Mix Test

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Mix Test - 3

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Weekly Quiz Competition

Question 1
1 / -0.25

Add: ab - bc, bc - ca, ca - ab

A
2bc

B
2ac

C
2ab

D
0

Solution

(ab - bc) + (bc - ca) + (ca - ab)
opening brackets we get,
ab - bc + bc - ca + ca - ab
solving like terms we get,
ab - ab - bc + bc - ca + ca
0 + 0 + 0 = 0
Question 2
1 / -0.25

A train can finish a journey in 10 hours, travelling at a speed of 56 km/h. If another faster train is to cover the same journey in 8 hours, what would be the average speed of the new train?

A
60 km/h

B
80 km/h

C
70 km/h

D
50 km/h

Solution

Speed and time are inversely related so with a decrease in time duration the speed has to increase to complete the journey.

In inverse proportion, the value of constant is given by x × y

10 × 56 = 8 × a (where a is the average speed of the train)

560/8 = a

70 km / hr = a
Question 3
1 / -0.25

Find the median of the data set, which shows the heights (in inches) of 10 students in Mr. Brajesh's class.

67, 62, 66, 63, 68, 69, 69, 69, 64 and 79

A
75

B
69

C
67.5

D
72

Solution

If we put serially all the numbers from 62 to 79 i.e. 62, 63, 64, 66, 67, 68, 69, 69, 79 so the middle number is in between 67 and 68, i.e.67.5 is the median
Question 4
1 / -0.25

The sum of x⁴ - xy + 2y² and -x⁴ + xy + 2y² is

A
Trinomial and polynomial

B
Monomial and polynomial in y

C
Binomial and Polynomial

D
Monomial and polynomial in x

Solution

Required sum = (x⁴ - xy + 2y²) + (- x⁴ + xy + 2y²)
= x⁴ - xy + 2y² - x⁴ + xy + 2y²
= [(x⁴ + (- x⁴))] + (-xy + xy) + (2y² + 2y²)
= 0 + 0 + 4y² = 4y²
4y² is a monomial and polynomial in y.
Question 5
1 / -0.25

If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

A
4

B
8

C
6

D
None of these

Solution

This is a question of inverse proportion as with the decrease in the number of children the number of sweets each student gets will increase

In inverse proportion, the constant value is given by x × y

24 × 5 = (24 - 4) × a (where a is the number of sweets each student gets)

120 = 20a

120/20 = a

6 sweets = a
Question 6
1 / -0.25

If 16 × 9 = 12 × m, the value of m is

A
9

B
16

C
13

D
None of these

Solution

16 × 9 = 12 × m
16 × 9/12 = m
144/12 = m
12 = m. So the answer is 12
Question 7
1 / -0.25

There are 2 Red, 3 Blue and 5 Black balls in a bag. A ball is drawn from the bag without looking into the bag. What is the probability of getting a non-blue ball?

A
3/5

B
7/10

C
2/5

D
None of these

Solution

Total number of balls = 10

Probability (of getting non-blue ball) = 1 - Probability of blue ball

= 1 - 3/10 = 7/10
Question 8
1 / -0.25

If a box of toffees is divided among 24 children, they will get 5 toffees each. How many toffees will each get if the number of children is reduced by 4?

A
6

B
8

C
10

D
12

Solution

This is a case of inverse proportion as with a decrease in the number of children the number of toffees each child gets will increase

In inverse proportion, the value of constant is given by x × y

24 × 5 = (24 - 4) × a ( where a is the number of toffees each child gets)

120 = 20a

120/20 = a

6 toffees = a
Question 9
1 / -0.25

Find the volume of a box, which is in the form of a rectangular prism, with a length of 6 in., a height of 3 in. and width of 5 in.

A
90 in³

B
80 in³

C
95 in³

D
100 in³

Solution

length = 6 in. , breadth = 5 in., height = 3 in.

Volume of a box = length × breadth × height

v = 6 × 5 × 3 = 90 in³

volume of a box is 90 in.³
Question 10
1 / -0.25

Which quantities in the previous question vary inversely with each other?

A
r and s

B
x and y

C
u and v

D
p and q

Solution

p 1² 2² 3² 4²

q 1³ 2³ 3³ 4³

If we multiply p and q with 1,2,3 and 4, we get the given result. But it is not given inversely.

r 2 5 10 25 50

s 25 10 5 2 0.5

If we multiply r. with 2.5 and s with 2.5, we will get the given result.

u 2 4 6 9 12

v 18 9 6 4 3

If u = 2, then v = 18
If u = 4, then v = 9
If u = 6, then v = 6
If u = 9, then v = 4
and if u = 12, then v = 3
It show, when u increases, then v decreases.

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p	1²	2²	3²	4²
q	1³	2³	3³	4³

r	2	5	10	25	50
s	25	10	5	2	0.5

Mix Test - 3

Result

Mix Test - 3

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Rank

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SHARING IS CARING

Question 1

2bc

2ac

2ab

0

Solution

Question 2

60 km/h

80 km/h

70 km/h

50 km/h

Solution

Question 3

75

69

67.5

72

Solution

Question 4

Trinomial and polynomial

Monomial and polynomial in y

Binomial and Polynomial

Monomial and polynomial in x

Solution

Question 5

4

8

6

None of these

Solution

Question 6

9

16

13

None of these

Solution

Question 7

3/5

7/10

2/5

None of these

Solution

Question 8

6

8

10

12

Solution

Question 9

90 in3

80 in3

95 in3

100 in3

Solution

Question 10

r and s

x and y

u and v

p and q

Solution

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90 in³

80 in³

95 in³

100 in³