English medium Class 10th स्टूडेंट्स के लिए कक्षा 10 Mathematics त्रैमासिक परीक्षा 2026 Model/Practice प्रश्न पत्र इस प्रकार हैं यह त्रैमासिक परीक्षा के ब्लू प्रिंट पर आधारित है इसमें महत्वपूर्ण प्रश्नों का समावेशन है . अभ्यास कर अपनी तैयारी जांचे
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| Time: 3:00 Hours | Maximum Marks: 75 |
Instructions:
1. All questions are compulsory.
2. Question numbers 1 to 5 are objective type questions carrying 1 mark each (Total 30 marks).
3. Question numbers 6 to 17 are short answer type questions carrying 2 marks each.
4. Internal choices (OR blocks) are provided from question number 6 onwards.
1. All questions are compulsory.
2. Question numbers 1 to 5 are objective type questions carrying 1 mark each (Total 30 marks).
3. Question numbers 6 to 17 are short answer type questions carrying 2 marks each.
4. Internal choices (OR blocks) are provided from question number 6 onwards.
Section – A (Objective Type Questions – 30 Marks)
Question 1. Choose and write the correct option: Marks: 6 × 1 = 6
- The HCF of 96 and 404 will be:
- If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then the value of α + β is:
- The condition for a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 to have no solution is:
- The value of the discriminant for the quadratic equation x² – 4x + 4 = 0 will be:
- The 10th term of the Arithmetic Progression (AP): 10, 7, 4, … is:
- The distance of the point (3, 4) from the origin is:
Question 2. Fill in the blanks: Marks: 6 × 1 = 6
- Every composite number can be expressed as a product of ________ numbers.
- A polynomial of degree 2 can have a maximum of ________ zeroes.
- In the equation x + 2y = 5, if x = 1, then the value of y will be ________.
- If the roots of a quadratic equation are real and equal, the value of the discriminant is ________.
- All equilateral triangles are ________.
- The point (0, 5) lies on the ________ axis.
Question 3. Write True or False: Marks: 6 × 1 = 6
- √2 is a rational number. ( )
- The degree of a zero polynomial is undefined. ( )
- A pair of linear equations always has a unique solution. ( )
- The roots of the equation x(x – 1) = 0 are 0 and 1. ( )
- The series 2, 4, 8, 16, … is an Arithmetic Progression (AP). ( )
- The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides. ( )
Question 4. Match the following columns correct pairs: Marks: 6 × 1 = 6
| Column ‘A’ | Column ‘B’ |
|---|---|
| 1. Product of two numbers | (A) Criterion for Similarity |
| 2. Degree of a linear polynomial | (B) Abscissa |
| 3. Standard form of a quadratic equation | (C) HCF × LCM |
| 4. nth term of an AP (a_n) | (D) 1 |
| 5. AAA (Angle-Angle-Angle) | (E) ax² + bx + c = 0 |
| 6. x-coordinate of any point | (F) a + (n – 1)d |
Question 5. Answer in one word or one sentence: Marks: 6 × 1 = 6
- What will be the LCM of numbers 15 and 20?
- What is a polynomial called whose degree is 3?
- In the linear equation y = mx + 3, if x = -2 and y = 5, what will be the value of m?
- Write the formula to find the discriminant (D) of the quadratic equation ax² + bx + c = 0.
- What is the common difference of the AP: 5, 8, 11, 14…?
- Write the coordinates of the mid-point of the line segment joining the points A(x₁, y₁) and B(x₂, y₂).
Section – B (Short Answer Type Questions – Questions 6 to 8)
Question 6. Marks: 2
Find the HCF of 6, 72, and 120 using the Prime Factorisation method.
Find the HCF of 6, 72, and 120 using the Prime Factorisation method.
OR
Show that 3 + 2√5 is an irrational number.
Question 7. Marks: 2
Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.Class 10th Mathematics Quarterly Practice Paper – Questions 8 to 23
Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.
ORFind the zeroes of the polynomial p(x) = x² – 3 and verify the relationship between the zeroes and the coefficients.
Section – B (Short Answer Type Questions – Questions 8 to 17)
Question 8. Marks: 2
By comparing the ratios a₁/a₂, b₁/b₂, and c₁/c₂, find out whether the pair of linear equations 2x – 3y = 8 and 4x – 6y = 9 is consistent or inconsistent.
By comparing the ratios a₁/a₂, b₁/b₂, and c₁/c₂, find out whether the pair of linear equations 2x – 3y = 8 and 4x – 6y = 9 is consistent or inconsistent.
OR
Solve the pair of linear equations x + y = 14 and x – y = 4 by the substitution method.
Question 9. Marks: 2
Check whether (x – 2)(x + 1) = (x – 1)(x + 3) is a quadratic equation.
Check whether (x – 2)(x + 1) = (x – 1)(x + 3) is a quadratic equation.
OR
Find the roots of the quadratic equation 2x² – x + 1/8 = 0 by factorization method.
Question 10. Marks: 2
Find the nature of the roots of the quadratic equation 2x² – 3x + 5 = 0.
Find the nature of the roots of the quadratic equation 2x² – 3x + 5 = 0.
OR
Find the value of k so that the quadratic equation 2x² + kx + 3 = 0 has two equal roots.
Question 11. Marks: 2
Find the 10th term of the Arithmetic Progression (AP): 2, 7, 12, …
Find the 10th term of the Arithmetic Progression (AP): 2, 7, 12, …
OR
Is -150 a term of the AP: 11, 8, 5, 2…? Give reasons.
Question 12. Marks: 2
How many terms of the AP: 24, 21, 18, … must be taken so that their sum is 78?
How many terms of the AP: 24, 21, 18, … must be taken so that their sum is 78?
OR
Find the sum of the first 1000 positive integers.
Question 13. Marks: 2
In the given figure, if DE || BC, find EC given that AD = 1.5 cm, DB = 3 cm, and AE = 1 cm.
In the given figure, if DE || BC, find EC given that AD = 1.5 cm, DB = 3 cm, and AE = 1 cm.
OR
State whether a triangle with side lengths 6 cm, 8 cm, and 10 cm forms a right-angled triangle.
Question 14. Marks: 2
If a line intersects sides AB and AC of a ΔABC at D and E respectively and is parallel to BC, prove that AD/AB = AE/AC.
If a line intersects sides AB and AC of a ΔABC at D and E respectively and is parallel to BC, prove that AD/AB = AE/AC.
OR
The sides of two similar triangles are in the ratio 4:9. Find the ratio of the areas of these triangles.
Question 15. Marks: 2
Find the distance between the points (2, 3) and (4, 1).
Find the distance between the points (2, 3) and (4, 1).
OR
Find a point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Question 16. Marks: 2
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally.
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally.
OR
If the points A(6, 1), B(8, 2), C(9, 4), and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
Question 17. Marks: 2
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
OR
Prove that the lengths of tangents drawn from an external point to a circle are equal.Section – C (Long Answer Type Questions – Questions 18 to 20)
Question 18. Marks: 3
Prove that √5 is an irrational number.
Prove that √5 is an irrational number.
OR
Given that HCF(306, 657) = 9, find LCM(306, 657).
Question 19. Marks: 3
Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are √(5/3) and -√(5/3).
Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are √(5/3) and -√(5/3).
OR
If the zeroes of the polynomial x³ – 3x² + x + 1 are a – b, a, and a + b, find the values of a and b.
Question 20. Marks: 3
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
OR
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?Section – D (Analytical Type Questions – Questions 21 to 23)
Question 21. Marks: 4
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
OR
Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis.
Question 22. Marks: 4
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
OR
Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m²? If so, find its length and breadth.
Question 23. Marks: 4
If the sum of the first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
If the sum of the first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
OR
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio (Basic Proportionality Theorem).शैक्षणिक सत्र 2026-27 के लिए हिन्दी माद्यम के छात्रों के सभी प्रकार की शैक्षणिक सामग्री एम् पी बोर्ड स्टडी डाट काम ( https://mpboardstudy.com/) पर उपलब्ध है जबकि अंग्रेजी माध्यम के लिए एम् पी बोर्ड इंग्लिश मीडियम डाट काम ( https://mpboardenglishmedium.com/) देखें . विमर्श पोर्टल डाट इन ( https://vimarshportal.in/) भी एक उपयोगी वेबसाईट है .
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