CBSE CLASS 10 MATHEMATICS QUESTION PAPER

Sample Paper – 2010

Class – X

Subject – Mathematics

Time: 3 hrs    
M.M. 80

                        

 General instructions:

1.   All the questions are compulsory

2.   The question paper consists of 30 questions divided into four sections A, B, C and D. Section A contain 10 questions of 1 mark each; section B contains 5 questions of 2 marks each, Section C contains 10 questions of 3 marks each, section D contains 5 questions of 6 marks each.  

3.   There is no overall choice. However, an internal choice has been provided in one question of 2 marks, three questions of 3 marks each and two questions of 6 marks each.

                                                       SECTION A

Q1. State fundamental theorem of arithmetic?

Q2. If a_n = 2 – 2n, find the value of 19 ^th term of an AP.

Q3. Find the HCF of 40 and 130.

Q4. 1 is zero of x³ – k, find the value of k.

Q5. Find the value of 2sin30⁰/ (tan²45⁰+cosce²45⁰).

Q6. Find the value of k, if the equation kx²+4x+4=0 have real and equal roots.

Q7. Find the value of x, if the mean of 10, 15, 5, x, 8 is 20.

Q8. Find the 30^th term of 10, 7, 4…

Q9.  What is the probability of sure event?

Q10. Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion.

                                 SECTION B

Q11. Prove that for number n ε N, 12ⁿ end with the digit zero.

Q12. Two concentric circles are of radii 5 cm and 3 cm. find the length of the chord of the larger circle which touches the smaller circle.

Q13. Draw a circle of radius 6 cm from a point 10 cm away from its centre , construct the pair of tangents to the the circle and measure their lengths.

Q14. Find the value of k for which the following points are collinear,  ( 7 , -2 ) , ( 5 , 1 ) , ( 3 , k )

                                          

Q15.  If tanA = 4/3 then find the value of sinA + cosA/ cosec A

OR

     Evaluate    2 cos67⁰/ sin 23⁰ - tan 40⁰ / cot 50⁰ – sin 90⁰

                                                       SECTION C

Q16.  2 woman and 5 men can together finish a piece of embroidery in 4 days, while 3 woman and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery, and that taken by 1 man alone.

Q17. Draw the graphs of the equations 2x-y+6=0 and 4x+5y-16=0. Also determine the coordinate of the vertices of the triangle formed by these lines and x axis.

OR

 Find the value of k of for which the following system of equations has infinitely many solutions   12x +k y = k   ,   k x+ 3 y = k-3

Q18. Solve the equation by using quadratic formula.

                abx² + (b² -ac) x – b c = 0

                               OR

The sum of the squares of two consecutive natural numbers is 421. Find the numbers.

Q19. The n^th term of an AP is given by a_n=9-5n, find the sum of first 15 terms of an AP.

Q20. Draw a pair of tangents to circle of radius 5 cm which are inclined to each other at an angle of 60⁰.

OR

Prove that: Tan A/ (1 –tan A) +cot A / (1 – tan A)= 1 + sec A .cosec A

Q21. Find the roots of the equation 9x²-15x+6=0 by method of    completing the square.

Q22. Prove that ( 4 , 3 ) , ( 6 , 4 ) , ( 5 , 6 ) and  ( 3 , 5 ) are the vertices of a rhombus.

                                                               

Q23. State and prove Basic Proportionality theorem.

   By using theorem in the given figure prove that 1/x   + 1/y = 1/z

                                  A                    B

                                               C

                                       X      z        y

                                     D                   F  

                                               F

Q24  Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h. how much area will it irrigate in 30 minutes, if 8 cm of standing water is needed.

 Q25. Find the sum of all natural numbers between 100 and 500 which are divisible by 8.

                                                       SECTION D

Q26. Find the mean, median and mode of the following frequency distribution table

 Classes:  5 – 10   10 – 15    15 – 20   20 – 25    25 - 30  30 – 35

 Frequency: 10       2           4         5          7          9

Q27.The angle of elevation of the bottom and top of a flag staff at the top of a building as seen from a point at a horizontal distance of 10 m from the foot of the building are 30⁰ and 45⁰ respectively. Find the height of the flag staff.

Q28.Prove that (TanA + sec A – 1)/(tanA – secA + 1)=(1 + sin A)/ cos A

OR

  Solve: 4/(x + y) = 6 / (x – y) +3, 1 / 2 (x +y) = 1/ 3(x-y) +3/2

Q29.In a∆ ABC, AD is a median and AE is perpendicular to BC.If BC= a, CA= b, AB=c, AD = p, AE = h and DE = x, prove that b²+c² = 2p² + ½ a².

Q30.  Solve for x, (2x + 2) / (x – 1) + (x – 2) / (x + 1) = 5 /2

                                  OR   

                                                                                  In a circle of radius 21 cm, an arc subtends an angle of 60⁰ at the centre. Find

(a)                     The length of an arc

(b)                     Area of the sector formed by the arc

(c)                     The area of the segment formed by the corresponding chord.