Bank Math

PrepBank · পাতা ১৪৭ / ১৬১ · ১৪,৬০১–১৪,৭০০ / ১৬,১২৪

১৪,৬০১.

Hassan completed 1/3 portion of a job in 8 days and left. Then Jashim was recruited and he worked for 5 days and left the job. Hassan again joined and completed the rest of the work in 12 days. How many days would Jashim require to complete the job alone?

ক
ক) 10 days
খ
খ) 24 days
গ
গ) 30 days
ঘ
ঘ) 36 days
ঙ
ঙ) None

সঠিক উত্তর: গ

গ) 30 days

উত্তর

সঠিক উত্তর: গ

গ) 30 days

গ

ব্যাখ্যা

হাসান ৮ দিনে করে ১/৩ অংশ
সে ১ দিনে করে ১/(৮x৩) = ১/২৪ অংশ
তাহলে ১২ দিনে করবে (১x১২)/২৪ = ১/২ অংশ।
অর্থাৎ, সে ২০ দিনে করে (১/৩)+(১/২) = ৫/৬ অংশ।
জসিম বাকি কাজ {১-(৫/৬))= ১/৬ অংশ করে ৫ দিনে
তাহলে পুরো কাজটি একা করতে জসিমের লাগবে (৫x৬)/১= ৩০ দিন।

১৪,৬০২.

Which of following can never be ending of a perfect square?

ক
ক) 00
খ
খ) 000
গ
গ) 1
ঘ
ঘ) 6

সঠিক উত্তর: খ

খ) 000

উত্তর

সঠিক উত্তর: খ

খ) 000

খ

ব্যাখ্যা

A perfect square never ends with odd number of zeros.

১৪,৬০৩.

30% of 50% of 4/7 of a number is 420. What is 20% of 3/7 of that number?

ক
360
খ
420
গ
480
ঘ
490

সঠিক উত্তর: খ

420

উত্তর

সঠিক উত্তর: খ

420

খ

ব্যাখ্যা

Question: 30% of 50% of 4/7 of a number is 420. What is 20% of 3/7 of that number?

Solution:
Let the number be x.

Then,
30% of 50% of 4/7 of x = 420
⇒ (30/100) × (50/100) × (4/7) × x = 420
⇒ 3/10 × 1/2 × 4/7 × x = 420
⇒ 12x/140 = 420
⇒ 3x/35 = 420
⇒ x = (420 × 35)/3
∴ x = 4900

Now,
20% of 3/7 of x
= (20/100) × (3/7) × 4900
= (1/5) × (3/7) × 4900
= (3/35) × 4900
= 420

১৪,৬০৪.

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15}. Find A ∩ (B ∪ C).

ক
ক) {7, 9, 11, 13, 15}
খ
খ) {7, 9, 11}
গ
গ) {3, 5, 7, 9, 11, 13}
ঘ
ঘ) {3, 5}

সঠিক উত্তর: খ

খ) {7, 9, 11}

উত্তর

সঠিক উত্তর: খ

খ) {7, 9, 11}

খ

ব্যাখ্যা

Question: If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15}. Find A ∩ (B ∪ C).

Solution:
B ∪ C = {7, 9, 11, 13} ∪ {11, 13, 15}
= {7, 9, 11, 13, 15}

A ∩ (B ∪ C) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15}
= {7, 9, 11}

১৪,৬০৫.

An iron rod that weights 24 kg is cut into pieces so that one of these pieces weighs 16 kg and is 34m long. If the weight of each piece is proportional to its length, how long is the other piece?

ক
ক) 11m
খ
খ) 17m
গ
গ) 34m
ঘ
ঘ) 64m

সঠিক উত্তর: খ

খ) 17m

উত্তর

সঠিক উত্তর: খ

খ) 17m

খ

ব্যাখ্যা

রডটির অপর ভাগের ওজন = (24 - 16)kg = 8 kg
ধরি
অপর ভাগের দৈর্ঘ্য = x মিটার

প্রশ্নমতে
16/34 = 8/x
x/8 = 34/16
x = (34 × 8)/16
x = 17

১৪,৬০৬.

Solve for x; log_x3 + log_x9 + log_x27 + log_x81 = 10.

ক
3
খ
1
গ
4
ঘ
2

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Solve for x; log_x3 + log_x9 + log_x27 + log_x81 = 10.

Solution:
Given that,
log_x3 + log_x9 + log_x27 + log_x81 = 10
⇒ log_x(3 × 9 × 27 × 81) = 10
⇒ log_x(3¹ × 3² × 3³ × 3⁴) = 10
⇒ log_x(3¹⁰) = 10
⇒ 10 log_x3 = 10
⇒ log_x3 = 10/10
⇒ log_x3 = 1
⇒ x¹ = 3
∴ x = 3

১৪,৬০৭.

In a right triangle, the length of one of the legs is 6 and the length of the hypotenuse is 10. What is the length of the other leg?

ক
8 units
খ
12 units
গ
5 units
ঘ
15 units

সঠিক উত্তর: ক

8 units

উত্তর

সঠিক উত্তর: ক

8 units

ক

ব্যাখ্যা

Question: In a right triangle, the length of one of the legs is 6 and the length of the hypotenuse is 10. What is the length of the other leg?

Solution:
Hypotenuse, c = 10 units
One leg, a = 6 units
Other leg, b = ?

Using the Pythagorean theorem,
⇒ a² + b² = c²
⇒ b² + 6² = 10²
⇒ b² + 36 = 100
⇒ b² = 100 - 36
⇒ b² = 64
⇒ b² = 8²
∴ b = 8

∴ The length of the other leg is 8 units.

১৪,৬০৮.

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

ক
ক) 30 days
খ
খ) 35 days
গ
গ) 40 days
ঘ
ঘ) 45 days

সঠিক উত্তর: ক

ক) 30 days

উত্তর

সঠিক উত্তর: ক

ক) 30 days

ক

ব্যাখ্যা

Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let time taken by B to complete a work be ′x′ days.
Therefore, time taken by A to the work =x + 50%x =1.5x days

Now,
Work done by B in one days = 1/x units
Work done by A in one day = 2/3x units

Thus, according to the question,
⇒1/x + 2/3x = 1/18
⇒5/3x = 1 /18
∴x =5 × 18/3 = 30

Hence, time taken by B to complete the work is 30 days

১৪,৬০৯.

Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

ক
ক) 11 a.m.
খ
খ) 10.30 a.m
গ
গ) 9.10 a.m.
ঘ
ঘ) 8 a.m
ঙ
ঙ) 10 a.m.

সঠিক উত্তর: ঙ

ঙ) 10 a.m.

উত্তর

সঠিক উত্তর: ঙ

ঙ) 10 a.m.

ঙ

ব্যাখ্যা

Assume both trains meet x hours after 7 a.m.
Distance covered by train starting from P in x hours = 20 x km
Distance covered by train starting from Q in (x − 1) hours = 25 (x − 1) km
Total distance = 110 km
⇒ 20 x + 25 (x − 1) = 110
⇒ 45 x = 135
⇒ x = 3
Hence, they meet 3 hours after 7 a.m.
i.e., they meet at 10 a.m.

Alternative method:
Distance travelled by first train in 1 hour = 20 km
Therefore, at 8 a.m., both trains will be (110 − 20) = 90 km apart.
Since the relative speed is (20 + 25) = 45 kmph,
they will cover this distance in 90/ 45 = 2 hours.
I.e. They will meet at 10 a.m.

১৪,৬১০.

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is?

ক
ক) 6 ml
খ
খ) 11 ml
গ
গ) 15 ml
ঘ
ঘ) 9 ml

সঠিক উত্তর: ক

ক) 6 ml

উত্তর

সঠিক উত্তর: ক

ক) 6 ml

ক

ব্যাখ্যা

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7

Let x ml of water be added
We get,
4.5/(4.5 + x) = 3/7
⇒ 9/(9 + 2x) = 3/7
⇒ 63 = 27 + 6x
⇒ 6x = 63 - 27
⇒ 6x = 36
⇒ x = 6

Hence 6ml of water is added.

১৪,৬১১.

A can run 22m while B runs 25m. In a kilometer race B beats A by -

ক
110m
খ
120m
গ
140m
ঘ
160m

সঠিক উত্তর: খ

120m

উত্তর

সঠিক উত্তর: খ

120m

খ

ব্যাখ্যা

Question: A can run 22m while B runs 25m. In a kilometre race B beats A by -

Solution:
while B covers 25m, A covers 22m
∴ B covers 1000m, A covers = (22 × 1000)/25 = 880m

∴ B beats A by = 1000 - 880 = 120m

১৪,৬১২.

If the measures of the angles in a triangle are in the ratio of 3 : 7 : 8, then the degrees in the largest angle:

ক
120°
খ
80°
গ
90°
ঘ
100°

সঠিক উত্তর: খ

80°

উত্তর

সঠিক উত্তর: খ

80°

খ

ব্যাখ্যা

Question: If the measures of the angles in a triangle are in the ratio of 3 : 7 : 8, then the degrees in the largest angle:

Solution:
মনে করি, ত্রিভুজের কোণ তিনটি যথাক্রমে 3x, 7x এবং 8x

আমরা জানি, ত্রিভুজের তিন কোণের সমষ্টি 180°

শর্তমতে,
3x + 7x + 8x = 180°
⇒ 18x = 180°
⇒ x = 180°/18
⇒ x = 10°

বৃহত্তম কোণটি হলো 8x
∴ বৃহত্তম কোণের মান = 8 × 10° = 80°

১৪,৬১৩.

The ratio of the ages of a father and his son is 5 : 2 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What is the son's present age?

ক
12 years
খ
16 years
গ
24 years
ঘ
28 years

সঠিক উত্তর: গ

24 years

উত্তর

সঠিক উত্তর: গ

24 years

গ

ব্যাখ্যা

Question: The ratio of the ages of a father and his son is 5 : 2 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What is the son's present age?

Solution:
ধরি, পিতার বর্তমান বয়স = 5x বছর
এবং পুত্রের বর্তমান বয়স = 2x বছর

ছয় বছর আগে,
পিতার বয়স = 5x − 6 বছর
পুত্রের বয়স = 2x − 6 বছর

শর্তমতে,
(5x − 6)/(2x − 6) = 3/1
⇒ 6x - 18 = 5x - 6
⇒ 6x - 5x = 18 - 6
⇒ x = 12

∴ পুত্রের বর্তমান বয়স = 2x = 2 × 12 = 24 বছর

১৪,৬১৪.

The ratio of the ages of A and B at present is 3 ∶ 1. Four years earlier the ratio was 4 ∶ 1. The present age of B is-

ক
12 years
খ
24 years
গ
18 years
ঘ
36 years

সঠিক উত্তর: ক

12 years

উত্তর

সঠিক উত্তর: ক

12 years

ক

ব্যাখ্যা

Question: The ratio of the ages of A and B at present is 3 ∶ 1. Four years earlier the ratio was 4 ∶ 1. The present age of B is-

Solution:
Given that,
Ratio of present ages of A and B = 3 ∶ 1.
Ratio of their ages 4 years ago = 4 ∶ 1.

Let the present ages of A and B be 3x and x, respectively.
Four years ago,
Age of A = 3x - 4
Age of B = x - 4

AQT,
(3x - 4)/(x - 4) = 4/1
⇒ 3x - 4 = 4(x - 4)
⇒ 3x - 4 = 4x - 16
⇒ 3x - 4x = - 16 + 4
⇒ - x = - 12
∴ x = 12

∴ Present age of B = 12 years.

১৪,৬১৫.

Find the amount if Tk. 2000 is invested at 10% compound interest p.a. for 3 years.

ক
2662
খ
2625
গ
2590
ঘ
2540

সঠিক উত্তর: ক

2662

উত্তর

সঠিক উত্তর: ক

2662

ক

ব্যাখ্যা

Question: Find the amount if Tk. 2000 is invested at 10% compound interest p.a. for 3 years.

Solution:
Given,
P = Tk. 2000
r = 10%
n = 3 years

We know,
C = P(1 + r)ⁿ
= 2000{1 + (10/100)}³
= 2000(1 + 1/10)³
= 2000(11/10)3
= 2000 × 1.1 × 1.1× 1.1
= 2662

১৪,৬১৬.

Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

ক
30.8 m
খ
60 m
গ
76.8 m
ঘ
40.5 m

সঠিক উত্তর: ক

30.8 m

উত্তর

সঠিক উত্তর: ক

30.8 m

ক

ব্যাখ্যা

Question: Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

Solution:

Le t the height of the second building AD be h.
EC = 100 - h
DC = AB = 40

From ΔECD we get,
EC/DC = tan60°
⇒ (100 - h)/40 = √3
⇒ 100 - h = 40 × √3
⇒ - h = - 100 + 40 × 1.73
⇒ - h = - 100 + 69.2
∴ h = 30.8 m

১৪,৬১৭.

A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2^nd and 3^rd day respectively, how long will it take the task to be completed?

ক
15 days
খ
14 days
গ
12 days
ঘ
10 days
ঙ
None of these

সঠিক উত্তর: ঙ

None of these

উত্তর

সঠিক উত্তর: ঙ

None of these

ঙ

ব্যাখ্যা

Question: A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2^nd and 3^rd day respectively, how long will it take the task to be completed?

Solution:
A একা ১ দিনে করে = ১/৩০ অংশ
B একা ১ দিনে করে = ১/১৫ অংশ
C একা ১ দিনে করে = ১/১০ অংশ

প্রথম ১০ দিনের জন্য হিসেব করে পাই,
প্রথম ১০ দিনে A কাজ করে ১০ দিন তথা = ১০/৩০ অংশ কাজ
প্রথম ১০ দিনে B কাজ করে ৫ দিন তথা = ৫/১৫ অংশ কাজ
প্রথম ১০ দিনে C কাজ করে ৩ দিন তথা = ৩/১০ অংশ কাজ
প্রথম ১০ দিনে A,B,C কাজ করে (১০/৩০) + (৫/১৫) + (৩/১০) = (১০ + ১০ + ৯)/৩০ = ২৯/৩০ অংশ
বাকি ১ - (২৯/৩০) = ১/৩০ অংশ কাজ করতে ১ দিন সময় লাগবে।

∴ মোট দিন = ১০ + ১ = ১১ দিন

১৪,৬১৮.

If log₈p = 25 and log₂q = 5 than-

ক
p = q
খ
p = q³
গ
p² = q⁴
ঘ
p = q¹⁵

সঠিক উত্তর: ঘ

p = q¹⁵

উত্তর

সঠিক উত্তর: ঘ

p = q¹⁵

ঘ

ব্যাখ্যা

Question: If log₈p = 25 and log₂q = 5 than-

Solution:
Given that,
⇒ log₈p = 25 and log₂q = 5
⇒ p = 8²⁵ and q = 2⁵
⇒ p = (2³)²⁵ and q = 2⁵ .........(1)
⇒ p = 2⁷⁵
⇒ p = (2⁵)¹⁵
∴ p = q¹⁵ ; [ From equation 1 ]

১৪,৬১৯.

60π cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters will be -

ক
24 meters
খ
88 meters
গ
196 meters
ঘ
240 meters
ঙ
300 meters

সঠিক উত্তর: ঘ

240 meters

উত্তর

সঠিক উত্তর: ঘ

240 meters

ঘ

ব্যাখ্যা

Question: 60π cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters will be -

Solution:
Let the length of the wire be h
Radius, r =(1/2) mm =1/20 cm.
We know,
Volume of a cylinder(wire) = πr²h

∴ π × (1/20) × (1/20) × h = 60π
⇒ h = 60 × 20 × 20
⇒ h = 24000

∴ The length of the wire = 24000 cm
= (24000/100) meters
= 240 meters

১৪,৬২০.

If 12 workers can build a wall in 6 days, how long would it take 9 workers to build the same wall?

ক
4 days
খ
6 days
গ
8 days
ঘ
9 days

সঠিক উত্তর: গ

8 days

উত্তর

সঠিক উত্তর: গ

8 days

গ

ব্যাখ্যা

Question: If 12 workers can build a wall in 6 days, how long would it take 9 workers to build the same wall?

Solution:
12 workers can build a wall in 6 days.
∴ 1 worker would take = 6 × 12 days = 72 days.
∴ 9 workers would take = 72/9 days = 8 days.

১৪,৬২১.

Two runner start running together for a certain distance, one at 5 km/h and another at 3 km/h. The former arrives one and half an hour before the latter. The distance in Km is:

ক
ক) 12
খ
খ) 20
গ
গ) 25
ঘ
ঘ) 30
ঙ
ঙ) 35

সঠিক উত্তর: খ

খ) 20

উত্তর

সঠিক উত্তর: খ

খ) 20

খ

ব্যাখ্যা

Let X be the distance, then
(x/5)−(x/8) = 3/2
x = 20km

১৪,৬২২.

What is 35% of (11 × 160)/56 ?

ক
9
খ
10
গ
11
ঘ
12

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

35% of (11 × 160)/56
= (35 × 11 × 160) ÷ (56 × 100)
= 11

১৪,৬২৩.

If log₁₀5 +log₁₀(5x + 1) = log₁₀(x + 5) + 1, then x is equal to-

ক
- 1
খ
- 2
গ
9
ঘ
- 4
ঙ
3

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Question: If log₁₀5 +log₁₀(5x + 1) = log₁₀(x + 5) + 1, then x is equal to-

Solution:
Given that,
⇒ log₁₀5 +log₁₀(5x + 1) = log₁₀(x+5) + 1
⇒ log₁₀5 +log₁₀(5x + 1) = log₁₀(x+5) + log₁₀10
⇒ log₁₀[5(5x + 1)] = log₁₀[10(x + 5)]
⇒ 5(5x + 1) = 10(x + 5)
⇒ 25x + 5 = 10x + 50
⇒ 25x - 10x = 50 - 5
⇒ 15x = 45
∴ x = 3

১৪,৬২৪.

The milk and water in a mixture are in the ratio 7 : 5. When 15 liters of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is:

ক
35 litres
খ
40 litres
গ
60 litres
ঘ
96 litres
ঙ
67 litres

সঠিক উত্তর: খ

40 litres

উত্তর

সঠিক উত্তর: খ

40 litres

খ

ব্যাখ্যা

Milk : Water
7 : 5
7 : 8
---------------
3 unit

∴ Remember water is added and not milk, so make milk equal but here milk is already equal
3 units = 15 litres
1 units = 5 litres
8 units = 40 litres
Total quantity of water in the new mixture = 40 litres

১৪,৬২৫.

Which of the following can be arranged into an English word?
a. ANSLAIT b. LSNIT c. OTATM d. WQRGS.

ক
ক) c
খ
খ) a
গ
গ) a & d
ঘ
ঘ) c & d

সঠিক উত্তর: খ

খ) a

উত্তর

সঠিক উত্তর: খ

খ) a

খ

ব্যাখ্যা

ANSLAIT কে rearrange করে পাওয়া যায় SALIANT

Which is a variant spelling of Salient
Salient means - প্রধান; অগ্রগণ্য; লক্ষণীয়; মুখ্য।

১৪,৬২৬.

A merchant selling 44 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

ক
55%
খ
50%
গ
33.33%
ঘ
None of the above

সঠিক উত্তর: গ

33.33%

উত্তর

সঠিক উত্তর: গ

33.33%

গ

ব্যাখ্যা

Question: A merchant selling 44 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth, the profit is = ?

Solution:
Profit = selling price of 11 m of cloth = 1/4 selling price of 44 m of cloth

Let the selling price of 44 meters of cloth = 4x
∴ profit = (1/4) × (4x) = x

So, cost price = selling price - profit = 4x - x = 3x

% Profit = (x/3x) × 100% = 33.33%

১৪,৬২৭.

The ratio of the volumes of two spheres is 27 : 8. What is the ratio of their surface areas?

ক
3√3 : 2√2
খ
3 : 2
গ
27 : 8
ঘ
9 : 4

সঠিক উত্তর: ঘ

9 : 4

উত্তর

সঠিক উত্তর: ঘ

9 : 4

ঘ

ব্যাখ্যা

Question: The ratio of the volumes of two spheres is 27:8. What is the ratio of their surface areas?

Solution:
Volume of a Sphere: V = (4/3)π(r)³
Surface Area of a Sphere: S = 4πr²

Given,

১৪,৬২৮.

A sum of Tk. 4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.

ক
Tk. 2520
খ
Tk. 3120
গ
Tk. 3320
ঘ
Tk. 2760

সঠিক উত্তর: খ

Tk. 3120

উত্তর

সঠিক উত্তর: খ

Tk. 3120

খ

ব্যাখ্যা

Question: A sum of Tk. 4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.

Solution:
Let A be the amount received at the end of the three years.

A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 × 11 × 6 × 5)/(10 × 5 × 4)
A = 7920

So the interest = 7920 - 4800 = 3120

১৪,৬২৯.

A sports club has 50 members. Of these, 37 play cricket, 30 play badminton and 21 play both cricket and badminton. How many members play neither cricket nor badminton?

ক
ক) 3
খ
খ) 4
গ
গ) 9
ঘ
ঘ) 17

সঠিক উত্তর: খ

খ) 4

উত্তর

সঠিক উত্তর: খ

খ) 4

খ

ব্যাখ্যা

Players who play at least one sport = 37 + 30 - 21 = 46
∴ Players who play neither cricket nor badminton = 50 - 46 = 4

১৪,৬৩০.

How many days are there in n weeks n days?

ক
(8n + 1) days
খ
6n days
গ
8n days
ঘ
9n days

সঠিক উত্তর: গ

8n days

উত্তর

সঠিক উত্তর: গ

8n days

গ

ব্যাখ্যা

Question How many days are there in n weeks n days?

Solution:
Number of days in n weeks = 7 × n = 7n days

∴ Number of days in n weeks n days = 7n + n days
= 8n days

১৪,৬৩১.

The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 26. Find the present worth.

ক
450
খ
550
গ
650
ঘ
750

সঠিক উত্তর: গ

650

উত্তর

সঠিক উত্তর: গ

650

গ

ব্যাখ্যা

Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 26. Find the present worth.

Solution:
Banker Gain = 26
True Discount = (Bnakers gain × 100)/(rate × time) = (26 × 100)/(10 × 2) = 130

Banker's Gain = Banker's Discount - True discount
⇒ 26 = Banker's discount - 130
∴ Banker's discount = 130 + 26 = 156

Now, banker's discount is the interest on the face value
Let the face value = x
So,
x × (10/100) × 2 = 156
⇒ x × 0.1 × 2 = 156
⇒ x = 156/0.2 = 780

Now,
Present Worth = Face value - True discount
= 780 - 130
= 650

১৪,৬৩২.

Which is the greatest three-digit number which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

ক
996
খ
975
গ
939
ঘ
972
ঙ
903

সঠিক উত্তর: খ

975

উত্তর

সঠিক উত্তর: খ

975

খ

ব্যাখ্যা

Question: Which is the greatest three-digit number which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

Solution:
Greatest three digit number = 999
LCM of 6, 9 and 12 = 36

On dividing 999 by 36,
Remainder = 27.

∴ The greatest three digit number divisible by 6, 9, and 12 = (999 - 27) = 972

As per the question, the required number is (972 + 3) = 975.

১৪,৬৩৩.

If p³ - q³ = (p - q) {(p + q)² - apq}, then find the value of a is-

ক
ক) 1
খ
খ) - 1
গ
গ) 3
ঘ
ঘ) - 3

সঠিক উত্তর: ক

ক) 1

উত্তর

সঠিক উত্তর: ক

ক) 1

ক

ব্যাখ্যা

⇒p³− q³= (p−q){(p + q)²- apq}
⇒(p − q){p²+ q²+ pq} = (p−q){p²+ q²+ 2pq - apq}
⇒p²+ q²+ pq = p²+q² + 2pq - apq
⇒ apq = pq
⇒a = 1

১৪,৬৩৪.

The sum of the ages of the father and daughter is 90 years. If five years ago the age of father was four times that of his daughter, find the present age of the daughter.

ক
ক) 19 years
খ
খ) 31 years
গ
গ) 28 years
ঘ
ঘ) 21 years

সঠিক উত্তর: ঘ

ঘ) 21 years

উত্তর

সঠিক উত্তর: ঘ

ঘ) 21 years

ঘ

ব্যাখ্যা

Question: The sum of the ages of the father and daughter is 90 years. If five years ago the age of father was four times that of his daughter, find the present age of the daughter.

Solution:
Let the age of daughter 5 years ago = x
The age of father 5 years ago = 4x

ATQ,
x + 5 + 4x + 5 = 90
⇒ 5x + 10 = 90
⇒ 5x = 80
∴ x = 16

Daughter present age = 16 + 5 = 21 years.

১৪,৬৩৫.

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

ক
38
খ
42
গ
45
ঘ
46
ঙ
40

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Volume of the block = (6 × 12 × 15) cm3
= 1080 cm3

Side of the largest cube = H.C.F of 6 cm, 12 cm, 15 cm
= 3 cm.

Volume of this cube = (3 × 3 × 3) cm3
= 27 cm3

Number of cubes = 1080/27
= 40.

১৪,৬৩৬.

The average of x, y and z is 45. x is as much more than the average as y is less than the average. Find the value of z.

ক
45
খ
35
গ
60
ঘ
15
ঙ
None of these

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The average of x, y and z is 45. x is as much more than the average as y is less than the average. Find the value of z.

Solution:
As the average is 45
Sum of x, y and z will be 135.
and Also given that ,
x - 45 = 45 - y
∴ x + y = 90,

therefore, 90 + z = 135
∴ z = 45

১৪,৬৩৭.

A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of -

ক
ক) Tk. 80
খ
খ) Tk. 115.20
গ
গ) Tk. 120
ঘ
ঘ) Tk. 125.40

সঠিক উত্তর: খ

খ) Tk. 115.20

উত্তর

সঠিক উত্তর: খ

খ) Tk. 115.20

খ

ব্যাখ্যা

For an income of Tk. 10, investment = Tk. 96
For an income of 12, investment
= Tk. (96/10) × 12
= Tk. 115.20

Hence, He must purchase a stock worth of Tk. 115.20

১৪,৬৩৮.

A train passes two bridges of lengths 700 m and 300 m in 100 seconds and 60 seconds respectively. The length of the train is

ক
ক) 200 m
খ
খ) 300 m
গ
গ) 150 m
ঘ
ঘ) 100 m

সঠিক উত্তর: খ

খ) 300 m

উত্তর

সঠিক উত্তর: খ

খ) 300 m

খ

ব্যাখ্যা

Question: A train passes two bridges of lengths 700 m and 300 m in 100 seconds and 60 seconds respectively. The length of the train is

Solution:
Let the length of the train be x m
Speed s = (x + 700)/100.................(1)
Speed s = (x + 300)/60................(2)

Now
(x + 700)/100 = (x + 300)/60
(x + 700)/5 = (x + 300)/3
5x + 1500 = 3x + 2100
5x - 3x = 2100 - 1500
2x = 600
x = 300

১৪,৬৩৯.

Two pipes, A and B, can fill a tank in 37.5 minutes and 45 minutes. If both pipes are open, after how many minutes should pipe B be closed to fill the tank in half an hour?

ক
5 minutes
খ
9 minutes
গ
10 minutes
ঘ
15 minutes

সঠিক উত্তর: খ

9 minutes

উত্তর

সঠিক উত্তর: খ

9 minutes

খ

ব্যাখ্যা

Question: Two pipes, A and B, can fill a tank in 37.5 minutes and 45 minutes. If both pipes are open, after how many minutes should pipe B be closed to fill the tank in half an hour?

Solution:
নল A দ্বারা 37.5 মিনিটে পূর্ণ হয় 1 অংশ
∴ 1 মিনিটে পূর্ণ হয় = (1/37.5) অংশ
∴ 30 মিনিটে পূর্ণ হয় = 30/37.5 = 300/375 = 4/5 অংশ

∴ পূর্ণ হওয়ার বাকি থাকে = 1 - (4/5)
= (5 - 4)/5
= 1/5 অংশ

B নল দ্বারা ,
1 অংশ পূর্ণ হতে সময় লাগে = 45 মিনিট
∴ 1/5 অংশ পূর্ণ হতে সময় লাগে = 45 × (1/5) = 9 মিনিট

∴ B নলটি 9 মিনিট পর বন্ধ করলে ট্যাংকটি 30 মিনিটে পূর্ণ হবে।

Shortcut:
(30/37.5) + (x/45) = 1 (whole)
⇒ 0.8 + (x/45) = 1
⇒ x/45 = 1 - 0.8 = 0.2
⇒ x = 0.2 × 45 = 9

১৪,৬৪০.

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

ক
2
খ
3
গ
4
ঘ
5
ঙ
6

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

Solution:
Let,
First term = a
Common difference = d

8th term = a + 7d = 39 ........... (1)
12th term = a + 11d = 59 ........... (2)

By (2) - (1) we get,
a + 11d - a - 7d = 59 - 39
⇒ 4d = 20
∴ d = 5

Hence,
a + 7 × 5 = 39
⇒ a = 39 - 35
∴ a = 4

১৪,৬৪১.

The distance between places A and B is 999 km. An express train leaves place A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hour 20 minutes. It reaches B at:

ক
ক) 12 pm
খ
খ) 6 am
গ
গ) 1.20 am
ঘ
ঘ) 11 pm

সঠিক উত্তর: গ

গ) 1.20 am

উত্তর

সঠিক উত্তর: গ

গ) 1.20 am

গ

ব্যাখ্যা

Question: The distance between places A and B is 999 km. An express train leaves place A at 6 am and runs at a speed of 55.5 km/hr. The train stops on the way for 1 hour 20 minutes. It reaches B at:

Solution:
Time will be taken by train if it does not stop = Distance/Speed
= 999 km/55.5 km/hr
Without stop = 18 hr

But if stops on the way for 1 hour 20 minutes before reaching B.
Total time = 18 hr + 1 hr 20 min
= 19 hour 20 minutes

Reaching time at B = 6 am + 19 hr 20 min
= 1.20 am

১৪,৬৪২.

If 30% of C = 25% of A and 2d% of C = A, find the value of d?

ক
ক) 40
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 80

সঠিক উত্তর: গ

গ) 60

উত্তর

সঠিক উত্তর: গ

গ) 60

গ

ব্যাখ্যা

Given that
30% of C = 25% of A
2d% of C = A

According to the questions,
⇒ (30/100) × C = (25/100) × A
⇒ (30/25) = A/C
⇒ 6/5 = A/C

From the above question,
⇒ 2d% of C = A
⇒ 2d/100 = A/C
⇒ 2d/100 = 6/5
⇒ 2d = (6/5) × 100
⇒2d = 120
⇒ d = 60

∴ The value of d is 60

১৪,৬৪৩.

Determine the roots of the equation (x + 3)(x - 3) = 40.

ক
- 3, 3
খ
- 5, 5
গ
- 6, 6
ঘ
- 7, 7

সঠিক উত্তর: ঘ

- 7, 7

উত্তর

সঠিক উত্তর: ঘ

- 7, 7

ঘ

ব্যাখ্যা

Question: Determine the roots of the equation (x + 3)(x - 3) = 40.

Solution:
Given,
(x + 3) (x - 3)=40
⇒ x² - 9 = 40
⇒ x² - 9 - 40 = 0
⇒ x² - 49 = 0
⇒ x² - 7² = 0
⇒ (x+7) (x-7) = 0
⇒ x + 7 = 0 or x - 7 = 0
∴ x = - 7 or x = 7.
Hence, the roots of the given equation are -7, 7.

১৪,৬৪৪.

A contractor employs 40 persons for doing a job in 60 days. After 20 days it was found that only one-fourth of work was finished. How many more persons are to be employed to finish the job as per schedule?

ক
40
খ
30
গ
20
ঘ
None of the above

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A contractor employs 40 persons for doing a job in 60 days. After 20 days it was found that only one-fourth of work was finished. How many more persons are to be employed to finish the job as per schedule?

Solution:
Work remains = 1 - (1/4) part = 3/4 part
Day remaining = 60 - 20 = 40 days

1/4 th work is done in 20 days by 40 person
∴ 1 part is done in 20 days by 40 × 4 person
∴ 1 part is done in 1 day by (40 × 4 × 20) person
∴ 3/4 part is done in 40 days by (40 × 4 × 20 × 3)/(40 × 4) = 60 person

∴ He needs = (60 - 40) = 20 more persons.

১৪,৬৪৫.

What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a reminder 2 but when divided by 13 leaves no remainder?

ক
ক) 962
খ
খ) 1053
গ
গ) 1142
ঘ
ঘ) 1056

সঠিক উত্তর: ক

ক) 962

উত্তর

সঠিক উত্তর: ক

ক) 962

ক

ব্যাখ্যা

L.C.M of 3, 5, 6, 8, 10 and 12 = 120
So, the required number is of the form 120k + 2.
Least value of k for which (120k + 2) is divisible by 13 is k = 8.
∴ Required number = (120 × 8 + 2) = 962.
Answer : 962

১৪,৬৪৬.

A invested Tk. 70000 in a business. After a few months, B joined him with Tk. 60000. At the end of the year, the total profit was divided between them in the ratio of 2 : 1. After how many months did B join?

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

সঠিক উত্তর: খ

5 months

উত্তর

সঠিক উত্তর: খ

5 months

খ

ব্যাখ্যা

Question: A invested Tk. 70000 in a business. After a few months, B joined him with Tk. 60000. At the end of the year, the total profit was divided between them in the ratio of 2 : 1. After how many months did B join?

Solution:
Let A work alone for ‘n’ months.
A’s input = 70000 × 12
B’s input = 60000 × (12 - n)

So, (70000 × 12)/[60000 × (12 - n] = 2 / 1
⇒(7 × 12) / [6 × (12 - n)] = 2 / 1
⇒ 12 - n = 7
∴ n = 5
Therefore, B joined after 5 months.

১৪,৬৪৭.

If x - 1/x = 3, the value of x³ - 1/x³ is-

ক
36
খ
63
গ
99
ঘ
18

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If x - 1/x = 3, the value of x³ - 1/x³ is-

Solution:
x - 1/x = 3

x³ - 1/x³
= (x - 1/x)³ + 3.x.(1/x)(x - 1/x)
= (x - 1/x)³ + 3(x - 1/x)
= (3)³ + 3 × 3
= 27 + 9
= 36

১৪,৬৪৮.

A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

ক
15%
খ
16%
গ
24%
ঘ
28%

সঠিক উত্তর: খ

16%

উত্তর

সঠিক উত্তর: খ

16%

খ

ব্যাখ্যা

Question: A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

Solution:
Given,
the price of the purse = 200 tk

∴ Price of the bag = 200 + (200 × 20%)
= 240 tk

Price of the wallet = 240 − (240 × 30%)
= 240 − 72
= 168 Tk

Difference is = (200 - 168) = 32 tk

∴ Percentage = (32 × 100)/200 = 16%

১৪,৬৪৯.

Find the equation of the line with x-intercept = 4 and y-intercept = 3.

ক
4x - 3y - 12 = 0
খ
4x + 3y - 12 = 0
গ
3x - 4y + 12 = 0
ঘ
3x + 4y - 12 = 0

সঠিক উত্তর: ঘ

3x + 4y - 12 = 0

উত্তর

সঠিক উত্তর: ঘ

3x + 4y - 12 = 0

ঘ

ব্যাখ্যা

Question: Find the equation of the line with x-intercept = 4 and y-intercept = 3.

Solution:
Given, x-intercept = 4,
So, the line passes through (4, 0).
y-intercept = 3,
So, the line passes through (0, 3).

We know,
The intercept form of a line is:
(x/a) + (y/b) = 1, where a = x-intercept, b = y-intercept.
⇒ (x/4) + (y/3) = 1
⇒ (3x + 4y)/12 = 1
⇒ 3x + 4y = 12
⇒ 3x + 4y - 12 = 0

∴ The equation of the line is 3x + 4y - 12 = 0

১৪,৬৫০.

If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is -

ক
4.8 cm
খ
8 cm
গ
6 cm
ঘ
5 cm

সঠিক উত্তর: ঘ

5 cm

উত্তর

সঠিক উত্তর: ঘ

5 cm

ঘ

ব্যাখ্যা

Question: If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is -

Solution:
According to question,
Length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, this is right angle triangle.

To find the length of the median to the greatest side of a triangle, we can use the formula:
Median = 1/2 * √(2b^2 + 2c^2 - a^2)
Where a, b, and c are the lengths of the sides of the triangle, and a is the greatest side.
In this case, the lengths of the sides are 6 cm, 8 cm, and 10 cm. The greatest side is 10 cm.
Using the formula:
Median = 1/2 * √(2 * 8² + 2 * 6² - 10²)
= 1/2 * √(128 + 72 - 100)
= 1/2 * √(100)
= 1/2 * 10
= 5 cm

So, the length of the median to the greatest side of the triangle is 5 cm.

১৪,৬৫১.

(log36/log6) =

ক
5
খ
8
গ
3
ঘ
2

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: (log36/log6) =

Solution:
(log36/log6)
= (log6²/log6)
= 2log6/log6
= 2

১৪,৬৫২.

The average age of A, B, C, D and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is

ক
48
খ
46
গ
42
ঘ
45

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The average age of A, B, C, D and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is-

Solution:
Total age of A, B, C and D
= 40 × 5
= 200 years

total age of A and B = 2 × 35 = 70 years
total age of C and D = 2 × 42 = 84 years

Age of E = 200 - 70 - 84 years
= 46 years

১৪,৬৫৩.

The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?

ক
38 kg
খ
37 kg
গ
35 kg
ঘ
34 kg

সঠিক উত্তর: খ

37 kg

উত্তর

সঠিক উত্তর: খ

37 kg

খ

ব্যাখ্যা

Question: The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?

Solution:
তিনজনের গড় ওজন ৩৩ কেজি
মোট ওজন = ৩৩ × ৩ কেজি
= ৯৯ কেজি

প্রতিজনের ওজন সর্বনিম্ন ৩১ কেজি
দুজনের সর্বনিম্ন ওজন = (৩১ × ২) কেজি
= ৬২ কেজি

একজনের সর্বোচ্চ ওজন হতে পারে = (৯৯ - ৬২) কেজি
= ৩৭ কেজি

১৪,৬৫৪.

Two trains, one from Dhaka to Chattogram and the other from Chattogram to Dhaka, start simultaneously. After they meet, the first train takes 4 hours to reach Chattogram, and the second train takes 9 hours to reach Dhaka. What is the ratio of their speeds?

ক
2 : 3
খ
1 : 2
গ
3 : 2
ঘ
5 : 3
ঙ
None of these

সঠিক উত্তর: গ

3 : 2

উত্তর

সঠিক উত্তর: গ

3 : 2

গ

ব্যাখ্যা

Question: Two trains, one from Dhaka to Chattogram and the other from Chattogram to Dhaka, start simultaneously. After they meet, the first train takes 4 hours to reach Chattogram, and the second train takes 9 hours to reach Dhaka. What is the ratio of their speeds?

Solution:
Time taken by Train₁ = 4 hours, And Train₂ = 9 hours.

∴ Ratio of speeds (Train₁ : Train₂) = Speed of Train₁/Speed of Train₂
= √(9/4) = 3/2 = 3 : 2

১৪,৬৫৫.

For what value of 'k' will the pair of equations 2x + 9y = 2 and 12x + ky = 37 does not have a unique solution?

ক
9
খ
54
গ
27
ঘ
36

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

2x + 9y = 2
⇒ 6 × 2x + 6 × 9y = 6 × 2
⇒ 12x + 54y = 12
The given equation 12x + ky = 37
The pair of equations 2x + 9y = 2 and 12x + ky = 37 does not have a unique solution if tha value of k is 54.

১৪,৬৫৬.

The marked price of a water cooler is Tk.4650. The shopkeeper offers an off-season discount of 18% on it. What is its selling price?

ক
ক) Tk.5487
খ
খ) Tk.3600
গ
গ) Tk.3813
ঘ
ঘ) Tk.4000

সঠিক উত্তর: গ

গ) Tk.3813

উত্তর

সঠিক উত্তর: গ

গ) Tk.3813

গ

ব্যাখ্যা

প্রশ্ন: The marked price of a water cooler is Tk.4650. The shopkeeper offers an off-season discount of 18% on it. What is its selling price?

সমাধান:
১৮% ছাড়ে,
গায়ে লিখা মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ৮২ টাকা
∴ গায়ে লিখা মূল্য ৪৬৫০ টাকা হলে বিক্রয়মূল্য (৮২ × ৪৬৫০)/১০০ টাকা
= ৩৮১৩ টাকা

১৪,৬৫৭.

Find the difference between the simple interest and the compound interest at 10% per annum for 2 years on a principal of Tk 3,000.

ক
Tk. 5
খ
Tk. 12
গ
Tk. 18
ঘ
Tk. 30

সঠিক উত্তর: ঘ

Tk. 30

উত্তর

সঠিক উত্তর: ঘ

Tk. 30

ঘ

ব্যাখ্যা

Question: Find the difference between the simple interest and the compound interest at 10% per annum for 2 years on a principal of Tk 3,000.

Solution:
We know, Simple Interest, I = pnr
and Compound Principal, C = p(1 + r)ⁿ

Simple Interest = 3,000 × 2 × (10/100) = 600 Tk

Compound Principal = 3,000 × (1 + 10/100)²
= 3,000 × (110/100)²
= (3,000 × 110 × 110)/(100 × 100)
= 3,630

So, Compound interest = 3,630 - 3,000 = 630 Tk

So, difference = 630 - 600 = 30 Tk.

১৪,৬৫৮.

The difference between the local value and the face value of 7 in the numeral 32675149 is -

ক
75142
খ
64851
গ
5149
ঘ
69993

সঠিক উত্তর: ঘ

69993

উত্তর

সঠিক উত্তর: ঘ

69993

ঘ

ব্যাখ্যা

Question: The difference between the local value and the face value of 7 in the numeral 32675149 is -

Solution:
32675149 -
Local value of 7 = 70000
Face value of 7 = 7
Difference =(70000 - 7) = 69993

১৪,৬৫৯.

Which of the following is irrational?

ক
√9
খ
4/3
গ
0.50
ঘ
√10

সঠিক উত্তর: ঘ

√10

উত্তর

সঠিক উত্তর: ঘ

√10

ঘ

ব্যাখ্যা

Question: Which of the following is irrational?

Solution:
√10 একটি অমূলদ সংখ্যা (irrational number)।
অমূলদ সংখ্যা (irrational number):
- যে সংখ্যাকে p/q আকারে প্রকাশ করা যায় না, যেখানে p ও q পূর্ণসংখ্যা এবং q ≠ 0, সে সংখ্যাকে অমূলদ সংখ্যা বলা হয়।
- পূর্ণবর্গ নয় এরূপ যে কোনো স্বাভাবিক সংখ্যার বর্গমূল কিংবা তার ভগ্নাংশ একটি অমূলদ সংখ্যা। যেমন, √2 = 1.414213..., √6 = 2.229489... ইত্যাদি অমূলদ সংখ্যা।
- কোনো অমূলদ সংখ্যাকে দুইটিপূর্ণ সংখ্যার অনুপাত হিসেবে প্রকাশ করা যায় না।
-অমূলদ সংখ্যাকে একটি মূলদ সংখ্যা দ্বারা গুণ করলে অমূলদ সংখ্যা পাওয়া যায়।
অর্থাৎ, non zero rational number × irrational number = irrational number.

১৪,৬৬০.

To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?

ক
36 days
খ
30 days
গ
40 days
ঘ
38 days

সঠিক উত্তর: ক

36 days

উত্তর

সঠিক উত্তর: ক

36 days

ক

ব্যাখ্যা

Question: To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?

Solution:
Let Y takes x days to complete the work
Then X will take 25% more i.e 125% of x days i.e 5/4x days.
So the one day work of X and Y together will be
(1/x) +{1/(5/4x)} = 1/20
⇒ (1/x) + (4/5x) = 1/20
⇒ 9/5x = 1/20
⇒ x = 36
∴ Y takes 36 days to complete the work.

১৪,৬৬১.

The average of the three numbers x, y and z is 45, x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is.

ক
ক) 3
খ
খ) 5
গ
গ) 7
ঘ
ঘ) 11

সঠিক উত্তর: গ

গ) 7

উত্তর

সঠিক উত্তর: গ

গ) 7

গ

ব্যাখ্যা

Question: The average of the three numbers x, y and z is 45, x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is.

Solution:
প্রশ্নমতে,
⇒ (x + y + z)/3 = 45
⇒ x + y + z = 135 ...................(1)

⇒ x = (y + z)/2 + 9
⇒ 2x - y - z = 18 .........................(2)

(1) + (2) নং যোগ করে পাই,
x + y + z = 135
2x - y - z = 18
3x = 153
∴ x = 51

(1) নং হতে পাই,
y + z = 135 - 51
y + z = 84 ........................(3)

আবার,
(y + z)/2 = y + 2
⇒ y + z = 2y + 4
⇒ z - y = 4 .................... (4)

(3) + (4) হতে পাই,
y + z = 84
z - y = 4
2z = 88
∴ z = 44

x ও z এর মধ্যে পার্থক্য = 51 - 44 = 7

১৪,৬৬২.

Which of the following must be odd?

ক
The product of two even numbers
খ
The product of two odd numbers
গ
The sum of an odd and an even number
ঘ
B & C
ঙ
The product of an odd and an even number

সঠিক উত্তর: ঘ

B & C

উত্তর

সঠিক উত্তর: ঘ

B & C

ঘ

ব্যাখ্যা

even × even is always even.
odd × even is always even.
so there is no possibility to find an odd number in the 1st and 5th options.
odd × odd is always odd.
odd + even is always odd.

১৪,৬৬৩.

5% loss is incurred when Rahim sells a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit?

ক
Tk. 1,260
খ
Tk. 1,200
গ
Tk. 1,300
ঘ
Tk. 1,450

সঠিক উত্তর: ক

Tk. 1,260

উত্তর

সঠিক উত্তর: ক

Tk. 1,260

ক

ব্যাখ্যা

Question: 5% loss is incurred when Rahim sells a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit?

Solution:
৫% ক্ষতিতে বিক্রয়মূল্য = ১০০ - ৫ = ৯৫ টাকা

বিক্রয়মূল্য ৯৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/৯৫ টাকা
বিক্রয়মূল্য ১১৪০ টাকা হলে ক্রয়মূল্য (১০০/৯৫) × ১১৪০ = ১২০০ টাকা

আবার,
৫% লাভে বিক্রয়মূল্য = ১০০ + ৫ = ১০৫ টাকা
ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১০৫ টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য ১০৫/১০০ টাকা
ক্রয়মূল্য ১২০০ টাকা হলে বিক্রয়মূল্য (১০৫/১০০) × ১২০০ = ১২৬০ টাকা

১৪,৬৬৪.

The height of a cylinder is four times the radius of the cylinder. If the volume of the cylinder is 256π cm³, what is the radius of the cylinder?

ক
ক) 4 cm
খ
খ) 8 cm
গ
গ) 16 cm
ঘ
ঘ) 24 cm

সঠিক উত্তর: ক

ক) 4 cm

উত্তর

সঠিক উত্তর: ক

ক) 4 cm

ক

ব্যাখ্যা

ধরি
সিলিন্ডারের ব্যাসার্ধ r cm
সিলিন্ডারের উচ্চতা 4r cm

আমরা জানি,
সিলিন্ডারের আয়তন= πr²h ঘন একক

প্রশ্নমতে,
πr²× 4r = 256π
4r³ = 256
r³= 64
r³ = 4³
r = 4

১৪,৬৬৫.

A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the remaining food lasts for 35 days, the number of men originally in the fort were -

ক
ক) 2500
খ
খ) 3000
গ
গ) 3500
ঘ
ঘ) 4000

সঠিক উত্তর: গ

গ) 3500

উত্তর

সঠিক উত্তর: গ

গ) 3500

গ

ব্যাখ্যা

Let, there be x men originally.
So, x men had provisions for 40 days whereas (x + 500) men consumed it in 35 days.
more men, Less days [Indirect proportion]
∴ (x + 500) : x = 40 : 35
⇒ 35(x+ 500) = 40x
⇒ 5x = 35 × 500
⇒ x = (35 × 500)/5
= 3500.

১৪,৬৬৬.

A two digit number is 4 times the sum of its digits. If the digits differ by 3, find the number.

ক
36
খ
47
গ
26
ঘ
14
ঙ
58

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: A two-digit number is 4 times the sum of its digits. If the digits differ by 3, find the number.

Solution:
Two digit number have:
Tens digit = a
Ones digit = b
So the number is:
10a + b

Condition 1:
The number is 4 times the sum of its digits.
10a + b = 4 (a + b)
⇒ 10a + b = 4a + 4b
⇒ 10a - 4a = 4b - b
⇒ 6a = 3b
⇒ 2a = b .......(1)

Condition 2:
The two digits differ by 3.
| a - b | = 3

From Condition 1:
| a - b | = 3
⇒ | a - 2a | = 3 [substituting b = 2a]
⇒ | - a | = 3
⇒ a = 3

so,
b = 2a
⇒ b = 2 × 3 = 6

So the number is = 36

১৪,৬৬৭.

Find the least number of six digits which is exactly divisible by 15, 21 and 28.

ক
ক) 100480
খ
খ) 100270
গ
গ) 100380
ঘ
ঘ) 100340

সঠিক উত্তর: গ

গ) 100380

উত্তর

সঠিক উত্তর: গ

গ) 100380

গ

ব্যাখ্যা

Least six-digit number is = 100000
Lcm of 15, 21, 28 is = 420
Then, 100000/420 = quotient 238 and remainder = 40
So, the number is = (100000 – 40) + 420 = 100380

১৪,৬৬৮.

A train passes two bridges of the lengths 600 m and 250 m in 100 seconds and 60 seconds respectively. The length of the train is -

ক
ক) 152 m
খ
খ) 125 m
গ
গ) 275 m
ঘ
ঘ) 120 m

সঠিক উত্তর: গ

গ) 275 m

উত্তর

সঠিক উত্তর: গ

গ) 275 m

গ

ব্যাখ্যা

Let the length of train x m
Speed of train = (length of train + length of bridge)/time taken in crossing
According to information we get,
⇒ (x + 600)/100 = (x + 250)/60
⇒ 60 (x + 600) = 100(x + 250)
⇒ 3 (x + 600) = 5(x + 250)
⇒ 5x + 1250 = 3x + 1800
⇒ 5x - 3x = 1800 - 1250
⇒ 2x = 550
⇒ x = 275 m

১৪,৬৬৯.

Find the smallest three digit number which is a multiple of 7.

ক
105
খ
103
গ
98
ঘ
None of these

সঠিক উত্তর: ক

105

উত্তর

সঠিক উত্তর: ক

105

ক

ব্যাখ্যা

Question: Find the smallest three digit number which is a multiple of 7.

Solution:
Smallest three digit number =100.
Divide this number by 7 and get the remainder as 2.
If you subtract 2 from the number the remaining number will be a multiple of 7, 100 - 2 = 98 which is two digit number.
Now if we add 7 so that we get the smallest three digit number which is a multiple of 7.
Required number = 98 + 7 = 105.

১৪,৬৭০.

Students of a class stand in a queue. If Raju is 22^nd in order from both ends, how many students are there in the queue?

ক
42
খ
44
গ
43
ঘ
45

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Students of a class stand in a queue. If Raju is 22^nd in order from both ends, how many students are there in the queue?

Solution:
এক দিক থেকে রাজুর অবস্থান ২২ তম অর্থাৎ সে সহ ২২ জন।
অপর দিক থেকে তার অবস্থান ২২ তম অর্থাৎ সে বাদে আরও ২১ জন আছে।
∴ ঐ সারিতে মোট ছাত্র আছে (২২ + ২১) জন = ৪৩ জন

১৪,৬৭১.

Arif bought a ticket of a cinema for Tk. 25 and later sold the ticket to Rafi for Tk. 75. What was the percent increase in the price of the ticket?

ক
100%
খ
54%
গ
30%
ঘ
200%

সঠিক উত্তর: ঘ

200%

উত্তর

সঠিক উত্তর: ঘ

200%

ঘ

ব্যাখ্যা

Question: Arif bought a ticket of a cinema for Tk. 25 and later sold the ticket to Rafi for Tk. 75. What was the percent increase in the price of the ticket?

Solution:
ক্রয়মূল্য = 25 টাকা
বিক্রয়মূল্য = 75 টাকা
∴ লাভ = 75 - 25 = 50 টাকা

25 টাকায় লাভ হয় = 50 টাকা
1 টাকায় লাভ হয় = 50 / 25 টাকা
∴ 100 টাকায় লাভ হয় = (50 × 100)/25 টাকা = 200 টাকা

∴ শতকরা লাভ 200%

১৪,৬৭২.

The least number which should be added to 2,497 so that the sum is exactly divisible 5, 6, 4 and 3 is

ক
ক) 23
খ
খ) 13
গ
গ) 3
ঘ
ঘ) 33

সঠিক উত্তর: ক

ক) 23

উত্তর

সঠিক উত্তর: ক

ক) 23

ক

ব্যাখ্যা

Question: The least number which should be added to 2,497 so that the sum is exactly divisible 5, 6, 4 and 3 is

Solution:
L.C.M. of 5, 6, 4, and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37)
= 23

১৪,৬৭৩.

A boy is sitting on the back seat of a car. When the driver suddenly starts the car, the boy experiences a backward force -

ক
ক) Always
খ
খ) Sometimes
গ
গ) Often
ঘ
ঘ) Never

সঠিক উত্তর: ক

ক) Always

উত্তর

সঠিক উত্তর: ক

ক) Always

ক

ব্যাখ্যা

থেমে থাকা বাস হঠাৎ চলতে শুরু করলে বাস যাত্রীরা সবসময় পিছনের দিকে হেলে পড়েন জড়তার কারণে।

চলন্ত বাস থেকে নামতে গেলে ঠিক তার বিপরীত ব্যাপারটি ঘটে। পুরাে শরীরটি গতিশীল অবস্থায় পা যখন মাটি স্পর্শ করে, শরীরের নিচের অংশ স্থির হয়ে গেলেও উপরের অংশ গতিশীল থেকে যায় এবং যাত্রী সামনে হুমড়ি খেয়ে পড়ে যায়। কোনাে বস্তুর দিক পরিবর্তনের ক্ষেত্রেও আমরা জড়তার প্রভাব অনুভব করি। যদি কোনাে বাস বা গাড়ি হঠাৎ বাক নেয়, যাত্রীরা অন্য পাশে ঝুঁকে পড়ে জড়তার কারণে।

১৪,৬৭৪.

In college Rahim scored 80 marks out of 150 in History and 95 marks out of 120 in English. If he wants to score 70% marks in 3 subjects, find the minimum marks he should score in Geography out of 100.

ক
ক) 70
খ
খ) 55
গ
গ) 76
ঘ
ঘ) None of these

সঠিক উত্তর: ঘ

ঘ) None of these

উত্তর

সঠিক উত্তর: ঘ

ঘ) None of these

ঘ

ব্যাখ্যা

Total marks = 150 + 120 + 100 = 370
Marks obtained in 2 subjects = 80+95 = 175
Total marks to be obtained = 370 × 70% = 259
∴ Minimum marks needed to be scored in Geography = 259 – 175 = 84

১৪,৬৭৫.

Find an equation for the line with x-intercept = 5, y-intercept = - 2.

ক
2x - 5y - 10 = 0
খ
5x - 2y - 10 = 0
গ
2x + 5y - 10 = 0
ঘ
2x - 5y + 10 = 0

সঠিক উত্তর: ক

2x - 5y - 10 = 0

উত্তর

সঠিক উত্তর: ক

2x - 5y - 10 = 0

ক

ব্যাখ্যা

Question: Find an equation for the line with x-intercept = 5, y-intercept = - 2.

Solution:
দেওয়া আছে,
রেখাটি x-অক্ষকে ছেদ করে (x₁, y₁) = (5, 0) বিন্দুতে
এবং y-অক্ষকে ছেদ করে (x₂, y₂) = (0, - 2) বিন্দুতে।

আমরা জানি,
ঢাল m = (y₂ - y₁)/(x₂ - x₁)
= (- 2 - 0)/(0 - 5)
= - 2/- 5
= 2/5.

এখানে,
m = 2/5
c = y এর ছেদক = - 2

∴সরলরেখার ঢালের সমীকরণ হতে পাই,
y = mx + c
⇒ y = (2/5)x + (- 2)
⇒ 5y = 2x - 10
⇒ 2x - 5y - 10 = 0.

∴ নির্ণেয় রেখাটির সমীকরণ হলো 2x - 5y - 10 = 0

১৪,৬৭৬.

The interest accrued on Tk. 2800 over 18 months at an annual rate of 10% using compound interest is-

ক
Tk. 434
খ
Tk. 634
গ
Tk. 430
ঘ
Tk. 728

সঠিক উত্তর: ক

Tk. 434

উত্তর

সঠিক উত্তর: ক

Tk. 434

ক

ব্যাখ্যা

Question: The interest accrued on Tk. 2800 over 18 months at an annual rate of 10% using compound interest is-

Solution:
Interest after 1 year or 12 months = 2800 × 1 × (10/100)
= 280
New principal = 2800 + 280
= 3080

6 months = 1/2 year

Now,
I = Pnr
= 3080 × (1/2) × (10/100)
= 154

∴ Total interest = 280 + 154 = Tk. 434

১৪,৬৭৭.

What is the original price of a T- shirt, if the sale price after 16% discount is Tk. 264?

ক
Tk. 300
খ
Tk. 310
গ
Tk. 314
ঘ
Tk. 318

সঠিক উত্তর: গ

Tk. 314

উত্তর

সঠিক উত্তর: গ

Tk. 314

গ

ব্যাখ্যা

Let the cost price of the T-shirt be Tk. y
or, y - 16% of y = 264
or, y - 16y/100 = 264
or, (1 - 16/100)y = 264
or, 84y/100 = 264
or, y = 314.28

১৪,৬৭৮.

ক
2
খ
15
গ
3
ঘ
24

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question:

Solution:

১৪,৬৭৯.

If a + b + c = 12, a + b = 4 and a + c =7, what is the value of a?

ক
ক) 2
খ
খ) - 1
গ
গ) 3/23
ঘ
ঘ) - 2

সঠিক উত্তর: খ

খ) - 1

উত্তর

সঠিক উত্তর: খ

খ) - 1

খ

ব্যাখ্যা

Question: If a + b + c = 12, a + b = 4, and a + c =7, what is the value of a?

Solution:
a + b + a + c = 4 + 7 = 11
⇒ 2a + b + c = 11

2a + b + c - a - b - c = 11 - 12
∴ a = - 1

১৪,৬৮০.

A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is-

ক
600
খ
750
গ
1000
ঘ
1250

সঠিক উত্তর: ঘ

1250

উত্তর

সঠিক উত্তর: ঘ

1250

ঘ

ব্যাখ্যা

Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is-

Solution:
speed = 5 × (5/18) m/sec
= 25/18 m/sec.

Distance covered in 15 minutes = (25/18) × 15 × 60 m
= 1250 m.

১৪,৬৮১.

A man swims 12 km downstream and 10 km upstream. If he takes 2 hours each time, what is the speed of the stream?

ক
1 km/hr
খ
0.5 km/hr
গ
1.5 km/hr
ঘ
0.7 km/hr

সঠিক উত্তর: খ

0.5 km/hr

উত্তর

সঠিক উত্তর: খ

0.5 km/hr

খ

ব্যাখ্যা

Question: A man swims 12 km downstream and 10 km upstream. If he takes 2 hours each time, what is the speed of the stream?

Solution:
Speed downstream = 12/2 = 6 km/hr
Speed upstream = 10/2= 5 km/hr

Speed of stream = (1/2)(speed downstream - speed upstream)
= (1/2)(6 - 5)
= 1/2
= 0.5

১৪,৬৮২.

How many Permutations of the letters of the word APPLE are there?

ক
30
খ
120
গ
60
ঘ
240

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: How many Permutations of the letters of the word APPLE are there?

Solution:
Here,
APPLE = 5 letters.
But two letters PP is of same kind.
So, required permutations,
= 5!/2!
= 120/2
= 60

১৪,৬৮৩.

In what ways the letters of the word "PUZZLE" can be arranged to form the different new words so that the vowels always come together?

ক
280
খ
450
গ
630
ঘ
120

সঠিক উত্তর: ঘ

120

উত্তর

সঠিক উত্তর: ঘ

120

ঘ

ব্যাখ্যা

Question: In what ways the letters of the word "PUZZLE" can be arranged to form the different new words so that the vowels always come together?

Solution:
The word PUZZLE has 6 different letters.

As per the question, the vowels should always come together.
Now, let the vowels UE as a single entity.
Therefore, the number of letters is 5 (PZZL = 4 + UE = 1)
Since the total number of letters = 4+1 = 5
So the arrangement would be in ⁵P₅ = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways.
Now, the vowels UE can be arranged in 2 different ways, i.e., ²P₂ = 2! = 2 × 1 = 2 ways
Hence, the new words, which can be formed after rearranging the letters = 120 ×2 = 240
As we known z is occurring twice in the word ‘PUZZLE’ so we will divide the 240 by 2.
So, the no. of permutation will be = 240/2 = 120

১৪,৬৮৪.

A man spent 1/2 of his money and then lost 1/4 of the remainder. He was left with Tk. 4,200. How much did he start with?

ক
ক) Tk. 10400
খ
খ) Tk. 11200
গ
গ) Tk. 10800
ঘ
ঘ) Tk. 12600

সঠিক উত্তর: খ

খ) Tk. 11200

উত্তর

সঠিক উত্তর: খ

খ) Tk. 11200

খ

ব্যাখ্যা

Question: A man spent 1/2 of his money and then lost 1/4 of the remainder. He was left with Tk. 4,200. How much did he start with?

Solution:
ধরি
মোট ছিল = x টাকা

সে খরচ করলো = x/2 টাকা
অবশিষ্ট থাকে = x - (x/2)
= (2x - x)/2
= x/2

হারিয়ে ফেলে = x/2 এর 1/4 = x/8

অবশিষ্ট থাকে = (x/2) - (x/8)
= (4x - x)/8
= 3x/8

প্রশ্নমতে,
3x/8 = 4200
⇒ 3x = 4200 × 8
⇒ x = (4200 × 8)/3
⇒ x =11200 টাকা

১৪,৬৮৫.

If a² + 2a/5 + 1/25 = 0, then (a - 2/5)² = ?

ক
ক) 16/25
খ
খ) 1/25
গ
গ) 9/25
ঘ
ঘ) 36/25

সঠিক উত্তর: গ

গ) 9/25

উত্তর

সঠিক উত্তর: গ

গ) 9/25

গ

ব্যাখ্যা

Question: If a² + 2a/5 + 1/25 = 0, then (a - 2/5)² = ?

Solution:
a² + 2a/5 + 1/25 = 0
⇒ a² + (1/5)² + 2 × a × 1/5 = 0
⇒ (a + 1/5)² = 0
⇒ a = - 1/5

{(- 1/5) - (2/5)}² = {(- 1 - 2)/5}²
= 9/25

১৪,৬৮৬.

The average age of a husband and his wife was 25 years at the time of their marriage. After five years they have a three-year old child. What is the average age of the family now?

ক
20 years
খ
21 years
গ
23 years
ঘ
25 years

সঠিক উত্তর: খ

21 years

উত্তর

সঠিক উত্তর: খ

21 years

খ

ব্যাখ্যা

Question: The average age of a husband and his wife was 25 years at the time of their marriage. After five years they have a three-year old child. What is the average age of the family now?

solution:
The average age of a husband and his wife was 25 years at the time of their marriage
Sum of age = 25 × 2 = 50

After five years, sum of their age = 50 + 5 + 5 = 60
Sum of age of the family = 60 + 3 = 63 years

∴the average age of the family is = 63/3 = 21 years

১৪,৬৮৭.

How many factors does 144 have?

ক
ক) 14
খ
খ) 15
গ
গ) 16
ঘ
ঘ) 17

সঠিক উত্তর: খ

খ) 15

উত্তর

সঠিক উত্তর: খ

খ) 15

খ

ব্যাখ্যা

প্রশ্নঃ How many factors does 144 have?
সমাধানঃ
144 এর উৎপাদকগুলো হলো = {1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}
অর্থাৎ, 144 এর উৎপাদক সংখ্যা : 15

১৪,৬৮৮.

A fair die is rolled once. What is the probability of getting an even number?

ক
1/3
খ
1/2
গ
1/6
ঘ
2/3

সঠিক উত্তর: খ

1/2

উত্তর

সঠিক উত্তর: খ

1/2

খ

ব্যাখ্যা

Question: A fair die is rolled once. What is the probability of getting an even number?

Solution:
A standard fair die has 6 faces.
{1, 2, 3, 4, 5, 6}

∴ Total possible outcomes = 6

And even numbers on a die, {2, 4, 6}
∴ Number of favorable outcomes = 3

∴ Probability of getting an even number = (Number of favorable outcomes)/(Total number of possible outcomes)
= 3/6
= 1/2

So the probability is 1/2.

১৪,৬৮৯.

The volume of a cuboid with length, breadth and height as 11x³, 12x⁵ and 13x⁷ respectively is:

ক
1716x¹⁵
খ
1015x⁹
গ
1050x
ঘ
1172x¹⁵

সঠিক উত্তর: ক

1716x¹⁵

উত্তর

সঠিক উত্তর: ক

1716x¹⁵

ক

ব্যাখ্যা

Question: The volume of a cuboid with length, breadth and height as 11x³, 12x⁵ and 13x⁷ respectively is:

Solution:
দেওয়া আছে
আয়তাকার ঘনবস্তুর (cuboid) দৈর্ঘ্য = 11x³
আয়তাকার ঘনবস্তুর (cuboid) প্রস্থ = 12x⁵
আয়তাকার ঘনবস্তুর (cuboid) উচ্চতা = 13x⁷

আয়তাকার ঘনবস্তুর আয়তন = (11x³) × (12x⁵) × (13x⁷)
= 1716x¹⁵

১৪,৬৯০.

In a football team, the average of 11 players is 28 years. Out of these, the average ages of three players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is 11 years older than the yougest player, what is the age of the youngest player?

ক
23
খ
24
গ
25
ঘ
26

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

প্রশ্ন: In a football team, the average of 11 players is 28 years. Out of these, the average ages of three players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is 11 years older than the yougest player, what is the age of the youngest player?

সমাধান:
11 জনের মোট বয়স = 11 × 28 = 308 বছর
3 জনের 3টি গ্রুপের 9 জনের মোট বয়স = (3 × 25) + (3 × 28) + (3 × 30) = 249 বছর
∴ ক্যাপ্টেন এবং সবচেয়ে জুনিয়র খেলোয়াড়ের বয়স = 308 - 249 = 59 বছর

ধরি,
ক্যাপ্টেনের বয়স = a
সবচেয়ে জুনিয়র খেলোয়াড়ের বয়স = a - 11

প্রশ্নমতে,
a + a - 11 = 59
⇒ 2a = 70
∴ a = 35
অতএব, সবচেয়ে জুনিয়র খেলোয়াড়ের বয়স = 35 - 11 = 24 বছর

১৪,৬৯১.

One of the factors of x⁴ + x² + 1 is -

ক
ক) x² - x - 1
খ
খ) x² + x + 1
গ
গ) (x + 1)²
ঘ
ঘ) x² + x - 1

সঠিক উত্তর: খ

খ) x² + x + 1

উত্তর

সঠিক উত্তর: খ

খ) x² + x + 1

খ

ব্যাখ্যা

x⁴ + x² + 1
= (x²)² + 2x².1 + 1 - x²
= (x² + 1)² - x²
= (x² + x + 1) (x² - x + 1)

১৪,৬৯২.

A trader sells his goods at a discount of 10%. He still makes a profit of 20%. If he sells the goods at the marked price only, his profit will be -

ক
ক) 33.33%
খ
খ) 30%
গ
গ) 28.35%
ঘ
ঘ) 22.35%

সঠিক উত্তর: ক

ক) 33.33%

উত্তর

সঠিক উত্তর: ক

ক) 33.33%

ক

ব্যাখ্যা

Question: A trader sells his goods at a discount of 10%. He still makes a profit of 20%. If he sells the goods at the marked price only, his profit will be -

Solution:
ডিসকাউন্ট এর পর বিক্রয়মূল্য = ১০০ - (১০০ এর ১০%) = ৯০ টাকা
২০% লাভে ক্রয়মূল্য ১০০ টাকা হলে বিক্রয়মূল্য ১২০ টাকা

∴ ৮০ টাকা বিক্রয়মূল্য হলে ক্রয়মূল্য = (১০০ × ৯০)/১২০ টাকা
= ৭৫ টাকা

প্রকৃত দামে বিক্রি করলে লাভ হত = ১০০ - ৭৫ = ২৫ টাকা

∴ শতকরা লাভ = (২৫ × ১০০)/৭৫ = ৩৩.৩৩%

১৪,৬৯৩.

The capacity of containing water of a tank is 8000 litres. The length of the tank is 2.56 metres and breadth is 1.25 metres. What is the depth of the tank?

ক
ক) 1.5 meters
খ
খ) 2 meters
গ
গ) 2.5 meters
ঘ
ঘ) 3.5 meters

সঠিক উত্তর: গ

গ) 2.5 meters

উত্তর

সঠিক উত্তর: গ

গ) 2.5 meters

গ

ব্যাখ্যা

Question: The capacity of containing water of a tank is 8000 litres. The length of the tank is 2.56 metres and breadth is 1.25 metres. What is the depth of the tank?

১৪,৬৯৪.

In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes. If the ratio of girls to boys in the class is 3 : 4, then what is the fraction of the students in the class having blue eyes?

ক
11/45
খ
11/70
গ
12/33
ঘ
14/45

সঠিক উত্তর: খ

11/70

উত্তর

সঠিক উত্তর: খ

11/70

খ

ব্যাখ্যা

Question: In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes. If the ratio of girls to boys in the class is 3 : 4, then what is the fraction of the students in the class having blue eyes?

Solution:
Let the number of girls be x
Since the ratio of the girls to boys is 3 : 4, the number of boys = 4x/3
Hence, the number of students in the class = x + (4x/3) = 7x/3

We are given that 10% of girls are blue-eyed,
∴ 10% of x = (10/100)x = x/10
Also, 20% of the boys are blue-eyed,
∴ 20% of 4x/3 = (20/100) × (4x/3) = 4x/15

Hence, the total number of blue-eyed students = (x/10) + (4x/15)
= 11x/30

Hence, the required fraction = (11x/30)/(7x/3)
= (11 × 3)/(30 × 7)
= 11/70

১৪,৬৯৫.

The average of the largest and smallest 3 digits numbers formed by 0, 3 and 8 would be-

ক
538
খ
598
গ
569
ঘ
583

সঠিক উত্তর: গ

569

উত্তর

সঠিক উত্তর: গ

569

গ

ব্যাখ্যা

Question: The average of the largest and smallest 3 digits numbers formed by 0, 3 and 8 would be-

Solution:
largest = 830
smallest = 308

Average = (830 + 308)/2
= 1138/2
= 569

১৪,৬৯৬.

The value of q, for which the equation x² + (q - 3)x + q = 0 has real and equal roots is-

ক
0
খ
1
গ
5
ঘ
7

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The value of q, for which the equation x² + (q - 3)x + q = 0 has real and equal roots is-

Solution:
দেয়া আছে,
x² + (q - 3)x + q = 0
x² + (q - 3)x + q = 0 কে কে ax² + bx + c = 0 সমীকরণের সাথে তুলনা করে পাই a = 1 , b = q - 3 , c = q
সমীকরণের মূলদ্বয় বাস্তব ও সমান হলে, নিশ্চায়ক = 0 হবে
b² - 4ac = 0
⇒ (q - 3)² - 4 × 1 × q = 0
⇒ q² - 2 × q × 3 + 9 - 4q = 0
⇒ q² - 6q + 9 - 4q = 0
⇒ q² - 10q + 9 = 0
⇒ q² - 9q - q + 9 = 0
⇒ q(q - 9) - 1(q - 9) = 0
⇒ (q - 9) (q - 1) = 0
∴ q = 1, 9

১৪,৬৯৭.

Five times the first of three consecutive even integers is 4 more than three times the third. The third integer is-

ক
10
খ
12
গ
14
ঘ
16
ঙ
None

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: Five times the first of three consecutive even integers is 4 more than three times the third. The third integer is-

Solution:
Let,
the three even integers = x, x + 2 and x + 4

ATQ,
5x = 3(x + 4) + 4
⇒ 5x = 3x + 12 + 4
⇒ 5x - 3x = 16
⇒ 2x = 16
∴ x = 8

∴ Third integer = x + 4 = 8 + 4 = 12

১৪,৬৯৮.

5 years ago, a man aged 28 got married. after 2 years, a baby child was born. What is the age ratio of the baby and father at present?

ক
ক) 11
খ
খ) 11 : 3
গ
গ) 1 : 11
ঘ
ঘ) 1 : 9

সঠিক উত্তর: গ

গ) 1 : 11

উত্তর

সঠিক উত্তর: গ

গ) 1 : 11

গ

ব্যাখ্যা

Question: 5 years ago, a man aged 28 got married. after 2 years, a baby child was born. What is the age ratio of the baby and father at present?

Solution:
the present age of the children is 3 years
the present age of the father is 33 years

so, the ratio is = 3 : 33
1 : 11

১৪,৬৯৯.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
25%
গ
50%
ঘ
37.5%

সঠিক উত্তর: ক

20%

উত্তর

সঠিক উত্তর: ক

20%

ক

ব্যাখ্যা

Question: The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

Solution:
Let price of book = 100tk
Price of pen = 100 + 100 × 25%
= 125 tk
Price of pen-holder = 100 + 100 × 50%
= 150 tk

Difference is = 150 - 125 = 25 tk

∴ Percentage = (25 × 100)/125
= 20%

১৪,৭০০.

The H. C. F of (9/10), (12/20), (15/25), (27/50) is?

ক
7/5
খ
3/100
গ
18/100
ঘ
5/7

সঠিক উত্তর: খ

3/100

উত্তর

সঠিক উত্তর: খ

3/100

খ

ব্যাখ্যা

Question: The H. C. F of (9/10), (12/20), (15/25), (27/50) is?

Solution:
Required H. C. F
= (H. C. F of 9, 12, 15, 27)/(L. C. M of 10, 20, 25, 50)
= 3/100