Bank Math

PrepBank · পাতা ১৫১ / ১৬১ · ১৫,০০১–১৫,১০০ / ১৬,১২৪

১৫,০০১.

20% ডিসকাউন্টের পরে একটি বইয়ের খরচ 400 টাকা দাঁড়ায়। তবে বইটির প্রকৃত মূল্য কত?

ক
500 টাকা
খ
480 টাকা
গ
320 টাকা
ঘ
333 টাকা

ব্যাখ্যা

প্রশ্ন: 20% ডিসকাউন্টের পরে একটি বইয়ের খরচ 400 টাকা দাঁড়ায়। তবে বইটির প্রকৃত মূল্য কত?

সমাধান:
20% ডিসকাউন্টে,
ক্রয়মূল্য দাড়ায় = (100 - 20) টাকা
= 80 টাকা

বইয়ের ক্রয়মূল্য 80 টাকা হলে প্রকৃত মূল্য = 100 টাকা
বইয়ের ক্রয়মূল্য 1 টাকা হলে প্রকৃত মূল্য = 100/80 টাকা
বইয়ের ক্রয়মূল্য 400 টাকা হলে প্রকৃত মূল্য = (100 × 400)/80 টাকা
= 500 টাকা

১৫,০০২.

Two-third of one-fifth of one-fourth of a number is 10. What is 30% of that number?

ক
60
খ
100
গ
270
ঘ
90

ব্যাখ্যা

Question: Two-third of one-fifth of one-fourth of a number is 10. What is 30% of that number?

Solution:
Let,
The number be x.

ATQ,
(2/3) × (1/5) × (1/4) × x = 10
⇒ (1/30) × x = 10
⇒ x = 10 × 30
∴ x = 300

30% of 300 = (30 × 300)/100 = 90

১৫,০০৩.

The radius of a cylinder is three times its height. If the volume of the cylinder is 243π cm³, what is the height of the cylinder?

ক
9 cm
খ
6 cm
গ
3 cm
ঘ
3.5 cm

ব্যাখ্যা

Question: The radius of a cylinder is three times its height. If the volume of the cylinder is 243π cm³, what is the height of the cylinder?

Solution:
Given that,
Volume, V = 243π cm³
Radius, r = 3h

We know,
V = πr²h
⇒ πr²h = 243π
⇒ (3h)²h = 243
⇒ 9h³ = 243
⇒ h³ = 243/9
⇒ h³ = 27
⇒ h³ = 3³
∴ h = 3

So the height is 3 cm

১৫,০০৪.

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

ক
3
খ
4
গ
15
ঘ
18
ঙ
20

ব্যাখ্যা

Question: A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

Solution:
Let the number of correct answers be X
The number of incorrect answers will be 22 - X
For each correct answer the student got 3.5 points for a total of 3.5X
For each incorrect answer one point was taken out which is equivalent to - (22 - X)
The total he got for that was 63.5

So in short you have the following equation and solution.
3.5X - (22 - X) = 63.5
⇒ 3.5X - 22 + X = 63.5
⇒ 4.5X = 63.5 + 22
⇒ 4.5X = 85.5
⇒ 4.5X/4.5 = 85.5/4.5
∴ X = 19

So incorrect answers will be 22 - X = 22 - 19 = 3.

১৫,০০৫.

Rakib obtained an amount of Tk. 8300 as simple interst on a certain amount at 8 p.c.p.a. after 5 years. What is the amount invested by Rakib?

ক
ক) Tk. 20750
খ
খ) Tk. 20700
গ
গ) Tk. 20720
ঘ
ঘ) Tk. 20760

ব্যাখ্যা

Question: Rakib obtained an amount of Tk. 8300 as simple interest on a certain amount at 8 p.c.p.a. after 5 years. What is the amount invested by Rakib?

Solution:
Suppose, Principal = Tk. 100
Then interest for 5 years at 8% = 5 × 8 = Tk. 40.

Now,
If interest is 40 taka then Principal = 100
∴ If interest is Tk. 8300 then Principal = (8300 × 100)/40 Tk.
= 20750 Tk.

১৫,০০৬.

A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water

ক
ক) 12 km/hr
খ
খ) 13 km/hr
গ
গ) 14 km/hr
ঘ
ঘ) 15 km/hr

ব্যাখ্যা

Let the speed of the water in still water = x
Given that speed of the stream = 3 kmph
Speed downstream
= (x+3) kmph
Speed upstream
= (x−3) kmph
He travels a certain distance downstream in 4 hour and come back in 6 hour.
ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour
since distance = speed × time,
we have
(x+3)4= (x−3)6
⇒ (x+3)2= (x−3)3
⇒ 2x+6= 3x−9
⇒ x= 6+9= 15 kmph

১৫,০০৭.

If WORLD is written as 34526 and EARTH is written as 78519, then ALERT is written as-

ক
84526
খ
38519
গ
82751
ঘ
28517

ব্যাখ্যা

Question: If WORLD is written as 34526 and EARTH is written as 78519, then ALERT is written as-

Solution:
WORLD is written as 34526
W = 3
O = 4
R = 5
L = 2
D= 6

EARTH is written as 78519
E = 7
A = 8
R = 5
T = 1
H = 9

So, ALERT will be
A = 8
L = 2
E = 7
R = 5
T = 1

∴ ALERT will be = 82751

১৫,০০৮.

M and N enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, M withdraws. If they receive profit in the ratio of 5 : 9. Find how long N's capital was used?

ক
ক) 9 months.
খ
খ) 10 months.
গ
গ) 11 months.
ঘ
ঘ) 12 months.

ব্যাখ্যা

Question: M and N enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, M withdraws. If they receive profit in the ratio of 5 : 9. Find how long N's capital was used?

Solution:
Let the capitals of N was used for X months.
According to the question,
(5 × 8)/(6 × X) = 5/9
⇒ X = 12 months

Hence capital of N was used for = 12 months.

১৫,০০৯.

In New jersey 90% of the population own a car, 15% own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?

ক
ক) 46/7%
খ
খ) 47/3%
গ
গ) 100/3%
ঘ
ঘ) 91/2%

ব্যাখ্যা

গাড়ি বা মোটরসাইকেল এর মালিক = ১০০%
গাড়ির মালিক = ৯০%
মোটরসাইকেলের মালিক = ১৫%

গাড়ি ও মোটরসাইকেল এর মালিক =(৯০ + ১৫)% - ১০০% = ১০৫% - ১০০% = ৫%
গাড়ির মালিকের মোটর সাইকেল রয়েছে = {(৫/১৫) × ১০০}% = ১০০/৩%

১৫,০১০.

The sum of three consecutive odd integers is 44 more than the last of the numbers. What is the middle number?

ক
21
খ
23
গ
25
ঘ
27

ব্যাখ্যা

Question: The sum of three consecutive odd integers is 44 more than the last of the numbers. What is the middle number?

Solution:
Let the odd is x
So,
2nd odd is x + 2
3rd odd is x + 4

According to the question,
Sum of the odd numbers = (x + 4) + 44
The equation,
x + ( x + 2) + (x + 4) = (x + 4) + 44
⇒ 3x + 6 = x + 48
⇒ 3x - x = 48 - 6
⇒ 2x = 42
⇒ x = 42/2
∴ x = 21
First number is 21
Second number is 23

∴ The middle number is 23

১৫,০১১.

In a class, 25 students play football, 15 students play cricket, and 5 students play both. 10 students play neither football nor cricket. What is the total number of students in the class?

ক
40
খ
50
গ
45
ঘ
55

ব্যাখ্যা

Question: In a class, 25 students play football, 15 students play cricket, and 5 students play both. 10 students play neither football nor cricket. What is the total number of students in the class?

Solution:
Let the number of students who play football = 25
Number of students who play cricket = 15
Number of students who play both football and cricket = 5
Number of students who play neither = 10

Number of students who play football or cricket:
n(F ∪ C) = n(F) + n(C) − n(F ∩ C)
n(F ∪ C) = 25 + 15 − 5 = 35

Add the students who play neither to get the total number of students:
Total students = n(F ∪ C) + neither = 35 + 10 = 45

১৫,০১২.

A worker earns Tk. 350 on the first day and spends Tk. 300 on the second day, earns Tk. 350 on the third day and again spends Tk. 300 on the fourth day and so on. On which day would he have had Tk. 1000?

ক
21^th day
খ
31^th day
গ
27^th day
ঘ
25^th day

ব্যাখ্যা

Question: A worker earns Tk. 350 on the first day and spends Tk. 300 on the second day, earns Tk. 350 on the third day and again spends Tk. 300 on the fourth day and so on. On which day would he have had Tk. 1000?

Solution:
১ম দিনে আয় করে ৩৫০ টাকা।
২য় দিনে ব্যয় করে ৩০০ টাকা।

∴ ২ দিনে তার জমা থাকে (৩৫০ - ৩০০) = ৫০ টাকা।

এখন, (১০০০ - ৩৫০) = ৬৫০ টাকা।

৫০ টাকা জমা থাকে ২ দিনে
১ টাকা জমা থাকে ২/৫০ দিনে
৬৫০ টাকা জমা থাকে (২ × ৬৫০)/৫০ দিনে
= ২৬ দিন।

২৬ দিন পর তার হাতে থাকে ৬৫০ টাকা
এবং ২৭ তম দিনে সে আয় করে ৩৫০ টাকা।
তাহলে মোট টাকা হয় (৬৫০ + ৩৫০) = ১০০০ টাকা,

সুতরাং ২৭ দিনে তার কাছে ১০০০ টাকা ছিল।

১৫,০১৩.

The average of x and y is 7, and z = 3x + 2. What is the average of y and z?

ক
ক) x + 8
খ
খ) 2x - 5
গ
গ) 2x + 11
ঘ
ঘ) 3x - 7

ব্যাখ্যা

(x + y)/2 = 7
⇒ x + y = 14
∴ y = 14 - x

Therefore,
(y + z)/2
= (14 - x + 3x + 2)/2
= (2x + 16)/2
= x + 8
------------------------------
x ও y গড় 7 এবং z = 3x + 2 হলে, y ও z এর গড় কত?

x ও y গড় 7 হলে,
(x + y)/2 = 7
⇒ x + y = 14
∴ y = 14 - x

অতএব,
y ও z এর গড়
= (y + z)/2
= (14 - x + 3x + 2)/2
= (2x + 16)/2
= x + 8
সুতরাং y ও z এর গড় x + 8

১৫,০১৪.

A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time the cistern will get filled?

ক
ক) 13 hours
খ
খ) 15 hours
গ
গ) 18 hours
ঘ
ঘ) 20 hours

ব্যাখ্যা

Question: A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time the cistern will get filled?

Solution:
The cistern fill in 1 hour = ( 1/6 ) - ( 1/9 ) part = 1/18 part
The cistern fill 1/18 part = 1 hour
The cistern fill full = ( 1 × 18 ) /1 hour = 18 hours

১৫,০১৫.

Which of the following fraction is smaller than 7/8 and greater than 4/9?

ক
ক) 17/41
খ
খ) 5/13
গ
গ) 9/10
ঘ
ঘ) 13/21

ব্যাখ্যা

Question: Which of the following fraction is smaller than 7/8 and greater than 4/9?

Solution:
7/8 = 0.875
4/9 = 0.444

Option (ক) 17/41 = 0.415
Option (খ) 5/13 = 0.385
Option (গ) 9/10 = 0.900
Option (ঘ) 13/21 = 0.690

Here, 0.444 < 0.690 < 0.875

So, Option (ঘ) 13/21 = 0.690 is smaller than 7/8 and greater than 4/9.

১৫,০১৬.

Vromor’s grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now, 8 years ago, what was the ratio of vromor’s age to that of her grandfather?

ক
ক) 1:2
খ
খ) 1:5
গ
গ) 3:8
ঘ
ঘ) None of these

ব্যাখ্যা

16 years ago, let V = x years and G = 8x years.
After 8 years from now, V = (x + 16 + 8)years and G = (8x + 16 + 8) years.
∴ 8x + 24 = 3 (x + 24)
⇒ 8x - 3x = 72 - 24
⇒ 5x = 48
8 years ago, V/g = (x + 8)/(8x + 8)
= {(48/5) + 8}/{8 × (48/5) + 8}
= (48 + 40)/(384 + 40) = 88/424
= 11/53
Answer: none of these.

১৫,০১৭.

If A = , then the trace of A is-

ক
9
খ
13
গ
15
ঘ
17

ব্যাখ্যা

Question: If A = , then the trace of A is-

Solution:
দেয়া আছে,
A =

ট্রেস (Trace): Matrix- এর Trace হলো একটি বর্গাকার ম্যাট্রিক্সের প্রধান কর্ণের সব উপাদানের যোগফল।
প্রধান কর্ণ: ম্যাট্রিক্সের উপরের বামদিকের কোণ থেকে নিচের ডানদিকের কোণ পর্যন্ত যে উপাদানগুলো থাকে, সেগুলোই প্রধান কর্ণ।

সুতরাং প্রদত্ত ম্যাট্রিক্স এর ট্রেস = 2 + 5 + 8 = 15

১৫,০১৮.

1 - [2 - {3 - (4 - 5) + 6} + 7] = ?

ক
1
খ
2
গ
- 2
ঘ
0

ব্যাখ্যা

Question: 1 - [2 - {3 - (4 - 5) + 6} + 7] = ?

Solution:
1 - [2 - {3 - (4 - 5) + 6} + 7]
= 1 - [2 - {3 - ( - 1) + 6} + 7]
= 1 - [2 - {3 + 1 + 6} + 7]
= 1 - [2 - 10 + 7]
= 1 - [- 1]
= 1 + 1
= 2

১৫,০১৯.

Three friends, Titu, Joyonto, and Rajib, start running around a circular track at the same time in the same direction. Titu completes a round in 120 seconds, Joyonto in 150 seconds, and Rajib in 180 seconds, all starting at the same point. After how much time will they meet again at the starting point?

ক
20 minutes
খ
25 minutes
গ
30 minutes
ঘ
40 minutes
ঙ
None

ব্যাখ্যা

Question: Three friends, Titu, Joyonto, and Rajib, start running around a circular track at the same time in the same direction. Titu completes a round in 120 seconds, Joyonto in 150 seconds, and Rajib in 180 seconds, all starting at the same point. After how much time will they meet again at the starting point?

Solution:
L.C.M. of 120, 150 and 180 = 1800
So, Titu, Joyonto, and Rajib will again meet at the starting point in 1800 sec
Now, 1800 sec = 1800/60 minutes
= 30 minutes

১৫,০২০.

A can do a work in 20 days, and B in 30 days. They work together for 6 days. How much of the work is left?

ক
1/3
খ
1/4
গ
1/2
ঘ
2/5

ব্যাখ্যা

Question: A can do a work in 20 days, and B in 30 days. They work together for 6 days. How much of the work is left?

Solution:
A 20 দিনে করতে পারে কাজটির 1 অংশ
A 1 দিনে করতে পারে কাজটির 1/20 অংশ

B 30 দিনে করতে পারে কাজটির 1 অংশ
B 1 দিনে করতে পারে কাজটির 1/30 অংশ

A ও B 1 দিনে করতে পারে কাজটির (1/20) + (1/30) অংশ
= (3 + 2)/60 অংশ
= 5/60 অংশ
= 1/12 অংশ

A ও B 6 দিনে করতে পারে কাজটির 6/12 অংশ
= 1/2 অংশ

কাজ বাকি থাকে = 1 - 1/2 অংশ
= (2 - 1)/2 অংশ
= 1/2 অংশ

১৫,০২১.

In a club 50% of the male voters and 80% of the female voters voted for candidate A. If candidate A received 70% of the total votes, what is the ratio of male to female voters?

ক
ক) 1/3
খ
খ) 3/4
গ
গ) 1/4
ঘ
ঘ) 1/2

ব্যাখ্যা

Let, Male voter = x and Female voter = y
50% of x + 80% of y = 70% of (x+y)
⇒ 50x/100 + 80y/100 = {70(x+y)}/100
⇒ (50x + 80y)/100 = (70x + 70y)/100
⇒ 80y – 70y= 70x – 50x
⇒ 10y = 20x
⇒ x/y = 10/20 = 1/2
∴ x : y = 1 : 2

১৫,০২২.

Kabir sold his wallet at a loss of 4% . Had he sold it for Tk 84 more, he would have gained 10%. What was the cost of the wallet?

ক
300Tk
খ
400Tk
গ
500Tk
ঘ
600Tk
ঙ
700Tk

ব্যাখ্যা

Question: Kabir sold his wallet at a loss of 4% . Had he sold it for TK 84 more, he would have gained 10%. What was the cost of the wallet?

Solution:
Let the original price of the wallet is x TK

∴ [x × (100% - 4%)] + 84 = x × (100% + 10%)
⇒ (x × 96%) + 84 = x × 110%
⇒ (96x + 8400)/100 = 110x/100
⇒ 110x - 96x = 8400
⇒ 14x = 8400
⇒ x = 600

১৫,০২৩.

If A : B = 5 : 4 and A : C = 6 : 5 then, C : B = ?

ক
ক) 24 : 25
খ
খ) 25 : 24
গ
গ) 3 : 2
ঘ
ঘ) None

ব্যাখ্যা

Question: If A : B = 5 : 4 and A : C = 6 : 5 then, C : B = ?

Solution:
A : B = 5 : 4
⇒ A/B = 5/4

A : C = 6 : 5
⇒ A/C = 6/5
⇒ C/A = 5/6

(A/B) × (C/A) = (5/4) × (5/6)
⇒ C/B = 25/24
⇒ C : B = 25 : 24

১৫,০২৪.

a = 2b = 3c and abc = 36, then find the value of c.

ক
√2
খ
2
গ
2√2
ঘ
4

ব্যাখ্যা

Question: a = 2b = 3c and abc = 36, then find the value of c.

Solution:
Given,
a = 2b = 3c
∴ a = 3c
and b = 3c/2

Now, abc = 36
⇒ 3c . (3c/2) . c = 36
⇒ 9c³/2 = 36
⇒ 9c³ = 72
⇒ c³ = 72/9
⇒ c³ = 8
⇒ c³ = 2³
∴ c = 2

১৫,০২৫.

If each side of the square is increased by 50%, what will be the ratio between the new area and the original area of the square?

ক
5 : 4
খ
9 : 4
গ
4 : 5
ঘ
4 : 9

ব্যাখ্যা

Question: If each side of the square is increased by 50%, what will be the ratio between the new area and the original area of the square?

Solution:
Let,
The side of original square is x
∴ The area of original square is x²

The side of new square is x + 50% of x = x + x/2 = 3x/2
∴ The area of new square is (9x²)/4

∴ The ratio between the new area and the original area of the square = (9x²)/4 : x²
= (9/4) : 1
= 9 : 4

১৫,০২৬.

If ÷ means ×, × means +, + means - and - means +, find the value of 28 × 3 + 5 - 2 ÷ 4.

ক
31
খ
34
গ
37
ঘ
39

ব্যাখ্যা

Question: If ÷ means ×, × means +, + means - and - means +, find the value of 28 × 3 + 5 - 2 ÷ 4.

Solution:
16 × 3 + 5 - 2 ÷ 4
= 28 + 3 - 5 + 2 × 4
= 28 + 3 - 5 + 8
= 31 - 5 + 8
= 39 - 5
= 34

১৫,০২৭.

If θ = 45°, then find the value of (3 + cot2θ)/(3 - cot2θ).

ক
0
খ
1
গ
1/√3
ঘ
√3
ঙ
undefined

ব্যাখ্যা

Question: If θ = 45°, then find the value of (3 + cot2θ)/(3 - cot2θ).

Solution:
(3 + cot2θ)/(3 - cot2θ)
= [3 + cot(2 × 45°)]/[3 - cot(2 × 45°)]
= (3 + cot90)°/(3 - cot90)°
= (3 + 0)/(3 - 0)
= 3/3
= 1

১৫,০২৮.

In a code, "STONE" is written as 12345 and "FLAME" is written as 67895. How is "FLOAT" written in the same code?

ক
67328
খ
67382
গ
76832
ঘ
12345
ঙ
67823

ব্যাখ্যা

Question: In a code, "STONE" is written as 12345 and "FLAME" is written as 67895. How is "FLOAT" written in the same code?

Solution:
STONE is written as 12345
S = 1
T = 2
O = 3
N = 4
E = 5

FLAME is written as 67895
F = 6
L = 7
A = 8
M = 9
E = 5

So, FLOAT will be
F = 6
L = 7
O = 3
A = 8
T = 2

∴ FLOAT = 67382

১৫,০২৯.

Find out the wrong term: 8, 14, 26, 48, 98, 194, 386

ক
98
খ
14
গ
48
ঘ
194

ব্যাখ্যা

Question: Find out the wrong term: 8, 14, 26, 48, 98, 194, 386

Solution:
Each term = (previous term × 2) - 2
Let’s check term by term.
1st term = 8
2nd = 8 × 2 - 2 = 16 - 2 = 14
3rd = 14 × 2 - 2 = 28 - 2 = 26
4th = 26 × 2 - 2 = 52 - 2 = 50 ; but the given term is 48 (wrong here)
5th = 50 × 2 - 2 = 100 - 2 = 98
6th = 98 × 2 - 2 = 196 - 2 = 194
7th = 194 × 2 - 2 = 388 - 2 = 386

The first mistake occurs at the 4th term. 26 should become 50, but it is written as 48.
So 48 is the wrong term. It should be replaced by 50.
Correct series should be 8, 14, 26, 50, 98, 194, 386

১৫,০৩০.

1000 tk. is being charged at 50% per annum. what is the interest for 2nd year at compound interest?

ক
ক) 1250 tk.
খ
খ) 1000 tk.
গ
গ) 750 tk.
ঘ
ঘ) 425 tk.

ব্যাখ্যা

Question: 1000 tk. is being charged at 50% per annum. what is the interest for 2nd year at compound interest?

solution:
১মবছরে চক্রবৃদ্ধি সুদাসল = 1000 (1 + 50/100)1
= 1000 (1 + 1/2)¹
= 1000 (3/2)¹
= 1500 টাকা

২য় বছরে চক্রবৃদ্ধি সুদাসল = 1000 (1 + 50/100)2
= 1000 (1 + 1/2)²
= 1000 (3/2)²
= 2250 টাকা

২য় বছরের জন্য সুদ = 2250 - 1500 টাকা
= 750 টাকা

১৫,০৩১.

If Tk. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4, then the first part is-

ক
Tk. 204
খ
Tk. 192
গ
Tk. 190
ঘ
Tk. 182

ব্যাখ্যা

Question: If Tk. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4, then the first part is-

Solution:

Given ratio = 1/2 : 2/3 : 3/4

= 6 : 8 : 9

The first part = 782 × (6/23)
= 204

১৫,০৩২.

Simplify: log_a10−log_a(10/a)

ক
ক) 0
খ
খ) 1
গ
গ) 100
ঘ
ঘ) -1

ব্যাখ্যা

log_a10−log_a(10/a)
=log_a10−[log_a10−log_aa]
=log_a10−log_a10+log_aa
=0+1=1

১৫,০৩৩.

If 1 + tan²θ = 4 and θ < 90°, than what is the value of θ = ?

ক
75°
খ
60°
গ
55°
ঘ
30°

ব্যাখ্যা

Question: If 1 + tan²θ = 4 and θ < 90°, than what is the value of θ = ?

Solution:
Given that,
1 + tan²θ = 4 and θ < 90°
⇒ sec²θ = 4 ; [sec²θ = 1 + tan²θ]
⇒ (secθ)² = (2)²
⇒ secθ = 2
⇒ secθ = sec60°
⇒ θ = 60°

১৫,০৩৪.

A card is randomly drawn from a deck of 52 cards. What is the probability of getting a king or Queen?

ক
ক) 3/13
খ
খ) 2/13
গ
গ) 1/13
ঘ
ঘ) 4/13

ব্যাখ্যা

Total number of kings is 4 out of 52 cards.
Total number of queens is 4 out of 52 cards
Number of favorable outcomes i.e. ‘a king or a queen’ is 4 + 4 = 8 out of 52 cards.
Therefore, probability of getting ‘a king or a queen’ = Number of favorable outcomes
∴ P(E) = Total number of possible outcomes = 8/52 = 2/13

১৫,০৩৫.

A clock was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

ক
Tk. 60
খ
Tk. 80
গ
Tk. 100
ঘ
Tk. 120

ব্যাখ্যা

Question: A clock was sold for Tk. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

Solution:
Let, the percentage of profit be x%
cost of the clock was x taka.

x + x × x/100 = 144
⇒ x + (x²/100) = 144
⇒ (x² + 100x) = 14400
⇒ x² + 100x - 14400 = 0
⇒ x² + 180x - 80x - 14400 = 0
⇒ x(x + 180) - 80 (x + 180) = 0
⇒ (x + 180) (x - 80) = 0
⇒ x = 80

১৫,০৩৬.

In an examination, 65% students passed in Mathematics and 60% students in English, 40% passed in both these subjects. If 90 students failed in Mathematics and English both, then what is the total number of students?

ক
850
খ
700
গ
600
ঘ
400

ব্যাখ্যা

Question: In an examination, 65% students passed in Mathematics and 60% students in English, 40% passed in both these subjects. If 90 students failed in Mathematics and English both, then what is the total number of students?

Solution:
Given that,
P(M) = 65%
P(E) = 60%
P(M ∩ E) = 40%

We know,
P(M U E) = P(M) + P(E) - P(M ∩ E)
= 65% + 60% - 40% = 85%
∴ P(M U E) = 85%
∴ passed students = 85%
∴ Failed students = 100% - 85% = 15%

Now,
We are given that 90 students failed in both subjects, which represents 15% of the total students. Let N be the total number of students.
⇒ 15% of N = 90
⇒ (15/100)N = 90
⇒ N = (90 × 100)/15
∴ N = 600

∴ The total number of students is 600.

১৫,০৩৭.

The greatest value of sin⁴θ + cos⁴θ is?

ক
1/2
খ
1
গ
2
ঘ
1/3

ব্যাখ্যা

Question: The greatest value of sin⁴θ + cos⁴θ is?

Solution:
We know,
sin²θ + cos²θ = 1
⇒ (sin²θ + cos²θ)² = 1² ; Squaring both sides
⇒ sin⁴θ + cos⁴θ + 2sin²θ.cos²θ = 1
⇒ sin⁴θ + cos⁴θ = 1 - 2sin²θ.cos²θ
⇒ sin⁴θ + cos⁴θ = 1 - 0 ; [Put θ = 90° , cos90° = 0]
∴ sin⁴θ + cos⁴θ = 1

So the greatest value of sin⁴θ + cos⁴θ is 1.

১৫,০৩৮.

The area of a hemisphere is 48Π m². What is the radius of the hemisphere?

ক
2m
খ
4m
গ
6m
ঘ
12m

ব্যাখ্যা

The area of a hemisphere is 48Π m². What is the radius of the hemisphere?
Let the radius of the hemisphere be r.
Therefore, 3Πr² = 48Π
or, r² = 16
or, r = 4m

১৫,০৩৯.

If a -1/a = 2 what is a³ – 1/a³?

ক
ক) 16
খ
খ) 10
গ
গ) 14
ঘ
ঘ) 12

ব্যাখ্যা

Given,
(a - 1/a) = 2
∴ a³ - 1/a³ = (a - 1/a)³ + 3.a.1/a(a - 1/a)
= 2³ + 3.2
= 8 + 6 = 14

১৫,০৪০.

Fresh apples contain 85% water, while dry apples contain 15% water. If the weight of dry apples is 300 kg, what was the total weight of the apples when fresh?

ক
1700 kg
খ
1570 kg
গ
1200 kg
ঘ
2000 kg

ব্যাখ্যা

Question: Fresh apples contain 85% water, while dry apples contain 15% water. If the weight of dry apples is 300 kg, what was the total weight of the apples when fresh?

Solution:
Given that,
Dry apples contain 15% water
∴ they contain 85% solid matter.
Fresh apples contain 85% water
∴ they contain 15% solid matter.

The amount of solid matter (pulp) never changes during drying.

Let the weight of fresh apples = x kg

Solid matter in fresh apples = 15% of x = 0.15x kg
Solid matter in dry apples = 85% of 300 kg = (85/100)× 300 = 255 kg

Since the solid matter remains the same,
0.15x = 255
⇒ x = 255 /0.15
⇒ x = (255 × 100)/15
∴ x = 1700 kg

The total weight of the apples when fresh was 1700 kg.

১৫,০৪১.

A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

ক
1% loss
খ
2% loss
গ
1% profit
ঘ
2% profit

ব্যাখ্যা

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

Solution:
Let cost price of goods = Tk. 100
The market price of goods = 110% of 100
= (110/100)×100
= Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
= Tk. 99

Loss = 100 - 99 = Tk. 1

∴ Loss % = (1/100) × 100 = 1%

১৫,০৪২.

On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

ক
4% increase
খ
4% decrease
গ
16% increase
ঘ
16% decrease

ব্যাখ্যা

Question: On increasing the price of tickets for a show by 20 % the audience decreases by 30%. What is the effect on revenue?

Solution:
Effect on revenue
= percent increase - percent decrease - (percent increase × percent decrease)/100
= 20 - 30 - (20 × 30)/100
= - 10 - 600/100
= -10 - 6
= - 16 %

'-' sign shows decrease in revenue.

১৫,০৪৩.

If '+' means '-', '-' means '×', '×' means '÷', and '÷' means '+', then what is the value of: 16 - 4 × 2 + 6 ÷ 3?

ক
46
খ
39
গ
29
ঘ
25

ব্যাখ্যা

Question: If '+' means '-', '-' means '×', '×' means '÷', and '÷' means '+', then what is the value of: 16 - 4 × 2 + 6 ÷ 3?

Solution:
Given,
'+' means '-', '-' means '×', '×' means '÷', and '÷' means '+'

Now,
16 - 4 × 2 + 6 ÷ 3

∴ the transformed expression will be: 16 × 4 ÷ 2 - 6 + 3
= 16 × 2 - 6 + 3
= 32 - 6 + 3
= 35 - 6
= 29

১৫,০৪৪.

Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6√3 long.

ক
75°
খ
30°
গ
45°
ঘ
60°

ব্যাখ্যা

Question: Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6√3 long.

Solution:

shadow = base = 6√3 m
height =18 m

let, angle of elevation θ

tanθ = 18/6√3
⇒ tanθ = 3/√3
⇒ tanθ = √3
⇒ tanθ = tan60°
∴ θ = 60°

১৫,০৪৫.

P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?

ক
6
খ
4
গ
5
ঘ
8

ব্যাখ্যা

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15
= 2/3
Remaining work = 1 - 2/3
= 1/3
Number of days in which P can finish the remaining work = (1/3)/(1/18)
= 6.

১৫,০৪৬.

A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

ক
Tk. 12
খ
Tk. 15
গ
Tk. 18
ঘ
Tk. 21

ব্যাখ্যা

Question: A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

Solution:
Dividend on Tk. 20 = Tk. (9/100) × 20 = Tk. 9/5

Tk. 12 is an income on Tk. 100.
∴ Tk. 9/5 is an income on = Tk. (100 × 9)/(12 × 5)
= Tk.15

১৫,০৪৭.

A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

ক
14%
খ
14.29%
গ
15.29%
ঘ
10%

ব্যাখ্যা

Question: A student bought a bag for Tk. 3500 and later sold it for Tk. 4000. Find the profit percentage he earned.

Solution:
Here,
CP = 3500, and SP = 4000
As SP > CP,
∴ Profit = SP - CP = 4000 - 3500 = 500

Profit% = (500/3500) ×100%
=100/7 %
= 14.29%

১৫,০৪৮.

A and B are two positive integers such that AB = 72. Which of the following cannot be the value of A + B?

ক
38
খ
27
গ
73
ঘ
20
ঙ
22

ব্যাখ্যা

Question: A and B are two positive integers such that AB = 72. Which of the following cannot be the value of A + B?

Solution:
Factor pairs of 72:
(1, 72) → A + B = 73
(2, 36) → A + B = 38
(3, 24) → A + B = 27
(4, 18) → A + B = 22
(6, 12) → A + B = 18
(8, 9) → A + B = 17

So, possible values of A + B are: 73, 38, 27, 22, 18, 17.

Among the options, 20 is not possible.

১৫,০৪৯.

If sin 17° = (x/y), then sec 17° is equal to

ক
{√(y² - x²)}/y
খ
{√(y² - x²)}/x
গ
y/{√(y² - x²)}
ঘ
x/{√(y² - x²)}

ব্যাখ্যা

Question: If sin 17° = (x/y), then sec 17° is equal to

Solution:
Given,
sin 17° = (x/y)

We know,
sin² θ + cos²θ = 1
∴ cos θ = √(1 - sin θ)

∴ cos 17° = √(1 - sin²17°)
= √{1 - (x²/y²)}
= √{(y² - x²)/y²}
= {√(y² - x²)}/y

∴ sec 17° = 1/cos 17°
= 1/[{√(y² - x²)}/y]
= y/{√(y² - x²)}

১৫,০৫০.

If 5^{(x + 3)} = 25^{(3x - 4)} then the value of x is = ?

ক
12/5
খ
11/5
গ
11/3
ঘ
7/5

ব্যাখ্যা

Question: If 5^{(x + 3)} = 25^{(3x - 4)} then the value of x is = ?

Solution:
5^{(x + 3)} = 25^{(3x - 4)}
⇒ 5^{(x + 3)} = 5^{2(3x - 4)}
⇒ 5^{(x + 3)} = 5^{6x - 8}
⇒ (x + 3) = (6x - 8)
⇒ x - 6x = - 8 - 3
⇒ - 5x = - 11
⇒ 5x = 11
∴ x = 11/5

১৫,০৫১.

A train crosses two bridges that are 420 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?

ক
200 meters
খ
240 meters
গ
280 meters
ঘ
300 meters

ব্যাখ্যা

Question: A train crosses two bridges that are 420 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?

Solution:
We know,
To cross a bridge, a train must cover the length of the bridge along with its own length.

Let the length of the train = x meters

Then,
For the first bridge, the distance covered by the train = (x + 420) meters
And,
For the second bridge, the distance covered by the train = (x + 200) meters

According to the question,
(x + 420)/60 = (x + 200)/40
⇒ 40(x + 420) = 60(x + 200)
⇒ 40x + 16800 = 60x + 12000
⇒ 60x - 40x = 16800 - 12000
⇒ 20x = 4800
⇒ x = 4800/20
⇒ x = 240

∴ The length of the train is 240 meters

১৫,০৫২.

Two pipes A and B can fill a pool in 5 hours and 6 hours respectively. If both pipes work together, how long will it take to fill the pool?

ক
ক) 20/11
খ
খ) 14/11
গ
গ) 30/11
ঘ
ঘ) 25/11

ব্যাখ্যা

Question: Two pipes A and B can fill a pool in 5 hours and 6 hours respectively. If both pipes work together, how long will it take to fill the pool?

Solution:
A, 1 ঘণ্টায় পূর্ণ করে (1/5) অংশ
B, 1 ঘণ্টায় পূর্ণ করে (1/6) অংশ

উভয় পাইপ একত্রে 1 ঘণ্টায় পূর্ণ করে (1/5) + (1/6) অংশ
= (6 + 5)/30
= 11/30

আবার,
11/30 অংশ পূর্ণ করে 1 ঘণ্টায়
∴ 1 অংশ পূর্ণ করে (1×30)/11 ঘণ্টায়
= 30/11 ঘণ্টা

১৫,০৫৩.

If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-

ক
18 days
খ
24 days
গ
25 days
ঘ
15 days
ঙ
None of these

ব্যাখ্যা

Question: If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-

Solution:
One day's work of,
(A + B) = 1/18.......(1)
One day's work of,
(A + C) = 1/12.......(2)
One day's work of,
(B + C) = 19.......(3)

Adding(1),(2)and(3),
⇒ 2 × (A + B + C) = 1/18 + (1/12) + (1/9)
⇒ 2 (A + B + C) = 1/4
⇒ (A + B + C) = 1/8
Now,
⇒ B = (1/8) - (A + C)
⇒ B= (1/8) - (1/12)
One day's work of B = (3 - 2)/24 = 1/24
∴ B need 24 days

১৫,০৫৪.

Mira is 30 times older than her son. 18 years later she will be thrice as old as her son. What is Mira's present age?

ক
ক) 36
খ
খ) 40
গ
গ) 52
ঘ
ঘ) 86

ব্যাখ্যা

Let, the present age of Mira is x
so her sons' present age is x/30
18 year later, the age of Mira will x+18 and the age of her son will (x/30)+18

ATQ,
x + 18 = 3{(x/30)+18}
or, x + 18= (3x/30) + 3.18 = (x/10) + 54
or, 10x + 180 = x + 540 [Multiplying both sides by 10]
or, 10x - x = 540 - 180
or, 9x = 360
or, x = 360/9
or, x = 40
So, The present age of Mira is 40.

১৫,০৫৫.

The angle of depression of a point situated at a distance of 70 m from the base of a tower is 60°. The height of the tower is -

ক
ক)
খ
খ) 70√3 m
গ
গ) 70 m
ঘ
ঘ) 35√3 m

ব্যাখ্যা

Question: The angle of depression of a point situated at a distance of 70 m from the base of a tower is 60°. The height of the tower is -

Solution:

Let,
Height of the tower AB = h meter.
Now, ∠DAC = ∠ACB = 60° and BC = 70 meter.

In ΔABC
tan60° = AB/BC
⇒ √3 = h/70
∴ h = 70√3

Height of the tower 70√3 meter.

১৫,০৫৬.

A, B and C start together from the same place to walk round a circular path of length 12 km. A walks at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

ক
24 hours
খ
18 hours
গ
16 hours
ঘ
12 hours

ব্যাখ্যা

Question: A, B and C start together from the same place to walk round a circular path of length 12 km. A walks at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

Solution:
Given that,
Circumference of circular path = 12 km
Speeds, A = 4 km/h
B = 3 km/h
C = 3/2 = 1.5 km/h

We know,
Time = Distance/Speed

Than,
Time for A = 12/4 = 3 hours
Time for B = 12/3 = 4 hours
Time for C = 12/1.5 = 8 hours

∴ Required time,
= LCM of 3, 4, 8.
= 24 hours.

∴ They will meet together at the starting place at the end of 24 hours.

১৫,০৫৭.

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

ক
11 : 20
খ
17 : 22
গ
15 : 21
ঘ
21 : 22

ব্যাখ্যা

Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Solution:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
⇒ (120/100) × 7x and (110/100) × 8x
⇒ 42x/5 and 44x/5

∴ The required ratio = 42x/5 : 44x/5 = 21 : 22.

১৫,০৫৮.

A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family in years?

ক
ক) 31(5/7)
খ
খ) 30(5/7)
গ
গ) 28(1/7)
ঘ
ঘ) 32(2/7)

ব্যাখ্যা

Total age of grandparents = 67 × 2
Total age of parents = 35 × 2
Total age of grandchildren = 6 × 3

Total age of all persons = 67 × 2 + 35 × 2 + 6 × 3 = 222
Total number of persons = 2 + 2 + 3 = 7

The average age of the family
= 222/7
= 31(5/7)

১৫,০৫৯.

Which one is factor of x³ - x - 6?

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

ব্যাখ্যা

ধরি
F(x) = x³- x - 6
F(2) = 2³ - 2 - 6
= 8 - 8
= 0

(x - 2) হলো, x³ - x - 6 এর একটি উৎপাদক ।

১৫,০৬০.

A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.

ক
34 m
খ
1156 m
গ
136 m
ঘ
Cannot be determined

ব্যাখ্যা

Question: A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.

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

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

One side of the square = 34 m.
So, perimeter of the square = 4 × 34
= 136 m

১৫,০৬১.

How many integers between 1 and 100 are divisible by 3 but not by 5?

ক
ক) 27
খ
খ) 29
গ
গ) 30
ঘ
ঘ) 31

ব্যাখ্যা

From 1 to 100 = 100/3 = 33.33 ≈ 33 integers are divisible by 3
From 1 to 100 = 100/15 = 6.67 ≈ 6 integers are divisible by both 3 and 5

So, 33 - 6 = 27 integers are divisible by 3 but not by 5

১৫,০৬২.

What is the slope of a line perpendicular to the line whose equation is 10x - y = 3?

ক
- 1/10
খ
1/10
গ
20
ঘ
- 2

ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 10x - y = 3?
(Officer Cash 2022 অনুযায়ী)

Solution:
সরল রেখার সাধারণ সমীকরণ,
y = mx + c ......(1) (এখানেm = ঢাল)

যদি কোনো রেখার ঢাল হয় m, তবে তার লম্ব (perpendicular) রেখার ঢাল হবে,
m' = - (1/m)

এখন,
10x - y = 3
y = 10x + 3
(1) নং এর সাথে তুলনা করে পাই,
m = 10

∴ লম্ব (perpendicular) রেখার ঢাল হবে, m' = - (1/10)

১৫,০৬৩.

A train 150 meters long takes 40 seconds to cross a 350-meter-long bridge. How much time will the train take to cross a 250-meter-long platform?

ক
28 seconds
খ
32 seconds
গ
35 seconds
ঘ
42 seconds

ব্যাখ্যা

Question: A train 150 meters long takes 40 seconds to cross a 350-meter-long bridge. How much time will the train take to cross a 250-meter-long platform?

Solution:
Length of train = 150 m
Length of bridge = 350 m
∴ Total distance to cross bridge = 150 + 350 = 500 m
Time taken = 40 seconds
∴ Speed of train = Total distance/Time
= 500/40 = 12.5 m/s

Length of platform = 250 m
∴ Total distance to cross platform = 150 + 250 = 400 m

∴ Time taken = Total distance/Speed
= 400/12.5 seconds
= 32 seconds

১৫,০৬৪.

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

ক
Monday
খ
Friday
গ
Sunday
ঘ
Tuesday

ব্যাখ্যা

Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Solution:

On 31st December, 2005 it was Saturday.

Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday

১৫,০৬৫.

A certain amount of money at simple interest turns into Tk. 1110 in 4 years and into Tk. 1200 in 5 years. The amount of money is:

ক
Tk. 750
খ
Tk. 840
গ
Tk. 660
ঘ
Tk. 800

ব্যাখ্যা

Question: A certain amount of money at simple interest turns into Tk. 1110 in 4 years and into Tk. 1200 in 5 years. The amount of money is:

Solution:
Simple interest for 1 years = Tk. (1200 - 1110)
= Tk. 90

∴ Simple interest for 4 years = Tk. (90 × 4)
= Tk. 360

∴ The amount of money is = Tk. (1110 - 360)
= Tk. 750

১৫,০৬৬.

A lamp is manufactured to sell for $35.00, which yields a profit of 25% of cost. If the profit is to be reduced to 15% of cost, what will be the new retail price of the lamp?

ক
ক) $31.50
খ
খ) $28.00
গ
গ) $21.00
ঘ
ঘ) $32.20

ব্যাখ্যা

In 25% profit,
If selling price is $125 then cost is $100
So, when selling price is $35 then cost = (100×35)/125 = $28
In 15% profit,
If cost is $100 then selling price = $115
So, when cost is $28, then selling price = (115×28)/100 = $32.20

১৫,০৬৭.

In how many ways can a leap year have 53 Mondays?

ক
8
খ
6
গ
4
ঘ
2

ব্যাখ্যা

Question: In how many ways can a leap year have 53 Mondays?

Solution:
In a leap year there are 366 days
52 weeks + 2 extra days.
So to have 53 Mondays one of these two days must be a Monday.
This can occur in only 2 ways.
(Sunday and Monday) or (Monday and Tuesday).
Thus number of ways = 2

১৫,০৬৮.

Find the maximum distance between two points on the perimeter of a rectangular garden whose length and breadth are 24 m and 7 m.

ক
25 m
খ
17 m
গ
31 m
ঘ
62 m

ব্যাখ্যা

Question: Find the maximum distance between two points on the perimeter of a rectangular garden whose length and breadth are 24 m and 7 m.

Solution:
একটি আয়তক্ষেত্রের পরিসীমার উপর অবস্থিত দুটি বিন্দুর মধ্যে সর্বাধিক দূরত্ব হলো এর কর্ণের দৈর্ঘ্য। কর্ণের দৈর্ঘ্য পিথাগোরাসের সূত্র ব্যবহার করে নির্ণয় করা যায়।

কর্ণের দৈর্ঘ্য = √(দৈর্ঘ্য^২ + প্রস্থ^২)
= √(24² + 7²)
= √(576 + 49)
= √625
= 25 মিটার

সুতরাং, দুটি বিন্দুর মধ্যে সর্বাধিক দূরত্ব হলো 25 মিটার।

১৫,০৬৯.

Pointing to a man in a photograph, Mitu said, "His brother's father is the only son of my grandfather."
How is Mitu related to the man in the photograph?

ক
Mother
খ
Aunt
গ
Sister
ঘ
Grandmother

ব্যাখ্যা

Question: Pointing to a man in a photograph, Mitu said, "His brother's father is the only son of my grandfather."
How is Mitu related to the man in the photograph?

Solution:
মিতু বলল: "His brother's father is the only son of my grandfather."

"His brother's father" = ছবির লোকটির বাবা
ছবির লোকটির বাবা = মিতুর দাদার একমাত্র ছেলে
ছবির লোকটির বাবা = মিতুর বাবা

অর্থাৎ মিতু এবং ছবির লোকটি ভাই-বোন।
মিতু মেয়ে হওয়ায় সে ছবির লোকটির বোন।

১৫,০৭০.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 9 cm and 13 cm. What is the area of the circle?

ক
ক) 154 cm²
খ
খ) 144 cm²
গ
গ) 124 cm²
ঘ
ঘ) 114 cm²

ব্যাখ্যা

The sides of the rectangle are 9 cm and 13 cm.
Perimeter of the rectangle =2(9 + 13)=44 cm
Circumference of circle =44 cm.

Here
2πr = 44
(22/7)r = 22
r/7 = 1
r = 7
Area of circle = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm²

১৫,০৭১.

The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of a quadratic equation as-

ক
x² - x + 360 = 0
খ
x² + x - 360 = 0
গ
x² + x + 360 = 0
ঘ
x² - x - 360 = 0

ব্যাখ্যা

Question: The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of a quadratic equation as-

Solution:
Let x and (x + 1) be the two consecutive integers.

According to the given,
x(x + 1) = 360
⇒ x² + x = 360
⇒x² + x - 360 = 0
⇒x²+ 18x - 17x - 360 = 0
⇒(x +18)(x - 17) = 0
x ≠ - 18,
∴ x = 17

One positive interger 17.
Other positive interger 17 + 1 = 18.

x² + x - 360 = 0 is the required quardratic equation.

১৫,০৭২.

Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

ক
62.5%
খ
37.5%
গ
24.8%
ঘ
None of these

ব্যাখ্যা

Question: Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

Solution:
let, Alom invest x taka at 15% per annum for 4 years and y taka at 12% per annum for 3 years

ATQ,
x × 0.15 × 4 = y × 0.12 × 3
⇒ x/y = 0.36/.6 = 3/5
⇒ x : y = 3 : 5

%percentage = (3/8) × 100%
= 37.5%

১৫,০৭৩.

The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

ক
30°
খ
45°
গ
60°
ঘ
90°

ব্যাখ্যা

Question: The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

Solution:

Let,
Height of the tree BC = x
Length of the shadow AB = √3x
The angle of elevation of the sun ∠C = θ

Now,
tanθ = BC/AB
⇒ tanθ = x/(√3x)
⇒ tanθ = 1/√3
⇒ tanθ = tan30°
∴ θ = 30°

১৫,০৭৪.

In a geometric progression, the 4^th term is 16 and the 7^th term is 128. Find the 10^th term.

ক
364
খ
510
গ
720
ঘ
1024

ব্যাখ্যা

Question: In a geometric progression, the 4^th term is 16 and the 7^th term is 128. Find the 10^th term.

Solution:
Let the first term = a
Common ratio = r
We know,
n-term = ar^{n - 1}

Then,
4^th term, ar³ = 16 ........(1)
7th term, ar⁶ = 128 ........(2)

Now, divide equation (2) by equation (1) then we get,
(ar⁶)/(ar³) = 128/16
⇒ r³ = 8
⇒ r³ = 2³
∴ r = 2

Then substitute r = 2 into equation (1)
a.(2)³ = 16
⇒ a × 8 = 16
∴ a = 2

Now, 10^thterm
= ar⁹
= 2 × 2⁹
= 2 × 2⁹
= 2¹⁰
= 1024

∴ The 10th term is 1024

১৫,০৭৫.

If 60 tk. is the cost for a quarter kg of potatoes, how much will 200 grams cost?

ক
48 tk.
খ
54 tk.
গ
66 tk.
ঘ
88 tk.

ব্যাখ্যা

Question: If 60 tk. is the cost for a quarter kg of potatoes, how much will 200 grams cost?

Solution:
Let the required weight be x kg.

Less weight, Less cost (Direct Proportion)

250 : 200 : : 60 : x
⇒ 250/200 = 60/x
⇒ 250x = (200 × 60)
⇒ x = (200 × 60)/250
∴ x = 48

১৫,০৭৬.

ক
0
খ
2a³
গ
1
ঘ
2b³
ঙ
None of these

ব্যাখ্যা

Question:

Solution:

১৫,০৭৭.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 16 cm and 50 cm. What is the area of the circle?

ক
1256 sq. cm.
খ
1386 sq. cm.
গ
1540 sq. cm.
ঘ
1078 sq. cm.

ব্যাখ্যা

Question: A circle and a rectangle have the same perimeter. The sides of the rectangle are 16 cm and 50 cm. What is the area of the circle?

Solution:
আয়তক্ষেত্রটির পরিসীমা = 2 × (16 + 50) সেমি
= 2 × 66 সেমি
= 132 সেমি।

যেহেতু বৃত্তের পরিধি ও আয়তক্ষেত্রের পরিসীমা সমান, তাই বৃত্তের পরিধিও 132 সেমি।

∴ বৃত্তের পরিধি, C = 2πr
⇒ 2πr = 132
⇒ r = 132/(2 × 22/7)
∴ r = 21 সেমি।

বৃত্তের ক্ষেত্রফল, A = πr²= (22/7) × (21)²= (22/7) × 441
= 1386 বর্গ সেমি।

সুতরাং, বৃত্তটির ক্ষেত্রফল হলো 1386 বর্গ সেমি।

১৫,০৭৮.

Four people are running around a circular ground from a point on the circumference at 8:00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again ?

ক
6:20 PM
খ
6:00 PM
গ
8:00 PM
ঘ
7:30 PM

ব্যাখ্যা

Question: Four people are running around a circular ground from a point on the circumference at 8:00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again ?

Solution:
L.C.M. of 40, 50, 60 and 30
= 600 minutes
= 10 hours
So, they meet again 10 hours after they start.
They meet together again = 8:00 am + 10 hours
= 6:00 pm

So they will meet together again at 6:00 PM.

১৫,০৭৯.

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25% . The percentage of water in the mixer is:

ক
ক) 8%
খ
খ) 10%
গ
গ) 20%
ঘ
ঘ) 15%

ব্যাখ্যা

25% লাভ হওয়ায়,
100 টাকার দুধ বিক্রয় করে = 100 + 25 = 125 টাকা
অর্থাৎ 125 টাকার পানি মিশ্রিত দুধ বিক্রয় করে = 100 টাকায়
100 টাকার পানি মিশ্রিত করে = (100 ×100)/125 = 80 টাকায়

দুধে পানির শতকরা পরিমাণ = (100 - 80)% = 20%

১৫,০৮০.

A rectangular sheet of paper, 10 cm long and 8 cm wide has squares of side 2 cm cut from each of its corner. The sheet is then folded to form a tray of depth 2 cm. What is the volume of this tray?

ক
32cm³
খ
49 cm³
গ
54 cm³
ঘ
48 cm³

ব্যাখ্যা

Question: A rectangular sheet of paper, 10 cm long and 8 cm wide has squares of side 2 cm cut from each of its corner. The sheet is then folded to form a tray of depth 2 cm. What is the volume of this tray?

Solution:
Length of tray = 10 - (2 × 2) = 10 - 4 = 6 cm.
Breadth of tray = 8 - (2 × 2) = 4 cm.
Depth of tray = 2 cm.
∴ Volume of tray = 6 × 4 × 2 = 48 cm³

১৫,০৮১.

The average of ten number is 7. If each number is multiplied by 10, then the average of the new set of number is-

ক
40
খ
50
গ
60
ঘ
70

ব্যাখ্যা

Question: The average of ten number is 7. If each number is multiplied by 10, then the average of the new set of number is-

Solution:
let, 7 numbers are a1, a2, a3,.......,a7
so, (a1 + a2 + a3+.......+a7)/10 = 7
a1 + a2 + a3+.......+a7 = 70

If each number is multiplied by 10, Then sum = (a1 × 10) + (a2 × 10) + (a3 × 10) + .... + (a7 × 10)
= 10 (a1 + a2 + a3+.......+a7)
= 10 × 70
= 700

then average will be = 700/10
= 70

১৫,০৮২.

In an election, 4% of the total votes cast are invalid. Of the valid votes, one candidate secures 55% and wins the election by a margin of 4,800 votes. Find the total number of votes cast.

ক
50000
খ
45000
গ
42000
ঘ
60000

ব্যাখ্যা

Question: In an election, 4% of the total votes cast are invalid. Of the valid votes, one candidate secures 55% and wins the election by a margin of 4,800 votes. Find the total number of votes cast.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000

১৫,০৮৩.

When we reverse the digits of the number 14, the increases by 27. How many other two digit numbers increases by 27 when their digits are reversed?

ক
6
খ
5
গ
4
ঘ
7
ঙ
None

ব্যাখ্যা

Question: When we reverse the digits of the number 14, the increases by 27. How many other two digit numbers increases by 27 when their digits are reversed?

Solution:
Let the numbers = (10x + y),
When the digits of the number are reversed the number becomes (10y + x)

According to question,
(10y + x) - (10x + y) = 27
Or, 9(y - x) = 27
∴ y - x = 3

Possible numbers are = (25, 36, 47, 58, 69)
Total other two digits possible numbers are 5

১৫,০৮৪.

A cistern 8m long and 5m wide contains water up to a depth of 1m 50cm. The total area of the wet surface is:

ক
64 m²
খ
49 m²
গ
59 m²
ঘ
79 m²

ব্যাখ্যা

Question: A cistern 8m long and 5m wide contains water up to a depth of 1m 50cm. The total area of the wet surface is:

Solution:
দেওয়া আছে,
চৌবাচ্চার দৈর্ঘ্য (l) = 8 m, প্রস্থ (b) = 5 m, এবং গভীরতা (h) = 1 m 50 cm = 1.5 m

ভেজা পৃষ্ঠের (wet surface) ক্ষেত্রফল নির্ণয়ের জন্য আমরা সমগ্র পৃষ্ঠের ক্ষেত্রফল থেকে উপরের তলের ক্ষেত্রফল বাদ দেবো।

আমরা জানি,
সমগ্র পৃষ্ঠের ক্ষেত্রফল = 2(lb + bh + lh) বর্গ একক

∴ ভেজা পৃষ্ঠের ক্ষেত্রফল = 2(lb + bh + lh) - lb বর্গ একক
= 2{(8 × 5) + (5 × 1.5) + (8 × 1.5)} - (8 × 5)
= 2(40 + 7.5 + 12) - 40
= 2(59.5) - 40
= 119 - 40
= 79 m²

সুতরাং, ভেজা পৃষ্ঠের (wet surface) মোট ক্ষেত্রফল 79 বর্গ মিটার।

১৫,০৮৫.

By selling an article for Tk. 100, a man gains Tk. 15. Then, his gain % is

ক
ক) 15%
খ
খ) (38/3)%
গ
গ) (69/4)%
ঘ
ঘ) (300/17)%

ব্যাখ্যা

Question: By selling an article for Tk. 100, a man gains Tk. 15. Then, his gain % is

Solution:
Selling price = Tk. 100
profit =Tk. 15
Cost price = S.P. - Profit
= 100 -15
= 85
Gain % = (Profit/C.P.) × 100
= (15/85) ×100
= (300/17)%

১৫,০৮৬.

A boy read 3/8th of a book on one day and 4/5th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain?

ক
240
খ
300
গ
600
ঘ
800

ব্যাখ্যা

Question: A boy read 3/8th of a book on one day and 4/5th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain?

Solution:
ধরি, বইয়ে মোট পৃষ্ঠা আছে = x টি
১ম দিনে পড়ে = 3x/8 অংশ
বাকি থাকে = x - (3x/8) = 5x/8 অংশ

২য় দিনে পড়ে = (5x/8) এর 4/5 অংশ
= x/2 অংশ

মোট পড়া হয়েছে = 3x/8 + x/2 = (3x + 4x)/8 = 7x/8

প্রশ্নমতে,
x - (7x/8) = 30
⇒ x/8 = 30
⇒ x = 30 × 8
∴ x = 240

মোট পৃষ্ঠা সংখ্যা 240

১৫,০৮৭.

In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was-

ক
151
খ
161
গ
171
ঘ
181

ব্যাখ্যা

Question: In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was-

Solution:
A : B = 3 : 2
B : C = 3 : 2
= {3 × (2/3)} : {2 × (2/3)}
= 2 : (4/3)

A : B : C = 3 : 2 : (4/3)
= 9 : 6 : 4

∴ A's share = 361 × (9/19)
= 171

১৫,০৮৮.

A man travels for 2 hours at 30 miles an hour and he covers 60 miles in the next 3 hours. What is the average speed per hour for the entire trip?

ক
ক) 18
খ
খ) 24
গ
গ) 36
ঘ
ঘ) 45

ব্যাখ্যা

লোকটি প্রথম 2 ঘণ্টায় অতিক্রম করে 30 × 2 মাইল
= 60 মাইল

লোকটি পরবর্তী 3 ঘণ্টায় অতিক্রম করে = 60 মাইল

গড় গতিবেগ = (60 + 60)/(2 + 3) মাইল
= 120/5
= 24 মাইল

১৫,০৮৯.

By selling 90 balls for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

ক
28
খ
30
গ
36
ঘ
38

ব্যাখ্যা

Question: By selling 90 chocolets for Tk. 160 a person loses 20%. How many chocolets should be sold for Tk. 96 so as to have a profit of 20%?

Solution:
S.P of 90 chocolets = Tk. 160
C.P of 90 chocolets = Tk. {160×(100/80)}
= Tk. 200

Desired S.P of 90 chocolets = Tk. (120/100) × 200
= Tk. 240

For Tk. 240 chocolets sold = 90
For Tk. 96 chocolets sold = (90/240) × 96
= 36

১৫,০৯০.

Aman is 20% more efficient than Atique. Atique alone can build a craft in 30 days. Find the number of days taken by Aman to finish the same piece of work?

ক
ক) 16 days
খ
খ) 21 days
গ
গ) 25 days
ঘ
ঘ) 27 days

ব্যাখ্যা

The ratio of times taken by Aman and Atique
= 120 : 100
= 6: 5
Suppose Aman takes x days to do the work.
6 : 5 = 30 : x
or, 6x = 150
x = 25 days

১৫,০৯১.

The average of 7 consecutive numbers is 20. What is the largest of these numbers?

ক
23
খ
22
গ
24
ঘ
21
ঙ
25

ব্যাখ্যা

Question: The average of 7 consecutive numbers is 20. What is the largest of these numbers?

Solution:
Let the 7 consecutive numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,

As per the given condition;

[x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)]/7 = 20

⇒ 7x + 21 = 140

⇒ 7x = 119

⇒ x =17

∴ The largest number = x + 6 = 17 + 6 = 23

১৫,০৯২.

Anik invested 25,200 taka in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

ক
Tk. 10000
খ
Tk. 11500
গ
Tk. 13200
ঘ
Tk. 14800

ব্যাখ্যা

Question: Anik invested 25,200 taka in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

Solution:
5% সুদের জন্য আসল x টাকা
10% সুদের জন্য আসল 110%x = 1.1x টাকা

5% হারে সুদ = x × 3 × 5/100 = 3x/20 টাকা
10% হারে সুদ = 1.1x × 3 × 10/100 = 3.3x/10 টাকা

(3x/20) + (3.3x/10) = 5760
⇒ (3x + 6.6x)/20 = 5760
⇒ 9.6x = 5760 × 20
⇒ x = (5760 × 20)/9.6
= 12000 tk.

10% সুদের হারের জন্য আসল = 1.1 × 12000
= 13200 tk.

১৫,০৯৩.

The area of a rectangle R with a width of 4 feet is equal to the area of a square S, which has a perimeter of 32 feet. The perimeter of the rectangle R is:

ক
21 ft
খ
24 ft
গ
36 ft
ঘ
40 ft

ব্যাখ্যা

Question: The area of a rectangle R with a width of 4 feet is equal to the area of a square S, which has a perimeter of 32 feet. The perimeter of the rectangle R is:

Solution:
ধরি, আয়তক্ষেত্র R এর দৈর্ঘ্য এবং প্রস্থ যথাক্রমে l, b.
বর্গের এক বাহু = a

প্রশ্নমতে,
4a = 32
∴ a = 8

এখানে,
আয়তক্ষেত্রের ক্ষেত্রফল = বর্গের ক্ষেত্রফল
∴ l × b = a²
⇒ l = a²/b
= 64/4
= 16

∴ আয়তক্ষেত্রের পরিসীমা = 2(l + b)
= 2(16 + 4)
= 40 feet

১৫,০৯৪.

In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

ক
1780
খ
1520
গ
1700
ঘ
1850

ব্যাখ্যা

Question: In an election with three candidates, Candidate A received 30% of the valid votes, and Candidate B received 45%. If 15% of the total votes were invalid and 8,000 votes were cast in total, how many valid votes did Candidate C receive?

Solution:
Invalid votes = 15% of 8000 = (15/100) × 8000 = 1200

∴ Valid votes = 8000 - 1200 = 6800
Now,
Votes for A and B = 30% + 45% = 75% of 6800 = (75/100) × 6800 = 5100

∴ Votes for C = 6800 - 5100 = 1700

∴ So Candidate C received 1700 valid votes.

১৫,০৯৫.

Water flows through a cylindrical pipe of an internal diameter of 7cm at the rate of 5m/s. The time, in minutes, the pipe would take to fill an empty rectangular tank of 4m × 3m × 2.31m is -

ক
24 min
খ
22 min
গ
30 min
ঘ
28 min
ঙ
32 min

ব্যাখ্যা

Question: Water flows through a cylindrical pipe of an internal diameter of 7cm at the rate of 5m/s. The time, in minutes, the pipe would take to fill an empty rectangular tank of 4m × 3m × 2.31m is -

Solution:
the total volume of the tank is = 400 × 300 × 231 cc
total water flow per second through the pipe is = πr²h
= (22/7) × (7/2)²× 500

∴ total time = (400 × 300 × 231)/{(22/7) × (7/2)²× 500}
= (400 × 300 × 231 × 4 × 7)/(22 × 49 × 500)
= 1440 s
= 24 min

১৫,০৯৬.

How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?

ক
ক) 8
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 14

ব্যাখ্যা

এখানে,
28 টি জুতা = 14 জোড়া জুতা
∴ আবরণ (case) প্রয়োজন হবে = 112/14 = 8 টি

১৫,০৯৭.

A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
DEW, ZAS, VWO, RSK, ?

ক
MPH
খ
NOG
গ
LME
ঘ
PQI

ব্যাখ্যা

Question: A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
DEW, ZAS, VWO, RSK, ?

Solution:

D, E, W ⇔ 4, 5, 23 ⇔ 4 - 4, 5 - 4, 23 - 4 ⇔ 0 [0 + 26 = 26], 1, 19 ⇔ Z, A, S [এখানে সংখ্যাগুলো দ্বারা বর্ণগুলোর অবস্থান বুঝানো হয়েছে]
Z, A, S ⇔ 26, 1, 19 ⇔ 26 - 4, 1 - 4, 19 - 4 ⇔ 22, - 3 [- 3 + 26 = 23], 15 ⇔ V, W, O
V, W, O ⇔ 22, 23, 15 ⇔ 22 - 4, 23 - 4, 15 - 4 ⇔ 18, 19, 11 ⇔ R, S, K
R, S, K ⇔ 18, 19, 11 ⇔ 18 - 4, 19 - 4, 11 - 4 ⇔ 14, 15, 7 ⇔ N, O, G

∴ ? এর স্থানে NOG হবে।

১৫,০৯৮.

If a + 9/a = 6; what is the value of (a² + 9/a²)?

ক
ক) 1
খ
খ) 10
গ
গ) 9
ঘ
ঘ) 15

ব্যাখ্যা

Question: If a + 9/a = 6; what is the value of (a² + 9/a²)?

Solution:
(a + 9/a)² = (6)²
a² + 81/a² + 18 = 36
a² + 81/a² - 18 = 0
(a - 9/a)² = 0
a - 9/a = 0
a = 9/a
a² = 9

so,
(a² + 9/a²) = 9 + 9/9 = 10

১৫,০৯৯.

A takes 2 hr more than B to walk D km. If A doubles his speed then he can make it in 1hr less than B. How much time does B require for walking D km ?

ক
ক) d/2 hours
খ
খ) 5 hours
গ
গ) 4 hours
ঘ
ঘ) 2d/3 hours

ব্যাখ্যা

Suppose B takes t hours to walk d km.
Then, A takes (t + 2) hours to walk d km.
With double speed, A will take = 1/2(t+2) hours.
∴ t − 1/2(t+2) = 1
⇒ {2t − (t+2)}/2 = 1
⇒ 2t − (t+2) = 2
⇒ t = 4
∴ B takes 4 hours to walk d km.

১৫,১০০.

Find the value of cosec(- π/6)

ক
- 1
খ
- 2
গ
- 1/2
ঘ
- 3/2

ব্যাখ্যা

Question: Find the value of cosec(- π/6)

Solution:
cosec(- π/6)
= - cosec(π/6)
= - 1/sin(π/6)
= - 1/sin30°
= - 1/(1/2)
= - 2