Mathematics (Paper-1) Mock Test - 5

For 12142c to be divisible by 3, (1 + 2 + 1 + 4 + 2 + c) must be a multiple of 3.
⇒ 10 + c = 12 or 15 or 18
∴ 'c' can be 2, 5 or 8.

5/7 x = 4/8 y
⇒  x/y = 28/40 = 7/10
x : y = 7 : 10

Assume present age of A = 3p years
And, present age of B = 4p years
Now, according to the question,
(3p + 20)/(4p + 20) = 7/8
Or, 8(3p + 20) = 7(4p + 20)
Or, 24p + 160 = 28p + 140
Or, 4p = 20
Or, p = 5
So, present age of A = 3p = 15 years

Number of Nestle chocolates = 5
Number of Dairy Milk chocolates = 18
Total number of chocolates = 18 + 5 = 23
Probability that a picked up chocolate is Nestle = 5/23

Factors of 48 are = 2 × 2 × 2 × 2 × 3
Since '3' is not in pair
So, divide by 3

3600 = 2 × 3 × 2 × 5 × 2 × 3 × 2 × 5
Pairing up, we get
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
So, to obtain a perfect cube, we need to multiply 3600 by 2 × 2 × 3 × 5 = 60.

Marked price of the bag = Rs. 5200
Discount = 15%
∴ Discount price = Rs. 15/100 × 5200
= Rs. 780
Selling price of the bag = Rs. (5200 – 780)
= Rs. 4420

It is an inverse proportion.
∴ 30 × 15 = 25 × d (where 'd' is the required number of days)
d = 30×15 / 25 = 18 days

2 hours = 2 × 60 = 120 min
30 km is covered in 15 min.
Distance covered in 2 hours = 30×120 / 15  = 240 km

37933056 = 4096 × 9261
Cube root of 37933056 = (Cube root of 4096) × (Cube root of 9261)
= 16 × 21
= 336

Let the side of the new cube be S.
According to the question,
Total volume of all the cubes = Volume of the new cube
11³ + 12³ + 13³ + 14³ = S³
1331 + 1728 + 2197 + 2744 = 8000 cm³ = S³
S = 20 cm

The two given angles are 58° and 62°.
Let the two unknown angles be 4x and 11x.
58° + 62° + 4x + 11x = 360­° (Sum of four angles of a quadrilateral)
15x + 120° = 360°
15x = 240°
x = 16°
The unknown angles are 4x and 11x.
i.e. 4 × 16° = 64° and 11 × 16° = 176°
Or 64° and 176°

Let the lengths of parallel sides be 3x and 5x.
Now, according to given information:
Area of trapezium = 384 cm²
1/2 (3x + 5y) × 12 = 384
8x = 384/6
x = 8
Lengths of parallel sides of trapezium = 3x and 5x = 3(8) and 5(8)
= 24 cm and 40 cm
So, length of the smaller side is 24 cm.

29645 = 5 × 7 × 7 × 11 × 11
Since 5 is not in pair so we multiply the number with 5 to get a perfect square.
∴ Number = 29645 × 5 = 148225

√2025 = 45
√1521 = 39
Sum = 45 + 39 = 84

49^1.5 : 9^2.5
= (7)^2 × 1.5 : (3)^{2 × 2.5}
= (7)³ : (3)⁵
= 343 : 243

Let the digit at the units place be x.
So, digit at the tens place = (15 - x)
Original number = 10(15 - x) + x
= 150 - 10x + x
= 150 - 9x

Now, after interchanging the digits, the number will become:
10x + 15 - x = 9x + 15

According to the question,
150 - 9x + 27 = 9x + 15
162 = 18x
x = 9

So, original number = 150 - 9x
= 150 - 9 × 9
= 150 - 81
= 69

Area of four walls of a room = 2(l + b) h = 168
⇒ 2(l + 6) 6 = 168
⇒ l + 6 = 14
⇒ l = 8 m

Let the number of sides be n.
Then,
72n = 360°
n = 360/72 = 5

Use identity (a + b)² = a² + 2ab + b².
(2a + 3b)² = 4a² + 9b² + 12ab
= 30 + 12
= 42

Cost price of 1 shampoo bottle = Rs. 180
∴ Cost price of 2 shampoo bottles = Rs. 360
Sales tax = 5%
∴ Sales tax paid = Rs. (5/100 × 360) 
= Rs. 18
∴ Buying price = Rs. (360 + 18)
= Rs. 378

4 men dig a pit in 16 days
1 men to dig a pit in 16 × 4 days = 64 days
Therefore, 8 men dig the same pit in (64/ 8) days = 8 days

The car covers 168 miles in 2 hours.
Speed of the car,
S = D/T = 168 / 2 = 84 miles/hour
The truck covers 348 miles in 3 hours.
Speed of the truck,
S = 348 / 3 = 116 miles/hour
Speed of the car : Speed of the truck
84 : 116
4 × 21 : 4 × 29
⇒ 21 : 29

(20.2)² - (19.8)²
Using a² - b² = (a + b)(a - b);
(20.2)² - (19.8)²
= (20.2 + 19.8) (20.2 - 19.8)
= (40) × (0.4)
= 16