Section-1
1) If x =/= -1, then find the Quotient of x^5 + x^4 +x^3 + x^2
x^3 +x^2 + x + 1
2) Insert 4 rational numbers between 3/4 and 1 without using a+b formulae
2
3) If A = {x : x (≡ N and x<20 } and
B = { x : x (≡ N and x< 5 }
then write the set A - B in the set-builder form.
4)For what value of K , the following system of equations has a unique solution.
x - Ky = 2
3x + 2y = -5.
5) " we can write a trinomial having degree 7".
Justify the above statement by giving one example.
6) Find the centroid of a triangle, whose vertices are (3,4) (-7,-2) and (10, -5).
7). The hand-borewell driller charges Rs.200/- for the first one meter only and raises drilling charges at the rate of Rs.30/- for every subsequent meter . Write a progression for the above data.
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Section-2
8) Write any three numbers of two digits . Find the L.C.M and H.C.F for the above numbers by the "Prime Factorization method."
9) " If we divide or multiply both sides of a linear equation by a non-zero number, then the roots of that linear equation will remain the same ." Is it true? If so, justify with an example.
10) In a flower garden, there are 23 plants in the first row, 21 plants in the second row,19 plants in the third row and so on. If there are 10 rows in that flower garden , then find the total number of plants in the last row with the help of the formula
tn = a + (n-1)*d
11) Give an example for each of the following:
(!) The product of two irrational numbers is rational number.
(!!) The product of two irrational numbers is an irrational number.
12) If A={x : x (≡ N, x<6} and
B ={ x: x (≡ N, 3<x<8}
then show that A - B =/= B - A with the help of Venn diagram.
13) Show that the points A(4,2), B(7,5), C(9,7) are collinear.
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Section -3
14) (A) Prove that 3 + 2√5 is an irrational number.
OR
(B) Name the type of the quadrilateral formed by joining the points A(-1,-2), B(1,0), C(-1,2) and D(-3,0) on a graph paper. Justify your answer.
15(A) Laxmi does not want to disclose the length, breadth and height of a cuboid of her project. She has constructed a polynomial x^3 - 6x^2+ 11x -6 by taking the values of length, breadth and height as its zeroes. Can you open the secret?(Find the measures of Length, breadth and height)?
OR
(B) Solve the pair of equations by reducing them to a pair of linear equations
5 + 1 = 2 and 6 - 3 = 1
x-1 y -2 x -1 y -2
16(A) Draw a graph for the following pair of linear equations in two variables and find their solution from the graph.
2x + y = 5
3x - 2y = 4
OR
(B) Draw a graph for the polynomial p(x) = x^2 + 3x - 4 and find its zeroes from the graph.
17(A) If nth term of the geometric progression 162, 54, 18,.....and 2/81, 2/27, 2/9.......are equal. Find the value of n.
OR
(B) If the sum of the 7 terms of Arithmetic Progression is 49 and that of first 17 terms is 289, then find the sum of the first 'n' terms.
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1) If x =/= -1, then find the Quotient of x^5 + x^4 +x^3 + x^2
x^3 +x^2 + x + 1
2) Insert 4 rational numbers between 3/4 and 1 without using a+b formulae
2
3) If A = {x : x (≡ N and x<20 } and
B = { x : x (≡ N and x< 5 }
then write the set A - B in the set-builder form.
4)For what value of K , the following system of equations has a unique solution.
x - Ky = 2
3x + 2y = -5.
5) " we can write a trinomial having degree 7".
Justify the above statement by giving one example.
6) Find the centroid of a triangle, whose vertices are (3,4) (-7,-2) and (10, -5).
7). The hand-borewell driller charges Rs.200/- for the first one meter only and raises drilling charges at the rate of Rs.30/- for every subsequent meter . Write a progression for the above data.
******************************************************
Section-2
8) Write any three numbers of two digits . Find the L.C.M and H.C.F for the above numbers by the "Prime Factorization method."
9) " If we divide or multiply both sides of a linear equation by a non-zero number, then the roots of that linear equation will remain the same ." Is it true? If so, justify with an example.
10) In a flower garden, there are 23 plants in the first row, 21 plants in the second row,19 plants in the third row and so on. If there are 10 rows in that flower garden , then find the total number of plants in the last row with the help of the formula
tn = a + (n-1)*d
11) Give an example for each of the following:
(!) The product of two irrational numbers is rational number.
(!!) The product of two irrational numbers is an irrational number.
12) If A={x : x (≡ N, x<6} and
B ={ x: x (≡ N, 3<x<8}
then show that A - B =/= B - A with the help of Venn diagram.
13) Show that the points A(4,2), B(7,5), C(9,7) are collinear.
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Section -3
14) (A) Prove that 3 + 2√5 is an irrational number.
OR
(B) Name the type of the quadrilateral formed by joining the points A(-1,-2), B(1,0), C(-1,2) and D(-3,0) on a graph paper. Justify your answer.
15(A) Laxmi does not want to disclose the length, breadth and height of a cuboid of her project. She has constructed a polynomial x^3 - 6x^2+ 11x -6 by taking the values of length, breadth and height as its zeroes. Can you open the secret?(Find the measures of Length, breadth and height)?
OR
(B) Solve the pair of equations by reducing them to a pair of linear equations
5 + 1 = 2 and 6 - 3 = 1
x-1 y -2 x -1 y -2
16(A) Draw a graph for the following pair of linear equations in two variables and find their solution from the graph.
2x + y = 5
3x - 2y = 4
OR
(B) Draw a graph for the polynomial p(x) = x^2 + 3x - 4 and find its zeroes from the graph.
17(A) If nth term of the geometric progression 162, 54, 18,.....and 2/81, 2/27, 2/9.......are equal. Find the value of n.
OR
(B) If the sum of the 7 terms of Arithmetic Progression is 49 and that of first 17 terms is 289, then find the sum of the first 'n' terms.
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