ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: How many prime numbers are there from 1 to 50?

Solution:

Question: If a + b = 7 and ab = 12, then what is 1/a + 1/b?

Solution:
1/a + 1/b
= (b + a)/ab
= (a + b)/(ab)
= 7/12

প্রশ্নটির লজিকে ভুল থাকায় প্রশ্নটি বাতিল করা হলো।
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Question: Sum of 4 consecutive even numbers is (P + 12) and there are 4 consecutive odd numbers in which 2nd highest number is 37 more than the 2nd lowest even number in the previous series. Sum of the Highest number of both series is 105. Find the value of P.
Solution:
Consecutive even numbers = (x - 3), (x - 1), (x + 1), (x + 3)
∴ x - 3 + x - 1 + x + 1 + x + 3 = P + 12
⇒ 4x = P + 12 ...............(1)

2nd lowest even number = (x - 1)
∴ (x - 1) + 37 = (x + 36) = 2nd highest odd number

Consecutive odd numbers = (x + 38), (x + 36), (x + 34) and (x + 32)
∴ (x + 3) + (x + 38) = 105
⇒ 2x + 41 = 105
⇒ 2x = 64
∴ x = 32

Now from (1),
4 × 32 = (P + 12)
⇒ 128 = (P + 12)
∴ P = 116

Question: In an examination, 41% of students failed in Economics, 35% of students failed in Geography and 39% of students failed in History, 5% of students failed in all the three subjects, 14% of students failed in Economics and Geography, 21% of students failed in Geography and History and 18% of students failed in History and Economics. Find the percentage of students who failed in only Economics.

Solution:

Now,
e = 5%
b + e = 14%
⇒ b = 9%

and, d + e = 18%
⇒ d = 13%
Therefore, Percentage of students who failed only in Economics = a = 41% - (b + e + d)
⇒ a = 41% - (9 + 5 + 13)%
⇒ a = 41% - 27%
⇒ a = 14%
Hence, 14% is the correct answer.

Question: What is the remainder when 3³⁷ is divided by 10?

Solution:

Question: A parking garage rents parking spaces for Tk. 10 per week or Tk. 30 per month. How much does a person save in a year by renting by the month rather than by the week?

Solution:

Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

Solution:
Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14 = 4/7.

Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is-

Solution:

Question: How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

Solution:
ধরি,
৯ টাকা টাকা দরের চিনি আছে ক কেজি
৭ টাকা দরের চিনি আছে  ২৭ কেজি

মোট ক্রয়মূল্য = ৯ক + ২৭ × ৭ টাকা = ৯ক + ১৮৯ টাকা 
মোট বিক্রয়মূল্য = (ক + ২৭) × ৯.২৪ টাকা = ৯.২৪ক + ২৪৯.৪৮ টাকা 

∴ লাভ = ৯.২৪ক + ২৪৯.৪৮ - ৯ক - ১৮৯ = ০.২৪ক + ৬০.৪৮ টাকা 

প্রশ্নমতে,
(৯ক + ১৮৯) এর ১০% = ০.২৪ক + ৬০.৪৮
বা, (৯ক + ১৮৯) × (১/১০) = ০.২৪ক + ৬০.৪৮
বা, ৯ক + ১৮৯ = ২.৪ক + ৬০৪.৮
বা, ৯ক - ২.৪ ক = ৬০৪.৮ - ১৮৯
বা, ৬.৬ক = ৪১৫.৮
বা, ক = ৪১৫.৮/৬.৬
∴ ক = ৬৩

Question: At a certain diner, a hamburger and coleslaw cost $3.95, and a hamburger and french fries cost $4.40. If french fries cost twice as much as coleslaw, how much do french fries cost?

Solution:

Question:

If ∠XYZ in the figure above is a right angle, what is the value of x?

Solution:

Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

Solution:

Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is-

Solution:
Let the duration of the flight be x hours.
Then,
600/x - 600/(x + 1/2) = 200
⇒ 600/x - 1200/(2x + 1) = 200
⇒ 3/x - 6/(2x + 1) = 1
⇒ (6x + 3 - 6x){x(2x + 1)} = 1
⇒ x(2x + 1) = 3
⇒ 2x² + x - 3 = 0
⇒ 2x² + 3x - 2x - 3 = 0
⇒ x(2x + 3) - 1(2x + 3) = 0

Question: The value of log₃2⋅log₄3⋅log₅4⋅log₆5⋅log₇6⋅log₈7 is-

Solution:
log₃2⋅log₄3⋅log₅4⋅log₆5⋅log₇6⋅log₈7
⇒ (log₃2 ⋅ log₄3) (log₅4 ⋅ log₆5) (log₇6 ⋅ log₈7)
⇒ log₄2 .log₆4. log₈6 [log_bM × log_ab = log_aM]
⇒ (log₄2 .log₆4) log₈6
⇒ log₆2 ⋅ log₈6
⇒ log₈2
⇒ 1/log₂8 
⇒ 1/log₂2³
= 1/(3log₂2)
= 1/(3​ × 1) [∵ log₂2 = 1]
= 1/3

∴ log₃2⋅log₄3⋅log₅4⋅log₆5⋅log₇6⋅log₈7 = 1/3

Question: Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?

Solution:

Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is-

Solution: