Class 10th Half Yearly Exam 2025 – Hello dear students, today in this post we have brought you complete preparation for the Class 10th Math Half Yearly Paper 2025 so that you can better prepare for your Class 10th Math Half Yearly Paper. If you are a Class 10th student and are preparing for the half yearly exam, then please read this post carefully.
Class 10th Math Half Yearly Paper 2025-26
Half Yearly Exam
Set – A
Class – 10th
Subject – Math
Time – 03:00 hours, Marks – 75
Instructions:
All questions are compulsory.
Answer the questions as per the instructions.
Questions 1 to 5 are objective type questions carrying 1 × 30 marks.
Questions 6 to 15 are worth 2 marks each, with a word limit of 30 words.
Questions 16 to 19 are worth 3 marks each, with a word limit of 75 words.
Questions 20 to 23 are worth 4 marks each, with a word limit of 120 words.
Question 1. Choose the correct option and write it down –
The LCM of 12, 15, and 21 is:
180
315
420
252
The nature of the roots of the equation x2 + x – 1 = 0 is:
Real and equal
Real and different
No real roots
None of these
The 5th term of the arithmetic progression 2, 5, 8, …… is:
a. 11 b. 14 c. 2 d. 3
The triangle formed with sides 8 cm, 15 cm, and 17 cm is:
Isosceles triangle
Right-angled triangle
Isosceles right-angled triangle
Equilateral triangle
The distance between the points (8, 6) and (0, 0) is:
√14
10
√10
14
The ratio of the circumference and diameter of a circle is:
π : 1
πr : 2
π : 2
r : 2
Answer: 1. c. 420, 2. b. Real and fraction, 3. b. 14, 4. b. Right triangle, 5. b. 10, 6. d. r : 2
Question 2: Fill in the blanks:
The product of two multiple terms is a _______.
In the equation 2x + y = k, if x = 2, y = 1, then the value of k is _______.
If a line divides two sides of a triangle in the same ratio, then it is _______ to the third side. (Parallel/Non-parallel)
The point (-5,-4) is in the _______ quadrant.
The radius passing through the point of contact is _______ on the tangent line.
If the area of a circle is 4π square cm, then its radius will be…
Answer: 1. Polynomial, 2. 5, 3. Parallel, 4. Third, 5. Perpendicular, 6. 2cm.
Question 3: Make the correct pair:
General form of a linear equation in two variables a. 1
If the discriminant of a quadratic equation D ≥ 0 b. cot 2A
The nth term of an arithmetic progression c. ax + by + c = 0
All are squares d. Then the roots are real and distinct
cos 2 A + sin 2 A e. a n = a + ( n – 1 ) d
cosec 2 A – 1 f b
Answer: 1. c, 2. d, 3. e, 4. a, 5. a, 6. b
Question 4: Write True/False:
The product of two numbers is equal to the product of their HCF and LCM.
A polynomial of degree n has at most n zeros.
Sinθ = cosθ for all values of θ.
When viewed from a horizontal plane, the line of sight makes an angle of depression with the horizontal.
A line intersecting a circle at two points is called a secant.
The radius of a circle is greater than its diameter.
Answer: 1. True, 2. True, 3. False, 4. False, 5. True, 6. False
Question 5: Write the answer in one word or one sentence.
Write the standard form of a quadratic equation.
What is a series called if the number of terms is not finite?
What are the coordinates of the origin?
If the shadow of a 10-meter-tall tree is 10√3 meters, find the angle of elevation of the sun.
Give the value of tan30°.
Write the statement of Thales’ theorem.
Answer: 1. ax2 + bx + c = 0, 2. Infinite series, 3. (0,0), 4. 30°, 5. 1/√3, 6. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two sides.
Question 6: Find the LCM and HCF of 26 by using the prime factorization method.
Or
Express the number 3825 as a product of prime factors.
Question 7: Prove that √3 is a rational number.
Or
Find the HCF and LCM of the numbers 26 and 91 and verify that the product of two numbers is equal to the product of their HCF and LCM.
Question 8: If the sum of the zeros of a polynomial is 0 and the product is also √5, find the polynomial.
Or
If the zeros of the polynomial x2 – x + 1 are α and β, find the values of 1/α and 1/β.
Question 9: Find a quadratic polynomial whose sum and product of zeros are -1/4 and 1/4, respectively.
Or
Find the zeros of the quadratic polynomial 3×2 – x – 4 and verify the truth of the relationship between the zeros and the coefficients.
Question 10: Solve the pair of equations
x – 2y = 0
3x + 4y = 20
by the substitution method.
Or
Solve the pair of linear equations
7x – 15y = 2
x + 2y = 3
by the elimination method.
Question 11: The height of a right-angled triangle is 7 centimeters less than its base. If the hypotenuse is 13 centimeters, find the other two sides.
Or
Find the roots of the quadratic equation 2×2 + x – 6 = 0 by the completing the square method.
Question 12: If one term of the A.P.: 11, 8, 5, 2… is -150?
Or
Find the sum of the first 24 terms of a list of numbers whose second term is given by an = 3 + 2n.
Question 13 The price of 5 oranges and 3 apples is Rs. 35, and the price of 2 oranges and 4 apples is Rs. 28. Find the price of one orange and the price of one apple.
Or
A fraction becomes 1/3 when one is subtracted from its numerator and becomes 1/4 when 8 is added to the denominator. Find the difference.
Question 14 In the figure, DE || BC | Find EC.
Or
The perimeters of two similar triangles are 25 cm and 15 cm, respectively. If one side of the first triangle is 9 cm, find the length of the corresponding side of the second triangle.
Question 15 Find the distance between the points (-5 7) and (-1 3).
Or
If point C (1, 2) divides the line segment joining A (25) and B into 34, find the coordinates of B.
Question 16 Prove that secA (1-sinA) (secA+tanA) = 1.
Or
Tan(A+B) = √3 and tan(A-B) = 1/√3, 0° < A+B < 90° A > B. Find the values of A and B.
Question 17 If sin A = 3/4, then calculate the values of cos A and tan A.
Or
If ABC, right-angled at B, has AB = 24 cm and BC = 7 cm, find the values of sin A and sin C.
Question 18 A circus artist performs a 20-meter long skit. It falls on a long string that is tightly stretched and tied to the top of a pole fixed to the ground. If the angle subtended by the string with the ground level is 30°, find its height.
Or
A 1.5-meter-tall boy is standing some distance away from a 30-meter-tall building. As he walks toward the taller building, the angle of elevation of the top of the building changes from 30° to 60°. Find how far he has walked toward the building.
Question 19: Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Or
Prove that a parallelogram circumscribing a circle is a rhombus.
Question 20: Find the area subtended by the minute hand of a clock, whose length is 21 cm, in 5 minutes.
Or
The cost of fencing a circular field at the rate of ₹24 per meter is ₹5280. This field needs to be plowed at the rate of ₹0.50 per square meter. Find the cost of plowing the field. (Take π = 22/7.)
Question 21: A boat travels 30 km upstream and 44 km downstream in ten hours. In 13 hours, it travels
40 km upstream and 55 km downstream. Find the speed of the current and the boat’s weight in still water.
Or
A fraction becomes 1/3 when one is subtracted from its numerator and becomes 1/4 when 8 is added to the denominator.
Find the fraction.
Question 22: From a point P on the ground, the angle of elevation of the top of a 10-meter-tall building is 30°. A flag is hoisted on the top of a building, and the angle of elevation of the flagpole from P is 45°. Find the length of the flagpole and the distance of the building from point P.
Or
An electrician needs to repair a fault on a 5-meter-high pole. To carry out the repair, what should be the length of the CD used to reach a point 1.3 meters below the top of the pole so that it reaches the desired position when tilted at an angle of 60° from the horizontal? Also, how far should the foot of the pole be from the foot of the CD? (You can use √3 = 1.73 here).
Question 23: Find the area of the shaded region in the figure, if the radii of the two concentric circles with center O are 7 cm and 14 cm, respectively, and ΔAOC = 40°.
Or
If a horse is tied to a peg at one corner of a square field with a side of 15 meters with a 5-meter rope, find:
a. The area of the field where the horse can graze.
b. The increase in the area that can be grazed if the horse is tied to a 10-meter rope instead of a 5-meter rope. (Use 3.14)
Description
Class 10th Maths ardhvaarshik paper 2024 – Hello dear students, today in this post we are going to tell you about the complete preparation of Class 10th Maths half yearly paper 2024.
