Class 10 Maths Question Paper 2024-25

• This is a model question paper for Class 10 Mathematics, for the session 2024-25.
• The full marks is 80 and the time allocated is 3 hours.

Instructions

• Answer in your own words as far as possible.
• There are 52 questions in total, divided into four sections: A, B, C, and D.

Section A

• Section A has 30 multiple-choice questions.
• Each question has four options, and you must choose the correct one.

Section B

• Section B includes question numbers 31 to 38.
• These are very short answer type questions, and you must answer any six.
• Each question carries 2 marks.

Section C

• Section C includes question numbers 39 to 46.
• These are short answer type questions, and you must answer any six.
• Each question carries 3 marks.

Section D

• Section D includes question numbers 47 to 52.
• These are long answer type questions, and you must answer any four.
• Each question carries 5 marks.

Questions

• The zeroes of P(x) = 𝑥²-27 are ± 3√3.
• If the graph of a polynomial intersects the x-axis at three points, it has 3 zeros or more than 3.
• There can be infinite rational numbers between two rational numbers.
• The HCF of two consecutive even numbers is 2.
• The linear equation ax+by+c = 0 in two variables x, y has infinite solutions.
• Lines represented by inconsistent pairs of equations are parallel.
• x² - 3x + 2 = 0 has a root 2.
• Two consecutive odd positive integers whose sum of squares is 290 are 11, 13.
• -10, -6, -2, 2... is in A.P (arithmetic progression).
• The 18th term of 1,4,7,10… is 52.
• If the ratio of areas of two similar triangles is 16:9, the ratio of their corresponding sides is 4:3.
• The diagonals of a rhombus are 6 cm and 8 cm, the length of each side will be 5cm.
• The point of intersection of two axes is called Origin.
• With 5 unit pairs from the Y-axis and point P on the X-axis, the coordinates of point P are (5,0).
• If Sin A = ¾, Cosec A is 4/3.
• (Sec A + Tan A) (1 – Sin A) equals Sec A.
• If tan A = √3, the value of A is 60°.
• When a pillar's shadow equals its height, the angle of elevation of the Sun is 45°.
• The angle of a semicircle is 90°.
• If the distance between the centers of two circles equals the sum of their radii, there are 1 common tangent lines.
• Chords equidistant from the center of a circle are equal.
• For spheres with a volume ratio of 8:27, the ratio of surface areas is 4 : 9.
• If the curved surface area of a sphere is 144π square cm, its radius is 12cm.
• The chance of getting heads when tossing a coin is 1/2.
• The probability of a sure event is 1.
• If a dice is tossed, the probability of getting an even number is 1/2.
• For x+2, 3x and 4x+1 in arithmetic progression, the value of x is 3.
• If the mean of 6,8,9,x and 13 is 10, the value of x will be 14.
• The mode of 2, 6, 4, 5, 0, 2, 1, 3, 2 is 2.
• The median of 8, 7, 12, 15, 10, 9, 11 will be.
• The HCF and LCM of numbers 6 and 20 can be found using prime factorization.
• The zeros of the quadratic equation 𝑥² - 7𝑥 + 12 can be determined.
• If the length of the shadow of a pillar is √3 times the height, the angle of elevation of the Sun is calculated.
• If the first term of AP is 2 and the common difference is 3, then to find the 8th term use formula for arithmetic progression.
• A square is made by bending a circular wire of radius 28cm, the length of the side of the square can be determined.
• If R(5, 6) is the mid-point of the line segment AB that connects points A(6, 5) and B(4, y), we may solve for the value of y.
• The height of a pillar is found when lights are at 60° and produce a shadow of 20m length.
• If the length of a cube's diagonal is 6√3 cm, the method to find entire surface area is area=6side^2 and diagonal=√3side to find for side.
• √𝟐 is an irrational number.
• 2𝐶𝑜𝑠𝑒𝑐² 30° + 𝑥𝑆𝑖𝑛² 60° = 10, method to find the value of x.
• To determine if -150 is a term of the arithmetic progression 11,8,5,2, solve for n using formula and if n is a positive integer, then -150 is a term.
• If there are 3 red and 5 black balls in a bag, one ball is being extracted to determine the probability of it being red.
• If the median of a given distribution is 28.5, we can determine the values of x and y by setting them to the median formula.
• Given a tower observed at 30° elevation and 30 meters away, the height can be derived using trigonometric functions.
• With hemisphere placed on a cubical block and area derived, the total surface area may be calculated.
• Knowing coordinates (1, 2), (4, y), ( x, 6) and (3, 5) which is a parallelogram the values the variables may be derived.
• In a solid contains a cone of height 120cm and radius 60cm, which sits on a hemisphere, which is then placed in a cylinder with water the volume of water remaining can be calculated as VCylinder - (VCone+VHemisphere).
• From the top of the 30° inclined motorway highway, we get formula for how a fast can travel to see angle increase to 60° and what steps to take from tht point.
• Given two tangents of circle from an external point angle is supplemetnted the tangent point.
• The equation to find (sinA + CosA+1) and (sinA-CosA-1) is Sec²A=1+tan²A.
• For a figure the diagonal quadrilateral intersecting at = and .
• A table with number cars observed and the frequncy of time we can note of each, also for observations from those with 100 intervals.