CBSE Guess Paper
Subject – Mathematics
Class - 10th
1. Show that 5 − 2 √3 is irrational number.
OR
Show that 5 - 3√2 is an irrational number.
2. Obtain all zeros of polynomial x4 + x3 − 34x2 − 4x +120 if two of its zeros are 2 and ‐2.
3. If α & β are the zeroes of polynomial x2 – 6x + k. Find k such that (α + β)2 - 2αβ = 24.
4. Two customers SEAROSE and POOJA are visiting a particular shop in the same week ( Tuesday to Saturday ). Each is equally likely to visit the shop on any day so on another day . What is the probability that both will visit the shop on (i) same day ?(ii) consecutive days?( iii )different days ?
5. Prove that, the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
6. Solve abx2 + (b2-ac) x – bc = 0 (a,b,c ε R).
7. Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
8. What is the probability of 53 Sundays in a leap year and non leap year? And what will be the probability of 54 Sundays in each year?
9. If a hexagon ABCDEF circumscribe a circle. Prove that AB+CD+EF=BC+DE+FA.
10. AB is the diameter of the circle AC= 6cm and BC= 8cm .Find the area of the shaded region.
11. A card contains cards numbered 1 to 100 one card is drawn at random find the probability that
(a) It is multiple of 3 but not multiple of 9
(b) A perfect square
(c) A perfect cube
12. Romila went to a stationery shop and purchased 2 pencils and 3 erasers for Rs 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs 18. Represent this situation algebraically and graphically.
13. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
14. A motorboat takes 6 hours to cover 100km down stream and 30km upstream. If the motorboat goes 75km down stream and returns back to its starting point in 8hours, find the speed of the motorboat in still water and the rate of the stream.
15. If the equation (1 + m2) x2 + 2 mcx + (c2 - a2) = 0 has equal roots, prove that c2 = a2(1 + m2).
16. 4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750. Find the cost of 1 chair and 1 table separately.
17. The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
18. Given ΔABC, ∠A = 900 ,and AD┴BC,Prove that AD2= BD.CD
19. The median of the following data is 32.5. Find x & y.
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | |
| Frequency | x | 5 | 9 | 12 | y | 3 | 2 | Total=40 |
20. Find the mean with the following given data:
| Class Interval | 0‐6 | 6-12 | 12-18 | 18-24 | 24-30 |
| Frequency | 6 | 8 | 10 | 9 | 7 |