Bank Math Master

Question: If x - 2 = √3 then what is the value of x⁴ + (1/x)⁴?

Solution:
Given,
x - 2 = √3
⇒ x = 2 + √3

∴ (1/x) = 2 - √3

∴ x + (1/x) = 2 + √3 + 2 - √3 = 4

∴ x² + (1/x²) = {x + (1/x)}² - 2 . x . (1/x)
= (4)² - 2
= 16 - 2
= 14

∴ x⁴ + (1/x)⁴ = {x² + (1/x²)}² - 2. x². (1/x²)
= (14)² - 2
= 196 - 2
= 194

Question: In a code SUMMER is written as RUNNER, WINTER is written as VIOUER, then how can SPRING be written in the same code?

Solution:
Given,
S          U       M         M         E       R
↓(- 1)  ↓(0)     ↓(+ 1)   ↓(+ 1)   ↓(0)  ↓(0)
R         U       N          N          E       R

W         I        N         T          E        R
↓(- 1)   ↓(0)   ↓(+ 1)   ↓(+ 1)  ↓(0)    ↓(0)
V          I        O         U         E        R

Similarly,

S         P        R         I         N       G
↓(- 1)  ↓(0)    ↓(+ 1)  ↓(+ 1) ↓(0)    ↓(0)
R        P        S          J        N        G

Question: If p + 3 + 1/p = 0 then what is the value of p² + 1/p² = ?

Solution:
Given,
p + 3 + 1/p = 0
⇒ p + 1/p = - 3
⇒ (p + 1/p)² = (- 3)² [
⇒ p² + 2. p. 1/p + 1/p² = 9
⇒ p² + 1/p² = 9 - 2
∴ p² + 1/p² = 7

Question: If REAL = 185112 and MAN = 13114, then PEACH will be equal to-

Solution:
REAL:
R = 18
E = 5
A = 1
L = 12
So, REAL = 185112 

MAN:
M = 13
A = 1
N = 14
So, MAN = 13114 

Apply the same logic to PEACH
P = 16
E = 5
A = 1
C = 3
H = 8
So, PEACH = 165138

Question: If a + b + c = 9, a² + b² + c² = 29 then what is the value of (ab + bc + ca) = ?

Solution:
Given,
a + b + c = 9,
a² + b² + c² = 29

We know,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = (a + b + c)² - (a² + b² + c²)
⇒ 2(ab + bc + ca) = (9)² - 29
⇒ 2(ab + bc + ca) = 81 - 29
⇒ 2(ab + bc + ca) = 52
∴ (ab + bc + ca) = 26

Question: What should be the value of "P" so that the expression (9 − 12x + Px²) becomes a perfect square?

Solution:
(9 − 12x + Px²)
= (3)² − 2 × 3 × 2x + (2x)² + Px² - (2x)²
= (3 - 2x)² + Px² - 4x²

∴ the expression becomes a perfect square if,
Px² - 4x² = 0
⇒ Px² = 4x²
∴ P = 4

Question: If x² + yz + zx + xy is divided by x + y, the result is-

Solution:
x² + yz + zx + xy
= x² + xy + zx + yz
= x(x + y) + z(x + y)
= (x + y)(x + z)

∴ divided by (x + y) the result = (x + y)(x + z)/(x +y) = (x + z)

Question: In a certain code, PLANE = 26435 and EARTH = 54917, how is PEART coded in the language?

Solution:
Given,
P   L  A   N  E
↓   ↓   ↓   ↓   ↓
2  6   4   3   5

and
E   A  R   T  H
↓   ↓   ↓   ↓   ↓
5   4  9   1   7

So 
P  E   A  R   T
↓   ↓   ↓   ↓   ↓
2   5  4   9   1

Question: If a + b = 7 and ab = 12, then  what is the value of (1/a²) + (1/b²)?

Solution:
Given,
a + b = 7 and ab = 12

∴ (1/a²) + (1/b²)
= (b² + a²)/(a²b²)
= (a² + b²)/(a²b²)
= {(a + b)² - 2ab}/(ab)²
= {(7)² - (2 × 12)}/(12)²
= (49 - 24)/144
= 25/144

Question: If A = 2, B = 4, C = 6, D = 8 and so on, what is the meaning of following number 36, 30, 38, 10

Solution:
Given,
A = 2, B = 4, C = 6, D = 8.......

∴ Each code = Letter position × 2

So
36 ÷ 2 = 18 → R
30 ÷ 2 = 15 → O
38 ÷ 2 = 19 → S
10 ÷ 2 = 5 → E

the meaning of following number = ROSE

Question: If a = b = 2c and abc = 256 then, b² = ?

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

ATQ,
abc = 256
⇒ b × b × (b/2) = 256
⇒ b³/2 = 256
⇒ b³ = 256 × 2
⇒ b³ = 512
⇒ b³ = 8³
∴ b = 8

∴ b² = 8² = 64

Question: If x = 3 + 2√2 then, what is the value of x^-1?

Solution:
Given,
x = 3 + 2√2
∴ 1/x = 1/(3 + 2√2)
⇒ x^-1 = (3 - 2√2)/(3 + 2√2)(3 - 2√2)
= (3 - 2√2)/(3)² - (2√2)²
= (3 - 2√2)/(9 - 8)
∴ x^-1 = (3 - 2√2)

Question: If x² - √5.x + 1 = 0 then, x² + 1/x² = ?

Solution:
Given,
x² - √5.x + 1 = 0
⇒ x² + 1 = √5.x
⇒ x²/x + 1/x = (√5.x)/x
⇒ x + 1/x = √5

Now,
x² + 1/x² = (x + 1/x)² - 2. x.1/x
= (√5)² - 2
= 5 - 2
= 3

Question: The square root of


Solution:

Question: If HCRAES is code SEARCH, which word has the code LATIPAC?

Solution:
Reversed HCRAES = SEARCH

So the code is just the reverse of the given word

Let’s reverse LATIPAC → CAPITAL

Question: 2, 3, 6, 9, 18, ......, 54 What is the missing number in the series?

Solution:
There are two separate series

1st one for even number
2 
2 × 3 = 6
6 × 3 = 18
18 × 3 = 54

2nd one for odd number
3
3 × 3 = 9
9 × 3 = 27

So the missing number = 27