ব্যাংক নিয়োগ বিষয়ভিত্তিক প্রস্তুতি

Question: Calculate the simple interest if the principal amount is Tk. 50000 and the rate is 2% for 4 years.

Solution:
S.I. = PNR/100
⇒ S.I. = (50000 × 2 × 4)/100
= 4000

Question: Find the minimum number of straight lines required to make the given figure.

Solution:

Required straight lines: AB, KL, DC, AC, BD, AD, EF, GH, IJ, BC, GK, GL, HK, HL = 14

Question: The equation 12x² + 4kx + 3 = 0 has real and equal roots, if-

Solution:
Here a = 12, b = 4k, c = 3
Since the given equation has real and equal roots
∴ b² - 4ac = 0
⇒ (4k)² - 4 × 12 × 3 = 0
⇒ 16k² - 144 = 0
⇒ 16k² = 144
⇒ k² = 9
⇒ k = ± 3

Question: Evaluate the compound interest on Tk. 10101 for 3 years at the rate of 9% per annum compounded annually.

Solution:
A = P (1 + R/100)ⁿ
⇒ A = 10101(1 + 9/100)³ = 10101(109/100)³ = 13081.08

C.I. = A - P = 13081.08 - 10101 = 2980.08.

Question: Choose analogous pair.
Shrub : Prune

Solution:
Shrub - ঝোপঝাড়
Prune - ছাঁটাই

Beard - দাড়ি
Shave - মুণ্ডণ, চাঁচা

Hair - চুল
Trim - ছাঁটা

Lawn - বনভূমি
Mow - কাস্তে দ্বারা কাটা

Wool - পশম
Shear - ফাড়িয়া ফেলা

ঝোপঝাড় যেমন ছাঁটাই করে সুন্দর করে রাখা হয়, তেমনি চুল ও ছেঁটে সুন্দর রাখা হয়।

Question: If x + y = 7, then the value of x³ + y³ + 21xy is?

Solution:

Question: Calculate the compound interest at the rate of 6% per annum for 2 years on the principal, which in 2 years at the rate of 2% per annum gives Tk. 8000 as simple interest.

Solution:
S.I. = PRT/100
⇒ P = (S.I. × 100) / (R × T)
∴ P = (8000 × 100)/(2 × 2) = 200000

A = 200000(1 + 6/100)² = 200000(53/50)² = 224720

C.I. = 224720 - 200000 = 24720.

Question: What is the value of the lesser root of the equation x² - 3x + 2 = 0?

Solution:
x² - 3x + 2 = 0
⇒ x² - 2x - x + 2 = 0
⇒ x(x - 2) - 1(x - 2)= 0
⇒ (x - 1)(x - 2) = 0
so the solutions to the equation are x₁ = 1, x₂ = 2.
The lesser one is obviously 1.

Question: 13, 25, 51, 101, 203, ?

Solution:
Here,
Two series exist:
1st: 13, 51, 203
2nd: 25, 101, ?

1st:
13
13 × 4 - 1 = 52 - 1 = 51
51 × 4 - 1 = 204 - 1 = 203

2nd:
25
25 × 4 + 1 = 100 + 1 = 101
101 × 4 + 1 = 404 + 1 = 405

Question: If x - 1/x = √5, then x + 1/x =?

Solution:
Given,
x - 1/x = √5

We know,
(x + 1/x)² = (x - 1/x)² + 4x.1/x
⇒ (x + 1/x)² = ( √5)² + 4 
⇒ (x + 1/x)² = 5 + 4 
⇒ (x + 1/x)² = 9 
⇒ (x + 1/x) = √9
∴ (x + 1/x) = 3

Question: Find the amount on Tk. 5000 at the rate of 20% per annum for 18 months when interest is compounded half yearly.

Solution:
n = 18/12 = 3/2
A = P (1 + R/200)²ⁿ = 5000 (1 + 20/200)²ⁿ
= 5000(1 + 1/10)^{2 × (3/2)}
= 5000 (1.1)³
= 6655

Question: The equation (x - 2)² + 1 = 2x - 3 is a-

Solution:
We have (x - 2)² + 1 = 2x - 3
⇒ x² + 4 - 2 × x × 2 + 1 = 2x - 3
⇒ x² - 4x + 5 - 2x + 3 = 0
∴ x² - 6x + 8 = 0, which is a quadratic equation.

Question: Mary is 16 years old. She is 4 times older than her brother. How old will Mary be when she is twice his age?

Solution:
Mary is 16 years old
She is 4 times older than her brother
∴ Age of her brother 16/4 = 4 years

Let after x years she will twice his age
∴ 16 + x = 2(4 + x)
⇒ 16 + x = 8 + 2x
⇒ x = 8

After 8 years she will twice his age
∴ Her age will be 16 + 8 = 24 years

Question: A man starts from a point and travels 12 km in the north direction. Again he went east for 6 km and changed direction and again went north for 8 km. Finally went west for 6 km. What is the direct distance between his destination and journey?

Solution:

ঐ ব্যক্তির যাত্রাস্থান A এবং গন্তব্য স্থান E
∴ তার গন্তব্য স্থান ও যাত্রা স্থানের সরাসরি দূরত্ব, AE = (12 + 8) কি.মি.
= 20 কি.মি.

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

Question: The quadratic equation whose one rational root is 3 + √2 is-

Solution:
one root is 3 + √2
∴ other root is 3 - √2

Sum of roots = 3 + √2 + 3 - √2 = 6
Product of roots = (3 + √2)(3 - √2) = (3)² - (√2)² = 9 - 2 = 7

∴ Required quadratic equation is x² - 6x + 7 = 0

Question: SUNDAY, MONDAY, WEDNESDAY, SATURDAY, WEDNESDAY
Which day comes next?

Solution:
SUNDAY
SUNDAY + 1 = MONDAY
MONDAY + 2 = WEDNESDAY
WEDNESDAY + 3 = SATURDAY
SATURDAY + 4 = WEDNESDAY
WEDNESDAY + 5 = MONDAY

Question: S.I. on Tk. 1500 at 7% per annum for a certain time is Tk. 210. Find the time.

Solution:
P = 1500
r = 7%
I = 210
n = ?

n = I/(Pr)
= (210 × 100)/(1500 × 7)
= 2 years