs of capacity 1.5 liters each. How many jugs are required to fill the same filter, if the capacity of the jug is 1.1 liters?

ক
ক) 11
খ
খ) 12
গ
গ) 13
ঘ
ঘ) 15

ব্যাখ্যা

প্রশ্নমতে ফিল্টারের ধারণক্ষমতা 11×1.5 = 16.5
তাহলে এই ফিল্টারের জন্য 1.1 লিটারের ধারণক্ষমতার জগ প্রয়োজন = 16.5/1.1 = 15 টি।

১০,৪৮০.

What is the H.C.F. of 6/15, 12/20, and 18/25?

ক
1/9
খ
5/36
গ
1/36
ঘ
1/50

ব্যাখ্যা

Question: What is the H.C.F. of 6/15, 12/20, and 18/25?

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

H.C.F. of numerators:
H.C.F.(6, 12, 18) = 6

L.C.M. of denominators:
15 = 3 × 5
20 = 2² × 5
25 = 5²

∴ L.C.M. = 2² × 3 × 5² = 4 × 3 × 25 = 300

∴ Required H.C.F. = 6/300 = 1/50

১০,৪৮১.

A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train?

ক
ক) 100.1 m
খ
খ) 223.1 m
গ
গ) 111.1 m
ঘ
ঘ) 120.3 m

ব্যাখ্যা

We know,
Speed =Distance/ Time
Speed =(10/15) 60 = 40×(5/18)m/sec
= 11.1 m/sec
Length of train = (Speed x Time)
= (11.11x10)
= 111.1 m

১০,৪৮২.

A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

ক
3 days
খ
4 days
গ
5 days
ঘ
6 days

ব্যাখ্যা

Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days

১০,৪৮৩.

If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

ক
6
খ
8
গ
10
ঘ
12
ঙ
None

ব্যাখ্যা

Question: If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?

Solution:

Let 'p' be the erasers available for a rupee.

Reduced price = (75/100) × 1

= Tk. 3/4

Tk. 3/4 will fetch p erasers
Tk. 1 will fetch p × (4/3) erasers

Therefore,
4p/3 = p + 2
⇒ p = 6

১০,৪৮৪.

A man invested Tk. 5940 in Tk.10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

ক
Tk. 864
খ
Tk. 846
গ
Tk. 468
ঘ
Tk. 684

ব্যাখ্যা

Question: A man invested Tk. 5940 in Tk.10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

Solution:
Number of shares =(5940/8.25) = 720

Face value = Tk.(720× 10)= Tk. 7200

Annual income = {(12/100) × 7200} = 864

১০,৪৮৫.

A hospital pharmacy charges $ 0.40 per fluidram of a certain medicine but allows a discount of 15 percent to Medicare patients. How much should the pharmacy charge a Medicare patient for 3 fluidounces of the medicine? (128 fluidrams = 16 fluidounces)

ক
$ 9.60
খ
$ 8.16
গ
$ 3.20
ঘ
$ 2.72

ব্যাখ্যা

Question: A hospital pharmacy charges $ 0.40 per fluidram of a certain medicine but allows a discount of 15 percent to Medicare patients. How much should the pharmacy charge a Medicare patient for 3 fluidounces of the medicine? (128 fluidrams = 16 fluidounces)

Solution:
16 fluidounces = 128 fluidrams
∴ 1 fluidounces = 128/16 fluidrams = 8 fluidrams
∴ 3 fluidounces = 3 × 8 = 24 fluidrams

Cost of 24 fluidrams = 24 × 0.40 = 9.6
Cost after 15% discount = 0.85 × 9.6 = 8.16

১০,৪৮৬.

A train covers a distance in 30 minutes. If it runs at a speed of 56 km/h on average. The speed at which the train must run to reduce the time of the journey to 20 minutes is-

ক
77 km/h
খ
81 km/h
গ
84 km/h
ঘ
88 km/h
ঙ
92 km/h

ব্যাখ্যা

Question: A train covers a distance in 30 minutes. If it runs at a speed of 56 km/h on average. The speed at which the train must run to reduce the time of the journey to 20 minutes is-

Solution:
Here,
Current speed = 56 km/h
Current time = 30 minutes
= 30/60 h
= 1/2 hour
New time = 20 minutes
= 20/60 h
= 1/3 h

We know,
Distance = Speed × Time
= 56 × (1/2)
= 28 km

∴ New speed = Distance/New time
= 28/(1/3)
= 84 km/h

১০,৪৮৭.

Arrange the following words according to the dictionary order:
1. Corporate
2. Correspond
3. Correlation
4. Convenience
5. Co-operate

ক
ক) 5, 1, 2, 4, 3
খ
খ) 4, 5, 1, 3, 2
গ
গ) 1, 2, 3, 5, 4
ঘ
ঘ) 4, 1, 5, 2, 3

ব্যাখ্যা

Dictionary এর ক্রম অনুসারে :

শব্দগুলোর সঠিক ক্রম :
4. Convenience
5. Co-operate
1. Corporate
3. Correlation
2. Correspond

অতএব, সঠিক উত্তর হলো "4, 5, 1, 3, 2".

১০,৪৮৮.

If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?

ক
1 days
খ
3 days
গ
6 days
ঘ
9 days

ব্যাখ্যা

Question: If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?

Solution:
3 spiders can make 3 webs in 3 days,
3 spiders can make 1 webs in 3/3 days,
1 spiders can make 1 webs in (3 × 3)/3 = 3 days

১০,৪৮৯.

If n is an integer, which of the following cannot be an integer?

ক
ক) (n -2)/2
খ
খ) √n
গ
গ) 2/(n +1)
ঘ
ঘ) √1/(n2 + 2)

ব্যাখ্যা

Choose n to be 0.
Then (n -2)/2
= (0 -2)/2
= -1 which is an integer.
So, eliminate
next, √n = √0 = 0.
Eliminate.
Next, 2/(n +1) = 2/1 = 2
eliminate,
Next, √1/(n² + 2)
= √1/2
= 1/√2 which is not an integer
So, the Answer is: √1/(n² + 2)

১০,৪৯০.

What is the minimum value of 2sin²θ + 3cos²θ ?

ক
1
খ
2
গ
3
ঘ
4

ব্যাখ্যা

Let x = 2sin²θ + 3cos²θ
⇒ x = 2sin²θ + 2cos²θ + cos²θ
⇒ x = 2(sin²θ + cos²θ) + cos²θ
⇒ x = 2 + cos²θ [since sin²θ + cos²θ = 1]
Therefore x will be the minimum when cosθ = 0.
Minimum value of x will be 2.

১০,৪৯১.

What is the solution of the inequality ।2x - 3। ≤ 1 ?

ক
ক) 1 ≤ x ≤ 2
খ
খ) - 1 ≤ x ≤ 2
গ
গ) - 1 ≤ x ≤ 3
ঘ
ঘ) - 2 ≤ x ≤ 2

ব্যাখ্যা

Question: What is the solution of the inequality ।2x - 3। ≤ 1 ?

Solution:
।2x - 3। ≤ 1
⇒ - 1 ≤ 2x - 3 ≤ 1
⇒ - 1 + 3 ≤ 2x - 3 + 3 ≤ 1 + 3
⇒ 2 ≤ 2x ≤ 4
⇒ 2/2 ≤ 2x/2 ≤ 4/2
1 ≤ x ≤ 2

১০,৪৯২.

100 oranges are bought at the rate of Tk. 350 and sold at the rate of Tk. 48 per dozen. The percentage of profit or loss is-

ক
ক) (100/7)% gain
খ
খ) (50/7)% loss
গ
গ) (80/7)% gain
ঘ
ঘ) (80/7)% loss

ব্যাখ্যা

Question: 100 oranges are bought at the rate of Tk. 350 and sold at the rate of Tk. 48 per dozen. The percentage of profit or loss is-

Solution:
C.P.of 1 orange = Tk.(350/100) = Tk.3.50
S.P.of 1 orange = Tk.(48/12 )= Tk. 4

Gain = Tk. (4 - 3.50) = Tk. 0.50
Gain% = {(0.50/3.50) × 100}% = (100/7)%

১০,৪৯৩.

If log₃[log₂(log₂x)] = 1, then x is equal to = ?

ক
128
খ
256
গ
512
ঘ
729

ব্যাখ্যা

Question: If log₃[log₂(log₂x)] = 1, then x is equal to = ?

Solution:
দেওয়া আছে, log₃[log₂(log₂(x)] = 1
⇒ log₂(log₂(x) = 3¹
⇒ log₂(log₂(x)= 3 ; [log_ab = c ⇒ b = a^c]
⇒ log₂(x) = 2³
⇒ log₂(x) = 8
⇒ x = 2⁸
∴ x = 256

১০,৪৯৪.

A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

ক
ক) 80 km/hr
খ
খ) 91 km/hr
গ
গ) 88 km/hr
ঘ
ঘ) 81 km/hr
ঙ
ঙ) 92km/hr

ব্যাখ্যা

Let length and speed of the train be x metre and y kmph
x/8.4 = (y − 4.5) × 5/18 ⋯ (1)
x/8.5 = (y − 5.4) × 5/18 ⋯ (2)
Dividing (1) by (2) gives,
8.5/8.4 = (y − 4.5)/(y − 5.4)
⇒ 8.4y − 8.4 × 4.5 = 8.5y − 8.5 × 5.4
⇒ 0.1y = 8.5 × 5.4 − 8.4 × 4.5
⇒ 0.1y = 45.9 − 37.8 = 8.1
⇒ y = 81

১০,৪৯৫.

A person crosses a 900 m long street in 5 minutes. What is his speed in km per hour?

ক
ক) 9.6 km/hr.
খ
খ) 10.6 km/hr.
গ
গ) 9.8 km/hr.
ঘ
ঘ) 10.8 km/hr.

ব্যাখ্যা

Question: A person crosses a 900 m long street in 5 minutes. What is his speed in km per hour?

Explanation:
Speed = 900m/(5 x 60) sec.
= 3 m/sec.

এখন কিলোমিটারে পরিণত করতে হলে-
= 3 × (18/5) km/hr
= 10.8 km/hr.

১০,৪৯৬.

An air conditioner can cool the hall in 40 miutes while another takes 60 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room?

ক
24 minutes
খ
26 minutes
গ
28 minutes
ঘ
None of these

ব্যাখ্যা

Question: An air conditioner can cool the hall in 40 miutes while another takes 60 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room?

Solution:
৪০ মিনিটে ঠান্ডা হয় সম্পূর্ণ অংশ
১ মিনিটে পূর্ণ হয় ১/৪০ অংশ

৬০ মিনিটে পূর্ণ হয় সম্পূর্ণ অংশ
১ মিনিটে পূর্ণ হয় ১/৬০ অংশ

দুটি মিলে পূর্ণ হয় ১/৪০ + ১/৬০
= ৩ + ২ / ১২০
= ৫/১২০ মিনিট
= ১/২৪ মিনিট

সম্পূর্ণ অংশ ঠান্ডা হতে সময় লাগে ২৪ মিনিট।

১০,৪৯৭.

If the clock in the mirror shows 7:25, what is the time on the real clock?

ক
3:35
খ
4:35
গ
5:25
ঘ
6:25

ব্যাখ্যা

Question: If the clock in the mirror shows 7:25, what is the time on the real clock?

Solution:
Actual time = 11:60 - time in the mirror
= 11:60 - 7:25
= 4:35

১০,৪৯৮.

A boat can travel with a speed of 14 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 76 km downstream.

ক
ক) 2 hours
খ
খ) 5 hours
গ
গ) 4 hours
ঘ
ঘ) 9 hours

ব্যাখ্যা

Speed downstream = (14 + 5) km/hr = 19 km/hr.

Time taken to travel 76 km downstream = (76/19) hours
= 4 hours

১০,৪৯৯.

Ahmed sold a T-shirt TK. 810 and gained 8%. How much did he purchase it for?

ক
ক) TK. 750
খ
খ) TK. 875
গ
গ) TK. 745
ঘ
ঘ) TK. 756

ব্যাখ্যা

ATQ, 108% = 810
Or, 100% = (100 × 810) / 108
= 750

১০,৫০০.

Determine x for which x² − 8x +15 is less than zero.

ক
- 2 < x < 7
খ
- 2 < x < 9
গ
1 > x > 6
ঘ
3 < x < 5
ঙ
- 3 < x > 5

ব্যাখ্যা

Question: Determine x for which x² − 8x +15 is less than zero.

Solution:
Given,
x² − 8x +15 < 0
⇒ x² - 3x - 5x + 15 < 0
⇒ x(x - 3) - 5(x - 3) < 0
⇒ (x - 3)(x - 5) < 0

The inequality will be true if x - 3 > 0 and x - 5 < 0 .
x - 3 > 0
or, x > 3

x - 5 < 0
or, x < 5
The inequality will be true if 3 < x < 5

∴ The solution of the inequality is 3 < x < 5