CAT 2025 Lesson : Class Discussion: Numbers - Surds & Indices: 1 to 8

Class Discussion - Surds & Indices

Question 1

Which of the following is the largest?

		$\sqrt[3]{2}$
		$\sqrt[5]{3}$
		$\sqrt[6]{5}$
		$\sqrt[10]{12}$

Question 2

x = -0.5

, then which of the following has the smallest value?
[CAT 2006]

		$2^\frac{1}{x}$
		$\dfrac{1}{x}$
		$\dfrac{1}{x^2}$
		$2^x$
		$\dfrac{1}{\sqrt{-x}}$

Question 3

The expression

\sqrt{\dfrac{4}{3}} - \sqrt{\dfrac{3}{4}}

is equal to :
[FMS 2010]

		$\dfrac{\sqrt{3}}{6}$
		$\dfrac{-\sqrt{3}}{6}$
		$\dfrac{\sqrt{-3}}{6}$
		$\dfrac{5\sqrt{3}}{6}$

Question 4

What is the square root of

37 - 20\sqrt{3}

		$5 - 2\sqrt{3}$
		$\sqrt{12} - 5$
		$10 - \sqrt{3}$
		More than one of the above

Question 5

In 2011, Plasma – a pharmaceutical company – allocated Rs.

4.5 \times 10^7

for Research and Development. In 2012, the company allocated Rs. 60,000,000 for Research and Development. If each year the funds are evenly divided among

2 \times 10^2

departments, how much more will each department receive this year than it did last year?
[IIFT 2012]

		Rs. $2.0 \times 10^5$
		Rs. $7.5 \times 10^5$
		Rs. $7.5 \times 10^4$
		Rs. $2.5 \times 10^7$

Question 6

Given

2^x = 8^{y + 1}

and

9^y = 3^{x - 9}

; the value of

x + y

is :
[FMS 2010]

		18
		21
		24
		27

Question 7

9^{2x - 1} - 81^{x - 1}

= 1944, then

x

is
[CAT 2017 S1]

		3
		$\dfrac{9}{4}$
		$\dfrac{4}{9}$
		$\dfrac{1}{3}$

Question 8

Given that

x^{2018}y^{2017}

\dfrac{1}{2}

and

x^{2016}y^{2019}

= 8, the value of

x^2 + y^3

is
[CAT 2018 S1]

		$\dfrac{31}{4}$
		$\dfrac{37}{4}$
		$\dfrac{33}{4}$
		$\dfrac{35}{4}$

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