Maths

1. The probability of an impossible event is: a) 0 b) 1 c) 0.5 d) Not defined Click to View Answer and Explanation Answer: a) 0 Explanation: An impossible event is something that cannot happen. Therefore, its probability is 0. 2. The probability of a sure or certain event is: a) 0 b) 1 c) […]

1. The mean of the first n natural numbers is: a) n/2 b) (n+1)/2 c) n d) (n-1)/2 Click to View Answer and Explanation Answer: b) (n+1)/2 Explanation: The sum of the first n natural numbers is n(n+1)/2. So, the mean = [n(n+1)/2] / n = (n+1)/2. 2. The median of the data: 6, 8,

1. The surface area of a cube with side 'a' is: a) a^2 b) 6a^2 c) a^3 d) 12a Click to View Answer and Explanation Answer: b) 6a^2 Explanation: A cube has six equal faces. Each face has an area of a^2. So, total surface area = 6a^2. 2. The volume of a cylinder with

1. The area of a circle with radius 'r' is: a) πr b) πr^2 c) 2πr d) r/π Click to View Answer and Explanation Answer: b) πr^2 Explanation: The formula to calculate the area of a circle is π times the square of its radius. 2. If the circumference of a circle is 44 cm,

1. To divide a line segment in a given ratio, which of the following is essential? a) Compass b) Divider c) Straightedge d) Protractor Click to View Answer and Explanation Answer: a) Compass Explanation: A compass is essential to mark arcs and create points that help in dividing a line segment in a given ratio.

1. If a line intersects a circle at two distinct points, then it is called a: a) Secant b) Tangent c) Chord d) Diameter Click to View Answer and Explanation Answer: a) Secant Explanation: A line that intersects a circle at two distinct points is termed as a secant. 2. The number of tangents that

1. From the top of a tower, the angle of depression of a point on the ground is 30°. If the tower's height is h, the distance of the point from the base of the tower is: a) h b) h/√3 c) h√3 d) 2h Click to View Answer and Explanation Answer: c) h√3 Explanation:

1. If sin θ = 3/5 and θ is an acute angle, then cos θ is: a) 4/5 b) 5/3 c) 5/4 d) 3/4 Click to View Answer and Explanation Answer: a) 4/5 Explanation: Using the Pythagorean identity, cos² θ = 1 – sin² θ. So, cos θ = √(1 – (3/5)²) = 4/5. 2.

1. If the coordinates of a point are (0, -3), it lies on: a) X-axis b) Y-axis c) Origin d) None of the above Click to View Answer and Explanation Answer: b) Y-axis Explanation: Any point with x-coordinate as 0 lies on the Y-axis. 2. The coordinates of the origin are: a) (1,1) b) (0,0)

1. Two triangles are congruent if: a) Their corresponding sides are equal b) Their corresponding angles are equal c) Both their corresponding sides and angles are equal d) None of the above Click to View Answer and Explanation Answer: c) Both their corresponding sides and angles are equal Explanation: Two triangles are congruent if both

1. Which of the following sequences is an arithmetic progression? a) 1, 3, 7, 11… b) 2, 6, 18, 54… c) 5, 5, 5, 5… d) 1, 4, 9, 16… Click to View Answer and Explanation Answer: a) 1, 3, 7, 11… Explanation: The difference between consecutive terms is constant. (3-1=2, 7-3=4, 11-7=4) 2. The

1. The general form of a quadratic equation is: a) ax^2 + bx + c = 0 b) ax + by + c = 0 c) ax^2 + bx = 0 d) ax^2 + c = 0 Click to View Answer and Explanation Answer: a) ax^2 + bx + c = 0 Explanation: A quadratic

1. Which of the following pair of equations has a unique solution? a) 2x + 3y = 7; 4x + 6y = 8 b) x + y = 4; 2x + 2y = 8 c) 3x – 2y = 1; 6x – 4y = 2 d) x – y = 1; x + y =

1. A polynomial of degree zero is called: a) Linear polynomial b) Quadratic polynomial c) Zero polynomial d) Constant polynomial Click to View Answer and Explanation Answer: d) Constant polynomial Explanation: A polynomial of degree zero has no variable term and is called a constant polynomial. 2. The degree of the polynomial 5x^3 – 4x^2

1. Every natural number is: a) An integer b) A real number c) An irrational number d) A prime number Click to View Answer and Explanation Answer: b) A real number Explanation: Natural numbers are a subset of real numbers. Thus, every natural number is a real number. 2. Which of the following is an

1. What is the probability of a certain event? a) 0 b) 0.5 c) 1 d) Cannot be determined Click to View Answer and Explanation Answer: c) 1 Explanation: A certain event is an event that will always happen, so its probability is 1. 2. If an event cannot happen at all, its probability is:

1. What is the mode of the data set: 5, 7, 9, 7, 6, 5, 5? a) 5 b) 7 c) 6 d) 9 Click to View Answer and Explanation Answer: a) 5 Explanation: The mode is the number that appears most frequently. Here, '5' appears three times, more than any other number. 2. The

1. Which formula represents the volume of a cylinder? a) πr^2h b) 2πrh c) πr^2 + h d) 2πr + h Click to View Answer and Explanation Answer: a) πr^2h Explanation: The volume of a cylinder is given by the product of its base area (πr^2) and its height (h). 2. The surface area of

1. Heron's formula is used to find the area of a triangle given: a) Its height and base b) The three angles c) The three side lengths d) Its altitude and median Click to View Answer and Explanation Answer: c) The three side lengths Explanation: Heron's formula calculates the area of a triangle when all

1. To bisect an angle using a ruler and compass, you should draw: a) An arc with the angle's vertex as the center b) A circle with the angle's vertex as the center c) A straight line from the angle's vertex d) Two arcs from the sides of the angle intersecting each other Click to

1. The radius of a circle is: a) The longest chord b) Half the diameter c) Tangent to the circle d) A line joining the center to any point on the circle Click to View Answer and Explanation Answer: d) A line joining the center to any point on the circle Explanation: Radius is a

1. The area of a parallelogram is the product of its: a) Base and height b) Diagonals c) Adjacent sides d) Perimeter Click to View Answer and Explanation Answer: a) Base and height Explanation: Area of a parallelogram = Base x Height. 2. Triangles on the same base and between the same parallels have: a)

1. How many angles does a quadrilateral have? a) 2 b) 3 c) 4 d) 5 Click to View Answer and Explanation Answer: c) 4 Explanation: By definition, a quadrilateral is a polygon with four angles. 2. The sum of the angles of a quadrilateral is: a) 180° b) 270° c) 360° d) 450° Click

1. Which of the following cannot represent the sides of a triangle? a) 3 cm, 4 cm, 7 cm b) 5 cm, 12 cm, 13 cm c) 6 cm, 8 cm, 10 cm d) 7 cm, 24 cm, 25 cm Click to View Answer and Explanation Answer: a) 3 cm, 4 cm, 7 cm Explanation:

1. If two parallel lines are intersected by a transversal, then the alternate interior angles are: a) Complementary b) Supplementary c) Equal d) Unequal Click to View Answer and Explanation Answer: c) Equal Explanation: For two parallel lines cut by a transversal, the alternate interior angles are congruent or equal. 2. An angle that measures