AP ICET 2nd May 2018 Shift-2

Let the work capacity of A,B,C be a,b,c units/day respectively. 
Let the amount of work be 120 units

Hence, we can frame the following equations:
a+b = 6
b+c = 4
a+c = 3
Adding up all these 3, we get: a+b+c = 6.5
From this, we can say that a = 2.5

Hence, the time required by A alone to get work done = 120/2.5 = 48 days 

The perimeter of this semicircle is given by 
$$2r+\pi\ r\ =\ 144$$
Solving this equation, we get: r = 28 cm 

Hence, area of the semicircle is = $$\pi\ \frac{r^2}{2}=1232\ sq\ cm$$

Draw a rough figure, write length of sides alongside and draw diagonals BE and BD. 
You can notice that BE is hypotenuse of triangle BAE and hence, BE = 2*(root 2)
Similarly, BD is also the hypotenuse of BCD and BD = 2*(root 2) 

Next, we can see that BDE becomes an equilateral triangle of side 2*(root 2)
Area of the entire pentagon = Area of the 2 right angled triangles BAE and BCD + Area of equilateral triangle BED
= 4 + 2*(root 3) sq units

Let the outer radius of pipe be R and inner radius be r. 

Also, we are given that 2*(22/7)*R = 440 cm ===> R = 70 cm 
Now, Volume of iron used in making the pipe = (22/7)*63*[(70*70)-(66*66)].......(as thickness is given as 4 cm)
Hence, Volume = 1,07,712 cubic cm

Area of a closed hemisphere = $$3\pi\ r^2$$ 

$$3\pi\ r^2$$ = 16632
r = 42 cm 

Now, Volume of the hemisphere = $$\frac{2}{3}\pi\ r^3$$

Volume = $$\frac{2}{3}\cdot\frac{22}{7}\ \cdot42^3$$ $$=\frac{2}{3}\cdot\frac{22}{7}\ \cdot42^3\ =\ 88\cdot42^2$$

Given, diagonal length of the square = 90 m

Side of the square = $$\frac{90}{\sqrt{2}}$$ m

Area of the square = $$\left(\frac{90}{\sqrt{2}}\right)^2$$ = 90 x 45 m$$^2$$

Area of rectangle = Area of square

$$\Rightarrow$$ l x 50 = 90 x 45

$$\Rightarrow$$  l = 81 m

Hence, the correct answer is Option D

Perimeter of the rectangular = 2(300+200) = 2 x 500 = 1000 m

Distance walked in 10 mins = 1000 m

Hence, Distance walked in 60 mins = 1000 x 6 = 6000 m = 6km

$$\therefore\ $$Speed of the person = 6kmph

Radius of the circular wheel = 14 cm

Circumference of the circular wheel = $$2\times\pi\times14$$ = $$2\times\frac{22}{7}\times14$$ = 88 cm

$$\therefore\ $$The number of revolutions required to cover a distance of 105.6 m = $$\frac{\text{Distance}}{\text{Circumference of the wheel}}$$

$$=\frac{105.6\times100}{88}$$

$$=120$$

Hence, the correct answer is Option A

We need a three digit number which is of the form 3x + 2 and when this number is divided by 13, the remainder must be 4.
The largest 3 digit number of this form can be when x = 332 and the number comes out to be 998. When divided by 13, the remainder is not 4.
The next can be when x = 331 which makes the number as 995. When divided by by 13, remainder is not 4. 
The next can be x = 330 which makes the number as 992. When divided by by 13, remainder is 4. 

Hence, answer is 992. 
Another approach can be directly taking options from largest to smallest and actually dividing by 13 to arrive at the answer.

Given,  $$a * b = a^2 + ab - b^2$$

$$4 * x = 6$$

$$\Rightarrow$$  $$4^2+4x-x^2=6$$

$$\Rightarrow$$  $$16+4x-x^2=6$$

$$\Rightarrow$$  $$x^2-4x-10=0$$

$$\Rightarrow$$  $$x^2-4x+4-14=0$$

$$\Rightarrow$$  $$\left(x-2\right)^2-14=0$$

$$\Rightarrow$$  $$\left(x-2\right)^2=14$$

Hence, the correct answer is Option C