# Practice Questions & Answers :: AMCAT

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**AMCAT**

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1. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

**Answer:**** Option D **

**Explanation:**

(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)

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2. The two trains of lengths 400m, 600m respectively, running at same directions. The faster train can Cross the slower train in 180sec, the speed of the slower train is 48km. then find the speed of the Faster train?

**Answer:**** Option D **

**Explanation:**

Length of the two trains = 600m + 400m = 1000m

Let's Assume Speed of the first train = x kmph

Speed of the second train= 48 Kmph

So Relative Speed = (x - 48) kmph =((x -48) * 5/18) m/sec

1000/((x -48) * 5/18) = 180

18000/(5x - 240) = 180

100 = 5X - 240

=> 5x = 340 => x = 68 kmph

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3. (0.1*0.1*0.1 + 0.02*0.02*0.02)/(0.2*0.2*0.2 + 0.04*0.04*0.04) is equal to

**Answer:**** Option A **

**Explanation:**

Lets assume 0.1 as a so 0.2 will be 2a

and 0.02 as b so 0.04 will be 2b

Simplify the give equation

(a*a*a + b*b*b)/(2a*2a*2a+2b*2b*2b) => (a^3+b^3)/(8*a^3+8*b^3)

=> (a^3+^3)/8(a^c+b^3) = 1/8 = 0.125

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4. If (a^2 + b^2 + 1/a^2 + 1/b^2) = 4, then the value of (a^2 + b^2) will be

**Answer:**** Option B **

**Explanation:**

Given (a^2 + b^2 + 1/a^2 + 1/b^2) = 4

Simplify the above eq.

=> a^2 + 1/a^2 +b^2 + 1/b^2 = 4

=> (a-1/a)^2 + 2 + (b - 1/b)^2 + 2 = 4

=> (a-1/a)^2 + (b - 1/b)^2 = 0

=> (a - 1/a) = 0; (b - 1/b) = 0

=> a = b = (+-)1

so (a^2+b^2) = 1+1 = 2

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5. if (2x + 2/x) = 1, then the value of (x^3 + 1/x^3) is

**Answer:**** Option C **

**Explanation:**

(2x + 2/x) = 1

=> (x + 1/x) = 1/2

(x^3+1/x^3) = (x+1/x)^3-3x*1/x(x+1/x)

= (1/2)^3-1/2 = (1/8 - 3/2) = (1-12)/8= -11/8

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6. If A:B = 2:3, B:C = 4:5 and C:D = 5:9,then A:D is equal to

**Answer:**** Option B **

**Explanation:**

A/B*B/C*C/D= 2/3*4/5*5/9

=> A/D = 8/27

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7. Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack.

Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then

**Answer:**** Option D **

**Explanation:**

Here is no explanation for this answer

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8. A scooterist covers a certain distance at 36 kmph. How many meters does he cover in 2 min?

**Answer:**** Option D **

**Explanation:**

Speed = 36 kmph = 36 * 5/18 = 10mps

So, Distance covered in 2 min = (10 * 2 * 60)m = 1200 meters.

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9. For what values of 'm' is y = 0, if y = x^2 + (2m + 1)x + m^2 - 1? x is a real number.

**Answer:**** Option D **

**Explanation:**

Here is no explanation for this answer

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10. First day of 1999 is sunday what day is the last day

**Answer:**** Option B **

**Explanation:**

Here is no explanation for this answer

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