CBSE Guess Paper
Subject – Mathematics
Class - X
1. Draw a ∠ABC such that BC=6cm, AB=5cm ∠ABC=60othen construct a triangle whose side is 4/3 times corresponding sides of ∠ ABC.
2. Name the type of quadrilateral formed by the points (1,7) (4,2) ( -1 ,-1) and (-4 ,4) are in order.
3. Show that any positive odd integer is of the form 6p+1 or 6p+5, where p is some integer.
4. Show that the square of any positive even integer is of the form 2q & every positive odd integer is of the form 2q + 1.
5. Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is
a. an even number
b. a number less than 14
c. a number which is a perfect square
d. a prime number less than 20.
6. If the roots of the equation (b-c) x2 +(c-a) x+ (a-b)=0 are equal then prove that 2b= a+c.
7. Find the roots of the equation 63/x + 72/(x+6)=3.
8. In a potato race, a bucket is placed at the starting point, which is 5m from the first potato and other potatoes are placed 3m apart in a straight line. There are ten potatoes in a line. A competitor starts from the bucket, picks up the nearest potato, runs back to pick up the next potato, runs to the buckets to drop it in and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
9. Solve the following system of linear equations: 3x - 5y = -1, x - y = –1.
10. A passenger train takes 2 hours less for journey of 300 km, if its speed is increased by 5 km/h from its usual speed, find its usual speed.
11. A man has only 20 paisa coins and 25 paisa coins in his purse. If he has 50 coins in all totaling Rs 11.25, how many coins of each kind does she has?
12. On dividing x3 + x2 + x – 2 by a polynomial g(x),the quotient and remainder were x2 + 2x + 1 and 2x - 1 respectively. Find g(x).
13. Find the largest number that will divide 398,436 and 542 leaving remainder 7,11,15,respectively.
The mean of following distribution is 53. Find the value of p.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 12 | 15 | 32 | P | 13 |
14. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
15. A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student X, takes food for 25 days, he has to pay Rs. 1750 as hostel charges whereas a student Y, who takes food for 28 days, pays Rs. 1900 as hostel charges. Find the fixed charge and the cost of food per day.