lcm and hcf questions answers pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (c)

Let $f_1(x) = x^3 + 3x^2y + 2xy^2$

= x $(x^2 + 3yx + 2y^2)$

= x $(x^2 + 2xy + xy + 2y^2)$

= x[x(x + 2y) + y(x + 2y)]

= x(x + y)(x + 2y)

and $f_2(x) = x^4 + 6x^3y + 8x^2y^2$

= $x^2(x^2 + 6xy + 8y^2)$

= $x^2(x^2 + 2xy + 4xy + 8y^2)$

= $x^2$[x (x + 2y) + 4y (x + 2y)]

= $x^2$(x + 2y) (x + 4y)

∴ HCF of $f_1 (x) and f_2$ (x) = x (x + 2y)

Answer: (d)

Let $f_1 (x) = x^2$ + bx – x – b

= x (x + b) – 1 (x + b)

= (x – 1) (x + b)

and $f_2 (x) = x^2$ + xa – x – a

= x (x + a) – 1 (x + a)

= (x + a) (x – 1)

∴ HCF of $f_1(x) and f_2$(x) = (x – 1)

Answer: (a)

Here 13850 and 17030 are two numbers which leaves remainder 17.

Now, 13850 – 17 = 13833

17013 – 17 = 17013

13833 = 159 × 3 × 29

17013 = 107 × 159

∴ HCF = 159.

It is the greatest number.

Answer: (c)

$x^3 + 3x^2 + 3x + 1 = (x + 1)^3$

$x^3 + 5x^2 + 5x + 4 = (x + 4) (x^2$ + x + 1)

$x^2$ + 5x + 4 = (x + 1)(x + 4)

L.C.M = $(x + 1)^3 (x + 4) (x^2$ + x +1)

Answer: (d)

HCF = 12. Then let the numbers be 12x and 12y.

Now 12x × 12y = 2160 ∴ xy = 15

Possible values of x and y are (1, 15); (3, 5); (5, 3); (15, 1)

∴ the possible pairs of numbers (12, 180) and (36, 60)