RRB NTPC CBT 1 2026 Mathematics Questions with Solutions

Explanation

Overall average = (n₁A₁ + n₂A₂ + n₃A₃) / (n₁ + n₂ + n₃)

Given: Group A: n₁ = 21, A₁ = 465 Group B: n₂ = 11, A₂ = 410 Group C: n₃ = 17, A₃ = 466

Total expenditure = (21 × 465) + (11 × 410) + (17 × 466) = 9765 + 4510 + 7922 = 22197

Total members = 21 + 11 + 17 = 49

Overall average spent per member = 22197 / 49 = 453

Explanation

Charles Babbage, an English mathematician and mechanical engineer, designed the Difference Engine and later the Analytical Engine in the 19th century. The Analytical Engine incorporated fundamental concepts of modern electronic computers, including an Arithmetic Logic Unit (ALU), control flow through conditional branching, and integrated memory, earning him the title of the 'Father of Computers'.

Explanation

Let the number of ₹1, ₹2, and ₹5 coins be 8x, 4x, and 3x respectively.

Total value = (1 × 8x) + (2 × 4x) + (5 × 3x) = 8x + 8x + 15x = 31x

Given total value = ₹930: 31x = 930 x = 30

Total number of coins = 8x + 4x + 3x = 15x = 15 × 30 = 450

Explanation

Average Speed = Total Distance / Total Time

Total Distance = (20 × 90) + (65 × 60) = 1800 + 3900 = 5700 m

Total Time = 90 + 60 = 150 min

Average Speed = 5700 / 150 = 38 m/min

Explanation

The 1991 economic reforms introduced Liberalization, Privatization, and Globalization (LPG) in India, dismantling the License Raj and opening the economy to international markets. Globalization enabled large Indian conglomerates to access foreign capital, acquire international companies, and expand into global markets. Concurrently, privatization and deregulation reduced state monopolies, lifted restrictions on production capacities, and fostered competitive market dynamics, enabling corporations like Reliance Industries and Tata Group to scale rapidly and establish themselves as global multinationals.

Explanation

Let the number of articles of type P, Q, and R purchased be 3x, 2x, and 3x, respectively.

Total cost = (280 × 3x) + (180 × 2x) + (120 × 3x) 6240 = 840x + 360x + 360x 6240 = 1560x x = 6240 / 1560 = 4

Number of articles of type Q purchased = 2x = 2 × 4 = 8.

Explanation

Dividing x⁴ - 83x² + 1 = 0 by x² gives: x² + 1/x² = 83

Using the identity (x - 1/x)² = x² + 1/x² - 2: (x - 1/x)² = 83 - 2 = 81 x - 1/x = 9

Using the algebraic expansion for x³ - 1/x³: x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x) x³ - 1/x³ = 9³ + 3(9) = 729 + 27 = 756

Substituting this into the given expression: √(x³ - x⁻³ + 28) = √(756 + 28) = √784 = 28

Explanation

Let x be the price at which P purchased the item.

Price at which P sells to Q = x × (1 + 77/100) = 1.77x Price at which Q sells to R = 1.77x × (1 - 50/100) = 0.885x

Given that R paid ₹ 2655: 0.885x = 2655 x = (2655 × 200) / 177 x = 15 × 200 = 3000

Explanation

The area of an equilateral triangle is given by the formula Area = (√3 / 4) × a², where a is the side length.

Substituting a = 8 cm into the formula:

Area = (√3 / 4) × 8² = (√3 / 4) × 64 = 16√3 sq. cm.

Using √3 ≈ 1.732:

Area = 16 × 1.732 = 27.712 ≈ 27.71 sq. cm.

Explanation

First, evaluate the square root in the expression: √2025 = 45

Next, perform the division step: 630 ÷ 45 = 14

Now, evaluate the multiplication on the left side of the equation: 19 × 7 × 14 = 19 × 98 = 1862

Substitute this value back into the equation: 1862 = y + 517

Solving for y: y = 1862 - 517 = 1345

Explanation

The difference between compound interest and simple interest for 2 years is given by the formula:

D = P × (r / 100)²

where D is the difference, P is the principal amount, and r is the annual interest rate.

Substituting D = 52 and r = 4:

52 = P × (4 / 100)² 52 = P × (1 / 25)² 52 = P / 625 P = 52 × 625 = 32500

Explanation

Let Cost Price = C and Marked Price = M.

First selling price = 3/10 × M = 0.3 M Since there is a loss of 16%, first selling price = (100 - 16)% of C = 0.84 C 0.3 M = 0.84 C M = 2.8 C

Second selling price = 69% of M = 0.69 M Substituting M = 2.8 C: Second selling price = 0.69 × 2.8 C = 1.932 C

Profit percentage = ((1.932 C - C) / C) × 100 = 93.2%

Explanation

The total surface area of the four walls and the ceiling is given by the formula: Area = 2h(l + b) + lb

Substituting length l = 20 m, breadth b = 10 m, and height h = 6 m: Area = 2 × 6 × (20 + 10) + (20 × 10) Area = 12 × 30 + 200 = 360 + 200 = 560 m²

Total cost of painting = Area × Rate Total cost = 560 × 15 = ₹8400