**Telangana**** SCERT Solution Class IX (9) Math Chapter 15 Proofs in Mathematics Exercise 15.1**

**1)**

(i) False, a month at least has 28 days usually either 30 or 31 days.

(ii) Ambiguous, In a given year makes sankranti may or may not fall on Friday.

(iii) Ambiguous, Sometimes in winter there can be temperature at 2 ̊C but not always.

(iv) True, As of now there exists no other planet except for earth which has life.

(v) False, Dogs cannot fly.

(vi) Ambiguous, In a leap year February has 29 days usually has 28 days.

**2.)**

(i) True, sum of interior angles of quadrilateral is always 360 ̊.

(ii) True, If you multiply any number with 2 it will produce an even number.

(iii) True, Rhombus has opposite sides parallel each other.

(iv) True.

(v) No, not all Square numbers can be written as the sum of two odd numbers. eg. 9 = 3+6

**3.)**

(i) Only neutral numbers can be represented as products of their prime factors.

(ii) True, eg. -> 2*3 =6 [ 3 odd number 6 is even]

(iii) Yes for all numbers 3x + 1 > 4 except for 0 and 1

3x 0+1 = 1<4; 3*1+4 =4

∴ when,

x>1 ; 3x +1 > 4

(iv) True, for any value of x

X^{3} ≥ 0. for x ≥ 0.

(v) Only in equilateral triangle the median bisects the angle.

**4.)**

Given,

X^{2} > y^{2} & x > y

For any negative integer value of x & y

The above equation is not valid.

For eg. ->

let,

x= -2 ; y = -4

∴ x^{2} = -2 x -2 = 4 y^{2} = -4 x -4 = 16

Clearly x^{2} < y^{2}

∴ The condition is not satisfied.