SSC CGL (Prelims) Maths: Geometry questions with solutions

Q1. In triangle LMN, \(\angle L = 118^\circ\) and \(LM = LN\). Find \(\angle N\).

1. 42°
2. 31°
3. 65°
4. 62°

Answer: 31°

Since \(LM = LN\), triangle LMN is isosceles with base \(MN\), so \(\angle M = \angle N\). The remaining angles sum to \(180^\circ - 118^\circ = 62^\circ\), so each base angle is \(62^\circ/2 = 31^\circ\).

Q2. In triangle ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to:

1. 14 cm
2. 16 cm
3. 12 cm
4. 10 cm

Answer: 10 cm

The centroid divides each median in the ratio 2:1, so the vectors of the medians from the centroid have lengths 8 cm and 6 cm. Since the medians are perpendicular, the side opposite the included angle can be found using coordinate geometry or vector relations, giving \(AB = 10\) cm.

Q3. What is the sum of the interior angles of a pentagon?

1. 360°
2. 540°
3. 720°
4. 900°

Answer: 540°

The sum of interior angles of an n-sided polygon is (n - 2) × 180°. For a pentagon, this becomes (5 - 2) × 180° = 540°.

Q4. A cone has a radius of 3 cm and height 4 cm. What is its volume? (Use \(\pi = 3.14\))

1. 37.68 cm³
2. 38 cm³
3. 36 cm³
4. 39 cm³

Answer: 37.68 cm³

The volume of a cone is \(\frac{1}{3}\pi r^2 h\). Substituting \(r=3\) cm, \(h=4\) cm, and \(\pi=3.14\), we get \(\frac{1}{3}\times 3.14 \times 9 \times 4 = 37.68\) cm³.

Q5. In a triangle, if one angle is 90° and another is 45°, what is the third angle?

1. 35°
2. 60°
3. 45°
4. 30°

Answer: 45°

The sum of angles in a triangle is 180°. So the third angle is 180° - 90° - 45° = 45°.

Q6. What is the perimeter of a square whose side is 13 cm?

1. 52 cm
2. 169 cm
3. 26 cm
4. 39 cm

Answer: 52 cm

The perimeter of a square is given by 4 × side. Here, side = 13 cm, so perimeter = 4 × 13 = 52 cm.