[Download PDF] TS ICET 23rd May 2019 Shift-1 Paper with Solutions

Instructions

For the following questions answer them individually

Question 71

A superfast express travelling at 100 kmph takes 2 hours more than another train travelling at 120 kmph to cover the distance betweenthe same two stations (in kms). Then the distance between the stations (in kms)is.

Video Solution

Question 72

A, B, C, D, E, F and G are sitting around a circular table and facing the centre: G is second to the left of C, C is to the immediate left of F, A is third to the left of E, B is between D and E. Which of the following is true?

Video Solution

Question 73

If * is defined by $$a * b = a^3 + b^3 - 3ab$$ for $$a, b \epsilon R$$, then $$\frac{(1 * 2) * (1 * 2)}{(1 * 1) * (1 * 1)} =$$

Video Solution

Question 74

If $$x \downarrow y = (x + y) + (x - y)^2$$ and $$x \uparrow y = (x + y)^3 - (x - y)^3$$ then the value $$\frac{(0 \downarrow 1) \uparrow (0 \downarrow 1)}{(1 \uparrow 2) \downarrow (1 \uparrow 2)} =$$

Video Solution

Question 75

For ab ≠ 0. if * is defined by $$a * b = \frac{a^2 + b^2}{ab}$$ then $$\frac{(1 * 2) * (2 * 1)}{(1 * 3) + (3 * 1)} =$$

Video Solution

Question 76

If $$a = 2^x, b = 4^y, c = 8^z$$ and $$a^{yz} . b^{zx} . c^{xy} = 4^6$$, then $$xyz = ...........$$

Video Solution

Solution

given that

$$a = 2^x, b = 4^y, c = 8^z$$ and

$$a^{yz} . b^{zx} . c^{xy} = 4^6$$ put the value of a,b and c

$$ 2^{xyz} . 4^{yzx} . 8^{zxy} = 4^6$$

$$ 2^{xyz} . 4^{yzx} . {2$$\times$$4}^{zxy} = 4^6$$

$$ 4^{xyz} . 4^{yzx} . 4^{zxy} = 4^6$$

$$ 4^{3zxy} = 4^6$$ when base are same then power will be equal

3xyz = 6

xyz = 2 Answer

Question 77

$$x^{x\sqrt{x}} = (x\sqrt{x})^{6x} \Rightarrow x =$$

Video Solution

Solution

given that

$$x^{x\sqrt{x}} = (x\sqrt{x})^{6x}$$

when base are same power will be equal

X^3x\2 = (x^3\2)^6x

x^3\2 = (3\2)6x

x = 81 Answer

Question 78

$$A + B + C = 427, 3A = 4B = 7C \Rightarrow A =$$

Video Solution

Solution

given that

$$A + B + C = 427, 3A = 4B = 7C \Rightarrow$$

B = A3\4 and C = A3\7 put the value

A + A3\4 + A3\7 = 427

(28A + 21A + 12A)\28=427

A = 196 Answer

Question 79

There are 50 paise and 25 paise coins in a bag whose value is Rs.45. If the total numberof coins is 100, then the number of 50 paise coins is

Video Solution

Solution

let we have x number of 50 paise cion and y number of 25 paise coin

then given

$$x\cdot\frac{1}{2}+y\cdot\frac{1}{4}=45$$ and x + y = 100

on solving both equation we get

x = 80 and y = 20

Question 80

$$\frac{2}{\sqrt{10 + 2\sqrt{21}}} - \frac{1}{\sqrt{12 + 2\sqrt{35}}} - \frac{1}{\sqrt{8 + 2\sqrt{15}}} =$$

Video Solution

Solution

given that

= $$\frac{2}{\sqrt{10 + 2\sqrt{21}}} - \frac{1}{\sqrt{12 + 2\sqrt{35}}} - \frac{1}{\sqrt{8 + 2\sqrt{15}}} $$

we know that $$\sqrt{21}$$ = 4.58 , $$\sqrt{35}$$ = 5.91 , $$\sqrt{15}$$ = 3.87

put the value in the equation we get

= $$\frac{2}{\sqrt{19}} - \frac{1}{\sqrt{19}} - \frac{1}{\sqrt{19}} $$

= 0 Answer

CAT Content

TS ICET 23rd May 2019 Shift-1

A superfast express travelling at 100 kmph takes 2 hours more than another train travelling at 120 kmph to cover the distance betweenthe same two stations (in kms). Then the distance between the stations (in kms)is.

A, B, C, D, E, F and G are sitting around a circular table and facing the centre: G is second to the left of C, C is to the immediate left of F, A is third to the left of E, B is between D and E. Which of the following is true?

If * is defined by $$a * b = a^3 + b^3 - 3ab$$ for $$a, b \epsilon R$$, then $$\frac{(1 * 2) * (1 * 2)}{(1 * 1) * (1 * 1)} =$$

If $$x \downarrow y = (x + y) + (x - y)^2$$ and $$x \uparrow y = (x + y)^3 - (x - y)^3$$ then the value $$\frac{(0 \downarrow 1) \uparrow (0 \downarrow 1)}{(1 \uparrow 2) \downarrow (1 \uparrow 2)} =$$

For ab ≠ 0. if * is defined by $$a * b = \frac{a^2 + b^2}{ab}$$ then $$\frac{(1 * 2) * (2 * 1)}{(1 * 3) + (3 * 1)} =$$

If $$a = 2^x, b = 4^y, c = 8^z$$ and $$a^{yz} . b^{zx} . c^{xy} = 4^6$$, then $$xyz = ...........$$

$$x^{x\sqrt{x}} = (x\sqrt{x})^{6x} \Rightarrow x =$$

$$A + B + C = 427, 3A = 4B = 7C \Rightarrow A =$$

There are 50 paise and 25 paise coins in a bag whose value is Rs.45. If the total numberof coins is 100, then the number of 50 paise coins is

$$\frac{2}{\sqrt{10 + 2\sqrt{21}}} - \frac{1}{\sqrt{12 + 2\sqrt{35}}} - \frac{1}{\sqrt{8 + 2\sqrt{15}}} =$$

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