5
Q:

# There are 6561 balls are there out of them 1 is heavy. Find the minimum number of times the balls have to be weighted for finding out the heavy ball ?

 A) 2414 B) 204 C) 87 D) 8

Explanation:

Suppose there are 9 balls

Let us give name to each ball B1 B2 B3 B4 B5 B6 B7 B8 B9

Now we will divide all the balls into 3 groups.

Group1 - B1 B2 B3

Group2 - B4 B5 B6

Group3 - B7 B8 B9

Step1 - Now weigh any two groups. Let's assume we choose Group1 on left side of the scale and Group2 on the right side.

So now when we weigh these two groups we can get 3 outcomes.

Weighing scale tilts on left - Group1 has a heavy ball.
Weighing scale tilts on right - Group2 has a heavy ball.
Weighing scale remains balanced - Group3 has a heavy ball.
Lets assume we got the outcome as 3. i.e Group 3 has a heavy ball.

Step2 - Now weigh any two balls from Group3. Lets assume we keep B7 on left side of the scale and B8 on right side.

So now when we weigh these two balls we can get 3 outcomes.

Weighing scale tilts on left - B7 is the heavy ball.
Weighing scale tilts on right - B8 is the heavy ball.
Weighing scale remains balanced - B9 is the heavy ball.
The conclusion we get from this Problem is that each time weigh. We element 2/3 of the balls.

As we came to conclusion that Group3 has the heavy ball from Step1, we remove 6 balls from the equation i.e (2/3) of 9.

Simillarly we do the ame thing for the Step2.

Now going with this conclusion. We have 6561 balls.

Step - 1

Divided into 3 groups

Group1 - 2187Balls

Group2 - 2187Balls

Group3 - 2187Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 2

Divided into 3 groups

Group1 - 729Balls

Group2 - 729Balls

Group3 - 729Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 3

Divided into 3 groups

Group1 - 243Balls

Group2 - 243Balls

Group3 - 243Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 4

Divided into 3 groups

Group1 - 81Balls

Group2 - 81Balls

Group3 - 81Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 5

Divided into 3 groups

Group1 - 27Balls

Group2 - 27Balls

Group3 - 27Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 6

Divided into 3 groups

Group1 - 9Balls

Group2 - 9Balls

Group3 - 9Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 7

Divided into 3 groups

Group1 - 3Balls

Group2 - 3Balls

Group3 - 3Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 8

So now when we weigh 2 balls out of 3 we can get 3 outcomes.

Weighing scale tilts on left - left side placed is the heavy ball.
Weighing scale tilts on right - right side placed is the heavy ball.
Weighing scale remains balanced - remaining ball is the heavy ball.
So the general answer to this question is, it is always multiple of 3 steps.

For 9 balls  $32$= 9. therefore 2 steps

For 6561 balls $38$ = 6561 therefore 8 steps

Q:

What does it mean to calculate frequencies within a dataset?

 A) to calculate the product of two variables to make a third variable B) to count the number of cases that fall into different subgroups within a dataset C) to count the number of times a dataset is used by a student D) to calculate the sum of a column of variables in a dataset

Answer & Explanation Answer: B) to count the number of cases that fall into different subgroups within a dataset

Explanation:

Frequency is what means how many times the event occurs in the same period.

0 55
Q:

Name a pair of complementary angles?

 A) B + C B) A + C C) C + C D) B + A

Explanation:

Complementary angles are those whose sum is 90.

Given here, is a right angled triangle, where anfle C is 90 deg. In this, sum of Angles A + C = 90, since, sum of angles in a right angled triangle = 180, angle C = 90 and

hence sum of A + B = 180 - C = 180 - 90 = 90.

Hence, the pair of cimplementary angles in the given triangle = Angle A + B.

2 160
Q:

Two angles whose sum is 90 are

 A) Supplementary angles B) corresponding angles C) Complimentary angles D) Alternate angles

Explanation:

Complimentary angles are those two angles whose sum is 90 whereas two angles whose sum is 180 are called Supplementary angles.

2 305
Q:

Smallest prime number greater than 200?

 A) 201 B) 205 C) 211 D) 203

Explanation:

From the trial and error method of division,

201 is divisible by 3

205 is divisible by 5

203 is divisible by 7

Hence, after eliminating three options, remained is 211 and is divisible by only 1 and itself.

Therefore, 211 is the smallest prime number greater than 200.

1 306
Q:

Which statement best compares a line and a point?

 A) A point has no dimension and a line has one dimension. B) A line can have line segments on it whereas a point cannot be on any line segment. C) point is a location whereas a line has several planes located on it D) A line can lie on a plane whereas a point cannot lie on a plane.

Answer & Explanation Answer: A) A point has no dimension and a line has one dimension.

Explanation:

A point has no dimension and a line has one dimension is the statement that best compares a line and a point.

1 480
Q:

9 tens 10 ones equals

 A) 910 B) 90 C) 91 D) 100

Explanation:

9 tens 10 ones equals

=> 9 x 10 + 10 x 1

=> 90 + 10

=> 100.

0 441
Q:

What is the value of 28 tens?

 A) 28 B) 2 C) 2800 D) 280

Explanation:

Here asked for the value of 28 tens

=> 28 x 10 = 280.

1 462
Q:

How many right angles does a square have?

 A) 2 B) 6 C) 4 D) 8