lcm and hcf Model Questions & Answers, Practice Test for ibps rrb clerk asst multipurpose prelims 2024

Answer: (a)

${x + 1.5x}/{y + 3.5y}$ = $25/51$

${2.5x}/{4.5y} = 25/51$

$x/y = {25 × 45}/{51 × 25} = 15/17$

Answer: (d)

LCM of p and q is 1

LCM = pq

Reciprocal = $1/{pq} = pq^{–1}$

Answer: (b)

$a^2 b^4 + 2a^2b^2 = a^2b^2(b^2$ + 2)

and $(ab)^7 – 4a^2b^9 = a^7b^7 – 4a^2b^9$

= $a^2b^2 (a^5b^5 – 4b^7$)

HCF of [($a^2b^4 + 2a^2b^2), ((ab)^7 – 4a^2b^9) = a^2b^2$

Answer: (a)

∵ p(x) × q(x) = LCM × HCF

∴ $(8x^3 + 32x^2$ + 32x) × q(x)

= 2x (x + 2) × 24x $(x + 2)^2$ (x – 2)

⇒ q(x) = ${48x^2 (x + 2)^3 (x - 2)}/{8x(x^2 + 4x + 4)}$

= ${6x(x + 2)^3 (x - 2)}/{(x + 2)^2}$

= 6x$(x^2 – 4) = 6x^3$ – 24x

Answer: (b)

Let $f_1 (x) = 36 (3x^4 + 5x^3 – 2x^2)$

= $36x^2 (3x^2$ + 5x – 2)

= 36 . $x^2$ {$3x^2$ + 6x – x – 2}

= 36 . $x^2$ {3x (x + 2) – 1 (x + 2)}

= 2 × 2 × 3 × 3 × x × x × (x + 2) (3x – 1)

$f_2 (x) = 9 (6x^3 + 4x^2$ – 2x)

= 9x ($6x^2$ + 4x – 2)

= 18x ($3x^2$ + 2x – 1)

= 18x ($3x^2$ + 3x – x – 1)

= 3 × 3 × 2 × x (3x – 1) (x + 1)

$f_3 (x) = 54(27x^4$ – x)

= 54x($27x^3$ – 1)

= 2 × 3 × 3 × 3 × x × (3x – 1) ($9x^2$ + 3x+ 1)

∴ HCF of $f_1(x), f_2(x), f_3(x)$

= 2 × 3 × 3 × x × (3x – 1)

= 18x (3x – 1)