Here are 25 multiple-choice questions on Geometry (including Coordinate Geometry) suitable for JKSSB and similar competitive exams, along with answers and explanations:
Geometry (including Coordinate Geometry)
Q1. What is the sum of the interior angles of a quadrilateral?
(a) 180 degrees
(b) 270 degrees
(c) 360 degrees
(d) 540 degrees
Answer: (c)
Explanation: The sum of interior angles of a polygon with ‘n’ sides is given by (n-2) 180 degrees. For a quadrilateral, n=4, so (4-2) 180 = 2 * 180 = 360 degrees.
Q2. Two lines are parallel if they:
(a) Intersect at a single point
(b) Form a right angle
(c) Are equidistant from each other at all points and never intersect
(d) Are always perpendicular
Answer: (c)
Explanation: Parallel lines maintain a constant distance between them and never meet, no matter how far they are extended.
Q3. An angle that measures exactly 90 degrees is called a:
(a) Acute angle
(b) Obtuse angle
(c) Right angle
(d) Straight angle
Answer: (c)
Explanation: A right angle is precisely 90 degrees. An acute angle is less than 90, an obtuse angle is more than 90 but less than 180, and a straight angle is 180 degrees.
Q4. What is the perimeter of a rectangle with length 12 cm and width 5 cm?
(a) 17 cm
(b) 34 cm
(c) 60 cm
(d) 120 cm
Answer: (b)
Explanation: Perimeter of a rectangle = 2 (length + width) = 2 (12 + 5) = 2 * 17 = 34 cm.
Q5. The diagonals of which quadrilateral always bisect each other at right angles?
(a) Rectangle
(b) Parallelogram
(c) Rhombus
(d) Trapezium
Answer: (c)
Explanation: In a rhombus, the diagonals bisect each other at 90 degrees. In a rectangle, they bisect each other but not necessarily at right angles (unless it’s a square). In a parallelogram, they bisect each other but not at right angles.
Q6. What is the area of a circle with a radius of 7 cm? (Use $\pi = \frac{22}{7}$)
(a) 22 cm²
(b) 44 cm²
(c) 154 cm²
(d) 308 cm²
Answer: (c)
Explanation: Area of a circle = $\pi r^2 = \frac{22}{7} 7^2 = \frac{22}{7} 49 = 22 * 7 = 154$ cm².
Q7. If two angles are complementary, their sum is:
(a) 45 degrees
(b) 90 degrees
(c) 180 degrees
(d) 360 degrees
Answer: (b)
Explanation: Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees.
Q8. The coordinates of the origin are:
(a) (1, 0)
(b) (0, 1)
(c) (1, 1)
(d) (0, 0)
Answer: (d)
Explanation: The origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0).
Q9. Which of the following points lies on the x-axis?
(a) (3, 2)
(b) (0, 5)
(c) (-4, 0)
(d) (1, -1)
Answer: (c)
Explanation: Points on the x-axis always have their y-coordinate as 0.
Q10. What is the distance between the points (2, 3) and (5, 7)?
(a) 3 units
(b) 4 units
(c) 5 units
(d) $\sqrt{26}$ units
Answer: (c)
Explanation: Distance formula = $\sqrt { (x_2 – x_1)^2 + (y_2 – y_1)^2 }$
Distance = $\sqrt { (5 – 2)^2 + (7 – 3)^2 } = \sqrt { 3^2 + 4^2 } = \sqrt { 9 + 16 } = \sqrt { 25 } = 5$ units.
Q11. The midpoint of the line segment joining (1, -2) and (3, 4) is:
(a) (2, 1)
(b) (4, 2)
(c) (1, 3)
(d) (2, 3)
Answer: (a)
Explanation: Midpoint formula = $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$
Midpoint = $(\frac{1 + 3}{2}, \frac{-2 + 4}{2}) = (\frac{4}{2}, \frac{2}{2}) = (2, 1)$.
Q12. The slope of a horizontal line is:
(a) 1
(b) -1
(c) 0
(d) Undefined
Answer: (c)
Explanation: A horizontal line has no change in y-coordinate, so its slope ($\frac{\text{change in y}}{\text{change in x}}$) is 0.
Q13. What is the equation of a line passing through the origin (0,0) with a slope of 3?
(a) y = x + 3
(b) y = 3x
(c) y = 3
(d) x = 3y
Answer: (b)
Explanation: The general equation of a line is y = mx + c, where m is the slope and c is the y-intercept. Since it passes through the origin, c = 0. So, y = 3x + 0 => y = 3x.
Q14. If a triangle has sides 3 cm, 4 cm, and 5 cm, it is a:
(a) Equilateral triangle
(b) Isosceles triangle
(c) Right-angled triangle
(d) Obtuse-angled triangle
Answer: (c)
Explanation: This is a Pythagorean triplet ($3^2 + 4^2 = 9 + 16 = 25 = 5^2$). A triangle with sides satisfying the Pythagorean theorem is a right-angled triangle.
Q15. The angle subtended by a diameter at any point on the circumference of a circle is always:
(a) Acute
(b) Obtuse
(c) Right angle (90 degrees)
(d) Straight angle (180 degrees)
Answer: (c)
Explanation: This is a fundamental theorem in geometry, often referred to as Thales’s Theorem or the inscribed angle theorem.
Q16. How many faces does a cube have?
(a) 4
(b) 6
(c) 8
(d) 12
Answer: (b)
Explanation: A cube is a three-dimensional solid object bounded by six square faces, eight vertices, and twelve edges.
Q17. The ratio of the circumference to the diameter of a circle is represented by which constant?
(a) e
(b) $\pi$
(c) $\phi$
(d) g
Answer: (b)
Explanation: The constant $\pi$ (pi) is defined as the ratio of a circle’s circumference to its diameter.
Q18. What is the degree measure of each angle in an equilateral triangle?
(a) 30 degrees
(b) 45 degrees
(c) 60 degrees
(d) 90 degrees
Answer: (c)
Explanation: An equilateral triangle has all three sides equal and all three angles equal. Since the sum of angles in a triangle is 180 degrees, each angle is 180/3 = 60 degrees.
Q19. If a point (x, y) is in the second quadrant, then:
(a) x > 0, y > 0
(b) x < 0, y > 0
(c) x < 0, y < 0
(d) x > 0, y < 0
Answer: (b)
Explanation: In the second quadrant, the x-coordinate is negative, and the y-coordinate is positive.
Q20. The volume of a cylinder with radius ‘r’ and height ‘h’ is given by:
(a) $\pi r^2 h$
(b) $2 \pi r h$
(c) $\frac{1}{3} \pi r^2 h$
(d) $4 \pi r^2 h$
Answer: (a)
Explanation: The volume of a cylinder is calculated by multiplying the base area (area of the circle, $\pi r^2$) by its height ‘h’.
Q21. Two angles forming a linear pair are always:
(a) Complementary
(b) Supplementary
(c) Equal
(d) Adjacent and acute
Answer: (b)
Explanation: A linear pair of angles are adjacent angles that form a straight line, meaning their sum is 180 degrees, making them supplementary.
Q22. A section of a straight line connecting two points is called a:
(a) Ray
(b) Line segment
(c) Line
(d) Angle
Answer: (b)
Explanation: A line segment has two distinct endpoints. A ray has one endpoint and extends infinitely in one direction. A line extends infinitely in both directions without endpoints.
Q23. The area of a triangle with base ‘b’ and height ‘h’ is given by:
(a) $b \times h$
(b) $\frac{1}{2} (b + h)$
(c) $\frac{1}{2} \times b \times h$
(d) $2 \times b \times h$
Answer: (c)
Explanation: The standard formula for the area of a triangle is half the product of its base and height.
Q24. If the product of the slopes of two lines is -1, then the lines are:
(a) Parallel
(b) Perpendicular
(c) Coincident
(d) Intersecting but not perpendicular
Answer: (b)
Explanation: Two non-vertical lines are perpendicular if and only if the product of their slopes is -1.
Q25. What is the name of a polygon with 8 sides?
(a) Pentagon
(b) Hexagon
(c) Heptagon
(d) Octagon
Answer: (d)
Explanation: A polygon with 5 sides is a pentagon, 6 sides is a hexagon, 7 sides is a heptagon, and 8 sides is an octagon.
