Himachal Padesh Patwari Exam 2019 Math Part Solved Paper

➤ (3p²qr³)*(-4p³qr²)*(7pq³r) is equal to:

• 84p⁶q⁶r⁶
• 84p⁶q⁵r⁵
• -84p⁶q⁶r⁶
• -84p⁶q⁵r⁵

Explanation: Multiply the terms and combine the exponents of like bases. The result is -84p⁶q⁵r⁵.

➤ 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)πd³
• (23/4)πd³
• (32/3)πd³
• (34/3)πd³

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.

➤ 2⁰*3⁰*4⁰*=?

• 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 cm³) of the cylinder is: (take pi=22/7).

• 770
• 1155
• 1540
• 2310

Explanation: Use the formula for the volume of a cylinder: V = πr²h. 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 cm²
• 1386 cm
• 1486 cm²
• 1320 cm²

Explanation: Use the circumference to find the radius and then use the formula for the area of a circle: A = πr².

➤ 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.