Mathematics-2017-paper(1)

                                Section-1

1) Write the nature of roots of the quadratic equation 2x^2 -5x +6 =0


2) Find the value of log√2 256 .


3) In a GP , tn = (-1)^n.2017 . Find the common ratio.


4) Srikar says that the order of the polynomial (x^2 - 5) (x^3 +1) is 6. Do you agree with him? How?


5) A(0,3), B(k,0), and AB = 5. Find the positive value of k. 
 

6) Show that the pair of linear equations 7x + y = 10 and 
     x + 7y = 10 are consistent. 


7) Represent A∩B through Venn diagram, where A={1,4,6,9,10} and B={perfect squares less than 25}

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                                           Section-2 

8) Write any two three digit numbers. Find their L.C.M and G.C.D by prime factorization method 


9) Find the sum of first 10 terms of an A.P,..... 3,15,27,39........ 


10) Which of √2 and 2 is a zero of polynomial p(x)=x^3 -2x? why?


11) The sum of a number and its reciprocal is (10/3). Find the number.



12) Two vertices of a triangle are (3,2) (-2,1) and its centroid is 
     (5/3, -1/3). Find the third vertex of the triangle. 



13) Find the angle made by the line joining (5,3) and (-1,-3) with the positive direction of X-axis.


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                                     Section-3

14). From the following Venn diagram , write the elements of the sets of A and B  and verify 
n(A⋃B) + n ( A∩B) = n(A) + n(B) 

Use Euclid's division lemma to show that the square of any positive integer is of the form 5n or 5n+1 or 5n+4, where n is a whole number. 


15) Find the sum of all three digit natural numbers, which are divisible by 3 but not divisible by 6

                                             OR

Divide 3x^4 - 5x^3 + 4x^2 + 3x - 5 by x^2 - 3 and verify the division algorithm.




16) The perimeter of a right-angled triangle is 60cm. and its hypotenuse is 25 cm. Then find the remaining two sides. 

                                    OR

The points C and D are on the line segment joining A(-4,7) and
B(5,13) such that AC=CD=DB. Then find co-ordinates of points C and D




17) Draw the graph for the polynomial p(x) = x^2 - 5x + 6 and find the zeroes from the graph.

                                               OR

Draw the graph of 2x + y = 6  and 2x -y + 2 = 0 and find the solutions from the graph. 

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