CBSE Guess Paper
Mathematics
Class - X
1. Prove that in a right angled triangle, the square of hypotenuse is equal to sum of the squares of other two sides.
2. If x sin3θ + y cos3θ = sinθ . cosθ and x sinθ = y cosθ prove x2 + y2 = 1.
3. On the same axes draw the graph of each of the following equations: 2x – y +1 =0; x – 5y +14 =0; x – 2y +8=0. Hence shade the region of the triangle so formed.
4. Obtained all the zeros of the polynomial x4 – 7x3 + 17x2 – 17x + 6. If two of its zeroes are 3 & 1.
5. If x = p secθ + q tanθ and y = p tanθ + q secθ, prove that x2 – y2 = p2 – q2.
6. Prove that the areas of two similar Δ’s are in the ratio of the squares of the corresponding altitudes.
7. 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 |
8. If tan(A+B) = 1 and sin (2A - B) = 1, find A and B.
9. A man travels 370 km partly by train and partly by car . If he covers 250 km by train and the rest by car it takes him 4 hours . But if he travels 130 km by train and the rest by car , he takes 18 minutes longer . Find the speed of the car and the train.
10. A number consisting of two digits is equal to 7 times the sum of its digits. When 27 is subtracted from the number, the digits interchange their places. Find the number.
11. Solve the following pair of equations graphically: x + 2y =5, 2x +3y = -4. Also find the points where the lines meet the x-axis.
12. A swimming pool is filled with three pipes with uniform flow. The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by third pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than the third pipe. Find the time required by each pipe to fill the pool separately.