Mix Test

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Mix Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If $a _{1} x + b _{1} y + c _{1}=0$ and $a _{2} x + b _{2} y + c _{2}=0$ have infinite number of solutions, then which one of the following is correct:

A
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

B
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

C
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

D
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Solution

If both equation $a _{1} x + b _{1} y + c _{1}=0$ and $a _{2} x + b _{2} y + c _{2}=0$ have the infinite solution, then the graph will be the pair of coincidents line, and the relation between the coefficient of both the equation is
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Hence, the correct option is (D).

Question 2

1 / -0

Directions For Questions

Direction: The table shows the number of national parks and wild life sanctuaries in different states. Study the table carefully and answer the following questions.

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7

...view full instructions

What is the ratio of National parks to Wild life sanctuaries?

41 ∶ 221

42 ∶ 223

41 ∶ 223

42 ∶ 221

Solution

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7
	Total = 42	Total = 221

∴ Required Ratio = 42 ∶ 221

Hence, the correct option is (D).

Question 3

1 / -0

Directions For Questions

Direction: The table shows the number of national parks and wild life sanctuaries in different states. Study the table carefully and answer the following questions.

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7

...view full instructions

The number of wild life sanctuaries in Maharashtra is how much percent more than the number of wild life sanctuaries in Himachal Pradesh?

40%

45%

50%

55%

Solution

Wild life sanctuaries in Maharashtra = 42

Wild life sanctuaries in Himachal Pradesh = 28

∴ Required percentage = $\frac{14}{28}$ × 100 = 50%

Hence, the correct option is (C).

Question 4

1 / -0

Directions For Questions

Direction: The table shows the number of national parks and wild life sanctuaries in different states. Study the table carefully and answer the following questions.

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7

...view full instructions

What is the average of all the national parks together?

5

7

6

4 Solution

State	National Parks
Madhya Pradesh	10
Himachal Pradesh	5
Gujarat	4
Maharashtra	6
Andaman and Nicobar	10
Uttarakhand	7
	Total = 42

∴ Required average = $\frac{42}{6}$ = 7

Hence, the correct option is (B).

Question 5

1 / -0

Directions For Questions

Direction: The table shows the number of national parks and wild life sanctuaries in different states. Study the table carefully and answer the following questions.

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7

...view full instructions

What is the total number of wild life sanctuaries in all the states together?

220

219

221

222 Solution

State	Wild life Sanctuaries
Madhya Pradesh	25
Himachal Pradesh	28
Gujarat	23
Maharashtra	42
Andaman and Nicobar	96
Uttarakhand	7
	Total = 221

∴ All states together has total 221 wild life sanctuaries.

Hence, the correct option is (C).

Question 6

1 / -0

Directions For Questions

Direction: The table shows the number of national parks and wild life sanctuaries in different states. Study the table carefully and answer the following questions.

State	National Parks	Wild life Sanctuaries
Madhya Pradesh	10	25
Himachal Pradesh	5	28
Gujarat	4	23
Maharashtra	6	42
Andaman and Nicobar	10	96
Uttarakhand	7	7

...view full instructions

Which state has least number of national parks?

Gujarat

Himachal Pradesh

Maharashtra

Uttarakhand

Solution

State	National Parks
Madhya Pradesh	10
Himachal Pradesh	5
Gujarat	4
Maharashtra	6
Andaman and Nicobar	10
Uttarakhand	7

∴ Gujarat has least number of National parks.

Hence, the correct option is (A).

Question 7
1 / -0

If $20 \%$ of $n$ is equal to $40$ , what is the value of $n$?

A
$200$

B
$2000$

C
$800$

D
$80$

Solution

Given,
$20 \% \text { of } n=40 $
$\Rightarrow \frac{20}{100} \times n=40 $
$\Rightarrow n=\frac{40 \times 100}{20} $
$\Rightarrow n=2 \times 100 $
$\Rightarrow n=200$
So, the value of $n$ is $200$.
Hence, the correct option is (A).
Question 8
1 / -0

Mr. Mike borrowed Rs. $8500$ at $4 \%$ per annum compound interest. The compound interest compounded annually for $2$ years is:

A
Rs. $9193.6$

B
Rs. $639.6$

C
Rs. $693.6$

D
Rs. $9139.6$

Solution

Given,
Principal $(P)=$ Rs. $8500$
Rate of interest $(r)=4 \%$
Time $(n)=2$ years
As we know,
Compound interest $=P\left(1+\frac{r}{100}\right)^{n}-P$
$\therefore$ Compound interest $=8500\left(1+\frac{4}{100}\right)^{2}-8500$
$=8500 \times \left(\frac{104}{100}\right)^{2}-8500$
$=8500 \times \left(\frac{26}{25}\right)^{2}-8500$
$= 8500 \times \frac{676}{625}-8500$
$= 8500\times \left(\frac{676}{625}-1\right)$
$= 8500\times \left(\frac{676-625}{625}\right)$
$= 8500\times \frac{51}{625}$
$=$ Rs. $693.6$
Hence, the correct option is (C).
Question 9
1 / -0

Which of the numbers given below is the square root of 16384?

A
132

B
128

C
118

D
122

Solution

The given number can be factored as shown below:
16384 = 2×2×2×2×2×2×2×2×2×2×2×2×2×2
The square root of 16384 = 2×2×2×2×2×2×2 =128.
Hence, the correct option is (B).
Question 10
1 / -0

Find the number of prime factor of 540.

A
2

B
4

C
6

D
8

Solution

Given:
The number = 540
Factorization = 2 × 270
⇒ 2 × 3 × 90
⇒ 2 × 3 × 2 × 45
⇒ 2 × 3 × 2 × 3 × 15
⇒ 2 × 3 × 2 × 3 × 3 × 5
⇒ 2² × 3³ × 5¹
Number of prime factors of N = p + q + r
Here, p = 2, q = 3 and r = 1
Number of prime factors of N = 2 + 3 + 1 = 6
∴ The number of prime factors of 540 is 6.
Hence, the correct option is (C).

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Re-Attempt Weekly Quiz Competition

Mix Test - 4

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Mix Test - 4

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SHARING IS CARING

Question 1

\(\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\)

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\)

\(\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

Solution

Question 2

41 ∶ 221

42 ∶ 223

41 ∶ 223

42 ∶ 221

Solution

Question 3

40%

45%

50%

55%

Solution

Question 4

5

7

6

4

Solution

Question 5

220

219

221

222

Solution

Question 6

Gujarat

Himachal Pradesh

Maharashtra

Uttarakhand

Solution

Question 7

\(200\)

\(2000\)

\(800\)

\(80\)

Solution

Question 8

Rs. \(9193.6\)

Rs. \(639.6\)

Rs. \(693.6\)

Rs. \(9139.6\)

Solution

Question 9

132

128

118

122

Solution

Question 10

2

4

6

8

Solution

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