Board : Central Board Of Secondary Education
Exam : Class X
Subject : Mathematics
Document Type : Sample Paper
Website : cbse.nic.in
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/cbse.nic.in/7040-Math06.pdf
Mathematics Sample Question Paper-I :
Class X :
Subject : Mathematics
Time : 3 Hours
Max Marks : 100
Related : Central Board Of Secondary Education Business Studies Model Question Paper : www.pdfquestion.in/7039.html
General Instructions :
1. All questions are compulsory.
2. The question paper consists of 25 questions divided into three sections A, B and C. Section A contains 10 questions of 3 marks each, Section B is of 10 questions of 4 marks each and Section C is of 5 questions of 6 marks each.
3. There is no overall choice. However, internal choice has been provided in two questions of three marks each, two questions of four marks each and two questions of six marks each.
4. In question on construction, the drawing should be neat and exactly as per the given measurements.
5. Use of calculators is not permitted. However, you may ask for Mathematical tables.
SECTION A :
Q1. Solve the following system of equations :
15x + 4y = 61
4x + 15y = 72
Q2. Reduce the following rational expression to its lowest terms :
Q3. PQ and RS are two parallel chords of a circle and the lines RP and SQ meet at O on producing (as shown in the given figure)
Prove that OP=OQ
x2 + 3x + 9
x2 — 25
x3 — 27
(x2 + 3x — 10)
Q4. A suit is available for Rs. 1500 cash or for Rs. 500 cash down payment followed by 3 monthly instalments of Rs. 345 each. Find the rate of interest charged under the instalment scheme.
Q5. A loan has to be returned in two equal annual instalments. If the rate of interest is 16% per annum compounded annually and each instalment is of Rs. 1682, find the sum borrowed and the total interest paid.
Q6. If (x — 2) is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller, find the numbers.
Q8. Which term of the A.P. 3, 15, 27, 39…. is 132 more than its 54th term ?
OR
Derive the formula for the sum of first n terms of an A.P. whose first term is ‘a’ and the common difference is ‘d’
Q9. Find the sum of the following arithmetic progression 1+3+5+7+…………….+199
Q10. Show that a line drawn parallel to the parallel sides of a trapezium divides the non nonparallel sides proportionally.
SECTION B :
Q11. Solve for x, + = , (x = -1, -2, -4)
Q12. Find graphically, the vertices of the triangle formed by the x-axes and the lines
2x — y + 8 = 0
8x + 3y — 24 = 0
Q13. Construct a triangle ABC in which BC = 13cm, CA = 5cm and AB = 12cm. Draw its incircle and measure its radius.
Q14. The total surface area of a closed right circular cylinder is 6512 cm², and the circumference of its base is 88 cm. Find the volume of the cylinder (use p = )
Q16. Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.
OR
Using distance formula, show that the points (-1, -1), (2, 3) and (8, 11) are collinear.
Q17. Find the ratio in which the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3). Hence find the value of p.
Q18. Compute the missing frequencies ‘f1’ and ‘f2’ in the following data if the mean is 166 and the sum of observations is 52.
Q19. An unbiased dice is tossed
i) Write the sample space of the experiment
ii) Find the probability of getting a number greater than 4
iii) Find the probability of getting a prime number.
Q20. The pie chart (as shown in the figure) represents the amount spent on different sports by a sports club in a year. If the total money spent by the club on sports is Rs. 1,08,000/-, find the amount spent on each sport.
SECTION C :
Q21. Prove that the angle subtended by an arc of a circle at its center is double the angle subtended by it at any point on the remaining part of the circle. Using the above result prove that the angle in a major segment is acute.
Q22. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Using the above, prove that the area of an equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.
Q23. From the top of a tower 60m. high, the angles of depression of the top and bottom of a building whose base is in the same straight line with the base of the tower are observed to be 30° and 60° respectively. Find the height of the building.
OR
An aeroplane flying horizontally at a height of 1.5km above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 seconds, its angle of elevation at the same point is observed to be 30°. Calculate the speed of the aeroplane in km/h.