RRB NTPC Algebra and Geometry 2 — Questions and Answers

Question 1: If one angle of a parallelogram is 60°, what is the adjacent angle?

60°
90°
120° (Correct answer)
150°

Correct answer: 120°

Adjacent angles of a parallelogram are supplementary (sum = 180°). Adjacent angle = 180° - 60° = 120°.

Properties of a parallelogram: (1) Opposite angles are equal. (2) Adjacent angles are supplementary (sum = 180°). (3) Opposite sides are equal and parallel. (4) Diagonals bisect each other. Given one angle = 60°, Adjacent angle = 180° - 60° = 120°. The four angles of this parallelogram are: 60°, 120°, 60°, 120°. Verification: 60 + 120 + 60 + 120 = 360° ✓ (sum of interior angles of a quadrilateral). A rectangle is a special parallelogram where all angles = 90°.

Question 2: Solve for x: 3x/4 - 2 = 7

9
10
12 (Correct answer)
15

Correct answer: 12

3x/4 - 2 = 7 → 3x/4 = 9 → 3x = 36 → x = 12.

Solving: 3x/4 - 2 = 7. Step 1: Add 2 to both sides: 3x/4 = 7 + 2 = 9. Step 2: Multiply both sides by 4: 3x = 36. Step 3: Divide both sides by 3: x = 12. Verification: 3(12)/4 - 2 = 36/4 - 2 = 9 - 2 = 7 ✓. When solving equations with fractions, multiplying both sides by the denominator (LCM if multiple fractions) is a key technique. Always verify your answer by substituting back.

Question 3: What is the volume of a cube with side 5 cm?

25 cm³
75 cm³
100 cm³
125 cm³ (Correct answer)

Correct answer: 125 cm³

Volume of cube = side³ = 5³ = 125 cm³.

Volume of a cube = a³ where a is the side length. V = 5³ = 5 × 5 × 5 = 125 cm³. Other properties of this cube: Surface area = 6a² = 6 × 25 = 150 cm²; Diagonal of face = a√2 = 5√2 cm; Space diagonal = a√3 = 5√3 cm. Key volume formulas for RRB NTPC: Cube = a³; Cuboid = l×b×h; Sphere = (4/3)πr³; Cylinder = πr²h; Cone = (1/3)πr²h. These solid geometry questions are regularly tested.

Question 4: The factorization of x² - 9 is:

(x - 3)²
(x + 3)(x - 3) (Correct answer)
(x + 9)(x - 1)
(x - 9)(x + 1)

Correct answer: (x + 3)(x - 3)

x² - 9 = x² - 3² = (x + 3)(x - 3), using the difference of squares identity a² - b² = (a+b)(a-b).

x² - 9 = x² - 3² This is a difference of squares. Identity: a² - b² = (a + b)(a - b). With a = x and b = 3: x² - 3² = (x + 3)(x - 3). Verification: (x + 3)(x - 3) = x² - 3x + 3x - 9 = x² - 9 ✓. Algebraic identities to know for RRB NTPC: a² - b² = (a+b)(a-b); a² + 2ab + b² = (a+b)²; a² - 2ab + b² = (a-b)²; a³ + b³ = (a+b)(a²-ab+b²); a³ - b³ = (a-b)(a²+ab+b²).

Question 5: The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)

5 cm
6 cm
7 cm (Correct answer)
8 cm

Correct answer: 7 cm

Circumference = 2πr → 44 = 2×(22/7)×r → 44 = 44r/7 → r = 7 cm.

Circumference = 2πr. Given: C = 44 cm, π = 22/7. 44 = 2 × (22/7) × r → 44 = (44/7) × r → r = 44 × 7/44 = 7 cm. Area = πr² = (22/7) × 49 = 154 cm². Key circle formulas: Circumference = 2πr = πd; Area = πr². Quick check: For radius 7 (using π=22/7): Circumference = 2×(22/7)×7 = 44 ✓. Common values: r=3.5→C=22; r=7→C=44; r=10.5→C=66; r=14→C=88.

Question 6: Two supplementary angles are in the ratio 2:3. What is the measure of the larger angle?

70°
90°
100°
108° (Correct answer)

Correct answer: 108°

Supplementary angles sum to 180°. Let angles be 2x and 3x. 2x + 3x = 180 → x = 36. Larger angle = 3×36 = 108°.

Supplementary angles: two angles that sum to 180°. Let the angles be 2x and 3x. 2x + 3x = 180° → 5x = 180° → x = 36°. Smaller angle = 2 × 36° = 72°. Larger angle = 3 × 36° = 108°. Verification: 72° + 108° = 180° ✓; Ratio: 72:108 = 2:3 ✓. Key angle relationships: Supplementary: sum = 180°; Complementary: sum = 90°; Vertically opposite angles are equal; Angles on a straight line sum to 180°; Angles around a point sum to 360°.

RRB NTPC Algebra and Geometry 2

If one angle of a parallelogram is 60°, what is the adjacent angle?