power indices and surds Model Questions & Answers, Practice Test for ssc chsl tier 1 2024

Answer: (a)

After 1st hit ball height will be = $1/2$(64)

After 2nd hit ball height will be = $(1/2)^2 (64)$

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After 16th hit ball height will be = $(1/2)^{16} (64)$

= $1/{2^{16}}(2^6) = 2^{-10}m$

Answer: (d)

$n^2 + 19n + 92 = (n^2$ + 18n + 81) + n + 11

To be perfect square

n + 11 = 0 ∴ n = –11

$n^2 + 19n + 92 = (n^2$ + 20n + 100) – n – 8

To be perfect square, –n –8 = 0

n = –8

ATQ, Sum = –11–8 = –19

Answer: (b)

Given that, a = 2 + $√3, 1/a = 2 - √3$

Now, $a^2 + a^{-2} = (a + 1/a)^2 - 2$

= $(2 + √3 + 2 - √3)^2 - 2$

= $(4)^2$ - 2 = 16 - 2 = 14

Answer: (c)

$3^x × 27^x = 9^{x + 4}$

∴ $3^x × 3^{3x} = 3^{2(x + 4)}$

⇒$3^{x + 3x} = 3^{2(x + 4)}$

Here base is same

So, x + 3x = 2(x + 4)⇒4x - 2x = 8

∴ x = $8/2$ = 4

Answer: (c)

$a√a + b√b$ = 32 ...(i)

$a√b + b√a$ = 31 ...(ii)

Squaring and subtracting equation (i) and (ii), we have

$(a - b)^2(a + b) = 63$

$(a–b)^2 (a + b) = 3^2$.7

∴ (a – b) = 3 and a + b = 7

⇒a = 5, b = 2

Now, ${5(a + b)}/7 = {5(5 + 2)}/7$ = 5