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Mixed Test (Maths)

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Let the transportation cost of red, blue, yellow and green toys be Rs. 15, Rs. 20, Rs. 25 and Rs. 30, respectively. Then, the difference between the total cost of transportation of all the toys and the cost of transportation of green toys is

Directions: Read the following passage and answer the given question.

Let there be four colours of toys in a shop, i.e. red, green, blue and yellow. There are 101 toys of red colour. The number of blue toys is 4 less than the number of green toys. The number of yellow toys is 3 more than the number of red toys and the number of green toys is 10 less than the number yellow toys. Now, let k, l, m and n be the numbers of red, blue, yellow and green toys, respectively.

  1. Rs. 5915

  2. Rs. 7325

  3. Rs. 6855

  4. Rs. 6385

  5. None of these


Correct Option: A
Explanation:

No. of red toys = 101 No. of yellow toys = 101 + 3 = 104  No. of green toys = 104 - 10 = 94  No. of blue toys = 94 - 4 = 90 Total transportation cost of all the toys = Rs. (101 x 15 + 90 x 20 + 104 x 25 + 94 x 30) = Rs. (1515 + 1800 + 2600 + 2820) = Rs. 8735 Total cost of transportation of green toys = Rs. (30 x 94) = Rs. 2820 Therefore, required difference in the cost = Rs. (8735 - 2820) = Rs. 5915

In the equation 2m + k = n, what is the value of m?

Directions: Read the following passage and answer the given question.

Let there be four colours of toys in a shop, i.e. red, green, blue and yellow. There are 101 toys of red colour. The number of blue toys is 4 less than the number of green toys. The number of yellow toys is 3 more than the number of red toys and the number of green toys is 10 less than the number yellow toys. Now, let k, l, m and n be the numbers of red, blue, yellow and green toys, respectively.

  1. 2

  2. 2/7

  3. -7/2

  4. 7/2

  5. None of these


Correct Option: D
Explanation:

No. of red toys = 101 = k No. of yellow toys = 101 + 3 = 104 = m No. of green toys = 104 - 10 = 94 = n No. of blue toys = 94 - 4 = 90 = l Therefore, 2m + 101 = 94 2m = 7 m = 7/2

The value of k + l is

Directions: Read the following passage and answer the given question.

Let there be four colours of toys in a shop, i.e. red, green, blue and yellow. There are 101 toys of red colour. The number of blue toys is 4 less than the number of green toys. The number of yellow toys is 3 more than the number of red toys and the number of green toys is 10 less than the number yellow toys. Now, let k, l, m and n be the numbers of red, blue, yellow and green toys, respectively.

  1. 191

  2. 199

  3. 185

  4. 190

  5. None of these


Correct Option: A
Explanation:

No. of red toys = 101 = k No. of yellow toys = 101 + 3 = 104 = m No. of green toys = 104 - 10 = 94 = n No. of blue toys = 94 - 4 = 90 = l Therefore, k + l = 101 + 90 = 191

The value of [k - {l - m} - (-n + 2k)] is

Directions: Read the following passage and answer the given question.

Let there be four colours of toys in a shop, i.e. red, green, blue and yellow. There are 101 toys of red colour. The number of blue toys is 4 less than the number of green toys. The number of yellow toys is 3 more than the number of red toys and the number of green toys is 10 less than the number yellow toys. Now, let k, l, m and n be the numbers of red, blue, yellow and green toys, respectively.

  1. -21

  2. 7

  3. 201

  4. -201

  5. None of these


Correct Option: B
Explanation:

No. of red toys = 101 = k No. of yellow toys = 101 + 3 = 104 = m No. of green toys = 104 - 10 = 94 = n No. of blue toys = 94 - 4 = 90 = l [k - {l + m} - (-n + 2k)] = [101 - {90 - 104} - (-94 + 202)] = [101 - {-14} - 108] = [101 + 14 - 108] = 7

The value of (k + l)2 + (m - n)2 is.

Directions: Read the following passage and answer the given question.

Let there be four colours of toys in a shop, i.e. red, green, blue and yellow. There are 101 toys of red colour. The number of blue toys is 4 less than the number of green toys. The number of yellow toys is 3 more than the number of red toys and the number of green toys is 10 less than the number yellow toys. Now, let k, l, m and n be the numbers of red, blue, yellow and green toys, respectively.

  1. 39701

  2. 42125

  3. 36581

  4. 75685

  5. None of these


Correct Option: C
Explanation:

No. of red toys = 101 = k No. of yellow toys = 101 + 3 = 104 = m No. of green toys = 104 - 10 = 94 = n No. of blue toys = 94 - 4 = 90 = l Therefore, the value of (k + l)2 + (m - n)2 = (101 + 90)(101 + 90) + (104 - 94)(104 - 94) = 191 x 191 + 10 x 10 = 36481 + 100 = 36581

Solve for x:

2x - 3 = 4x + 2

  1. 5/2

  2. -5/2

  3. -2/5

  4. 2/5

  5. None of these


Correct Option: B
Explanation:

2x - 3 = 4x + 2 Or 2x - 4x = 2 + 3 Or -2x = 5 Or x = -5/2

If 2x + 3 = 4, then the value of (4x + 2) will be

  1. 0

  2. 2

  3. 4

  4. -6

  5. None of these


Correct Option: C
Explanation:

2x + 3 = 4 Or 2x = 1 Or 4x = 2 Therefore, 4x + 2 = 4

What is the value of (2k + 3l) if 2k(I + 2) = 4 and I + 4 = 2I + 2?

  1. 7

  2. 1/2

  3. 8

  4. 13/2

  5. None of these


Correct Option: A
Explanation:

Given: I + 4 = 2I + 2 Or 2I - I = 4 - 2 Or I = 2 Now, 2k x 4 = 4 Or 2k = 1 Or k = 1/2 Therefore, 2k + 3I = 1 + 6 = 7

Which of the following is a perfect square?

  1. 23252

  2. 23523

  3. 23527

  4. 23528

  5. 48841


Correct Option: E
Explanation:

48841 = 221 x 221

Deepali has to travel a distance of 300 km. She walked for 2 hours at speed of 60.2 km/hr and the next 3 hours at 35.3 km/hr. How much distance does she still need to walk to complete the whole journey?

  1. 74.1 km

  2. 73.1 km

  3. 74.7 km

  4. 73.7 km

  5. None of these


Correct Option: D
Explanation:

Total distance to be covered = 300 km Total distance covered in 2 hours = (60.2 x 2) km = 120.4 km Total distance covered in next 3 hours = (35.3 x 3) km = 105.9 km Total distance covered in 5 hours = (120.4 + 105.9) km = 226.3 km Remaining distance to be covered = (300 - 226.3) km = 73.7 km

Solve for j if 3j + k = 2, k + 3m = 6 and 3m = 6m - 9.

  1. -1/3

  2. 5/3

  3. -13/3

  4. 3/5

  5. None of these


Correct Option: B
Explanation:

6m - 9 = 3m Or 3m = 9 Or m = 3 Now, k + 9 = 6 Or k = -3 Also, 3j + k = 2 Or 3j = 5 Or j = 5/3

Let k be a number which is 2 more than 3 times the even prime number and l be a number which 2 less than 4 times the first odd prime number. Then, the value of (k + l)(k + 2)(l - 3) will be

  1. 588

  2. 1260

  3. 1980

  4. 180

  5. None of these


Correct Option: B
Explanation:

k = 3 x 2 + 2 = 8 and l = 4 x 3 - 2 = 10 Therefore, (8 + 10)(8 + 2)(10 - 3) = 18 x 10 x 7 = 1260

Which of the following expressions is/are monomial(s)?

  1. 3xy + 2

  2. x

  3. xz + c + 2

  4. x2

  5. Both (2) and (4)


Correct Option: E
Explanation:

This is the correct answer.

Which of the following is a binomial expression?

  1. zx + 2

  2. xz + 2 + j

  3. xz

  4. z

  5. None of these


Correct Option: A
Explanation:

It is a binomial expression.

What is the value of 301 x 101 + 10 x 215 when rounded off to the nearest ten?

  1. 32560

  2. 32550

  3. 32551

  4. 33000

  5. None of these


Correct Option: B
Explanation:

301 x 101 + 10 x 215 = 30401 + 2150 = 32551 Therefore, when rounded off to the nearest ten, it becomes 32550.

What is the value of (201 x 25) + (51 x 13) when rounded off to the nearest hundred?

  1. 5680

  2. 5688

  3. 5700

  4. 5690

  5. None of these


Correct Option: C
Explanation:

201 x 25 + 51 x 13 = 5025 + 663 = 5688 When rounded off to the nearest hundred, it becomes 5700.

Which of the following expressions is/are correct with respect to commutative law?

  1. 2564 x 26485 = 26485 x 2564

  2. 256487/7 = 7/256487

  3. 25635 + 2654 = 2654 + 25635

  4. Both (1) and (3)

  5. None of these


Correct Option: D
Explanation:

Options 1 and 3 both are correct. Hence, it is the most appropriate option.

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