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Quadratic Equations

Quadratic Equations Qustion 1 Divide 27 into 2 parts such that the sum of their reciprocals is 3/20. Qustion 2 A rectangular feild 16m long and 10m wide. There is a path of uniform width all around it having an atea of 120m^2. form the quadrotic equation for the givn problem? Qustion 3 An employer finds that he increases the weekly wages of each worker by Rs 3 and employs 1 worker less, He reduces his weekly wage bill from Rs 816 to Rs 781. Taking the original weekly wage of each worker as Rs 'x', form an equation in 'x' and solve it to find the weekly wage of each worker. QUSTION 4 Swati can raw a boat at a speed of 5km/h in still water. If she takes 1houer more to row the boat 5.25 km upstream and them to return downstream. Ten find the speed of the still water. Quadratic Equation: ax 2 + bx + c = 0 a = b = c = X 1 = X 2 =

Coordinate Geometry

Coordinate Geometry QUESTION 1 Find the coordinate of the point A , where AB is diameter of a circle whose center is (2, -3) and B is the point (1,4). QUESTION 2 Find the coordinate of a point A, where AB is diameter of the circle (-2, 2) and B is point with coordinate (3, 4). QUESTION 3 Find the ratio in which the segment joining the points (1, -3) and (4, 5) is divided by x-axis? Also find the coordinate of this point on x-axis. QUESTION 4 Write coordinates of a point P on x-axis which is equidistant from the point A (-2, 0) and B(6, 0). QUESTION 5 Find the point on y-axis which is equidistant from the point (5, -8) and (-3, 2). QUESTION 6 The line segment joining the point A(2, 1) and (5, -8) is triscted at the point P and Q sch that P is nearer to A. If P also lies on the line given 2x -y + = 0, find the value of k. QUESTION 7 Find the distance of a point P (x, y) from the origin. QUESTION 8 Find the ratio in which P(4, m) divides the line segment joini

Real Numbers

Real Numbers Question 1 Find the rational number between root 2 and root 3? Question 2 Tow positive integers a and b can be written as a = x^3y^2 and b= xy^3. x, y are prime numbers, then LCM (a, b). Question 3 Find the HCF of 1260 and 7344 using Euclid's algorithm. Question 4 Show that every positive integer is of the form 4q+1 or9 4q+3 where q is some integer. Question 5 Prove that root 2 is an irrational number. Question 6 Prove that 2+(root 3/5) is an irrational number, given that root 3 is an irrational number. Question 7 Prove that 2+5 root 3 is an irrational number. Question 8 What is the HCF of smallest prime number and the smallest composite number? Question 9 Given that root 2 is irrrational, prove that (5+3 root 2) is an irrational number. Question 10 Find HCFand LCM of 404 and 96 and verifiy that HCF*LCM = Product of the two given numbers. Question 11 Write whether ( 2 root 45 + 3 root 20)/( 2 root 5 ) on simplification gives an irrationa

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