power indices and surds Model Questions & Answers, Practice Test for ssc steno grade c d 2024

Answer: (a)

From option (a) $[(5^{-2})^{-2}]^{-2} = 5^{-8} = 1/{5^8}$

From option (b) $[(5^{-2})^2]^{-2} = 5^8 = 5^8$

From option (c) $[(2^{-5})^{-2}]^{-2} = 5^{-20} = 1/{5^{20}}$

From option (d) $[(2^{-5})^2]^{-2} = 5^{20} = 5^{20}$

Now, smallest number $[(2^{-5})^{-2}]^{-2}$

Answer: (c)

Given x = $2^{1/3} + 2^{-1/3}$

x = $2^{1/3} + 1/{2^{1/3}}$

Cubing on both sides, we get

$x^3 = (2^{1/3})^3 + (1/{2^{1/3}})^3 + 3.2^{1/3} . 1/{2^{1/3}} (2^{1/3} + 1/{2^{1/3}})$

⇒$x^3 = 2 + 1/2 + 3(x)$

⇒$x^3 = {4 + 1 + 3x × 2}/2$

⇒$2x^3$ = 5 + 6x

⇒$2x^3$ – 6x – 5 = 0

∴ option (a) is correct.

Answer: (a)

Given that, $√{1 + {93}/{196}} = 1 + x/{14}$

⇒$√{{289}/{196}} = 1 + x/{14}⇒{17}/{14} = 1 + x/{14}$

⇒$x/{14} = {17}/{14} -1 ⇒x = 3$

Answer: (b)

x = $√3 + √2$

$1/x = 1/{√3 + √2} = {√3 - √2}/{(√3 + √2)(√3 - √2)}$

= $√3 - √2$

⇒$x^3 + x + 1/x + 1/{x^3}$

= $x + 1/x + x^3 + 1/{x^3}$

= $(x + 1/x) + (x + 1/x)^3 -3(x + 1/x)$

= $(√3 + √2 + √3 - √2) + (√3 + √2 + √3 - √2)^3$

-3$(√3 + √2 + √3 - √2)$

= $2√3 + (2 √3)^3 - 3(2 √3)$

= $2√3 + 24√3 - 6 √3$

= $20√3$

So, option (b) is correct

Answer: (a)

Given, $ a^x = c^q = band c^y = a^z = d$

Now, $a^x = c^q$

⇒$a^{x.z} = c^{q.z}⇒(a^z)^x = (c^z)^q$

Here, $a^z = c^y⇒(c^y)^x = c^{zq}$

⇒yx = zq