Explore topic-wise InterviewSolutions in .

No, it is not a right angle triangle.

Explanation:

As we know, in a right-angled triangle the hypotenuse is the longest side. Of all the three sides given here, 17cm must be hypotenuse.

According to Pythagoras  theorem,

(Hypotenuse)² = (other side1)² + (other side 2)² 
here, (17)²  is not equal to (12)²  +(14)² 
So the given triangle is not right-angled triangle.

(i) x³ + 64 = (x)³ + (4)³ = (x + 4)(x² + 16 – 4x)

(ii) 1-125y³ = (1)³ – (5y)³ = (1 – 5y)(1 + 25y² + 5y)

(iii) \(\frac{p^{3}}{343}+8 q^{3}=\left(\frac{p}{7}\right)^{3}+(2 q)^{3}\) 

\(=\left(\frac{p}{7}+2 q\right)\left(\frac{p^{2}}{49}+4 q^{2}-\frac{2}{7} p q\right)\)

(iv) 7m⁴n – 7mn⁴ = 7mn(m³ – n³) 

= 7mn[(m)³– (n)³] 

= 7mn[(m – n)(m² + n² + mn)]

(v) x⁷y⁷ – xy = xy(x⁶y⁶ – 1) 

= xy[(x²y²)³ – (1)³]

= y[(x²y² – 1)(x⁴y⁴ + 1 + x²y²]

= xy [(xy)² – (1)²) (x⁴y⁴ – 1 + 2x²y² xy²)]

= xy (xy + 1)(xy – 1)[(x²y² + 1)² – (xy)²]

= xy(xy + 1)(xy – 1)(x²y² + 1 + xy)(x²y² + 1 – xy)

Following example to understand all the logical operators available in Python programming language:

#!/usr/b in/python

a = 10 

b = 20 

c = 0 

if (a and b): 

print “Line 1 – a and b are true” 

else: 

print “Line 1 – Either a is not true or b is not true”

if (a or b): 

print “Line 2 – Either a is true or b is true or both are true” 

else: 

print “Line 2 – Neither a is true nor b is true”

a = 0 

if ( a and b ): 

print “Line 3 – a and b are true” 

else: 

print “Line 3 – Either a is not true or b is not true”

if ( a or b ): 

print “Line 4 – Either a is true or b is true or both are true” 

else: 

print “Line 4 – Neither a is true nor b is true” 

if not( a and b) : 

print “Line 5 – a and b are true” 

else: 

print “Line 5 – Either a is not true or b is not true”

When you execute the above program it produces following result:

Line 1 – a and b are true 

Line  2 – Either a is true or b is true or both are true

 Line  3 – Either a is not true or b is not true

Line  4 – Either a is true or b is true or both are true

 Line  5 – a and b are true