Mathematics Test 87

Result

Mathematics Test 87

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Question 1
4 / -1

if |z - 2| + |z + 2| = 3 , then locus of z is :-

A
Circle

B
St. line

C
Ellipse

D
No real curve

Solution

|z - 2| + |z + 2| = 3

Let z₁ = 2 and z₂ = –2

⇒ |z₁ – z₂| = 4
⇒ |z₁ – z₂| < 3

So, No real curve
Question 2
4 / -1

If (x + iy)⁵ = a + ib then (y + ix)⁵ is equal to :-

A
b + ia

B
b – ia

C
a + ib

D
a – ib

Solution

(x + iy)⁵ = a + bi

i⁵(y – ix)⁵ = a + bi

(y – ix)⁵ = b – ia

⇒ (y + ix)⁵ = b + ia
Question 3
4 / -1

Let S(k) = 1 + 3 + 5 + ..... + (2k–1) = 3 + k², then which of the following is true ?

A
S(1) is true

B
S(k) ⇒ S(k+1)

C
S(k) S(k+1)

D
Principle of mathematical induction can be used to prove that formula

Solution

S(K) = 1 + 3 + 5 + ..... + (2K–1) = 3 + K²

S(1) is not true

let S(K) is true then

S(K+1) = 1 + 3 + 5 + ..... + (2K–1) + (2K+1) = S(K) + (2K + 1)

= 3 + K² + 2K + 1 = 3 + (K+1)²

Hence S(k) ⇒ S(k+1)