FA JULY 2014 X MATHEMATICS

JAWAHAR NAVODAYA VIDYALAYA HOTHPETH GULBARGA

FORMATIVE  TEST (JULY-2014)

Mathematics: X                              Time to be allowed: 1 Hour                                   Max marks:50

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QUESTIONS OF ONE MARK EACH

1.       For some integer m,every even integer is of the form    is -----

a)      m              b)  m+1                  c)  2m             d) 2m+1

2.      Euclids division algorithm states that for every positive integers a, and b there exist unique integers ‘q’ and “r” such that  a=bq+r , where

a)     0        b) 0≤ q            

c) 0 ≤ r < b.       d) 0        

3.      Condition for inconsistent solution of pair of linear equation a₁x+b₁y+c₁=0and a₂x+b₂y+c₂=0 will have -------

                         a) ≠ ,     .b) ≠ =     c)  =  =   d)  =  ≠

4.      How many solutions do the pair of linear equations in two variable have, if their graph is       intersecting in only one  point.

                 a)  One solution.  b) Two solution.   c)  Three solutions     d) infinite number of solutions

5.      Which of the fallowing is not a graph of  a quadratic polynomial?

a)                                                           b)

 

c)                                                              d)

 

                                                                                                                                         

QUESTIONS OF TWO  MARKS EACH

6.      Obtain the HCF of 867 and 255 using Euclids division algorithm.

7.      Write the quadratic polynomial whose zeroes are , -5 and 4.

8.      If  -4 is one of the zeroes of the polynomial : x² –x –(2k+2) =0 then find the value of ‘k’.

9.      Find the sum and product of the zeroes of the quadratic  polynomial:  2 x²  - 4x - 5=o

10. Without drawing the graph of pair of linear equation:2x+5y+7=0 and 4x+10y = -14, predict its nature.

11. For what value of ‘k’ will the fallowing pair of linear equations: kx+3y =k-3, and 12x + ky =k, have an infinite number of solution.

12.    Is   8x7x6x5+ 5 a composite? If so justify.

 QUESTIONS OF THREE  MARKS EACH

13.      The cost of 3 Mathematics books and  2 English books together  is Rs2250 where as  2 Mathematics books and 3 English books is 2750. Obtain the cost of each Mathematics book and English book separately.  Hence find what is the amount to be paid towards the purchase of 5 Mathematics Books and 2 English books.

14.  Solve the system of equations:   + =8,        &       + = 9.

15.    Find the zeroes of quadratic polynomial 4x²-4x-3 and verify the relation between the zeroes and its coefficients.

16. If the polynomial: x⁴+2x³+8x²+12x+18 is divided by the another polynomial x² +5 then remainder comes -out to be px +q, find the value of p and q.

17.    Prove that 5-2√3   is an irrational.

QUESTIONS OF THREE  MARKS EACH

18. A boat goes 32 km up stream and 36 km downstream in 7 hours, Also it covers 40km up  stream  and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.

19.  solve the fallowing system   of equations graphically:3x+y-12=0 and x-3y+6=0 shade the region bounded by these lines and abscissa, also find the ratio of areas of triangles formed by  two given lines and   x-axis and Y-axis .

20. If two zeroes of polynomial, p(x) = x⁴ -6x³ -26x² +138x -35 are 2 +√3, then find the other zeroes.

21. If two zeroes of p(x) = 5x⁴ -5x³ -33x² +3x +18 , are + √3/5  ,  &   -  √3/5 then find the other zeroes.