Bank Math

PrepBank · পাতা ১৫৯ / ১৬১ · ১৫,৮০১–১৫,৯০০ / ১৬,১২৪

১৫,৮০১.

A student is ranked 13th from right and 8th left. How many students are there in total?

ক
ক) 18
খ
খ) 19
গ
গ) 20
ঘ
ঘ) 21
ঙ
ঙ) 22

ব্যাখ্যা

Number of students = (13 + 8) - 1 = 20

১৫,৮০২.

If 6,250 Taka is invested at 12% simple interest, how much time will it take for the interest to reach 3,000 Taka?

ক
4 years
খ
5 years
গ
6 years
ঘ
7 years

ব্যাখ্যা

Question: If 6,250 Taka is invested at 12% simple interest, how much time will it take for the interest to reach 3,000 Taka?

Answer:
Given,
P = 6250 Taka
I = 3000 Taka
r = 12% = 0.12
Time = n

We know,
I = Pnr
n = I/Pr
n = 3000/(6250×0.12)
n = 4 years

১৫,৮০৩.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

ক
Tk. 3972
খ
Tk. 4100
গ
Tk. 3784
ঘ
Tk. 4248

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

Solution:
Given that,
Increase in amount after 6 years = 60%

We know,
A = P(1 + r/100)n
simple Interest = (principal × rate × time)/100

Now,
Let the amount at the 1^st year be 100x
∴ Increased in amount = 60% of 100x = 60x
⇒ 60x = (100x × 6 × r)/100
⇒ 6r = 60
⇒ r = 60/6 = 10
∴ r = 10%

∴ Compound Interest after 3 years = P(1 + r/100)ⁿ - P
= 12000(1 + 10/100)³ - 12000
= 12000 × (11/10)³ - 12000
= 12000 × (11/10) × (11/10) × (11/10) - 12000
= 15972 - 12000
= Tk. 3972

∴ The required answer is Tk. 3972

১৫,৮০৪.

A, B and C enter into a partnership with a certain capital in which A's contribus10,000. If out of a total profit of Tk. 1000, A gets Tk. 500, B gets Tk. 300 then C's capital is

ক
ক) Tk. 4,000
খ
খ) Tk. 3,600
গ
গ) Tk. 4,800
ঘ
ঘ) Tk. 4,400

ব্যাখ্যা

According to the problem,
Total profit is = 1000 TK,
A’s profit = 500 TK
B’s profit = 300 TK
∴ C’s profit is = (Total profit – (A + B)’ profit) = (1000 − 800) = 200

∴ Profit Ratio between A, B and C is
⇒ 500 : 300 : 200
⇒ 5 : 3 : 2
Let their capitals be 5x, 3x, and 2x respectively.

According to the problem,
A’s contribution is TK. 10000.
∴ 5x = 10000
⇒ x = 2000

∴ C’s share = 2x
= 2 × 2000
= 4000Tk

১৫,৮০৫.

A and B can finish a job together in x days. If A alone can complete the job in x + 3 days, and B alone can complete it in x + 12 days, what is the value of x?

ক
8
খ
4
গ
6
ঘ
9
ঙ
18

ব্যাখ্যা

Question: A and B can finish a job together in x days. If A alone can complete the job in x + 3 days, and B alone can complete it in x + 12 days, what is the value of x?

Solution:
A's 1 day's work = 1/(x + 3) part
B's 1 day's work = 1/(x + 12) part
(A + B)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/[(x + 3)(x + 12)] = 1/x
⇒ (2x + 15)/(x² + 15x + 36) = 1/x
⇒ 2x² + 15x = x² + 15x + 36
⇒ x² = 36
∴ x = 6

১৫,৮০৬.

In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 3 men take to eat 40kg of rice?

ক
ক) 12 days
খ
খ) 18 days
গ
গ) 36 days
ঘ
ঘ) None

ব্যাখ্যা

Question: In a training camp, 18 men can eat 20kg of rice in 3 days. How long will 3 men take to eat 40kg of rice?

Solution:
18 জন 20কেজি চাল খায় = 3দিনে
18 জন 1কেজি চাল খায় = 3/20দিনে
1 জন 1 কেজি চাল খায় = 3 × 18/20দিনে
3 জন 1 কেজি চাল খায় = (3 × 18)/(20 × 3) দিনে
3 জন 40 কেজি চাল খায় = (3 × 18 × 40)/(20 × 3)দিনে
= 36 দিনে

১৫,৮০৭.

In a business, A and C invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested by A and B was 3 : 2. If Tk. 2730 was their profit, how much amount did B receive?

ক
ক) Tk. 840
খ
খ) Tk. 1260
গ
গ) Tk. 630
ঘ
ঘ) Tk. 230

ব্যাখ্যা

Question: In a business, A and C invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested by A and B was 3 : 2. If Tk. 2730 was their profit, how much amount did B receive?

Solution:
A : B = 3 : 2 = 6 : 4
A : C = 2 : 1 = 6 : 3
A : B : C = 6 : 4 : 3

B's share = (4/13) × 2730 = Tk. 840

১৫,৮০৮.

A sum of Tk. 312 was divided among 100 boys and girls in such a way that each boys gets Tk. 3.6 and each girl Tk. 2.4. The number of girls is :

ক
35
খ
40
গ
42
ঘ
45

ব্যাখ্যা

Question: A sum of Tk. 312 was divided among 100 boys and girls in such a way that each boys gets Tk. 3.6 and each girl Tk. 2.4. The number of girls is :

Solution:
ধরি,
বালিকার সংখ্যা = x জন
বালকের সংখ্যা = (100 - x) জন

1 জন বালক পায় 3.60 টাকা
(100 - x) জন বালক পায় = 3.60 (100 - x) টাকা

1 জন বালিকা পায় = 2.40 টাকা
x জন বালিকা পায় = 2.40x টাকা

প্রশ্নমতে,
3.60(100 - x) + 2.40x = 312
⇒ 360 - 3.60x + 2.40x = 312
⇒ 360 - 1.2x = 312
⇒ 360 - 312 = 1.2x
⇒ 1.2x = 48
⇒ x = 48/1.2
⇒ x = 40

১৫,৮০৯.

The average of the first 6 numbers out of 7 is 25, and the average of the last 6 numbers is 29. If the first number is 10, what is the 7th number?

ক
30
খ
32
গ
34
ঘ
36

ব্যাখ্যা

Question: The average of the first 6 numbers out of 7 is 25, and the average of the last 6 numbers is 29. If the first number is 10, what is the 7th number?

Solution:
Given that,
First number = 10
Average of first 6 = 25
Average of last 6 = 29

Let,
the seven numbers be A₁, A₂, A₃, A₄, A₅, A₆, A₇
A₁ = 10

Sum of first 6 numbers = 6 × 25 = 150 …(1)
Sum of last 6 numbers = 6 × 29 = 174 …(2)

Subtract equation (1) from (2):
(A₂ + A₃ + A₄ + A₅ + A₆ + A₇) - (A₁ + A₂ + A₃ + A₄ + A₅ + A₆) = 174 - 150
⇒ A₇ - A₁ = 24
⇒ A₇ - 10 = 24
⇒ A₇ = 34

∴ The 7th number is 34.

১৫,৮১০.

In what time will the simple interest on 1200 Tk. at 4% per annum be the same as that on 600 Tk. at 8% per annum in 2 years?

ক
2 years
খ
3 years
গ
4 years
ঘ
8 years

ব্যাখ্যা

Question: In what time will the simple interest on 1200 Tk. at 4% per annum be the same as that on 600 Tk. at 8% per annum in 2 years?

Solution:
the interest of 600 Tk. at 8% per annum in 2 years is = 600 × 2 × 8%
= 96 Tk.

let, the time is n years.
I = 96 Tk.
P = 1200 Tk.
r = 4%

as we know,
I = Pnr
n = I / Pr
= 96 / (1200 × 4%)
= 2 years

১৫,৮১১.

Two hundred gallons of fuel oil are purchased at Tk. 910 per gallon and are consumed at a rate of Tk. 700 worth of fuel per hour. At this rate, how many hours are required to consume the 200 gallons of fuel oil?

ক
140
খ
220
গ
260
ঘ
322
ঙ
330

ব্যাখ্যা

Question: Two hundred gallons of fuel oil are purchased at Tk. 910 per gallon and are consumed at a rate of Tk. 700 worth of fuel per hour. At this rate, how many hours are required to consume the 200 gallons of fuel oil?

Solution:
The cost for the two hundred gallons is 910 × 200 = Tk. 182000

Thus, the number of hours to consume 200 gallons of fuel is 182000/700 = 260

১৫,৮১২.

A box contains three colored marbles, such that the number of blue, yellow and grey marbles is 8, 7 and 5 respectively. Find the probability of picking two marbles, one being blue marble and the other being grey marble.

ক
3/19
খ
5/19
গ
2/19
ঘ
4/19

ব্যাখ্যা

Question: A box contains three colored marbles, such that the number of blue, yellow and grey marbles is 8, 7 and 5 respectively. Find the probability of picking two marbles, one being blue marble and the other being grey marble.

Solution:
From the given data,
Number of blue marbles = 8
Number of yellow marbles = 7
Number of grey marbles = 5

∴ Probability = (⁸C₁ × ⁵C₁)/²⁰C₂
= (8 × 5)/190
= 40/190
= 4/19.
Hence, option(4) is correct.

১৫,৮১৩.

The roots of the equation 9x² - bx + 81 = 0 will be equal, if the value of b is

ক
ক) ±9
খ
খ) ±18
গ
গ) ±27
ঘ
ঘ) ±54

ব্যাখ্যা

When roots are equal, b² = 4ac
⇒ b² = 4×9×81
⇒ b² = 36×81 = 6 × 6 × 9 × 9
∴ b = ± 54

১৫,৮১৪.

A certain amount becomes Tk. 3000 at a simple interest of 12%. Keeping the time period the same, if the rate of simple interest is increased by 3%, the amount will become 300 Tk/- more than in the previous setting. What is the amount? Also find the time period.

ক
ক) Tk. 1500 and 7 years
খ
খ) Tk. 1800 and 5.5 years
গ
গ) Tk. 1900 and 8.25 years
ঘ
ঘ) Tk. 2000 and 20 years

ব্যাখ্যা

Let Simple Interest be S
Original sum 'P' and Time 'T' remains the same
Also, 3% increase in rate of interested means, New rate = 15%
Increase of 300 Rs/- in the final amount means, New amount = Tk. 3300/-

So, Amount 2 - Amount 1 = (P + S₁) - (P + S₂) = S₁ - S₂
∴ 3300 - 3000 = S₁ - S₂
∴ S₁ - S₂ = 300

∴ {(P × R × T)/100} - {(P × 12 × T)/100 = 300
3PT/100 = 300
PT = 10000
For R = 15%,

Simple interest = (P × 15 × T)/100
= (10000 × 15)/100
= Tk. 1500

Original sum = Amount - Interest = 3300 - 1500 = Tk. 1800 (Principle amount)

Also, PT = 10000
T = 10000/1800
= 5.55 years.

১৫,৮১৫.

If a man sells 1/4th of his goods sold at a profit of 10% and the remaining goods at a loss of 20%, what is his percentage profit or loss?

ক
12.5%
খ
15%
গ
12%
ঘ
25%

ব্যাখ্যা

Question: If a man sells 1/4th of his goods sold at a profit of 10% and the remaining goods at a loss of 20%, what is his percentage profit or loss?

সমাধান:
ধরি
মোট পণ্য = ১০০ টি
১০০টি পণ্যের মোট ক্রয়মূল্য = ১০০ টাকা

১০% লাভে,
২৫টি পণ্যের বিক্রয়মূল্য = (২৫ × ১১০)/১০০ = ২৭.৫ টাকা

২০% ক্ষতিতে
৭৫টি পণ্যের বিক্রয়মূল্য = (৭৫ × ৮০)/১০০ = ৬০ টাকা

∴ মোট বিক্রয়মূল্য = (২৭.৫ + ৬০) টাকা = ৮৭.৫ টাকা

∴ ক্ষতি = ১০০ - ৮৭.৫ = ১২.৫
∴ শতকরা ক্ষতি = {(১২.৫/১০০) × ১০০}% = ১২.৫%

১৫,৮১৬.

Three containers A, B and C are having mixtures of milk and water in the ratio 20 : 28, 18 : 30 and 8 : 40 respectively. Find the ratio of milk to water, if the mixtures of all the three containers are mixed together?

ক
ক) 6 : 5
খ
খ) 5 : 6
গ
গ) 53 : 115
ঘ
ঘ) 23 : 49
ঙ
ঙ) None of the Above

ব্যাখ্যা

At, A ; M : W = 20 : 28 = 5 : 7 = 5/12 : 7/12
At, B; M : W = 18 : 30 = 3 : 5 = 3/8 : 5/8
At C ; M : W = 8 : 40 = 1 : 5 = 1/6 : 5/6
M : W = (5/12 + 3/8 + 1/6) : ( 7/12 + 5/8 + 5/6)
= (20 + 18 + 8)/48 : (28 + 30 + 40)/48
= 46 : 98
= 23 : 49

১৫,৮১৭.

For what value of k (k > 0) will the lines 3x + 4y = 1 and 2x + Ky = 7 be parallel?

ক
8/5
খ
3/4
গ
7/3
ঘ
8/3

ব্যাখ্যা

Question: For what value of k (k > 0) will the lines 3x + 4y = 1 and 2x + Ky = 7 be parallel?

Solution:
Two lines are parallel if their slopes are equal.
Rewrite both equations in slope-intercept form (y = mx + c).

Now first line,
3x + 4y = 1
⇒ 4y = - 3x + 1
⇒ y = (- 3/4)x + 1/4
∴ Slope m₁ = - 3/4

And second line,
2x + Ky = 7
⇒ Ky = - 2x + 7
⇒ y = (- 2/K)x + 7/K (since k > 0, k ≠ 0)
∴ Slope m₂ = - 2/k

For the lines to be parallel:
m₁ = m₂
⇒ - 3/4 = - 2/k
⇒ 3/4 = 2/k
⇒ 3k = 8
∴ k = 8/3

So the lines will be parallel when k = 8/3.

১৫,৮১৮.

A dishonest shopkeeper mixed cheaper quality rice, priced at Tk. 10/KG with good quality rice, priced at Tk. 25/KG, and sells the mixture at Tk. 15/KG. Find the ratio in which he mixes the two qualities of rice.

ক
2 : 1
খ
2 : 3
গ
3 : 2
ঘ
4 : 3

ব্যাখ্যা

Question: A dishonest shopkeeper mixed cheaper quality rice, priced at Tk. 10/KG with good quality rice, priced at Tk. 25/KG, and sells the mixture at Tk. 15/KG. Find the ratio in which he mixes the two qualities of rice.

Solution:

Thus, the ratio of quantities of cheaper and good quality rice = 10 : 5 = 2 : 1

১৫,৮১৯.

If x and y are positive real numbers, then (2x⁰ - 5y⁰)⁴ = ?

ক
64
খ
16
গ
25
ঘ
81

ব্যাখ্যা

Question: If x and y are positive real numbers, then (2x⁰ - 5y⁰)⁴ = ?

Solution:
We know that for any positive real number,
x⁰ = 1 and y⁰ = 1

So, (2x⁰ - 5y⁰)⁴
= (2 × 1 - 5 × 1)⁴
= (2 - 5)⁴
= (- 3)⁴
= 81

The value of (2x⁰ - 5y⁰)⁴ is 81

১৫,৮২০.

একটি পরীক্ষায় বালিকাদের পাশ নম্বর এবং বালকদের পাশ নম্বর যথাক্রমে ৩৫% এবং ৪০%। একজন বালক ৪৮৩ নম্বর পেয়েও ১১৭ নম্বরের জন্য ফেল করলো। বালিকাদের পাশ নম্বর কত?

ক
৫১৫
খ
৫২৫
গ
৫৩০
ঘ
৫৩৫
ঙ
৫৪০

ব্যাখ্যা

প্রশ্ন: একটি পরীক্ষায় বালিকাদের পাশ নম্বর এবং বালকদের পাশ নম্বর যথাক্রমে ৩৫% এবং ৪০%। একজন বালক ৪৮৩ নম্বর পেয়েও ১১৭ নম্বরের জন্য ফেল করলো। বালিকাদের পাশ নম্বর কত?

সমাধান:
ধরি,
মোট নম্বর = ক
তাহলে, বালিকাদের পাশ নম্বর = ৩৫ক/১০০ = ৭ক/২০
বালকের পাশ নম্বর = ৪৮৩ + ১১৭ = ৬০০

প্রশ্নমতে,
৪০ক/১০০ = ৬০০
⇒ ৪০ক = ৬০০০০
∴ ক = ১৫০০

∴ বালিকাদের পাশ নম্বর = (৭ × ১৫০০)/২০ = ৫২৫

১৫,৮২১.

If x + 1/x = 6; find the value of 3x/(6x² - 5x + 6)?

ক
ক) 1/11
খ
খ) 3/32
গ
গ) 3/31
ঘ
ঘ) 5/27

ব্যাখ্যা

Question: If x + 1/x = 6; find the value of 3x/(6x² - 5x + 6)?

Solution:

১৫,৮২২.

The value of is?

ক
ক) 1
খ
খ) 0
গ
গ) - 1
ঘ
ঘ) √3

ব্যাখ্যা

Question: The value of is?

Solution:

১৫,৮২৩.

What should come in place of both the question marks in the equation -
?/√128 =√162/?

ক
6
খ
12
গ
18
ঘ
24

ব্যাখ্যা

Let, x/√128 = √162/x
⇔ x² = √(128 × 162)
⇔ x² = √(64 × 2 × 18 × 9)
⇔ x² = √(8² × 6² × 3²)
⇔ x² = 8 × 6 × 3
⇔ x² = 144
⇔ x = √144
⇔ x = 12

১৫,৮২৪.

The height of an equilateral triangle with a side 2 cm is -

ক
ক) √3 cm
খ
খ) √2 cm
গ
গ) √5 cm
ঘ
ঘ) √7 cm
ঙ
ঙ) 4√5 cm

ব্যাখ্যা

আমরা জানি, সমবাহু ত্রিভুজের শীর্ষবিন্দু হতে ভূমির উপর অঙ্কিত লম্ব ভূমিকে সমদ্বিখণ্ডিত করে
তাই, BD = DC = 1 cm
পীথাগোরাসের সূত্র অনুসারে ΔABD হতে পাই,
⇒ AB² = BD² + AD²
⇒ AD² = AB² - BD² = 2² - 1²
∴ AD = √3

১৫,৮২৫.

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

ক
3 : 4
খ
4 : 3
গ
5 : 3
ঘ
Data inadequate
ঙ
None of these

ব্যাখ্যা

Question: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Solution:
(20 × 16) = 320 women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/320

(16 × 15) = 240 men can complete the work in 1 day.
1 man's 1 day's work = 1/240

So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4 : 3

১৫,৮২৬.

Find the H.C.F. of p(x) = 2x³ - 3x² - 2x + 3 and q(x) = 3x² + 8x + 5.

ক
(2x + 1)
খ
(x + 1)
গ
(2x - 3)
ঘ
(x - 1)

ব্যাখ্যা

Question: Find the H.C.F. of p(x) = 2x³ - 3x² - 2x + 3 and q(x) = 3x² + 8x + 5.

Solution:
Given that,
p(x) = 2x³ - 3x² - 2x + 3 and q(x) = 3x² + 8x + 5

Now,
The factors of p(x) = 2x³ - 3x² - 2x + 3
⇒ x²(2x - 3) - 1(2x - 3)
⇒ (x² - 1)(2x - 3)
⇒ (x + 1)(x - 1)(2x - 3)

And,
The factors of q(x) = 3x² + 8x + 5
⇒ 3x² + 5x + 3x + 5
⇒ x(3x + 5) + 1(3x + 5)
⇒ (3x + 5)(x + 1)

∴ The required H.C.F. is (x + 1).

১৫,৮২৭.

Five friends are standing in a line for a photo. Alice is to Bob's immediate right. Charlie is between David and Eve. Bob is to the left of David. Who is in the middle of the line?

ক
Charlie
খ
David
গ
Alice
ঘ
Eve

ব্যাখ্যা

Question: Five friends are standing in a line for a photo. Alice is to Bob's immediate right. Charlie is between David and Eve. Bob is to the left of David. Who is in the middle of the line?

Solution:
Alice is to Bob's immediate right: Bob ⇔ Alice
Charlie is between David and Eve: David ⇔ Charlie ⇔ Eve
Bob is to the left of David: Bob ⇔ David

Combining these pieces of information:
Bob ⇔ Alice ⇔ David ⇔ Charlie ⇔ Eve

The person standing in the middle of the line is David.

১৫,৮২৮.

Bob invested in a stock that increased in value by 17% to 25.74. What was the actual increase in the stock’s value?

ক
ক) 3.74
খ
খ) 3.47
গ
গ) 4.25
ঘ
ঘ) 4.47

ব্যাখ্যা

17% বৃদ্ধিতে বর্তমান মূল্য = 117 টাকা
বর্তমান মূল্য 117 টাকা হলে পূর্ব মূল্য = 100 টাকা
∴ বর্তমান মূল্য 25.74 টাকা হলে পূর্ব মূল্য = (100 × 25.74)/100 টাকা
= 22 টাকা
∴ প্রকৃত মূল্য বৃদ্ধি = 25.74 - 22 = 3.74

১৫,৮২৯.

The compound interest on Tk 30,000 at 7% per annum is TK.4357. The period (in years) is:

ক
ক) 2
খ
খ) 2.5
গ
গ) 3
ঘ
ঘ) 4

ব্যাখ্যা

Amount = Tk.(30000+4347) = Tk.34347
let the time be n year
Then,
30000(1+7/100)n = 34347
(107/100)n = 34347/30000 = 11449/10000 = (107/100)2
n = 2year

১৫,৮৩০.

A boat covers a certain distance in half an hour downstream with the speed of 20km/hr in still water and the speed of the current is 4km/hr. Then the distance travelled by the boat is:

ক
6km
খ
7km
গ
12km
ঘ
4km

ব্যাখ্যা

Given that,
The speed of a boat in still water is 20 km/hr
The speed of the stream is 4 km/hr.
Then,
The speed downstream = (20 + 4) km/hr
= 24 km/hr
The distance travelled in half an hour = 24 x 1/2
= 12 km
Hence the distance travelled by the boat is 12 km.

১৫,৮৩১.

A person takes a loan of 200 taka at 5% simple interest. He returns 100 taka at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay-

ক
ক) 100 taka
খ
খ) 110 taka
গ
গ) 110.5 taka
ঘ
ঘ) 115.5 taka

ব্যাখ্যা

Question: A person takes a loan of 200 taka at 5% simple interest. He returns 100 taka at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay-

Solution:
১ বছরে সুদ = ২০০ × ৫/১০০ টাকা
= ১০ টাকা

১ বছর শেষে সে ১০০ টাকা ফেরত দেয়।

বাকি আছে = ২১০ - ১০০ টাকা
= ১১০ টাকা

১১০ টাকা এক বছরে সুদাসলে হয় = ১১০ + ১১০ × ৫/১০০
= ১১৫.৫ টাকা

অতএব, ২য় বছর শেষে তাকে ১১৫.৫ টাকা দিতে হবে।

১৫,৮৩২.

Find the equation of the vertical line passing through the point (5, - 3).

ক
y = - 3
খ
x = - 3
গ
y = 5
ঘ
x = 5

ব্যাখ্যা

Question: Find the equation of the vertical line passing through the point (5, - 3).

Solution:
একটি উল্লম্ব রেখা (vertical line) হলো এমন একটি সরলরেখা যা Y-অক্ষের সমান্তরাল। এই ধরনের রেখার একটি বিশেষ বৈশিষ্ট্য হলো, এই রেখার উপর অবস্থিত প্রতিটি বিন্দুর x-স্থানাঙ্ক (x-coordinate) একই থাকে, কিন্তু y-স্থানাঙ্ক (y-coordinate) পরিবর্তিত হতে পারে।

উল্লম্ব রেখার (vertical line) সাধারণ সমীকরণ হলো: x = a
যেখানে a একটি ধ্রুবক সংখ্যা এবং রেখার প্রতিটি বিন্দুর x এর মান একই থাকে।

প্রশ্নে বলা হয়েছে রেখাটি (5, - 3) বিন্দুর মধ্য দিয়ে যায়।
যেহেতু, আমরা জানি, একটি উল্লম্ব রেখার প্রতিটি বিন্দুর x-স্থানাঙ্ক একই থাকে, এবং এই বিন্দুর x-স্থানাঙ্ক হলো 5, সুতরাং, রেখাটির সমীকরণ হবে:
x = 5

১৫,৮৩৩.

What is the reciprocal of the sum of the reciprocals of 7 and 6?

ক
1/13
খ
42/13
গ
13/42
ঘ
1/26

ব্যাখ্যা

Question: What is the reciprocal of the sum of the reciprocals of 7 and 6?

Solution:
Let,
a = 7, b = 6, and sum = s
s = (1/a) + (1/b)
= (1/7) + (1/6)
= (6 + 7)/42
= 13/42

∴ The reciprocal of the sum = 1/(13/42)
= 42/13

১৫,৮৩৪.

A man lends Tk. 10000 in four parts. If he gets 8% on TK. 2000, 7.5% on TK. 4000 and 8.5% on TK. 1400, what percent must he get for the remainder, if the average interest is 8.13%?

ক
7
খ
9.25
গ
9
ঘ
10.5
ঙ
None of these

ব্যাখ্যা

Question: A man lends Tk. 10000 in four parts. If he gets 8% on TK. 2000, 7.5% on TK. 4000 and 8.5% on TK. 1400, what percent must he get for the remainder, if the average interest is 8.13%?

Solution:
∵ [(2000 × 8 × 1)/100] + [(4000 × 7.5 × 1)/100] + [(1400 × 8.5 × 1)/100] + [(2600 × R × 1)/100] = (10000 × 8.13 ×1)/100
⇒ 160 + 300 + 119 + 26R = 813
⇒ 26R = 234
⇒ R = 9%

১৫,৮৩৫.

A wheel rotates 10 times per minute and moves 20 feet during each rotation, How many feet does the wheel move in 1 hour.

ক
1200
খ
600
গ
12,000
ঘ
None

ব্যাখ্যা

Question: A wheel rotates 10 times per minute and moves 20 feet during each rotation, How many feet does the wheel move in 1 hour.

Solution:
Number of rotation per hour = 10 × 60 = 600 ft
Movement of the wheel per hour = 600 × 20 = 12000 ft

১৫,৮৩৬.

6 pipes, working 10 hours a day, can empty a cistern in 3 days. How many hours a day must 9 pipes work to empty the cistern in one day?

ক
38 hours
খ
26 hours
গ
32 hours
ঘ
20 hours
ঙ
None of the above

ব্যাখ্যা

Question: 6 pipes, working 10 hours a day, can empty a cistern in 3 days. How many hours a day must 9 pipes work to empty the cistern in one day?

Solution:
By applying the MDH method,
it can be written as,

6 × 10 × 3 = 9 × x × 1
⇒ x = 20 hours

১৫,৮৩৭.

A man was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know how old I am". What is the age of the man?

ক
18
খ
24
গ
27
ঘ
36

ব্যাখ্যা

Question: A man was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know how old I am". What is the age of the man?

Solution:
Let the age of the man be = p years
Then,
⇒ 3(p + 3) - 3(p - 3) = p
⇒ 3p + 9 - 3p + 9 = p
⇒ p = 18
∴ The age of the man is 18 years.

১৫,৮৩৮.

A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up than to row down the river. Find the rate of stream -

ক
ক) 5.2 km/hr
খ
খ) 2.5 km/hr
গ
গ) 3.5 km/hr
ঘ
ঘ) 5.3 km/hr
ঙ
ঙ) None of these

ব্যাখ্যা

Let rate of stream be y km/hr, distance be d km
time upstream = 2 (time downstream)
⇒ d/(7.5 − y) = 2d/(7.5 + y)
⇒ 2( 7.5 − y ) = 7.5 + y
⇒ 15 − 2 y = 7.5 + y
⇒ 3 y = 7.5
⇒ y = 2.5

১৫,৮৩৯.

If x²= 2.89, what is the value of x?

ক
ক) 0.7
খ
খ) 1.6
গ
গ) 1.7
ঘ
ঘ) 2.7

ব্যাখ্যা

Question: If x²= 2.89, what is the value of x?

Solution:
x² = 2.89
⇒ x = √2.89
= √(289/100)
= 17/10
= 1.7

১৫,৮৪০.

I have two inlet pipes in my tank. Pipe P is diametrically bigger than Q and can fill a tank alone in 22 hours while Pipe Q takes 11 hours longer than Pipe P to fill the tank. If I open both the inlet pipes together, how long will they take to fill the tank?

ক
ক) 19/22 hours
খ
খ) 1(1/11) hours
গ
গ) 13(1/5) hours
ঘ
ঘ) 18 hours

ব্যাখ্যা

Tank filled or work done by P in 1 hour = 1/22
Tank filled or work done by Q in 1 hour (Q takes 11 hrs more than P) = 1/33

Tank filled or work done by both pipes in 1 hour = 1/22 + 1/33 = 5/66
So the entire tank is full in = 66/5 = 13(1/5) hours.

১৫,৮৪১.

A pole 90 meters long breaks into two parts without complete separation and makes an angle of 30° with the ground. Find the length of the broken part of the pole.

ক
45 meters
খ
50 meters
গ
60 meters
ঘ
30 meters

ব্যাখ্যা

Question: A pole 90 meters long breaks into two parts without complete separation and makes an angle of 30° with the ground. Find the length of the broken part of the pole.

Solution:

ধরি, খুঁটির মোট দৈর্ঘ্য = 90 m
ভাঙা অংশটির দৈর্ঘ্য, AC = x
অবশিষ্ট অংশটির দৈর্ঘ্য, AB = (90 - x)

আমরা জানি,
sin θ = লম্ব/অতিভুজ
sin 30°= BC/CD
∴ 1/2 = (90 - x)/x
⇒ x = 2(90 - x)
⇒ x = 180 - 2x
⇒ 3x = 180
∴ x = 60 m

অতএব, খুঁটির ভাঙা অংশটির দৈর্ঘ্য = 60 meters।

১৫,৮৪২.

The ages of Sakil and Lamia are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their present ages?

ক
6 years
খ
8 years
গ
10 years
ঘ
12 years

ব্যাখ্যা

Question: The ages of Sakil and Lamia are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their present ages?

Solution:
Let, their ages are 7x, 3x

ATQ,
(7x + 6)/(3x + 6) = 5/3
⇒ 3(7x + 6) = 5(3x + 6)
⇒ 21x + 18 = 15x + 30
⇒ 21x - 15x = 30 - 18
⇒ 6x = 12
∴ x = 2

The difference in their ages is = 7x - 3x
= 4x
= 4 × 2
= 8 years

১৫,৮৪৩.

An observer 1.6 m tall is 20√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

ক
21.6 m
খ
23.2 m
গ
24.72 m
ঘ
20 m

ব্যাখ্যা

Question: An observer 1.6 m tall is 20√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

Solution:

Here,
Height of the observer AB = 1.6 m
Distance between observer and tower AC = 20√3 m
∴ CE = AB = 1.6 m
Height of the tower is CD = CE + DE.

From ΔBDE we get,
BE = AC = 20√3 m

Now,
tan30° = DE/BE
⇒ 1/√3 = DE/(20√3)
⇒ DE = (20√3)/√3
∴ DE = 20

∴ The height of the tower is = CE + DE = 1.6 + 20 m = 21.6 m

১৫,৮৪৪.

In a class with a certain number of students if one new student weighing 50 kg is added, then average weight of class is increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?

ক
ক) 46
খ
খ) 42
গ
গ) 27
ঘ
ঘ) 47

ব্যাখ্যা

Let x be the number of students in the class and y be the average weight of the class
Now according to question,
(xy + 50)/(x + 1) = y + 1
x + y = 49 .......... (i) Again,
(xy + 50 + 50)/(x + 2) = y + 1.5
1.5x + 2y = 97.......... (ii) From equation (i) and (ii), we get y = 47
Answer: 47

১৫,৮৪৫.

The average of the first six multiples of 3 is-

ক
12.5
খ
9.25
গ
8
ঘ
10.5

ব্যাখ্যা

Question: The average of the first six multiples of 3 is-

Solution:
The first six multiples of 3 are,
3, 6, 9, 12, 15, 18

The sum of these multiples is,
3 + 6 + 9 + 12 + 15 + 18 = 63

∴ Average = 63/6 = 10.5
The average of the first six multiples of 3 is 10.5

১৫,৮৪৬.

If A is to the south of B and C is to east of B, in what direction is A with respect to C?

ক
ক) north-east
খ
খ) north-west
গ
গ) south-east
ঘ
ঘ) south-west

ব্যাখ্যা

Question: If A is to the south of B and C is to east of B, in what direction is A with respect to C?

Solution:

১৫,৮৪৭.

Calculate the area of a triangle whose sides are 13 meters, 14 meters, and 15 meters.

ক
84 m²
খ
62 m²
গ
74 m²
ঘ
58 m²

ব্যাখ্যা

Question: Calculate the area of a triangle whose sides are 13 meters, 14 meters, and 15 meters.

Solution:
We know,
Area of a scalene triangle = √{s(s - a)(s - b)(s - c)}
where, s = (a + b + c)/2
= (13 + 14 + 15)/2 = 42/2
= 21

∴ Area = √{21(21 - 13)(21 - 14)(21 - 15)}
= √(21 × 8 × 7 × 6 )
= √(9 × 4 × 196)
= 3 × 2 × 14
= 84 m²

১৫,৮৪৮.

If x + (1/x) = 2, then the value of x⁷ + (1/x⁵) =?

ক
2⁵
খ
2
গ
2¹²
ঘ
2⁷

ব্যাখ্যা

Question: If x + (1/x) = 2, then the value of x⁷ + (1/x⁵) =?

Solution:
x + (1/x) = 2
⇒ x² + 1 = 2x
⇒ x² - 2x + 1 = 0
⇒ (x - 1)² = 0
∴ x = 1

x⁷ + (1/x⁵)
= 1⁷ + 1/1⁵
= 1 + 1
= 2

১৫,৮৪৯.

At a conference, everyone shakes hands with everybody else. If there were 105 handshakes, how many people were at the conference?

ক
12
খ
14
গ
15
ঘ
19

ব্যাখ্যা

Question: At a conference, everyone shakes hands with everybody else. If there were 105 handshakes, how many people were at the conference?

Solution:
ধরি, কনফারেন্সে x সংখ্যক লোক ছিল।
দুজন ব্যক্তির মধ্যে একটি হ্যান্ডশেক হয়, যা Combination দিয়ে প্রকাশ করা যায়।

প্রশ্নমতে,
^xC₂ = 105
⇒ x!/(2!(x - 2)!) = 105
⇒ {x(x - 1)(x - 2)!}/{2 × 1 × (x - 2)!} = 105
⇒ x(x - 1)/2 = 105
⇒ x(x - 1) = 210
⇒ x² - x - 210 = 0
⇒ x² - 15x + 14x - 210 = 0
⇒ x(x - 15) + 14(x - 15) = 0
⇒ (x - 15)(x + 14) = 0

হয় x - 15 = 0 অথবা x + 14 = 0
∴ x = 15 অথবা x = -14

যেহেতু লোকসংখ্যা ঋণাত্মক হতে পারে না, তাই x = 15

অতএব, কনফারেন্সে 15 জন লোক ছিল।

১৫,৮৫০.

10 boys or 20 girls can do a task in 10 days both. If 5 boys and 5 girls is assigned for the task, how much time will it take to complete half of the task ?

ক
20/3 days
খ
20/7 days
গ
40/3 days
ঘ
25/6 days

ব্যাখ্যা

Question: 10 boys or 20 girls can do a task in 10 days both. If 5 boys and 5 girls is assigned for the task, how much time will it take to complete half of the task ?

Solution:
10 boys can do in one day = 1/10
5 boys can do in ne day = 1/20

20 girls can do in one day = 1/10
∴ 5 girls can do in one day = 1/40

so in one day 5 boys and 5 girls can do = 1/20 + 1/40
= 3/40

∴ time required to do the full task = 40/3 days
∴ time to do half the task = 20/3 days

১৫,৮৫১.

What is the probability of getting a sum of six if two dice are thrown at once?

ক
ক) 5/36
খ
খ) 7/36
গ
গ) 2/3
ঘ
ঘ) 1/36

ব্যাখ্যা

We know, the probability of an event = Favorable outcomes / Total outcomes.
In a case of two dices, Total outcomes = 6 × 6 = 36
A.T.Q favorable outcome is a sum of 6,
Ways of obtaining a sum of 6 (1,5), (5,1), (2,4), (4,2) and (3,3).
Thus, there are 5 ways in which 6 can be obtained using two dices.
Therefore, required probability, P = 5/36

১৫,৮৫২.

A coin is tossed four times, if H = head and T = tail, what is the probability of the tosses coming up in the order HHTH?

ক
1/8
খ
3/8
গ
1/16
ঘ
1/4

ব্যাখ্যা

Question: A coin is tossed four times, if H = head and T = tail, what is the probability of the tosses coming up in the order HHTH?

Solution:
Here, Coin is tossed four times.
The total possible outcomes = 16
Outcome = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Favourable outcome = 1 [HHTH]
∴ Probability = 1/16

১৫,৮৫৩.

The equation cos²θ = (x + y)²/4xy is only possible when ?

ক
x > y
খ
x = -y
গ
x < y
ঘ
x = y

ব্যাখ্যা

Question: The equation cos²θ = (x + y)²/4xy is only possible when ?

Solution:
Given that,
cos²θ = (x + y)²/4xy
⇒ 1 = (x + y)²/4xy ; [Max value of cos²θ = 1 ]
⇒ 4xy = (x + y)²
⇒ 4xy = x² + y² + 2xy
⇒ 0 = x² + y² - 2xy
⇒ (x - y)² = 0
⇒ x - y = 0
⇒ x = y

Therefore, the given equation is possible only when x = y.

১৫,৮৫৪.

There are 3 green, 4 orange and 5 white color bulbs. If a bulb is picked at random, what is the probability of having either a green or a white bulb?

ক
ক) 2/3
খ
খ) 3/4
গ
গ) 4/3
ঘ
ঘ) 2/5

ব্যাখ্যা

সবুজ রঙের বাল্ব = 3
কমলা রঙের বাল্ব = 4
সাদা রঙের বাল্ব =5

মোট বাল্ব আছে = 3 + 4 + 5 = 12 টি

মোট সবুজ ও সাদা বাল্ব আছে = (3 + 5) = 8টি
একটি সবুজ বা সাদা বাল্ব পাওয়ার সম্ভাবনা = 8/12 = 2/3

১৫,৮৫৫.

16, 25, 36, 72, 144, 196, 225

ক
ক) 36
খ
খ) 72
গ
গ) 196
ঘ
ঘ) 225

ব্যাখ্যা

Each of the numbers except 72 is a perfect square.

১৫,৮৫৬.

স্কীম A থেকে স্কীম B তে তিনগুণ বিনিয়োগ করা হলো। বার্ষিক ৮% সরল সুদে ৪ বছরের জন্য A তে এবং বার্ষিক ১৩% হারে ২ বছরের জন্য B তে বিনিয়োগ করা হলো। দুইটি স্কীম থাকে বার্ষিক সুদ আয় ১৩২০ টাকা। স্কীম A তে কত টাকা বিনয়োগ করা হলো?

ক
৯৮৮ টাকা
খ
১০৪০ টাকা
গ
১২০০ টাকা
ঘ
৮০০ টাকা
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: স্কীম A থেকে স্কীম B তে তিনগুণ বিনিয়োগ করা হলো। বার্ষিক ৮% সরল সুদে ৪ বছরের জন্য A তে এবং বার্ষিক ১৩% হারে ২ বছরের জন্য B তে বিনিয়োগ করা হলো। দুইটি স্কীম থাকে বার্ষিক সুদ আয় ১৩২০ টাকা। স্কীম A তে কত টাকা বিনয়োগ করা হলো?

সমাধান:
ধরি,
A তে বিনিয়োগের পরিমাণ = ক টাকা
B তে বিনিয়োগের পরিমাণ = ৩ক টাকা

প্রশ্নমতে,
{(ক × ৪ × ৮)/১০০} + {(৩ক × ২ × ১৩)/১০০} = ১৩২০
⇒ (৩২ক/১০০) + (৭৮ক/১০০) = ১৩২০
⇒ (৩২ক + ৭৮ক)/১০০ = ১৩২০
⇒ (১১০ক/১০০) = ১৩২০
⇒ ক = (১৩২০ × ১০০)/১১০
∴ ক = ১২০০

১৫,৮৫৭.

If radius of a circle is increased by 30% then its area is increased by

ক
ক) 40%
খ
খ) 70%
গ
গ) 50%
ঘ
ঘ) 69%

ব্যাখ্যা

Question: If radius of a circle is increased by 30% then its area is increased by

Solution:
ধরি,
ব্যাসার্ধ = r
∴ ক্ষেত্রফল = πr²

30% বৃদ্ধিতে ব্যাসার্ধ = 130r/100
এবং ক্ষেত্রফল = π×(130r/100)²
= π(169r²/100)

ক্ষেত্রফল বৃদ্ধি = 169πr²/100 - πr²
(169/100 - 1)πr²
= (69/100)πr²

∴ ক্ষেত্রফল বৃদ্ধির হার = (69πr² × 100)/(100 × πr²)
= 69%

১৫,৮৫৮.

The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is -

ক
ক) 30
খ
খ) 34
গ
গ) 44
ঘ
ঘ) 24

ব্যাখ্যা

Required number = (Sum of all numbers) - [(Sum of first 5 numbers) + (Sum of last 3 numbers)]
= 50 x 9 - (54 x 5 + 3 x 52)
= 450 - (270 + 156)
= 450 - 426
= 24

১৫,৮৫৯.

Animesh takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Animesh can do the work alone in -

ক
12 days
খ
15 days
গ
18 days
ঘ
20 days

ব্যাখ্যা

Question: Animesh takes twice as much as Bimol or thrice as much time as Rafi to finish a piece of work. Working together, they can finish the work in 3 days. Animesh can do the work alone in -

Solution:
Let, Animesh, Bimol, and Rafi take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively.

Now,
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, Animesh takes = 6 × 3 = 18 days

১৫,৮৬০.

If x + 1/x = 3 then x − 1/x =?

ক
ক) √5
খ
খ) √13
গ
গ) √7
ঘ
ঘ) 0

ব্যাখ্যা

x + 1/x = 3
Or, (x + 1/x)² = 9
Or, (x - 1/x)² + 4.x.1/x = 9
Or, (x - 1/x)² = 9 - 4 = 5
Or, (x - 1/x) = √5

১৫,৮৬১.

কমলার দাম ৮% কমে যাওয়ায় ৫০০ টাকায় পূর্বাপেক্ষা ১ হালি কমলা বেশি পাওয়া যায়। এক ডজন কমলার বর্তমান মূল্য কত?

ক
১৪০ টাকা
খ
১৩০ টাকা
গ
১২০ টাকা
ঘ
১৫০ টাকা
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: কমলার দাম ৮% কমে যাওয়ায় ৫০০ টাকায় পূর্বাপেক্ষা ১ হালি কমলা বেশি পাওয়া যায়। এক ডজন কমলার বর্তমান মূল্য কত?

সমাধান:
কমলার দাম ৮% কমে যাওয়ায়,
১০০ টাকায় কমে = ৮ টাকা
১ টাকায় কমে = ৮/১০০ টাকা
৫০০ টাকায় কমে = (৮ × ৫০০)/১০০ টাকা
= ৪০ টাকা

শর্তমতে, ৪০ টাকায় পাওয়া যায় ১ হালি বা ৪টি কমলা।
∴ ১ টি কমলার দাম = ৪০/৪ = ১০ টাকা
∴ ১২টি কমলার দাম = ১২ × ১০ = ১২০ টাকা

১৫,৮৬২.

In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?

ক
ক) 4 : 1
খ
খ) 5 : 1
গ
গ) 6 : 1
ঘ
ঘ) 8 : 1

ব্যাখ্যা

Question: In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?

Solution:
Let he has to make milk to water ratio 1 : x to earn 20% profit
Let the cost price of milk be C/L

Then According to the question,
C × (x + 1) = C × (120/100)
⇒ x + 1 = 6/5
⇒ x = 6/5 - 1
⇒ x = 1/5

So milk to water ratio = 1 : x
= 1 : 1/5
= 5 : 1

১৫,৮৬৩.

Which one of the following is not a prime number?

ক
31
খ
61
গ
71
ঘ
91

ব্যাখ্যা

Question: Which one of the following is not a prime number?

Solution:
91 is divisible by 7.
So, it is not a prime number.

• ১ এর চেয়ে বড় যে সকল সংখ্যাকে শুধু ১ এবং ঐ সংখ্যা ছাড়া আর কোনো সংখ্যা দ্বারা ভাগ করা যায় না, তাদেরকে মৌলিক সংখ্যা বলে।
অর্থাৎ মৌলিক সংখ্যার উৎপাদক হবে দুইটি ১ এবং শুধুমাত্র সেই সংখ্যাটি।

১৫,৮৬৪.

In a certain code MONKEY is written as XDJMNL. How is 'TIGER' written as?

ক
QCFHS
খ
JDFHS
গ
QDFHS
ঘ
QDFIS

ব্যাখ্যা

Question: In a certain code MONKEY is written as XDJMNL. How is 'TIGER' written as?

Solution:
এখানে, শব্দটিকে প্রথমে উল্টানো হয়, তারপর উল্টানো শব্দের অক্ষরগুলোর আগের অক্ষরটি নেয়া হয়।
MONKEY কে উল্টিয়ে পাওয়া যায় YEKNOM
YEKNOM শব্দের অক্ষরগুলোর আগের অক্ষরটি নেয়া হলে XDJMNL

অনুরূপভাবে,
TIGER কে উল্টিয়ে পাওয়া যায় REGIT
REGIT শব্দের অক্ষরগুলোর আগের অক্ষরটি নেয়া হলে QDFHS

১৫,৮৬৫.

Anika is taller than Bristi but shorter than Kabir. Rafi is shorter than Bristi. Shawon is taller than Anika but shorter than Kabir. Who is the smallest among them?

ক
Kabir
খ
Anika
গ
Bristi
ঘ
Shawon
ঙ
Rafi

ব্যাখ্যা

Question: Anika is taller than Bristi but shorter than Kabir. Rafi is shorter than Bristi. Shawon is taller than Anika but shorter than Kabir. Who is the smallest among them?

Solution:
From the given statements,
Anika > Bristi
Kabir > Anika
∴ Kabir > Anika > Bristi

Rafi < Bristi
∴ Bristi > Rafi

And
Shawon > Anika
Kabir > Shawon
∴ Kabir > Shawon > Anika

Full order from tallest to smallest,
Kabir > Shawon > Anika > Bristi > Rafi

Therefore, Rafi is the smallest among them.

১৫,৮৬৬.

cosθ√(sec²θ - 1) = ?

ক
- sinθ
খ
sinθ
গ
cosθ
ঘ
2cosθ

ব্যাখ্যা

Question: cosθ√(sec²θ - 1) = ?

Solution:
cosθ√(sec²θ - 1)
= cosθ√tan²θ
= cosθ (sinθ/cosθ)
= sinθ

১৫,৮৬৭.

In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

ক
100
খ
200
গ
220
ঘ
150

ব্যাখ্যা

Question: In a cash box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170, then what is the number of 10 paisa coin?

Solution:
let, there are x numbers of 10 paisa, 25 paisa and 50 paisa coins.

We know that,
1 tk = 100 paisa

ATQ,
10x/100 + 25x/100 + 50x/100 = 170
⇒ x {(10/100) + (25/100) + (50/100)} = 170
⇒ x (1/10 + 1/4 + 1/2) = 170
⇒ x{(2 + 5 + 10)/20} = 170
⇒ 17x/20 = 170
⇒ x = (170 × 20)/17
∴ x = 200

১৫,৮৬৮.

A train having length 150 m passes a platform of 550 m length. The time taken for it is 56 seconds. In how much time will this train take to pass a platform of 250 m length?

ক
24 seconds
খ
30 seconds
গ
28 seconds
ঘ
32 seconds

ব্যাখ্যা

Question: A train having length 150 m passes a platform of 550 m length. The time taken for it is 56 seconds. In how much time will this train take to pass a platform of 250 m length?

Solution:
We know,
When a train passes a platform, the total distance to be covered is,
Length of train + Length of platform

Case 1:
Distance covered = 150 m + 550 m = 700 m
Time taken = 56 seconds
∴ Speed of the train = Distance/Time
= 700/56
= 12.5 m/s

Case 2:
Length of new platform = 250 m
∴ Total distance to be covered now = 150 + 250 = 400 m
Time taken to pass the new platform = Distance/Speed
= 400m/12.5 m/s
= 32 seconds

So the train will take 32 seconds to pass the platform of 250 m length.

১৫,৮৬৯.

The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

ক
ক) 15 cm
খ
খ) 25 cm
গ
গ) 35 cm
ঘ
ঘ) 45 cm

ব্যাখ্যা

7 m = 700 cm
3 m 85 cm = 385 cm
12 m 95 cm = 1295 cm
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm
= 35 cm

১৫,৮৭০.

Nasim has saved 135 Taka by purchasing a blanket with 15% discount on it. what is the quoted price of the blanket in Taka?

ক
Tk. 300
খ
Tk. 400
গ
Tk. 700
ঘ
Tk. 900

ব্যাখ্যা

Question: Nasim has saved 135 Taka by purchasing a blanket with 15% discount on it. what is the quoted price of the blanket in Taka?

Solution:
15% ছাড়ে,
15 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100 টাকা
1 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য 100/15 টাকা
∴ 135 টাকা ছাড় পাওয়া যায় যখন তালিকামূল্য (100 × 135)/15 টাকা
= 900 টাকা

১৫,৮৭১.

If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?

ক
11 burners
খ
5 burners
গ
13 burners
ঘ
7 burners
ঙ
3 burners

ব্যাখ্যা

Question: If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?

Solution:
Given that,
5 burners 5 hours a day for 7 days is Tk. 525
Total burner-hours = (5 × 5 × 7) burner-hours
= 175 burner-hours

Cost per burner-hour =(525 ÷ 175)
= 3 Tk

∴ 750 Tk. total burner-hour = (750 ÷ 3) burner-hours
= 250 burner-hours

Let, the number of burners = x

ATQ,
x × 5 × 10 = 250
⇒ x × 50 = 250
⇒ x = 250 ÷ 50
∴ x = 5

১৫,৮৭২.

What is the probability of getting a sum of 10 from two throws of a dice?

ক
2/5
খ
3/10
গ
1/12
ঘ
7/10

ব্যাখ্যা

Question: What is the probability of getting a sum of 10 from two throws of a dice?

Solution:
Total events = (6 × 6) = 36
events to get a sum of 10 is -
{(6, 4), (5, 5), (4, 6)}

probability = 3/36 = 1/12

১৫,৮৭৩.

A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in-

ক
4 hours
খ
6 hours
গ
8 hours
ঘ
9 hours

ব্যাখ্যা

Question: A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in-

Solution:
Ratio of times taken by A and B = 100/80 = 5/4
Let
B takes x days to do the work

ATQ,
5/4 = (15/2)/x
⇒ 5/4 = (15/2)/x
⇒ 5x = (15 × 4)/2
⇒ 5x = 30
∴ x = 6 hours

১৫,৮৭৪.

In how many different ways can the letters of the word ''CANDIDATE'' be arranged in such a way that the vowels always come together?

ক
4320
খ
1440
গ
720
ঘ
840

ব্যাখ্যা

There are 9 letters in the given word, out of which 4 are vowels.
In the word ''CANDIDATE'' we treat the vowels ''AIAE'' as one letter.
Thus, we have CNDDT(AIAE).
Now, we have to arrange 6 letters, out of which D occurs twice.
Therefore,
Number of ways of arranging these letters = 6!/2!
= 720/2
= 360 ways.
Now,
AIAE has 4 letters, in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = 4!/2! = (1 × 2 × 3 × 4)/2
= 12
Therefore, required number of words = (360 × 12)
= 4320.

১৫,৮৭৫.

The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.

ক
65
খ
72
গ
76
ঘ
80

ব্যাখ্যা

Question: The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.

Solution:
let one number is x
other is 184 - x

x/3 = {(184 - x)/7} + 8
⇒ (x/3) - {(184 - x)/7 = 8
⇒ {7x - (3 × 184) + 3x} /21 = 8
⇒ 10x - 552 = 168
⇒ 10x = 720
⇒ x = 720/10 = 72

Another number = 180 - 72
= 108

∴ Smaller number is 72

১৫,৮৭৬.

The ages of Habib and Labib are in the ratio of 7 : 5 respectively. After 10 years, the ratio of their ages will be 9 : 7. What is the difference between their ages?

ক
ক) 5 years
খ
খ) 4 years
গ
গ) 10 years
ঘ
ঘ) 6 years

ব্যাখ্যা

Let
Habib's age be 7x years,
Labib's age = 5x years

Now
(7x + 10)/(5x + 10) = 9/7
49x + 70= 45x + 90
49x - 45x = 90 - 70
4x = 20
x = 5

The difference between their ages = 7x - 5x years
= 2x years = 10years

১৫,৮৭৭.

Two pipes A and B can fill a tank in 20 and 30 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?

ক
12 hours
খ
13 hours
গ
15 hours
ঘ
18 hours

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 20 and 30 hours respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution:
Part filled by A in 1 hour = 1/20

Part filled by B in 1 hour = 1/30

Part filled by (A + B) in 1 hour
= 1/20 + 1/30 = 5/60 = 1/12

∴ Both pipes can fill the tank in 12 hours

১৫,৮৭৮.

If the sum of two numbers is 34 and their H. C. F and L. C. M are 2 and 144 respectively, the sum of the reciprocals of the two numbers is-

ক
15/144
খ
11/144
গ
17/144
ঘ
13/144

ব্যাখ্যা

Question: If the sum of two numbers is 34 and their H. C. F and L. C. M are 2 and 144 respectively, the sum of the reciprocals of the two numbers is-

Solution:
Let the two numbers are, x and y then
x + y = 34
and xy = H. C. F × L. C. M = 2 × 144 = 288

Sum of their reciprocals = (1/x) + (1/y)
= (x + y)/xy
= 34/288
= 17/144

১৫,৮৭৯.

A book is sold for Tk. 575 the amount of profit is equal to the amount of loss if it is sold for Tk. 385, the cost price for this book is-

ক
ক) Tk. 450
খ
খ) Tk. 480
গ
গ) Tk. 490
ঘ
ঘ) Tk. 520

ব্যাখ্যা

Given,
Selling price of book = Tk. 575
Let cost price of book be Tk. a.
⇒ Profit = 575 - a

Given,
Selling price of book = Tk. 385
⇒ Loss = a - 385

Then,
⇒ 575 - a = a - 385
⇒ 2a = 960
⇒ a = 480

∴ cost price of a book is Tk. 480

১৫,৮৮০.

The average of 15 numbers is 48. If the average of first 7 numbers is 44 and the average of last 7 numbers is 50, what is the middle number?

ক
64
খ
62
গ
60
ঘ
58

ব্যাখ্যা

Question: The average of 15 numbers is 48. If the average of first 7 numbers is 44 and the average of last 7 numbers is 50, what is the middle number?

Solution:
Let
The middle number be x

Total sum of 15 numbers,
= 15 × 48
= 720

Sum of first 7 numbers,
= 7 × 44
= 308

Sum of last 7 numbers,
= 7 × 50
= 350

∴ Sum of first 7 numbers + x + Sum of last 7 numbers = 720
⇒ 308 + x + 350 = 720
⇒ 658 + x = 720
⇒ x = 720 - 658
∴ x = 62

So the middle number be 62.

১৫,৮৮১.

Amit works twice as fast as Sagor. If Sagor can complete a work in 12 days independently, the number of days in which Amit and Sagor can together finish the work is-

ক
4 days
খ
5 days
গ
6 days
ঘ
7 days
ঙ
None

ব্যাখ্যা

Question: Amit works twice as fast as Sagor. If Sagor can complete a work in 12 days independently, the number of days in which Amit and Sagor can together finish the work is-

Solution:
Ratio of times taken by Amit and Sagor = 2 : 1
So, the ratio of time taken = 1 : 2

Since, Sagor takes 12 days, Amit takes 6 days

∴ (Amit + Sagor)'s 1 day work = (1/6) + (1/12) part
= 3/12 part
= 1/4

∴ (Amit + Sagor) can finish the work in (4/1) = 4 days

১৫,৮৮২.

If a pen cost Tk.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?

ক
Tk. 55.55
খ
Tk. 66.66
গ
Tk. 50.50
ঘ
Tk. 50

ব্যাখ্যা

Question: If a pen cost Tk.50 after 10% discount, then what is the actual price or marked price (MP) of the pen?

Solution:
Since, we know;
MP - D = SP ..................(1)
where MP is marked price, D is discount, SP is selling price.

Percentage discount, D% = D/MP × 100
⇒ D = (D% × MP)/100 ........(2)

Substitute value of D in (1).
MP - (D% × MP)/100 = SP
⇒ MP × (100 - D%)/100 = SP

Putting the given values in formula
MP × (100 - 10)/100 = 50
⇒ MP × (90/100) = 50
⇒ MP = (50 × 100)/90
∴ MP = 55.55

Alternative:
SP Tk. 90 when MP Tk. 100
∴ SP Tk. 1 when MP Tk. (100/90)
∴ SP Tk. 50 when MP Tk. (100 × 50)/90
= Tk. 55.55

১৫,৮৮৩.

Simple interest obtained on a sum of Tk. 8000 for 4 years is Tk. 3200. Find the rate percent.

ক
8%
খ
10%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: Simple interest obtained on a sum of Tk. 8000 for 4 years is Tk. 3200. Find the rate percent.

Solution:
Here,
p = Tk. 8000
n = 4 years
I = Tk. 3200

Now,
I = pn(r/100)
⇒ 3200 = 8000 × 4 × (r/100)
⇒ 3200 = 32000 × (r/100)
⇒ r = 10%

১৫,৮৮৪.

Recollecting the progress of an assignment, a group of 24 men said that they finished a project together in 10 days. Find the number of days required to complete the same work if 30 men had worked on the same project.

ক
ক) 3 days
খ
খ) 6 days
গ
গ) 7.5 days
ঘ
ঘ) 8 days

ব্যাখ্যা

24 men complete work in 10 days.
In 1 day work done by 24 men = 1/10
In 1 day work done by 30 men = ?
∴ ? × 24 = (1/10) × 30
∴ ? = 1/8 = Amount of work done by 30 men in one day.

Thus in this case,
30 men complete the entire work in 8 days.
[If A completes a work in ''n'' days, in 1 days he completes 1/n amount of work; Conversely, if A completes 1/n amount of work in 1 day, he completes the entire work in 'n' days.]

১৫,৮৮৫.

If (5√5 × 5³)/5 ^{- 3/2} = 5^{a + 2}, then the value of a is-

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

ব্যাখ্যা

Question: If (5√5 × 5³)/5 ^{- 3/2} = 5^{a + 2}, then the value of a is-

Solution:
Given that
(5√5 × 5³)/5^{- 3/2} = 5^{a + 2}
⇒ (5^{1 + (1/2) + 3})/5^{- 3/2} =5^{a + 2}
⇒ 5^{1 + (1/2) + 3 + (3/2)} = 5^{a + 2}
⇒ 1 + (1/2) + 3 + (3/2) = a + 2
⇒ (2 + 1 + 6 + 3)/2 = a + 2
⇒ 12/2 = a + 2
⇒ 6 = a + 2
a = 4

১৫,৮৮৬.

Modric puts Tk. 100 in the bank for two years at 10% interest compounded annually. At the end of the two years, what will be his balance?

ক
ক) Tk. 100.00
খ
খ) Tk. 105.00
গ
গ) Tk. 110
ঘ
ঘ) Tk. 121

ব্যাখ্যা

Question: Modric puts Tk. 100 in the bank for two years at 10% interest compounded annually. At the end of the two years, what will be his balance?

Solution:
Here,
p = 100
n = 2
r = 10% = 10/1000 = 1/10
C = ?

We know,
C = p(1 + r)ⁿ
= 100{1 + (1/10)}²
= 100(11/10)²
= 100 (121/100)
= 121

১৫,৮৮৭.

A cyclist moving on a circular track of radius 105 meters completes one revolution in 3 minutes. What is the average speed of cyclist (approx.)?

ক
ক) 330 m/min
খ
খ) 260 m/min
গ
গ) 220 m/min
ঘ
ঘ) 240 m/min

ব্যাখ্যা

Question: A cyclist moving on a circular track of radius 105 meters completes one revolution in 3 minutes. What is the average speed of cyclist (approx.)?

Solution:
Distance covered in one complete revolution
= 2πr
= (2 × 105 × 22)/7
= 660 m

Average speed = 660/3 = 220 m/min

১৫,৮৮৮.

A is twice old as B. Three years ago A was three times as old as B. How old is A now?

ক
15 years
খ
17 years
গ
12 years
ঘ
10 years
ঙ
9 years

ব্যাখ্যা

Let age of B is x

So age of A is 2x

3 YEARS AGO :

Age of A is 2x-3

Age of B is x-3

BUT IT IS GIVEN THAT 3 YEARS AGO :

3(B)=A

3(x-3)=2x-3

3x-9=2x-3

x=6 i.e Age of B is 6 years.

So age of A now is 2x= 2×6= 12 years

১৫,৮৮৯.

If x is divided by 7, then the remainder is 5. If 3x is divided by 7, what is the remainder?

ক
2
খ
1
গ
3
ঘ
4
ঙ
5

ব্যাখ্যা

ATQ,
X = 7 × 1 + 5 = 12
Then, 3X = 3 × 12 = 36
So, 36 ÷ 7 = 5, remainder 1

১৫,৮৯০.

If the side length of a square is increased by 20%, by what percentage is the area of the square increased?

ক
20%
খ
125%
গ
44%
ঘ
150%

ব্যাখ্যা

Question: If the side length of a square is increased by 20%, by what percentage is the area of the square increased?

Solution:
ধরা যাক, বর্গক্ষেত্রের মূল বাহুর দৈর্ঘ্য = a একক
সুতরাং, মূল ক্ষেত্রফল = a² বর্গ একক

বাহুর দৈর্ঘ্য ২০% বৃদ্ধির পর নতুন বাহুর দৈর্ঘ্য = a + (a × 20/100)
= a + 0.2a
= 1.2a একক

নতুন ক্ষেত্রফল = (1.2a)²
= 1.44a² বর্গ একক

ক্ষেত্রফল বৃদ্ধি = নতুন ক্ষেত্রফল - মূল ক্ষেত্রফল
= 1.44a² - a²
= 0.44a² বর্গ একক

শতকরা বৃদ্ধির হার = (ক্ষেত্রফল বৃদ্ধি/মূল ক্ষেত্রফল) × 100%
= (0.44a²/a²) × 100%
= 44%

সুতরাং, বর্গক্ষেত্রটির ক্ষেত্রফল 44% বৃদ্ধি পাবে।

১৫,৮৯১.

A person took a loan of Tk. 2500 with simple interest for as many years as the rate of interest. If they paid Tk. 1600 as interest at the end of the loan period, what was the rate of interest?

ক
5%
খ
6%
গ
8%
ঘ
10%

ব্যাখ্যা

Question: A person took a loan of Tk. 2500 with simple interest for as many years as the rate of interest. If they paid Tk. 1600 as interest at the end of the loan period, what was the rate of interest?

Solution:
ধরি, সুদের হার = r%
যেহেতু সময় এবং সুদের হার সমান,
∴ সময়, n = r বছর
আসল (P) = 2500 টাকা
মোট সুদ (I) = 1600 টাকা
আমরা জানি,
সরল সুদ, SI = (P × r × n)/100
⇒ 1600 = (2500 × r × r)/100 [এখানে, n = r]
⇒ 1600 = 25 × r²
⇒ r² = 1600/25
⇒ r² = 64
⇒ r = √64
⇒ r = 8

∴ সুদের হার ছিল 8%।

১৫,৮৯২.

A water tank has a radius of 40 inches and a height of 150 inches. Find the area.

ক
47771.4 sq. inches
খ
477714 sq. inches
গ
47777.4 sq. inches
ঘ
477774 sq. inches

ব্যাখ্যা

Question: A water tank has a radius of 40 inches and a height of 150 inches. Find the area.

Solution:
Water tank is cylindrical in nature.
Total Surface Area of a cylinder is given by, 2πr(h + r)
TSA = 2 × 22/7 × 40(150 + 40)
TSA = 2 × 22/7 × 40 × 190
TSA = 44/7 × 7600
TSA = 334400/7

∴ Area = 47771.4 sq. inches.

১৫,৮৯৩.

If 3x/4 = 1, then x is greater than 3/4 approximately by what percent?

ক
58
খ
62
গ
78
ঘ
80
ঙ
None

ব্যাখ্যা

Question: If 3x/4 = 1, then x is greater than 3/4 approximately by what percent?

Solution:
Given that,
3x/4 = 1
⇒ 3x = 4
∴ x = 4/3

∴ Difference = x - (3/4) = (4/3) - (3/4)
= (16 - 9)/12
= 7/12

∴ Percentage increase = (Difference/Original) × 100%
= {(7/12)/(3/4)} × 100%
= (7/9) × 100%
= 77.78%
= 78%

∴ Rounded to the nearest whole number 78%. (Correct answer গ)

১৫,৮৯৪.

A and B are two positive integers such that A × B = 96. Which of the following cannot be the value of A + B?

ক
49
খ
20
গ
28
ঘ
35

ব্যাখ্যা

Question: A and B are two positive integers such that A × B = 96. Which of the following cannot be the value of A + B?

Solution:
Factor pairs of 96:
(1, 96) → A + B = 97
(2, 48) → A + B = 50
(3, 32) → A + B = 35
(4, 24) → A + B = 28
(6, 16) → A + B = 22
(8, 12) → A + B = 20

So, possible values of A + B are:
97, 50, 35, 28, 22, 20
Among options, 49 is not possible.

১৫,৮৯৫.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

ক
ক) 1/3
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/7

ব্যাখ্যা

Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
ধরি,
পাত্রের মিশ্রণের পরিমাণ ৮ লিটার।

মিশ্রণে পানির পরিমাণ ৩ লিটার
মিশ্রণে সিরাপের পরিমাণ ৫ লিটার

পাত্রের পানি ও সিরাপের পরিমাণ অর্ধেক অর্ধেক করতে ক লিটার মিশ্রণ অপসারণ করে পানি দিতে হবে।

ক লিটার মিশ্রণে পানির পরিমাণ ৩ক/৮ লিটার
ক লিটার মিশ্রণে সিরাপের পরিমাণ ৫ক/৮ লিটার

পানি মিশানোর পর,
নতুন মিশ্রণে পানির পরিমাণ হবে (৩ - ৩ক/৮) + ক লিটার
=(২৪ - ৩ক)/৮ + ক লিটার
= (২৪ + ৫ক)/৮ লিটারনতুন মিশ্রণে সিরাপের পরিমাণ হবে (৫ - ৫ক/৮) লিটার
= (৪০ - ৫ক)/৮ লিটার

শর্তমতে,
(২৪ + ৫ক)/৮ = (৪০ - ৫ক)/৮
বা, ২৪ + ৫ক = ৪০ - ৫ক
বা, ১০ক = ১৬
বা, ক = ৮/৫

৮ লিটার মিশ্রণ ৮ লিটারের সম্পূর্ণ বা ১ অংশ
∴ ৮/৫ লিটার মিশ্রণ ৮ লিটারের (৮/৫)/৮ অংশ
= ১/৫ অংশ

১৫,৮৯৬.

A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 3 hours more upstream than downstream. What is the distance (in km)?

ক
ক) 48 km
খ
খ) 50 km
গ
গ) 64 km
ঘ
ঘ) 72 km

ব্যাখ্যা

Speed of the man in still water = 12 km/h
Speed of the current = 4 km/h
Speed of the man along the current = (12 + 4) km/h = 16 km/h
Speed of the man against the current = (12 - 4) km/h = 8 km/h

Let, The distance is x km
Now
x/8 – x/16 = 3
=(2x - x)/16 = 3
= x/16 = 3
∴ x = 48 km

১৫,৮৯৭.

0.777777 ÷ 0.011 =?

ক
77.07
খ
0.70707
গ
70
ঘ
70.707

ব্যাখ্যা

Question: 0.777777 ÷ 0.011 =?

Solution:
0.777777 ÷ 0.011 = 70.707

১৫,৮৯৮.

A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

ক
1/108
খ
2/9
গ
1/5
ঘ
1/2

ব্যাখ্যা

Question: A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

Solution:
6 + 6 + 3 = 15, number of ways = 3!/2! = 3
6 + 5 + 4 = 15, number of ways = 3! = 6
5 + 5 +5 = 15, number of ways = 1
Total ways = 10

If first throw was a four = (4, 5, 6), (4, 6, 5) = 2 ways

Probability = 2/10 = 1/5

১৫,৮৯৯.

The difference between two numbers is 5 and the difference between their square is 65. What is the smaller number?

ক
4
খ
5
গ
11
ঘ
13

ব্যাখ্যা

Question: The difference between two numbers is 5 and the difference between their square is 65. What is the smaller number?

Solution:
Let the numbers be x and y
Then,
x - y = 5.........(i)
x² - y² = 65
Or (x + y)(x - y) = 105
5(x + y) = 65
x + y = 13 ....... (ii)

by adding (i) and (ii) we get,
2x = 5 + 13
2x = 18
x = 9

From (ii) we get
x + y = 13
9 + y = 13
y = 13 - 9
y = 4

Hence, the smaller number is 4

১৫,৯০০.

Solve for y, √(2y - 3) = 5

ক
y = 28
খ
y = 5.5
গ
y = 4
ঘ
y = 14

ব্যাখ্যা

Question: Solve for y, √(2y - 3) = 5

Solution:
Given that,
⇒ √(2y - 3) = 5
⇒ (√(2y - 3))² = 5²⇒ 2y - 3 = 25
⇒ 2y = 25 + 3
⇒ 2y = 28
⇒ y = 28/2
∴ y = 14