CBSE Board Sample Paper

Subject – Mathematics

Class – X

Time:3Hours                                                                        M.M.80

General Instructions:

(i)    All question are compulsory.
(ii)    The questions paper consists of 34 questions divided into 4 sections-A,B,C and D. Section-A comprises of ten question of 01 marks each. Section-B comprises of 8 question of 02 marks each. Section-C comprises of ten question of 03 marks each and Section-D comprises of six questions of 04 marks each.
(iii)    Use of calculator is not permitted.

Sections-A

1. Which one is not polynomial .

         a. x³-3x²+x+1               b.√5x²+x+1                   c. 8x^-2+x+1                 d. All are polynomia

2. Ratio of areas of two similar triangles whose corresponding sides are 8 cm and 12cm is

        a. 4/9                  b. 6/9                 c. 2/3                    d. 3/2

3. secA (1-sinA) (secA + tanA) equals to

                 a. sec²A + tan²A                         b. 1                    c. –1                 d. none

4. Remainder when 3x³+16x²+21x+20 is divided by x+4

            a. 10                     b. –10                    c. 0                               d. none

5. State Euclid’s division algorithm, find the HCF of 18864 and 6075.

6. If α , β and γ are roots of the equation x³–3 x² – x + 3 = 0, then find (i) α + β + γ         (ii) αβγ

7. If 4 cotA = 3, find the value of   (sinA - 4cosA)/(sinA + 4cosA).

8. If one zero of polynomial 5x² + 13x + a is reciprocal of the other, find the value of other.

9. Find he value of ‘k’ if following system of equations has no solutions: 3x-y-5=0 ; 6x-2y-k=0.

10. The point of intersection of ogives is given by ( 20.5, 30.4). What is median?

Section-B

11. Consider the number 6,Where n is a natural number.Check whether for any value ends with the digit zero.

12. Solve for and , x/a + y/b = 2, ax – by = a² – b².

13. Five years ago, A was thrice as old as B and 10 years hence A shall be twice as old as B. what are the present ages of A and B?

14. The angles of a triangle are in an AP. The least angle being half the greatest. Find the angles.

15. Find all zeros of the polynomial x⁴ + x³ - 9x² – 3x + 18, if it is given that two of its zero as are – √3 and √3.

16. Is 7x5x3x2+3 a composite number. Justify your answer.

17. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

18. If one diagonal of a trapezium divides the other diagional in ratio 1:2,Prove that one of the parallel side is double the other.

Section-C

19. A and B are friends and A is elder to B by 2 years. A’s father D is twice as old as A and B is twice as old as his sister C. if the ages of D and C differ by 40 years, find the age of A.

20. The polynomial x⁴ +bx³ +59 x² +cx +60 is exactly divisible by x² +4 x +3. Find the values of b and c.

21. A party of tourists booked a room in a hotel for Rs 1200 , three of the members failed to pay as a result others had to pay Rs 20 more (each) . How many tourists were there in the party.

22. Find the median of following data :

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
frequency	7	14	13	12	20	11	15	8

23. Show that any positive odd integer is of the form 6p+1 or 6p+5, where p is some integer.

24. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

25. Prove that 3√5 + 2 is an irrational number.

26. A polygon has 10 sides .The lengths of the sides starting with the smallest form an AP .If the perimeter of the polygon is 420 Cm and the length of the longest side is twice that of the shortest side .Find the first term and the common difference of the AP.

27. Obtain all zeros of polynomial x⁴ + x³ – 34x² – 4x + 120 if two of its zeros are 2 and -2.

28. A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find  the interest at the end of 30 years making use of this fact.

Section-D

29. If x = sinA & y = b tanA then Prove that a²/x² – b²/y² = 1.

30. If sinA + cosesA = 3, find the value of (sin⁴A + 1)/sin²A.

31. Draw the graphs of the pair of linear equation x – y + 2 = 0, 4x – y -4 = 0.Calculate the area of the triangle formed by the lines so drawn and the x – axis.

32. The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10km, the charges paid are Rs 75 and for a journey of 15km, the charge paid are Rs 110. What will a person have to pay for travelling a distance of 25 km?

34. Obtain all the zeroes of the polynomial f(x)=3x⁴+6x³-2x²-10x-5 if two of its zeroes are √5/3 and - √5/3.

35. A piece of cloth costs Rs 200. If the piece was 5 m longer and each metre of cloth costs Rs 2 less the cost of piece would have remained unchanged. How long is the piece and what is the original rate per metre.