Section-1
1) Find the value of log5 125
2) If A = {1 , 1, 1, 1, 1 }, then write A in set-builder form.
4 9 16 25
3) Write an example for a quadratic polynomial that has no zeroes.
4) If b^2 - 4ac > 0 in ax^2 + bx + c = 0, then what can you say about roots of the equation?(a=/=0)
5) Find the sum of first 200 natural numbers.
6) For what values of m, the pair of equations 3x + my = 10 and 9x + 12y = 30 have a unique solution.
7) Find the mid-point of the line segment joining the points
(-5,5) and (5,-5)
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Section-2
8) If x^2 + y^2 = 7xy; then show that 2log(x+y) = logx + logy +2log3
9) Length of a rectangle is 5 units more than its breadth. Express its perimeter in polynomial form.
10)Measures of sides of a triangle are in Arithmetic Progression. Its perimeter is 30 cm, and the difference between the longest and shortest side is 4cm; then find the measures of the sides.
11) Show that the points A(-3,3), B(0,0), C(3,-3) are collinear.
12) Solve the following pair of linear equations by Substitution method. 2x - 3y = 19 and 3x - 2y = 21.
13) If 9x^2 + kx + 1 = 0 has equal roots , find the value of k.
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Section-3
14) Use Euclid's division lemma to show that the cube of any positive integer is of the form 7m or 7m + 1 or 7m+6.
OR
Prove that √2 - 3√5 is an irrational number.
15) Draw the graph for the polynomial p(x) = x^2 - 3x + 2 and find the zeroes from the graph.
OR
Draw the graph for the following pair of linear equations in two variables and find their solution from the graph.
3x - 2y = 2 and 2x + y = 6
16) Sum of the squares of two consecutive positive even integers is 100; find those numbers by using quadratic equations.
OR
X is a set of factors of 24 and Y is a set of factors of 36, then find sets X ∪ Y and X∩Y by using Venn diagram and comment on the answer.
17) Find the sum of all the three digit numbers, which are divisible by 4.
OR
Find the co-ordinates of the points of trisection of the line segment joining the points (-3,3) and (3,-3)
1) Find the value of log5 125
2) If A = {1 , 1, 1, 1, 1 }, then write A in set-builder form.
4 9 16 25
3) Write an example for a quadratic polynomial that has no zeroes.
4) If b^2 - 4ac > 0 in ax^2 + bx + c = 0, then what can you say about roots of the equation?(a=/=0)
5) Find the sum of first 200 natural numbers.
6) For what values of m, the pair of equations 3x + my = 10 and 9x + 12y = 30 have a unique solution.
7) Find the mid-point of the line segment joining the points
(-5,5) and (5,-5)
*******************************************************
Section-2
8) If x^2 + y^2 = 7xy; then show that 2log(x+y) = logx + logy +2log3
9) Length of a rectangle is 5 units more than its breadth. Express its perimeter in polynomial form.
10)Measures of sides of a triangle are in Arithmetic Progression. Its perimeter is 30 cm, and the difference between the longest and shortest side is 4cm; then find the measures of the sides.
11) Show that the points A(-3,3), B(0,0), C(3,-3) are collinear.
12) Solve the following pair of linear equations by Substitution method. 2x - 3y = 19 and 3x - 2y = 21.
13) If 9x^2 + kx + 1 = 0 has equal roots , find the value of k.
*******************************************************
Section-3
14) Use Euclid's division lemma to show that the cube of any positive integer is of the form 7m or 7m + 1 or 7m+6.
OR
Prove that √2 - 3√5 is an irrational number.
15) Draw the graph for the polynomial p(x) = x^2 - 3x + 2 and find the zeroes from the graph.
OR
Draw the graph for the following pair of linear equations in two variables and find their solution from the graph.
3x - 2y = 2 and 2x + y = 6
16) Sum of the squares of two consecutive positive even integers is 100; find those numbers by using quadratic equations.
OR
X is a set of factors of 24 and Y is a set of factors of 36, then find sets X ∪ Y and X∩Y by using Venn diagram and comment on the answer.
17) Find the sum of all the three digit numbers, which are divisible by 4.
OR
Find the co-ordinates of the points of trisection of the line segment joining the points (-3,3) and (3,-3)
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