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Class Discussion: Numbers

Cd Numbers

MODULES

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Number Theory: 1 to 8
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Factors & Remainders: 1 to 8
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Factors & Remainders: 9 to 16
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Divisibility: 1 to 8
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Divisibility: 9 to 16
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Number Systems: 1 to 8
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Surds & Indices: 1 to 8
ALL MODULES

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

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Class Discussion - Surds & Indices

Question 1

Which of the following is the largest?

23\sqrt[3]{2}32​
35\sqrt[5]{3}53​
56\sqrt[6]{5}65​
1210\sqrt[10]{12}1012​

Question 2

If x=−0.5x = -0.5x=−0.5, then which of the following has the smallest value?
[CAT 2006]

21x2^\frac{1}{x}2x1​
1x\dfrac{1}{x}x1​
1x2\dfrac{1}{x^2}x21​
2x2^x2x
1−x\dfrac{1}{\sqrt{-x}}−x​1​

Question 3

The expression 43−34\sqrt{\dfrac{4}{3}} - \sqrt{\dfrac{3}{4}}34​​−43​​ is equal to :
[FMS 2010]

36\dfrac{\sqrt{3}}{6}63​​
−36\dfrac{-\sqrt{3}}{6}6−3​​
−36\dfrac{\sqrt{-3}}{6}6−3​​
536\dfrac{5\sqrt{3}}{6}653​​

Question 4

What is the square root of 37−20337 - 20\sqrt{3}37−203​?

5−235 - 2\sqrt{3}5−23​
12−5\sqrt{12} - 512​−5
10−310 - \sqrt{3}10−3​
More than one of the above

Question 5

In 2011, Plasma – a pharmaceutical company – allocated Rs. 4.5×1074.5 \times 10^74.5×107 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 2×1022 \times 10^22×102 departments, how much more will each department receive this year than it did last year?
[IIFT 2012]

Rs. 2.0×1052.0 \times 10^52.0×105
Rs. 7.5×1057.5 \times 10^57.5×105
Rs. 7.5×1047.5 \times 10^47.5×104
Rs. 2.5×1072.5 \times 10^72.5×107

Question 6

Given 2x=8y+12^x = 8^{y + 1}2x=8y+1 and 9y=3x−99^y = 3^{x - 9}9y=3x−9 ; the value of x+yx + yx+y is :
[FMS 2010]

18
21
24
27

Question 7

If 92x−1−81x−19^{2x - 1} - 81^{x - 1}92x−1−81x−1 = 1944, then xxx is
[CAT 2017 S1]

3
94\dfrac{9}{4}49​
49\dfrac{4}{9}94​
13\dfrac{1}{3}31​

Question 8

Given that x2018y2017x^{2018}y^{2017}x2018y2017 = 12\dfrac{1}{2}21​ and x2016y2019x^{2016}y^{2019}x2016y2019 = 8, the value of x2+y3x^2 + y^3x2+y3 is
[CAT 2018 S1]

314\dfrac{31}{4}431​
374\dfrac{37}{4}437​
334\dfrac{33}{4}433​
354\dfrac{35}{4}435​
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