Simplification Model Questions & Answers, Practice Test for ibps so prelims 2024 2025

Answer: (c)

$x^4 – x^2$ + 7x + 5

= (x + 2) ($ax^3 + bx^2$ + cx + d) + k

= $ax^4 + (b + 2a) x^3 + (c + 2b)x^2$ + (d + 2c)x + 2d + k

On Equating the coefficient, we get

a = 1, b + 2a = 0, c + 2b = –1

d + 2c = 7, 2d + k = 5

⇒a = 1, b = –2, c = 3, d = 1

Answer: (d)

$1248×{5/6}-1150×{4/5}$

= 1040 – 920 = 120

Answer: (a)

a + 2b=1.6 ….(1)

$7/{a+b/2}$=10

$14/{2a+b}=10$

2a+b=1.4

By equation (1) and (2) ……(2)

a=0.4, b=0.6

Answer: (c)

Given, x + y + z = 2s

Also, (s – x) + (s – y) – z = 2s – (x + y + z)

= 2s – 2s = 0

∴ $(s – x)^3 + (s – y)^3 – z^3$ + 3(s – x) (s – y) (z) = 0

(∵ a + b + c = 0⇒$a^3 + b^3 + c^3$ = 3abc)

⇒$(s – x)^3 + (s – y)^3 + 3(s – x) (s – y) (z) = z^3$

Answer: (b)

We can simply check the product of the constants in each option whether it yields the constant term or not i.e. –72.

Therefore, in option (a), there would be no constant term as each term will contain a variable x.

In option (b), we get the product of the constants as –1 × 6 × –12 i.e. 72.

In option (c), we get the product of the constants as –1 × 6 × 12 i.e. –72.

In option (d), we get the product of the constants as 1 × –6 × –12 i.e. 72.

Thus, option (c) is correct.