Half Yearly Exam Class 10 Maths Question Paper | Class 10 Maths Question Paper Half Yearly Exam

Class – X Time.                        Allowed – 3 Hours

Subject – Mathematics.          Max. Marks – 90

General Instruction:-

1. All questions are compulsory.

2. The question paper consists of 31 questions divided into four sections – A, B, C and D.

3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each. 

Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks 

each.   

SECTION A

1. Can two numbers have 18 as their HCF and 380 as their LCM? Give reason.

2. Without actual division, state the type of decimal expansion of the number.

3. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. Also, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent this situation algebraically.

4. In the given figure, DE║CB. Find the length of AE.

SECTION B

5. Find the LCM and HCF of 120 and 144 by fundamental theorem of arithmetic.

6. Solve for x and y:-

 x + 31y = 63

 31x + 47y = 15

7. Form a quadratic polynomial whose one zero is √5 and the product of zeroes is -2√5.

8. ABC is an isosceles triangle right angled at C. Prove that AB2= 2AC2

9. If sinθ =1/2, then find the value of (2cot2θ + 2).

10. The mean of 10 observations is 15.3. If two observations 6 and 9 are replaced by 8 and 14

respectively. Find the new mean.

SECTION C

11. Prove that 7 - 2√2 is irrational.

12. Find the quotient and remainder if polynomial 6x4+ 8x3+ 17x2+ 21x + 7 is divided by polynomial 3x2+ 4x + 1.

13. The sum of digits of a two digit number is 12 The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. 

14. Prove that the area of an equilateral triangle on the side of a square is half the area of equilateral triangle formed on its diagonal.

 

15. In the given figure below └PSR = 900 ,PQ =10 c.m., QS = 6 c.m. and QR = 9c.m. Calculate the length PR.

16. Prove that tan²θ – sin²θ = tan²θ.sin²θ

 

SECTION  D

21. A sweet seller has 420 kaju barfis and 130 badam barfis. He wants to stack them in such a way that each stack has the same number and they take up the least area of the tray. What is the maximum number of barfi’s that can be placed in each stack of this purpose? In India, sweets and festivals are inseparably linked with each other. According to you what values are associated with the celebration of festivals?