**HP Patwari Math Question Paper with Answers**

The HP Patwari Math Question Paper with Answers is a crucial resource for candidates preparing for the Himachal Pradesh Patwari Exam. This collection focuses specifically on mathematical concepts that are integral to the exam, covering topics such as arithmetic, algebra, geometry, and data interpretation. By practicing with this question paper, candidates can familiarize themselves with the exam format, improve their problem-solving skills, and enhance their speed and accuracy in tackling math problems.

**HP Patwari Math Question Paper**

Each question in the HP Patwari Math Question Paper with Answers is accompanied by detailed solutions, allowing candidates to understand the methodology behind each answer. This resource not only aids in self-assessment but also helps identify areas needing improvement, making it an essential tool for aspirants aiming to succeed in the competitive HP Patwari Exam.

**HP Patwari Math Question Paper with Answers**

### ➤ (3p^{2}qr^{3})*(-4p^{3}qr^{2})*(7pq^{3}r) is equal to:

- 84p
^{6}q^{6}r^{6} - 84p
^{6}q^{5}r^{5} - -84p
^{6}q^{6}r^{6} **-84p**^{6}q^{5}r^{5}

*Explanation: Multiply the terms and combine the exponents of like bases. The result is -84p ^{6}q^{5}r^{5}.*

### ➤ Arjun is twice as old as Shreya. Five years ago his age was three times Shreya’s age. Find their present ages:

- 10 years, 12 years
- 5 years, 10 years
- 15 years, 30 years
**12 years, 24 years**

*Explanation: Let Shreya’s age be x. Then Arjun’s age is 2x. Five years ago, their ages were (x-5) and (2x-5). According to the problem, 2x-5 = 3(x-5). Solving this gives x = 12 and 2x = 24.*

### ➤ If the radius of a square is 2d/3, then its volume is:

**(32/81)πd**^{3}- (23/4)πd
^{3} - (32/3)πd
^{3} - (34/3)πd
^{3}

*Explanation: The radius of a square is related to the side length. Using the given radius, compute the volume by substituting the value into the volume formula for a square.*

### ➤ The value of (-1)^{1000} is:

- -1
**1**- 1000
- -1000

*Explanation: Any negative number raised to an even power results in a positive number. Thus, (-1) ^{1000} equals 1.*

### ➤ The compound interest on Rs. 1000 at 10% per annum for 2 years is:

- Rs. 1210
**Rs. 210**- Rs. 200
- Rs. 190

*Explanation: Use the compound interest formula A = P(1 + r/n) ^{nt} where P = 1000, r = 0.10, n = 1, and t = 2. The compound interest is Rs. 210.*

### ➤ Mohan purchased a car for Rs. 8000 and sold it after one year at a loss of 25%. Find the selling price of the car:

- Rs. 7000
**Rs. 6000**- Rs. 10000
- Rs. 9000

*Explanation: A 25% loss on Rs. 8000 means the selling price is 75% of Rs. 8000, which is Rs. 6000.*

### ➤ A train covers a distance of 3750 Km in 25 hours, how much average distance the same train will cover in one hour?

- 140 Km
- 175 Km
**150 Km**- 130 Km

*Explanation: Average speed is total distance divided by total time. Here, 3750 Km / 25 hours = 150 Km per hour.*

### ➤ 2^{0}*3^{0}*4^{0}*=?

**1**- 24
- 0
- None of these

*Explanation: Any non-zero number raised to the power of 0 is 1.*

### ➤ The sum of 0.42+0.042+0.0042-0.00042 is:

- 0.42424
**0.46578**- 0.42654
- 0.42528

*Explanation: Adding and subtracting the decimals gives a total of 0.46578.*

### ➤ L.C.M of 4, 6, 12, 15 = ?

- 180
**60**- 75
- 120

*Explanation: The least common multiple of the numbers is 60.*

### ➤ (3/4)^{7} *(4/3)^{7} =?

**1**- 0
- 14
- -1

*Explanation: Multiply the fractions with the same exponent, resulting in (3/4) ^{7} * (4/3)^{7} = 1.*

### ➤ Find the smallest square number which is exactly divisible by 4, 9, and 10:

**900**- 400
- 490
- 360

*Explanation: The smallest square number divisible by 4, 9, and 10 is 900.*

### ➤ If 567567567 is divided by 567, then the quotient will be:

- 111
- 10101
**1001001**- 301

*Explanation: Dividing 567567567 by 567 gives a quotient of 1001001.*

### ➤ Circumference of the base of a right circular cylinder is 44 cm and its height is 15 cm. The volume (in cm^{3}) of the cylinder is: (take pi=22/7).

- 770
- 1155
- 1540
**2310**

*Explanation: Use the formula for the volume of a cylinder: V = πr ^{2}h. Given circumference, find the radius and then calculate the volume.*

### ➤ If 56-45+ √x = 17, then x=?

**36**- 25
- 16
- 9

*Explanation: Solve the equation 56 – 45 + √x = 17 to find x = 36.*

### ➤ If the circumference of a circle is 132 cm. The area of the circle is:

**1386 cm**^{2}- 1386 cm
- 1486 cm
^{2} - 1320 cm
^{2}

*Explanation: Use the circumference to find the radius and then use the formula for the area of a circle: A = πr ^{2}.*

### ➤ If the sum of two consecutive even numbers is 66, then the smaller one is:

- 34
**32**- 42
- 24

*Explanation: Let the consecutive even numbers be x and x+2. Solving x + (x+2) = 66 gives x = 32.*

### ➤ Find the missing number in the series 2, 5, 11, 20, 32, 47, ____, 86.

- 60
**65**- 58
- 62

*Explanation: The pattern in the series suggests that the missing number is 65.*

### ➤ The population of a village is 5000 and it increases at the rate of 2% every year. After 2 years the population will be:

- 5108
- 5200
**5202**- 5300

*Explanation: Use the compound interest formula for population growth to find the population after 2 years.*

### ➤ If a train 240 m long passes a pole in 16 seconds, then the speed of the train is:

- 36 Km/h
**54 Km/h**- 60 Km/h
- 72 Km/h

*Explanation: Calculate the speed using the formula: Speed = Distance / Time. Convert meters per second to kilometers per hour.*

### ➤ A man got a 10% increase in his salary. If his new salary is Rs. 1,54,000, then the original salary is:

- Rs. 1,50,000
- Rs. 1,60,000
**Rs. 1,40,000**- Rs. 1,45,000

*Explanation: Use the percentage increase formula to find the original salary from the new salary.*

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