Download X SAMPLE PAPERS Maths SA 1 (with Solution) 2012-2014

CLASS X  SAMPLE PAPERS  SCIENCE  SA 1 (with Solution) 2012-2014
1. X SCIENCE SAMPLE PAER- 1	2. X SCIENCE SAMPLE PAER-2
3. X SCIENCE SAMPLE PAER-3	4. X SCIENCE SAMPLE PAER- 4
5. X SCIENCESAMPLE PAER- 5	Source: kv1madurailibrary
CLASS X SAMPLE PAPERS Maths SA 1 (with Solution) 2012-2014
1. X MATHSSAMPLE PAER- 1	2. X MATHS SAMPLE PAER-2
3. X MATHS SAMPLE PAER 3	4. X Maths SAMPLE PAER- 4
5. X MATHS SAMPLE PAER-5	Source: kv1madurailibrary

10th maths Chapter Polynomial extrascore questions

Math Adda  

Chapter: POLYNOMIALS        

LEVEL-I

1. The zeroes of the polynomial 2x²-3x-2 are

a. 1, 2        b. -1/2,1    

c. ½,-2      d. -1/2,2                       [Ans- (d)]

2. If a and b are zeroes of the polynomial 2x²+7x-3, then the value of a² +b² is

a. 49/4                b. 37/4       

c. 61/4                d. 61/2                                                      
Ans-( c ) 

3. If the polynomial 6x³+16x²+px -5 is exactly divisible by 3x+ 5 , then the value of p is

a. -7      b. -5     

c.5        d.7                                                                                  
[Ans- (d )]

4. If 2 is a zero of the polynomials 3x2+ax-14 and 2x3+bx2+x-2, then the value of 2 - 2b is

a. -1       b. 5         

c. 9       d. -9                         

[Ans-( c ) ]

5. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is

(a) 3x² – x +3√ 2 (b) 3x² + x - 3√2 (c) 3x² + 3√2x +1 (d) 3x² – 3√2x +1         
[ Ans: (d)]

LEVEL-II

1. If 1 is a zero of the polynomial p(x) = ax² -3(a-1) x -1, then find the value of a.       
Ans: a=1

2. For what value of k, (-4) is zero of the polynomial x² – x – (2k+2)?                          
Ans: k=9

3. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and -2. 
Ans: x² -3x-2

4. Find the zeroes of the quadratic polynomial 2x²-9-3x and verify the relationship between the zeroes and the coefficients.                                   Ans: 3, -3/2

5. Write the polynomial whose zeroes are 2 +√3 and 2 - √3.          Ans: p(x)=x2-4x+1

LEVEL – III

1. Find all the zeroes of the polynomial 2x³+x²-6x-3, if two of its zeroes are -√3 and √3. 
Ans: x=-1/2

2. If the polynomial x⁴ + 2x³ + 8x²+12x+18 is divided by another polynomial x² + 5, the remainder comes out to be  px+q. 

Find the value of p and q.                                                         Ans:p=2,q=3

3. If the polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, the remainder  comes out to  be (ax+b), find a and b.                      Ans:a=1, b=2

4. If two zeroes of the polynomial f(x)= x³-4x²-3x+12 are √3 and -√3, then find its third zero. Ans: 4

5. If a, b are zeroes of the polynomial x²-2x-15 then form a quadratic polynomial whose zeroes are  (2a) and (2b).              Ans: x²-4x-60

LEVEL – IV

1. Find other zeroes of the polynomial p(x)=2x⁴ +7x³19x²-14x +30 if two of its zeroes are √2 and -
√2.

Ans: 3/2 and -5

2. Divide 30x⁴ +11x³-82x²-12x-48 by (3x² +2x-4) and verify the result by division algorithm.

3. If the polynomial 6x⁴ +8x³-5x²+ax+b is exactly divisible by the polynomial 2x²-5, then find the 
value of a and b.     
Ans: a = -2 0 , b = - 2 5

4. Obtain all other zeroes of 3x⁴ -15x³+13x²+25x-30, if two of its zeroes are and ±√5/3. 
Ans: 
±√5/3,3,2

5. If a, b are zeroes of the quadratic polynomial p(x)=kx²+4x+4 such that a² +b²=24, find the value 
of k.                                                                        
Ans: k=2/3 or k= -1

SELF EVALUATION

1. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find (a) a/b +b/a (b) a² +b²

2. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a² - b²

3. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a³ +b³

4. What must be added to 6x⁵+5x⁴+11x³-3x²+x+5 so that it may be exactly divisible by 3x² -2x+4 ?

5. If the square of difference of the zeroes of the quadratic polynomial f(x)= x²+px+45 is equal to 144, 
find the value of p.

Sample Paper – 2012 Class – X Subject – Mathematics

1. A motorboat takes 6 hours to cover 100km down stream and 30km upstream. If the motorboat goes 75km down stream and returns back to its starting point in 8hours, find the speed of the motorboat in still water and the rate of the stream.

2. Solve the following system of linear equations: 3x - 5y = -1, x - y = -1


3. The polynomial x4 +bx³ +59 x² +cx +60 is exactly divisible by x² +4 x +3. Find the values of b and c.


4. If the equation (1 + m2) x2 + 2 mcx + (c2 - a2) = 0 has equal roots, prove that c2 = a2(1 + m2)


5. A polygon has 10 sides .The lengths of the sides starting with the smallest form an AP .If the perimeter of the polygon is 420 Cm and the length of the longest side is twice that of the shortest side

6. A train covers a distance of 90 Km at uniform speed .Had the speed been 15 Km /hr more . it would have taken 30 minutes less for the journey find the original speed of the train

CBSE NCERT MATH 10th Sample Question Papers for Term I

(September 2011)

Science (Class IX & X)

Mathematics (Class IX & X)

Social Science (Class IX)

CBSE Maths Sample Papers X 2011- 2012 Sem. 1

cbse maths papers 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

                                                             SECTIONC

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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