surds and indices Model Questions & Answers, Practice Test for ibps po prelims 2023

Answer: (c)

? = $(27)^{18} ÷ (27)^3 = (27)^{18 – 3}$

= $(27)^{15}$ (∴ $a^m ÷ a^n = a^{m–n}$)

Answer: (b)

$64^{3.1} × 8^{4.3} = 8^{?}$

⇒$(8^2)^{3.1} × (8)^{4.3} = 8^{?}⇒8^{6.2} × 8^{4.3} = 8^{?}$

⇒$8^{6.2 + 4.3} = 8^{?}⇒8^{10.5} = 8^{?}$

? = 10.5

Answer: (c)

$(5)^(3.5) × (5)^(4.8) × (5)^(2.4) ÷ (5)^(?) = (5)^{(5.1)}$

⇒$5^{3.5 + 4.8 + 2.4 - ?} = 5^{5.1}$

⇒$5^{10.7-?} = 5^{5.1}$

⇒10.7 – ? = 5.51

⇒? = 10.70 – 5.1 = 5

Answer: (a)

(0.064) × $(0.4)^7 = (0.4)^{?} × (0.0256)^2$

$(0.4)^3 × (0.4)^7 = (0.4)^{?} × (0.4)^{4 × 2}$

$(0.4)^{3+7} = (0.4)^{?} × (0.4)^8$

${(0.4)^{10}}/(0.4)^8 = (0.4)^{?}$

$(0.4)^{10 – 8} = (0.4)^{?}$

2 =?

Answer: (d)

Let $3^{x^2}= a$ and $3^{3+6}=b$

the given equation reduces to

$a^2-2ab+b^2=0⇒(a-b)^2$

⇒a=b

$∴3x^2=3^{x+6}[a^m=a^n$ then m=n]

$⇒x^2=x+6⇒x^2-x-6=0$

⇒$x^2-3x+2x-6=0⇒x(x-3)+2(x-3)=0$

⇒(x-3)(x+2)=0⇒x=3 or x=-2