AP ICET 26th April 2019 Shift-1

5 men in 6 days in 6 hours per day$$=5\times 6\times 6=180$$hours

Therefore, 180 hours will be taken to produce 10 toys 

Therefore 1 toy$$=\dfrac {180}{10}=18$$hours

16 toys can be prepare in$$=16\times 18=288$$hours

When,12 men prepare 16 toys$$=\dfrac {288}{12}=24$$hours per day

Then by working 8 hours per day it will be$$=\dfrac {24}{8}=3$$days

Therefore in 3 days 12 men can prepare 16  toys for working 8 hours a day.

Let a is the length of the side of the equilateral triangle.

We know that the area of the equilateral triangle $$=\dfrac{\sqrt{3}a^2}{4}$$

So, $$\dfrac{\sqrt{3}a^2}{4}=4\sqrt3$$

$$a^2=4\times 4 $$

$$a=4$$

Hence, perimeter of the triangle $$=3a=12$$cm

As per given in the question,

Let,the length be $$7x$$ and breadth be $$5x$$

We know that the area of the rectangle $$=length\times breadth$$

So, $$3500=7x\times 5x$$

$$\Rightarrow 3500=35\times x^2$$

$$x=10$$cm

We know that the perimeter of the rectangle $$ =2(length+breadth)$$

hence, perimeter $$=2(7x+5x)$$

$$\Rightarrow 2\times 12x$$

$$\Rightarrow 24\times 10=240$$

therefore,the perimeter of the rectangle is 240 cm

given,

surface area of cube$$=6\times a^2$$

according to the given condition,

$$6\times a^2$$=726

$$a^2$$=$$\frac{726}{6}$$

a=11

hence,volume of cube will be=$$a^3$$

=$$11^3$$

=1331 cubic cm

Therefore the volume of the cube is 1331 cubic cm

given,

radius of sphere=10 cm

volume of each spherical ball=$$\frac{volume of sphere}{8}$$

$$\frac{4\times \pi\times r^3}{3}$$=$$\frac{1}{8}$$ $$\frac{4\times \pi\times 10^3}{3}$$

$$r^3$$=$$\frac{1000}{8}$$

$$r^3$$=$$\frac{10^3}{2^3}$$

r=$$\frac{10}{2}$$

r=5

surface area of each ball=$$4\times \pi\times r^2$$

=$$4\times \pi\times 5^2$$

=$$4\times 25\times \pi$$

=$$100\pi$$

Let, Length be l, breadth be  b

As per the condition given in the question,

$$b = l \times \dfrac{3}{4}$$

$$\Rightarrow 4b = 3l or 3l-4b = 0 ---------(i) $$ 

$$\Rightarrow  2(l+b) = 1050$$

$$\Rightarrow l+b = 525$$

$$\Rightarrow  l = 525 - b ------- (ii) $$ 

Put the value of "l' from equation (ii) in the equation (i)

$$ \Rightarrow 3(525 - b) - 4b = 0$$

$$ \Rightarrow 1575-3b-4b = 0$$

$$ \Rightarrow 1575 = 76$$

$$ \Rightarrow b = 225m ------(iii)$$

Put the value of b from equation (iii) in the equation (ii)

$$ l = (525-b)$$

$$ l = (525-225)$$

$$ l = 300m$$ ------------(iv)

Area of plot in square metres will be = l \times b 

Put the value of l and b from equation (iii) and (iv)

$$A = 300 \times 225$$

$$A = 67,500$$

Therefore, area of the plot is square metre is 67500 metres

Let, the hight of triangular field be = h

  Then base = 3x 

Now cost per hectare 73.44 is Rs 991.44

So, area of field = $$ \dfrac{991.44}{73.44}$$

$$ \Rightarrow 13.5$$

we know that area of triangle = $$ \dfrac{1}{2} \times b \times h$$

Then,

$$ \Rightarrow \dfrac{1}{2} \times 3h \times h = 13.5$$

$$ \Rightarrow 3h^2 = 27$$

$$ \Rightarrow h^2 = \dfrac{27}{3}$$

$$ \Rightarrow h^2 = 9$$

$$ \Rightarrow h = 3$$

In meters it will be   

   $$ \Rightarrow (h \times 100)m$$

  $$ \Rightarrow (3 \times 100)m $$ 

   $$ \Rightarrow 300m$$                            

As per given question,

volume of cuboid=72 cu. mts

Let the length of the cuboid be$$=x$$

breadth$$=\dfrac{2}{3}\times x$$

then height$$=\dfrac{3}{4}\times \dfrac{2}{3}\times x$$

as we know volume of cuboid$$= length \times breadth \times height$$

$$\Rightarrow x\times \dfrac{2}{3}\times x \dfrac{1}{2} \times x$$

$$\dfrac{1}{3}\times x^3=72$$

$$x^3=216$$

x=6

then length=6

breadth$$=\dfrac{2}{3}\times 6=4$$

height$$=\dfrac{3}{4}\times \dfrac{2}{3} \times 6=3 $$

as we know suface area of cuboid$$=2(lb+bh+hl)$$

surface area$$=2(6\times 4+4\times 3+3\times 6) $$

surface area= 108 sq.mts