[Download PDF] TS ICET 24th May 2019 Shift-1 Paper with Solutions

Instructions

For the following questions answer them individually

Question 81

$$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ........}}}} =$$

Video Solution

Solution

short cut $$2 \times 3 = 6$$

Longer Method

$$\sqrt{6 + \sqrt{6}.....} = x$$

$$6 + x = x^2$$

$$x^2 - x - 6 = 0$$

$$(x - 3)(x + 2) = 0$$

$$x = 3, x = -2$$

x = -2 not possible

So answer is x = 3

Hence the answer is option C

Question 82

What is the least value of x such that 43x4567 is divisible by 11?

Video Solution

Solution

43x4567 is divisible by 11
So, 4+x+5+7 - (3+4+6) is divisible by 11
So, x+16 - 13 is divisible by 11
So, x+3 is divisible by 11
So, x = 8

Hence the answer is option D

Question 83

The number of positive integers between 1 and 2087 that are divisible by 31 is:

Video Solution

Solution

First no 31

Last no

31) 2087 (67

186

227

217

10

$$1 \rightarrow 67$$

Total no = 67

Hence the answer is option C

Question 84

What is the largest four digit number that leaves a remainder 4 when it is divided by 36, 48 and 64?

Video Solution

Solution

No = LCM (36, 48, 64)k + 4

= 576k + 4

= 576) 9999 ( 17

576

4239

4032

207

9999 - 207 + 4

9999 - 203

= 9796

Hence the answer is option C

Question 85

What is the minimum number of square tiles required to pave a floor of dimensions 24.78 meters x 22.26 meters?

Video Solution

Solution

HCF 2478 2226

252

$$2 \times 126$$

$$2 \times 18 \times 7$$

HCF = $$2 \times 3 \times 7$$

= 42

No.of tiles $$2478 \times 2226$$

42 $$\times$$ 42

$$\Rightarrow 59 \times 53$$

= 3127

Hence the answer is option B

Question 86

$$\frac{3.61}{0.361} = \frac{361}{x} \Rightarrow x =$$

Video Solution

Question 87

If the recurring decimal number $$1.\overline{27}$$ is equal to the rational number $$\frac{p}{q}$$ then p - q =

Video Solution

Question 88

The difference between the largest and the smallest of the following rational numbers is:
$$\frac{3}{5}, \frac{3}{8}, \frac{2}{3}, \frac{4}{9}, \frac{1}{2}, \frac{6}{11}$$

Video Solution

Question 89

What is the least fraction to be added to the sum of the following fractions to make it an integer?
$$3\frac{1}{3}, 6\frac{11}{12}, 4\frac{7}{36}, 5\frac{1}{12}, 7\frac{1}{4}$$

Video Solution

Question 90

If the length of a rectangle is increased by 15%and the breadth decreased by 10% then the percentage change in its area is:

Video Solution

CAT Content

TS ICET 24th May 2019 Shift-1

$$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ........}}}} =$$

What is the least value of x such that 43x4567 is divisible by 11?

The number of positive integers between 1 and 2087 that are divisible by 31 is:

What is the largest four digit number that leaves a remainder 4 when it is divided by 36, 48 and 64?

What is the minimum number of square tiles required to pave a floor of dimensions 24.78 meters x 22.26 meters?

$$\frac{3.61}{0.361} = \frac{361}{x} \Rightarrow x =$$

If the recurring decimal number $$1.\overline{27}$$ is equal to the rational number $$\frac{p}{q}$$ then p - q =

The difference between the largest and the smallest of the following rational numbers is:$$\frac{3}{5}, \frac{3}{8}, \frac{2}{3}, \frac{4}{9}, \frac{1}{2}, \frac{6}{11}$$

What is the least fraction to be added to the sum of the following fractions to make it an integer?$$3\frac{1}{3}, 6\frac{11}{12}, 4\frac{7}{36}, 5\frac{1}{12}, 7\frac{1}{4}$$

If the length of a rectangle is increased by 15%and the breadth decreased by 10% then the percentage change in its area is:

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The difference between the largest and the smallest of the following rational numbers is:
$$\frac{3}{5}, \frac{3}{8}, \frac{2}{3}, \frac{4}{9}, \frac{1}{2}, \frac{6}{11}$$

What is the least fraction to be added to the sum of the following fractions to make it an integer?
$$3\frac{1}{3}, 6\frac{11}{12}, 4\frac{7}{36}, 5\frac{1}{12}, 7\frac{1}{4}$$