[Download PDF] TS ICET 23rd May 2019 Shift-2 Paper with Solutions

Instructions

For the following questions answer them individually

Question 71

If $$t_1$$ is the time elapsed between 9:25 a.m to 2:50 p.m, and if $$t_2$$ is the time elapsed between 10:10 a.m to 5:15 p.m then $$t_1 : t_2 =$$

Video Solution

Question 72

Six persons P. O, R. S, T and Uare sitting around a roundtable facing the centre of the table. Tis between P and S, R is to the immediate left of U and to the immediate mght of O and O is to the immediate mght of S. Who is sitting between R and S?

Video Solution

Question 73

If $$\alpha$$ denotes multiplication, $$\beta$$ denotes division, $$\gamma$$ denotes addition and $$\delta$$ denotes subtraction, then,
$$6 \delta \left[\left\{(6 \gamma 4)\beta 8\right\}\alpha 2\right] =$$

Video Solution

Question 74

For any real numbers a and b. if ab=a+b—ab then
(12)(34)=

Video Solution

Question 75

If Z denote the set of integers then the number of elements in the set $$A = \left\{(a,b) : 2a^{2} + 3b^{2} = 25 ;a, b \epsilon Z \right\}$$ is

Video Solution

Question 76

$$x^{y}=y^{x}\Rightarrow \left(\frac{x}{y}\right)^{\frac{y}{x}} =$$

Video Solution

Solution

given that

$$x^{y}=y^{x}$$

so we can write that $$y = x^\frac{y}{x}$$

and substituting the value to

$$x^\frac{y}{x}$$

we get $$\frac{x}{x^\frac{y}{x}^\frac{x}{y} $$

= {x^$$\frac{x}{y}$$ $$frac {x^1}$$

x^$$\frac{x}{y}-1$$ answer

Question 77

$$x^{x\sqrt{x} = \left(x\sqrt{x}\right)^x} \Rightarrow x = .............$$

Video Solution

Solution

$$x^{x\sqrt{x} = \left(x\sqrt{x}\right)^x} \Rightarrow$$

Question 78

$$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 5 : 7 \Rightarrow a : b : c =$$

Video Solution

Solution

$$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 5 : 7 \Rightarrow a : b : c =?$$

now we have from above eq $$a:\frac{1}{3},b:\frac{1}{5},c:\frac{1}{7}$$

let take LCM of 3,5 and 7 we get lcm=105

now we have $$a:b:c:=\frac{1}{3}times105:\frac{1}{5}times105:\frac{1}{7}times105$$

after solving we get

$$a:b:c:=35:21:15$$ answer

Question 79

If for the natural numbers $$a, b, c, a^{3} + b^{3} + c^{3} = 8072$$ and $$a : b = b : c = 3 : 2$$, then $$a =$$

Video Solution

Solution

$$a,b,c,a^{3}+b^{3}+c^{3}=8072$$ and $$a:b=b:c=3:2$$ then $$a= ? $$

let $$\frac{a}{b}=\frac{3}{2}times\frac{3x}{3}$$ and $$\frac{b}{c}=\frac{3}{2}times\frac{2x}{2}$$

then we get

$$a=9x,b=6x,c=4x$$

now put the value of a,b,and c in equation $$a,b,c,a^{3}+b^{3}+c^{3}=8072$$

now we have eq $${9x}^3+{6x}^3+{4x}^3=8072$$

then we get $${729x^3+216x^3+64x^3}=8072$$

then $$1009x^3=8072$$

$$x=2$$

put the value of x and we get

$$a=18,b=12,c=8$$ answer

Question 80

$$\frac{1}{\sqrt{5} - 1} - \frac{1}{2 - \sqrt{3}} + \frac{1}{\sqrt{3} - \sqrt{2}} - \frac{1}{\sqrt{2} - 1} + 1 =$$

Video Solution

CAT Content

TS ICET 23rd May 2019 Shift-2

If $$t_1$$ is the time elapsed between 9:25 a.m to 2:50 p.m, and if $$t_2$$ is the time elapsed between 10:10 a.m to 5:15 p.m then $$t_1 : t_2 =$$

Six persons P. O, R. S, T and Uare sitting around a roundtable facing the centre of the table. Tis between P and S, R is to the immediate left of U and to the immediate mght of O and O is to the immediate mght of S. Who is sitting between R and S?

If $$\alpha$$ denotes multiplication, $$\beta$$ denotes division, $$\gamma$$ denotes addition and $$\delta$$ denotes subtraction, then, $$6 \delta \left[\left\{(6 \gamma 4)\beta 8\right\}\alpha 2\right] =$$

For any real numbers a and b. if a*b=a+b—ab then(1*2)*(3*4)=

If Z denote the set of integers then the number of elements in the set $$A = \left\{(a,b) : 2a^{2} + 3b^{2} = 25 ;a, b \epsilon Z \right\}$$ is

$$x^{y}=y^{x}\Rightarrow \left(\frac{x}{y}\right)^{\frac{y}{x}} =$$

$$x^{x\sqrt{x} = \left(x\sqrt{x}\right)^x} \Rightarrow x = .............$$

$$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 5 : 7 \Rightarrow a : b : c =$$

If for the natural numbers $$a, b, c, a^{3} + b^{3} + c^{3} = 8072$$ and $$a : b = b : c = 3 : 2$$, then $$a =$$

$$\frac{1}{\sqrt{5} - 1} - \frac{1}{2 - \sqrt{3}} + \frac{1}{\sqrt{3} - \sqrt{2}} - \frac{1}{\sqrt{2} - 1} + 1 =$$

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If $$\alpha$$ denotes multiplication, $$\beta$$ denotes division, $$\gamma$$ denotes addition and $$\delta$$ denotes subtraction, then,
$$6 \delta \left[\left\{(6 \gamma 4)\beta 8\right\}\alpha 2\right] =$$

For any real numbers a and b. if ab=a+b—ab then
(12)(34)=