Algebra Easy Questions and Answers

(ad – bc)² + (ac + bd)²
= a²d² + b²c² – 2abcd + a²c² +
b²d² + 2abcd
= a²d² + b²c² + a²c² +
b²d²
= a²d² + b²d² + b²c² + a²c²
= d²(a² + b²) + c²(b² + a²)
= (a² + b²) (c² + d²)
= 2 × 1 = 2

Correct Option: D

Tricky Approach
x² = y + z
⇒ x² + x = x + y + z
⇒ x (x + 1) = x + y + z ....(i)
Similarly,
y (y + 1) = x + y + z .........(ii)
and, z (z + 1) = x + y + z ...(iii)

∴	1	+	1	+	1
	x + 1		x + 1		z + 1

=	x	+	y	+	z
	x + y + z		x + y + z		z + y + z

⇒	x + y + z	= 1
	x + y + z

Correct Option: B

Tricky Approach
x² = y + z
⇒ x² + x = x + y + z
⇒ x (x + 1) = x + y + z ....(i)
Similarly,
y (y + 1) = x + y + z .........(ii)
and, z (z + 1) = x + y + z ...(iii)

∴	1	+	1	+	1
	x + 1		x + 1		z + 1

=	x	+	y	+	z
	x + y + z		x + y + z		z + y + z

⇒	x + y + z	= 1
	x + y + z

p	+	q	=	p² + q²
p	+	q	=	pq

=	(p + q) - 2pq
	pq

=	100 - 2 × 5	=	90	= 18
	5		5

Correct Option: D

p	+	q	=	p² + q²
p	+	q	=	pq

=	(p + q) - 2pq
	pq

=	100 - 2 × 5	=	90	= 18
	5		5

a^1/3 =11 ⇒ a = 11³ = 1331
∴ a² – 331a = a(a – 331)
= 1331 (1331 – 331)
= 1331 × 1000 = 1331000

Correct Option: B

a^1/3 =11 ⇒ a = 11³ = 1331
∴ a² – 331a = a(a – 331)
= 1331 (1331 – 331)
= 1331 × 1000 = 1331000

1.5x = 0.04y

⇒	x	=	0.04	=	4	=	2
	y		1.5		150		75

⇒	y	=	75
	x		2

Now,	y² − x²
	y² + 2xy + x²

=	(y − x)(y + x)
	(y + x)²

=	y − x
	y + x

=	y	− 1
	x

	y	+ 1
	x

=	75	− 1
	2

	75	+ 1
	2

=	73
	77

Correct Option: B

1.5x = 0.04y

⇒	x	=	0.04	=	4	=	2
	y		1.5		150		75

⇒	y	=	75
	x		2

Now,	y² − x²
	y² + 2xy + x²

=	(y − x)(y + x)
	(y + x)²

=	y − x
	y + x

=	y	− 1
	x

	y	+ 1
	x

=	75	− 1
	2

	75	+ 1
	2

=	73
	77

If p + q = 10 and pq = 5, then the numerical value of	p	+	q	will be
	q		p

If 1.5x = 0.04y, then the value of	y² − x²	is
	y² + 2xy + x²

Algebra

Algebra

Aptitude

Correct Option: D

Correct Option: B

Correct Option: D

Correct Option: B

Correct Option: B