AIEEE Questions

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The quadratic equation whose roots are reciprocal of 2x2+5x+3=0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)(1/x)+ 5(1/x) + 3 = 0

=> 3x2+5x+2=0

Let the cost price of a ball is Rs.x
Given, on selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls
The equation is :
17x - 720 = 5x
Solving the equation
we get x = 60
Therefore, cost price of a ball is Rs. 60.

Sumo wrestling is the Japan origin game in which the two heavy weight wrestlers fight in a marked circle to throw the opponent out of the circle to win the game. And the two participants in the game are called Sumos.

Hence, sumo wrestling is the national sport of Japan.

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

2 x 28p + q = 28p - q

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

$$\begin{gathered} 283q + 2q + 283q - 2q = 67260 \\ => 285q + 28q = 67260 \\ => q = 3 kmph \\ => x =3q = 9 kmph \end{gathered}$$

Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.

The given number series is 8, 11, 19, 23, 32, ?

It follows a pattern that

8 + 11 = 19

11 + 12 = 23

19 + 13 = 32

23 + 14 = 37

32 + 15 = 47

....

Hence, the next number in the given series = 37.

Let sum = S. Then, amount = 7S/6

S.I. = 7S/6 - S = S/6; Time = 3 years.

Rate = (100 x S) / (S x 6 x 3) = 5 5/9 = 50/9 %.