Integers Test

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Integers Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Simplify:(-6) × (-2) =

A
-8

B
+8

C
-12

D
+12

Solution

-6 ×-2 = + 12
Question 2
1 / -0

Simplify: 1× 0 =

A
1

B
0

C
2

D
10

Solution

The multiplicative identity property states that any timeyou multiply an integer by 1, the result, or product, is that original number.
To write out this property using variables, we can say thatn × 1 = n. It doesn't matter if n equals to one, one million or 3.566879. Theproperty always hold true. Let us take an integer 0 then,
0 × 1 = 1 × 0 = 0
Hence,
1 × 0 = 0.
Question 3
1 / -0

the|−|−7|−3| is equal to

A
-7

B
7

C
10

D
-10

Solution

|−|−7|−3|
=|−7−3|
=|−10|
=10.
Question 4
1 / -0

$G i v e n t h a t, [- 51 \times x] = 204 a n d [- 33 \times y] = - 297, t h e n f i n d t h e v a l u e o f [- x \times y] .$

A
-39

B
33

C
36

D
-36

Solution

Given,−51×x= 204 and −33 × y = −297
Therefore,x= $\frac{204}{51} = - 4$
and y= $\frac{- 297}{- 33} = 9$
$T h u s - x \times y = - (- 4) \times 9 = 36$
Question 5
1 / -0

Thesimplified value of y⁴÷ y of y³÷y²×y⁵÷y³ is

A
2

B
0

C
-1

D
1

Solution

y⁴÷ yofy³ ÷ y² × y⁵ ÷ y³
= y⁴ ÷ y×y³ ÷ y² × y²
= $\frac{y^{4}}{y^{4}} \times \frac{y^{4}}{y^{4}} = 1 \times 1 = 1$
Question 6
1 / -0

8−[12−(−2×−4(4of−4))] =

A
-132

B
132

C
0

D
Noneof these

Solution

8 − [12 − (−2 × −4 (4of−4))]
= 8 − [12− (−2 × −4 × −16)]
= 8 − [12− (−128)]
= 8 − [12 + 128]
= 8 − 140
= − 132
Question 7
1 / -0

Evaluate $\frac{(- 16) \times (- 8) \times (- 81)}{(- 18) \times 32}$

A
-18

B
18

C
16

D
-16

Solution

Given, $\frac{(- 16) \times (- 8) \times (- 81)}{(- 18) \times 32}$
As there are 3 negative numbers in the numerator and 11 inthe denominator, the answer will be positive.
Canceling out the common factors and simplifying we get
$\frac{(- 16) \times (- 8) \times (- 81)}{(- 18) \times 32} = \frac{4 \times 81}{9 \times 2} = 18$
Question 8
1 / -0

Thevalue of
$\frac{0.9 \times 0.9 \times 0.9 + 0.1 \times 0.1 \times 0.1}{0.9 \times 0.9 - 0.9 \times 0.1 + 0.1 \times 0.1}$ on simplificationis

A
0

B
-1

C
2

D
1

Solution

$\begin{aligned} [SOL] \frac{0.9 \times 0.9 \times 0.9 + 0.1 \times 0.1 \times 0.1}{0.9 \times 0.9 - 0.9 \times 0.1 + 0.1 \times 0.1} \\ = \frac{(0.9)^{3} + (0.1)^{3}}{(0.9)^{2} - 0.9 \times 0.1 + (0.1)^{2}} \\ {We know thata}^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) \\ Then \frac{(0.9 + 0.1) [(0.9)^{2} - 0.9 \times 0.1 + (0.1)^{2}]}{(0.9)^{2} - 0.9 \times 0.1 + (0.1)^{2}} \end{aligned}$
=(0.9+0.1)=1
Question 9
1 / -0

Whatis the number to be multiplied by (−7)⁻¹ so as to get 10⁻¹as the product?

A
$\frac{- 7}{10}$

B
$\frac{7}{10}$

C
$\frac{9}{10}$

D
$\frac{- 3}{10}$

Solution

let the number be x According to the question:
⇒ (−7)⁻¹ x = 10⁻¹
⇒ $\frac{1}{- 7} x = \frac{1}{10}$
Applying cross multiplication
$\Rightarrow x = \frac{- 7}{10}$
Question 10
1 / -0

Simplifyto its nearest integer.
199.989 × 5.011 =?

A
1100

B
1250

C
950

D
1000

Solution

199.989 × 5.011 = 1002.144 ≈ 1000
Hence option d is the correct answer.
Question 11
1 / -0

Value of 2²× (−3)²×2²× (−4)²is

A
2034

B
2403

C
2304

D
None of these

Solution

2²×(−3)²×2²×(−4)²
=4×+9×4×16
=2304
Question 12
1 / -0

Thevalue of 357×193 – 357×93 is-

A
555,931

B
1,210,321

C
53,912

D
35,700

Solution

Solvingthe given expression,
357 × 193 − 357 × 93
= 357 × (193 − 93)
= 357 × 100 = 35700
Question 13
1 / -0

IfP³Q < 0 and Q > 0, which of the following must be negative?

A
PQ

B
p₂Q

C
P⁴

D
$- \frac{P}{Q}$

Solution

IfQ is positive P³ must be negative. Therefore, P must be negative. IfQ is positive and P is negative, the product PQ must be negative.
Question 14
1 / -0

If2 × 2 = 8 and 4 × 3=36
Then the value of 3× 7 is ___.

A
84

B
147

C
63

D
23

Solution

We can observe that,
2 × 2 = 4 and 4 × 2 = 8
Similarly,
4 × 3 = 12 and 12 × 3 = 36
Hence,
3 × 7 = 3 × 7 × 7 = 147
Question 15
1 / -0

$\frac{1 \div \frac{2}{3} \times \frac{3}{4}}{1 \div \frac{2}{3} \times \frac{3}{4}}$ onsimplification is

A
$\frac{3}{16}$

B
$\frac{9}{16}$

C
$\frac{1}{16}$

D
$\frac{7}{16}$

Solution

$\begin{aligned} \Rightarrow & [SOL] \frac{1 \div \frac{2}{3} \times \frac{3}{4}}{1 + \div \frac{2}{3} of \frac{4}{3}} \\ \Rightarrow & \frac{1 \div \frac{2}{3} \times \frac{3}{4}}{1 \div \frac{2}{3} \times \frac{4}{3}} \\ \Rightarrow & \frac{1 \times \frac{1}{2}}{1 \times \frac{8}{9}} \\ \Rightarrow & \frac{1 \times 2}{1 \times \frac{8}{9}} \\ \Rightarrow & \frac{\frac{1}{2}}{\frac{2}{9}} = \frac{9}{16} \end{aligned}$

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Re-Attempt Weekly Quiz Competition

Integers Test - 4

Result

Integers Test - 4

Score

-

Rank

-

SHARING IS CARING

Question 1

-8

+8

-12

+12

Solution

Question 2

1

0

2

10

Solution

Question 3

-7

7

10

-10

Solution

Question 4

-39

33

36

-36

Solution

Question 5

2

0

-1

1

Solution

Question 6

-132

132

0

Noneof these

Solution

Question 7

-18

18

16

-16

Solution

Question 8

0

-1

2

1

Solution

Question 9

-710

710

910

-310

Solution

Question 10

1100

1250

950

1000

Solution

Question 11

2034

2403

2304

None of these

Solution

Question 12

555,931

1,210,321

53,912

35,700

Solution

$\frac{- 7}{10}$

$\frac{7}{10}$

$\frac{9}{10}$

$\frac{- 3}{10}$

p₂Q

P⁴

$- \frac{P}{Q}$

$\frac{3}{16}$

$\frac{9}{16}$

$\frac{1}{16}$

$\frac{7}{16}$