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10th math sample paper 2012

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                                                            SECTION – A

1. State Euclid’s division lemma.
2. If one zero of polynomial 5x2+13x+a  is reciprocal of the other, find the value of other.
3. In ΔABC, DE||BC meeting AB at D and AC at E. If AB/BD= 4and CE = 2 cm,
    find the length of AE.
4. If 4 cotA = 3, find the value of (sinA- 4cos) / (sinA+ 4cos)
5.  Find the value of 4cot2θ − 4cos ec2θ .
6. Find the value of   sin 36 / 2cos54  -  2sec 41/3cos ec49
7. Why is 11/30a non‐terminating decimal number?
8. Find he value of ‘k’ if following system of equations has no solutions: 3x-y-5=0 ; 6x-2y-k=0.
9. If cosA = 3/5, find 9cot2 A−1.
10. The point of intersection of o gives is given by ( 20.5, 30.4). What is median ?                                                          
                                                            SECTION – B

11. Is 7×5×3×2+3 a composite number. Justify your answer.
12. Find the zeros of polynomial 7x2 −6−11x and verify the relation between zeros and coefficients of polynomial.
13. Solve for x and y : a/x- b/y = 0; ab2/x - a b /y= a2 + b2
14. Find A if sin(A+36)=cosA,where A+36 is acute angle.
15. In figure EF || DC|| AB, prove that           ED/ AE  =   FC/BF


16. In an equilateral Δ ABC, Ad is altitude drawn from A to BC. Prove that 3AB2=4AD2.
17. Find the mode marks from following data:
Marks Obtained       0-10        10-20              20-30    30-40   40-50
No. of Students          6               8                     5            4          4

18. Following table gives the scores of 100 candidates in an entrance examination: Find mode.

Marks              100-150   150-200    200-250   250-300  300-350  350-400
No. of Students            16           15       14                 32            11            12

                                                            SECTION-C

19. Show that any positive odd integer is of the form 6p+1 or 6p+5, where p is some integer.
20. show that 5−2Ö3 is irrational number.OR Show that 5Ö2  / 3
21. A number consists of two digits whose sum is 9. If 27 is added to the number, the digits are interchanged. Find the number.
22. Obtain all zeros of polynomial x4+x3−34x2−4x+120 if two of its zeros are 2 and -2.
23. prove that: cos / (1+sinA)   +   (1+ sinA) /cosA= 2sec
24. If cosθ +sinθ = 2 cosθ , then show that cosθ −sinθ = 2 sinθ .
25. D is any point on the side BC of Δ ABC such that <ADC = <BAC .Prove that
CA /CD=CB/CA.
26. Δ ABC and Δ DBC are on the same base BC. AD and BC intersect at O.
 Prove that ar DABC /  ar DDBC   =   AO/ DO.

27. Using step deviation method, calculate arithmetic mean of the following:
Class Interval   0-20   20- 40  40-60 60-80 80-100 100-120
Frequency         20       35        52      44      38           31

OR ,    Find the value of ‘p’ if mean of following data is 53.
Class                  0-20    20-40     40-60     60-80     80-100
Frequency             12         15           32       p         13

28. 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
29. On dividing P(x) = 3x3−2x2+5x−5 by a polynomial g(x), we get quotient and remainder as
 x2 − x + 2 and-7 respectively. Find g(x).

30. Prove that : (1 + sinA -cos A)  ¸ (sinA- 1 + cosA )  =  (cosA) ¸(1- sinA)

OR  (sec. cosec(90-A ) tan .cot(90-A ) + (sin255+ sin235) ¸ (tan10. tan 20. tan30. tan70. tan80)
31. Prove that in a triangle the line drawn parallel to one side ,divides the other two sides proportionally.
 OR,
Prove that in a right angled triangle, the square of hypotenuse is equal to sum of the squares of other two sides.

32. If x   =   psecθ+qtanθ and y=p tanθ + q secθ , prove that x2−y2   =  p2−q2.
33. 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.

34. Daily pocket expenses of (in Rs) of 80 students of a school are given in the table below:

Expenses                                0-5    5-10   10-15    15-20     20-25     25-30     30-35
No. of students.                         5       15      20           10         10          15            5

Change the data into a’ more than type table’ and hence draw ‘more than type ogive.
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