simplification Model Questions & Answers, Practice Test for ssc chsl tier 1 2024

Answer: (c)

${36}/{11} = 3 + 1/{x + 1/{y + 1/z}} 3/{11} = 1/{x + 1/{y + 1/z}} $

⇒$x + 1/{y + 1/z} = {11}/3 = 3 + 2/3$

⇒x = 3, $1/{y + 1/z} = 2/3⇒y + 1/z = 3/2⇒y + 1/z = 1 + 1/2$

⇒y = 1, z = 2

⇒x + y + z = 3 + 1 + 2 = 6

Answer: (c)

x + 3 is a factor of $x^3 + 3x^2$ + 4x + k

x + 3 = 0 ∴ x = – 3

Now $x^3 + 3x^2$ + 4x + k = 0

$(–3)^3 + 3x(–3)^2$ + 4 × (–3) + k = 0

–27 + 27 – 12 + k = 0

k – 12 = 0

∴ k = 12

Answer: (c)

49+$√{?}$ = 87

or = 87 – 49 = 38

or ? = $(38)^2$ = 1444

Answer: (b)

?=${7857 + 3596 + 4123}/96$

=${15576}/96$=162.25

Answer: (c)

$x/1 = {√{a + 2b} + √{a - 2b}}/{√{a + 2b} - √{a - 2b}}$

Applying componendo and dividendo, we get

${x + 1}/{x - 1} = {2√{a + 2b}}/{2 √{a - 2b}}$

⇒${x + 1}/{x - 1} = {√{a + 2b}}/{√{a - 2b}}$

Squaring on both sides, we get

${(x + 1)^2}/{(x - 1)^2} = {a + 2b}/{a - 2b}$

Again applying componendo and dividendo, we get

${x^2 + 1 + 2x + x^2 + 1 - 2x}/{x^2 + 1 + 2x - x^2 - 1 + 2x} = {2a}/{4ab} = a/{2b}$

⇒${2(x^2 + 1)}/{4x} = a/{2b}$

⇒${x^2 + 1}/x = a/b$

⇒$bx^2$ + b = ax

⇒$bx^2$ – ax + b = 0

∴ Option (a) is correct