LEARNING MATERIAL CLASS - X

Transcription

1 MINIMUM TARGET 40 LEARNING MATERIAL CLASS - X Kindly select 10 units as per choice of the student Topics Marks 1. Irrationality of numbers (5 questions) 3. Polynomials(long division) (5 questions) 4 3. Quadratic equations (10 questions) 4 4. Graphical method of solution of linear equations in two variables(4 questions)4 5. Arithmetic progression(0 questions) 5 6. Geometry (6 theorems)4 7. Construction(10 questions) 3 8. Coordinate geometry (0 questions)5 9. Statistics (10 questions)4 10. Probability(10 questions)4 11. Mensuration (5 questions) 5 1. Trigonometry (5 questions) 5 Total Marks (110questions)50 MINIMUM LEARNING MATERIAL

2 1. Prove that is an irrational number.. Prove that 3is an irrational number. 3. Prove that 3 is irrational Prove that3 + 5is irrational. 5. Prove that 4-5 3is irrational. TARGET 40 1.Irrationality of numbers. Polynomials(long division) 6. Find all the other zeroes of the polynomial p (x) =x 4-7 x 3 +19x -14x +30 if two of zeroes are and - 7. Find all the zeroes of p(x)= x 4 3x 3 3x + 6x, if you know that two of its zeroes are and Find all the other zeroes of the polynomial p (x) = x 4 + 3x 3 -x -9x -6 if two of zeroes are 3 and Obtain all the other zeroes of the polynomial p (x) = x 4-6 x 3 +3 x +3x - if two of zeroes are 1 and Find the other two zeroes of p (x) = 3 x 4 +6x 3 -x -10x -5. if two of zeroes are 5 and Quadratic equations 11. Find the roots of the following quadratic equations, (i) 3x 5x + = 0 (ii) x + 4x + 5 = 0 (iii) x x + 1 = 0 (iv) x + x 156 = 0 1. The product of two consecutive positive integers is 306. We need to find the integers. 13. Find two numbers whose sum is 7 and product is Find two consecutive positive integers, sum of whose squares is The sum of two numbers is 15, if the sum of their reciprocals is 3, find the numbers Solve the quadratic equation 1 4 3x (i ) + = (ii) + = (iii) x +1 x + x x -4 x - 3 = 5 x If the roots of the Equation (a-b)x +(b-c)x+(c-a)=0 are equal. Prove that a=b+c 18. For what value of k does x + kx + 3 = 0 have equal roots? 19. For what value of k does (k-1) x + (k-1) x + = 0 have equal roots? 0. Find the values of k,so that quadratic equation have two equal roots kx (x ) + 6 = 0 4. Graphical method of solution of linear equations in two variables

3 1. Draw the graphs of the equations x y + 1 = 0 and 3x + y 1 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region..solve the following system of linear equations graphically: x 3y 17 = 0 and 4x + y 13 = 0. Shade the region bounded by the above lines and x-axis. 3.Solve the following system of linear equations graphically: x + 3y = 4 and 3x y = 5. Shade the region bounded by the above lines and y-axis. 4. Draw the graphs of the equations 5x y = 5 and 3x y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis. 5. Arithmetic progression(two questions) The nth term of the AP a n = a + (n 1) d. 5. The first term of an AP is -7 and the common difference 5, find its 18 th term and general term. 6. Determine the AP whose 3rd term is 5 and the 7th term is If the 7 th term of an AP is 1 and its 9 th term is 1, find its 63 rd term Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 1. 9.Which term of the AP : 1, 18, 15,... is 81? 30. Which term of the AP : 1, 18, 15,... is 81? Also, is any term 0? Give reason for your answer. 31. Which term of the AP : 3, 15, 7, 39,... will be 13 more than its 54th term? 3. How many multiples of 4 lie between 10 and 50? 33. How many three-digit numbers are divisible by 7? 34.An AP consists of 50 terms of which 3rd term is 1 and the last term is 106. Find the 9th term. n n Sum of n terms of AP Sn : = {a +(n -1}d} and S n = {a + a n } 35.Find the sum of first terms of an AP in which d = 7 and nd term is Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively. 37.How many terms of the AP : 4, 1, 18,... must be taken so that their sum is 78? 38.How many terms of the AP : 9, 17, 5,... must be taken to give a sum of 636? 39.Find the sum of the first 40 positive integers divisible by The sum of 5th term and 9th term of an AP is 7 and the sum of 7th and 1th terms is 97. Find the AP. 41. Find the sum of series Find the sum of AP in -5 + (-8) + (-11) (-30). 43. If sum of n terms of an AP is n +5, then prove that a n =4n Find the sum of all multiples of 7 lying between 500 and 900.

4 6.Geometry- 6 theorems 45.State and prove Basic Proportionality Theorem. 46.State and prove Pythagoras Theorem. 47.State and prove converse of Pythagoras Theorem. 48. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 49.Prove that a tangent at any point on the circle is perpendicular to the radius through the point of contact. 50.Prove that the lengths of the tangents from an external point to a circle are equal. 7. Construction TYPE-1 51.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides areof the corresponding sides of the first triangle. 3 5.Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1times the corresponding sides of the isosceles triangle. 53.Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then construct a triangle whose sides are 3 of the corresponding sides of the triangle ABC Draw a triangle ABC with side BC = 7 cm, B = 45, A = 105. Then, construct a triangle whose sides are 4times the corresponding sides of ABC Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5 /3 times the corresponding sidesof the given triangle. TYPE- 56.Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. 57.Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. 58.Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. 60. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and B = 90. BD is the perpendicular from B on AC. The circle through B, C, and D is drawn. Construct the tangents

5 from A to this circle. 8. Coordinate geometry (two questions) TYPE 1 Distance Formula 61.Show that the points (1, 7), (4, ), ( 1, 1) and ( 4, 4) are the vertices of a square. 6. Prove that the points (3, 0) (4, 5) (-1, 4) and (-,-1) taken in order form a rhombus 63. Find the value of P if the point A (0,) is equidistant from (3, p)and ( p,3) 64. Find the point on the x-axis which is equidistant from (, 5) and (, 9). 65. Find the values of y for which the distance between the points P(, 3) and Q(10, y) is 10 units. TYPE Section Formula 66.Find the coordinates of the point which divides the join of ( 1, 7) and (4, 3) in the ratio : Find the ratio in which the line segment joining the points ( 3, 10) and (6, 8) is divided by ( 1, 6). 68. Find the coordinates of the points of trisection of the line segment joining (4, 1) and (, 3). 69. Find the coordinates of the points which divide the line segment joining A(, ) and B(, 8) into four equal parts. 70. Find the ratio in which the line segment joining A(1, 5) and B( 4, 5) is divided by the x-axis. Also find the coordinates of the point of division. TYPE 3 Midpoint Formula 71. If P (, p) is the midpoint of line segment joining the points A(6, -5) and B(-, 11), find the value of p? 7. If P (4, -) is the midpoint of line segment joining the points A(5k, 3) and B(-k, -7), find the value of k? 73. If A(1, ), B(4, 3) and C(6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D 74. If (1, ), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. 75. Find the length of median AD if vertices are A (1, 1),B ( 4, 6) and C ( 3, 5). TYPE 4 Area of a triangle 76.Find the area of a triangle whose vertices are (1, 1), ( 4, 6) and ( 3, 5). 77. Find the area of the quadrilateral whose vertices, taken in order, are ( 4, ), ( 3, 5), (3, ) and (, 3). 78. For what value of p are the points (, 1) (p,-1) and (-1, 3) collinear? 79. In each of the following find the value of k, for which the points are collinear. (i) (7, ), (5, 1), (3, k) (ii) (8, 1), (k, 4), (, 5)

6 80. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, 1), (, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. 9. Statistics 81. Find the mean of the following frequency distribution by a suitable method. C.I Frequency The arithmetic mean of the following distribution is 50. Find the missing frequency p. C.I Frequency P 83. Find the mode of the following data: C.I Frequenc y The following table shows the ages of the patients admitted in a hospital during a year: Age (in years) No. of participants Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. 85. Find the median of the following data. C.I Frequency Find the mean, mode and median of the following frequency distribution by a suitable method. C.I Frequency Find the missing frequencies in the following frequency distribution table if n = 100 and median is 3. C.I Frequency 10 f f The following distribution gives the daily income of 50 workers of a factory. Daily income (in Rs.) No. of workers Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive. 89. The following table gives production yield per hectare of wheat of 100 farms of a village.

7 Production yield (in kg/ha) No. of farms Change the distribution to a more than type distribution, and draw its ogive. 90. Write the following frequency distribution as less than type and more than type cumulative frequency distribution. Also find the median C.I Frequency Probability One card is drawn from a well-shuffled deck of 5 cards. Find the probability of getting: (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds (vii) a black queen (viii) a Jack a queen or a king (ix) neither an ace nora king (x) a non-face card (xi) a black king or a red queen(xii)a black face card 9. From a well shuffled pack of 5 cards black aces and black queens are removed. From the remaining cards a card is drawn at random find the probability ofdrawing (i) a king or a queen. (ii) a red card 93. From a pack of 5 playing cards, Jacks, queens, kings and aces of red colour are removed. From the remaining a card is drawn at random. Find the probability thatthe card drawn is (i) a black queen (ii) a red card (iii) a black Jack (iv) a honorable card 94. All the three face cards of spade are removed from a well shuffled pack of 5 cards &card is drawn from the remaining pack. Find the probability of getting a) a black face card b) a queen of diamond c) a spade d) a black card 95. In a single throw of two dice, find probability of getting a) doublets b) a total of A black die and a white die are thrown at the same time. Write all the possibleoutcomes. (a) What is the probability that the sum of the two numbers that turn up is8? (b) Find the probability of obtaining (i) a total of 6 (ii) a total of 10 (iii) Thesame no. on both dice 97. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green? (iv) not red? (v) either red or green 98. Cards marked with numbers 1,,3,..5 are placed in a box and mixedthoroughly and one card is drawn at random from the box what is the probabilitythat the number on the card is (i) a prime number? (ii) a multiple of 3 or 5? (iii) an odd number?

8 (iv) neither divisible by 5 nor by 10? (v) perfect square (vi) a two digit number. 99. Find the probability of having 53 Sundays in (i) a leap year (ii) a non leap year 100. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag. 11.Mensuration 101. In the adjoining figure, AB is a diameter of the circle with centre O and OA = 7 cm. Find the area of the shaded region. 10. ABCP is a quadrant of a circle of radius 14 cm. With AC as diameter a semicircle is drawn. Find the area of the shahded region A container, shaped like a right circular cylinder, having diameter 1 cm and height 15 cm is full of ice-cream. This ice-cream is to be filled into cones of height 1 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream A wooden article was made by scooping out a hemishphere from each end of a solid cylinder. If the height of the cylinder is 0 cm and radius of the base is 3.5 cm. Find the total surface area of the article A container open at the top, is in the form of frustum of a cone of height 4 cm with radii of its lower and circular ends as 8 cm and 0 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 1 per litre. 1.Trigonomentry 106. If sin 3A + cos (A-6), where 3A is an acute angle. Find the value of A the angle of elvation of an aeroplane from a point on the ground is 45. After flight for 15 seconds the elevation changes to 30. If the aeroplane is flying at a height of 3000 m. Find the speed of the aeroplane Without using trigonometric tables, evaluate-

9 cos 0 + cos 70 x sec 60 sec 50 - cot 40 -cot 58 cot3-4tan 13 tan 37 tan 45 tan 53 tan The angle of elevation of the top of a hill from foot of a tower is 60 and the angle of elevation of the top of the tower from the foot the hill is 30. If tower is 50m high, then find the height of the hill Two pillars of equal height are on either sides of a road, which is 100m wide. The angles of the top of the pillars are 60 and 30 at a point on the road between the pillars. Find the position of the point between the pillars. Also, find the height of each pillar. TIME: 60 MIN PRACTICE PAPER 1 M.M Prove that is an irrational number.. Find all the other zeroes of the polynomial p (x) =x -7 x 3 +19x -14x +30 if two of zeroes are and - 3. Find the roots of the following quadratic equations 3x 5x + = 0 4. Draw the graphs of the equations x y + 1 = 0 and 3x + y 1 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. 5. The first term of an AP is -7 and the common difference 5, find its 18 th term and general term ORFind the sum of first terms of an AP in which d = 7 and nd term is State and prove Basic Proportionality Theorem. 7. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides areof the corresponding sides of the first triangle Show that the points (1, 7), (4, ), ( 1, 1) and ( 4, 4) are the vertices of a square. ORIf P (, p)

10 is the midpoint of line segment joining the points A(6, -5) and B(-, 11), find the value of p? 9. Find the mean of the following frequency distribution by a suitable method. C.I Frequency One card is drawn from a well-shuffled deck of 5 cards. Find the probability of getting: (i) a king of red colour (ii) a face card (iii) a red face card (iv) a spade TIME: 60 MIN PRACTICE PAPER M.M Prove that 3is an irrational number.. Find all the zeroes of p(x)= x 4 3x 3 3x + 6x, if you know that two of its zeroes are and Find the roots of the following quadratic equations x + x 156 = 0 4. Solve the following system of linear equations graphically: x 3y 17 = 0 and 4x + y 13 = 0. Shade the region bounded by the above lines and x-axis. 5. Determine the AP whose 3rd term is 5 and the 7th term is 9. ORFind the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively. 6. State and prove Pythagoras Theorem. 7. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. 8. Find the coordinates of the point which divides the join of ( 1, 7) and (4, 3) in the ratio : 3.ORFind the area of a triangle whose vertices are (1, 1), ( 4, 6) and ( 3, 5). 9. The arithmetic mean of the following distribution is 50. Find the missing frequency p. C.I Frequency p 10. From a well shuffled pack of 5 cards black aces and black queens are removed. From the remaining cards a card is drawn at random find the probability of drawing (i) a king or a queen. (ii) a red card TIME: 60 MIN PRACTICE PAPER 3 M.M. 40

11 1. Prove that 3 is irrational. 5. Find all the other zeroes of the polynomial p (x) = x 4 + 3x 3 -x -9x -6 if two of zeroes are 3 and Solve the quadratic equation: + = x +1 x + x Solve the following system of linear equations graphically: x + 3y = 4 and 3x y = 5. Shade the region bounded by the above lines and y-axis. 5. If the 7 th term of an AP is 1 and its 9 th term is 1, find its 63 rd term.orhow many terms of the AP : 9 7 4, 1, 18,... must be taken so that their sum is 78? 6. State and prove converse of Pythagoras Theorem. 7. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1times the corresponding sides of the isosceles triangle. 8. Prove that the points (3, 0) (4, 5) (-1, 4) and (-,-1) taken in order form a rhombusorif P (4, -) is the midpoint of line segment joining the points A(5k, 3) and B(-k, -7), find the value of k? 9. Find the mode of the following data: C.I Frequenc y From a pack of 5 playing cards, Jacks, queens, kings and aces of red colour are removed. From the remaining a card is drawn at random. Find the probability thatthe card drawn is (i) a black queen (ii) a red card (iii) a black Jack (iv) a honorable card TIME: 60 MIN PRACTICE PAPER 4 M.M Prove that3 + 5is irrational.. Obtain all the other zeroes of the polynomial p (x) = x 4-6 x 3 +3 x +3x - if two of zeroes are 1 and 4 3. Solve the quadratic equation - 3 = x 5 x Draw the graphs of the equations 5x y = 5 and 3x y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis. 5. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 1.ORHow many terms of the AP : 9, 17, 5,... must be taken to give a sum of 636? 6. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 7. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at -1

12 a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. 8. Find the ratio in which the line segment joining the points ( 3, 10) and (6, 8) is divided by ( 1, 6).ORFind the area of the quadrilateral whose vertices, taken in order, are ( 4, ), ( 3, 5), (3, ) and (, 3). 9. The following table shows the ages of the patients admitted in a hospital during a year: Age (in years) No. of participants Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency. 10. All the three face cards of spade are removed from a well shuffled pack of 5 cards &card is drawn from the Remaining pack. Find the probability of getting a) a black face card b) a queen of diamond c) a spade d) a black card TIME: 60 MIN PRACTICE PAPER 5 M.M Prove that 4-5 3is irrational.. Find the other two zeroes of p (x) = 3 x 4 +6x 3 -x -10x -5. if two of zeroes are 5 and If the roots of the Equation (a-b)x +(b-c)x+(c-a)=0 are equal. Prove that a=b+c 4. Draw the graphs of the equations x y + 1 = 0 and 3x + y 1 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. 5. Which term of the AP : 1, 18, 15,... is 81?OR Find the sum of the first 40 positive integers divisible by Prove that a tangent at any point on the circle is perpendicular to the radius through the point of contact. 7. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then construct a triangle whose sides are 3 of the corresponding sides of the triangle ABC Find the value of P if the point A (0,) is equidistant from (3, p)and ( p,3)orif A(1, ), B(4, 3) and C(6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D 9. Find the median of the following data. C.I Frequency In a single throw of two dice, find probability of getting a) doublets b) a total of 11

13 TIME: 60 MIN PRACTICE PAPER 6 M.M Prove that is an irrational number.. Find all the other zeroes of the polynomial p (x) =x 4-7 x 3 +19x -14x +30 if two of zeroes are and - 3. For what value of k does (k-1) x + (k-1) x + = 0 have equal roots? 4. Solve the following system of linear equations graphically: x 3y 17 = 0 and 4x + y 13 = 0. Shade the region bounded by the above lines and x-axis. 5. Which term of the AP : 1, 18, 15,... is 81? Also, is any term 0? Give reason for your answer.or The sum of 5th term and 9th term of an AP is 7 and the sum of 7th and 1th terms is 97. Find the AP. 6. Prove that the lengths of the tangents from an external point to a circle are equal. 7. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of Find the coordinates of the points of trisection of the line segment joining (4, 1) and (, 3).ORFor what value of p are the points (, 1) (p,-1) and (-1, 3) collinear? 9. Find the mean, mode and median of the following frequency distribution by a suitable method. C.I Frequency A black die and a white die are thrown at the same time. Write all the possible outcomes. (a) What is the probability that the sum of the two numbers that turn up is8? (b) Find the probability of obtaining (i) a total of 6 (ii) a total of 10 (iii) The same no. on both dice TIME: 60 MIN PRACTICE PAPER 7 M.M Prove that 3is an irrational number.. Find all the zeroes of p(x)= x 4 3x 3 3x + 6x, if you know that two of its zeroes are and Find the values of k,so that quadratic equation have two equal roots kx (x ) + 6 = 0 4. Solve the following system of linear equations graphically: x + 3y = 4 and 3x y = 5. Shade the region bounded by the above lines and y-axis. 5. Which term of the AP : 3, 15, 7, 39,... will be 13 more than its 54th term? OR Find the sum of series State and prove Basic Proportionality Theorem. 7. Draw a triangle ABC with side BC = 7 cm, B = 45, A = 105. Then, construct a

14 triangle whose sides are 4times the corresponding sides of ABC Find the point on the x-axis which is equidistant from (, 5) and (, 9). ORIf (1, ), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. 9. Find the missing frequencies in the following frequency distribution table if n = 100 and median is 3. C.I Frequency 10 f f A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green? (iv) not red? (v) either red or green TIME: 60 MIN PRACTICE PAPER 8 M.M Prove that 3 is irrational Find all the other zeroes of the polynomial p (x) = x 4 + 3x 3 -x -9x -6 if two of zeroes are 3 and The product of two consecutive positive integers is 306. We need to find the integers. 94.Draw the graphs of the equations 5x y = 5 and 3x y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis. 95. How many multiples of 4 lie between 10 and 50? ORFind the sum of AP in -5 + (-8) + (-11) (-30). 96.State and prove Pythagoras Theorem. 97. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. 98. Find the coordinates of the points which divide the line segment joining A(, ) and B(, 8) into four equal parts. OR In each of the following find the value of k, for which the points are collinear. (7, ), (5, 1), (3, k) 99. The following distribution gives the daily income of 50 workers of a factory. Daily income (in Rs.) No. of workers Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive Cards marked with numbers 1,,3,..5 are placed in a box and mixedthoroughly and one card is drawn at random from the box what is the probabilitythat the number on the card is (i) a prime number? (ii) a multiple of 3 or 5? (iii) an odd number?(iv) neither divisible by 5 nor by 10?

15 TIME: 60 MIN PRACTICE PAPER 9 M.M Prove that3 + 5is irrational.. Obtain all the other zeroes of the polynomial p (x) = x 4-6 x 3 +3 x +3x - if two of zeroes are 1 and 3. Find two numbers whose sum is 7 and product is Draw the graphs of the equations x y + 1 = 0 and 3x + y 1 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. 5. How many three-digit numbers are divisible by 7? OR If sum of n terms of an AP is n +5, then prove that a n =4n State and prove converse of Pythagoras Theorem. 7. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5 /3 times the corresponding sidesof the given triangle. 8. Find the values of y for which the distance between the points P(, 3) and Q(10, y) is 10 units. ORFind the length of median AD if vertices are A (1, 1), B ( 4, 6) and C ( 3, 5). 9. The following table gives production yield per hectare of wheat of 100 farms of a village. -1 Production yield (in kg/ha) No. of farms Change the distribution to a more than type distribution, and draw its ogive. 10. Find the probability of having 53 Sundays in (i) a leap year (ii) a non leap year TIME: 60 MIN PRACTICE PAPER 10 M.M Prove that 4-5 3is irrational.. Find the other two zeroes of p (x) = 3 x 4 +6x 3 -x -10x -5. if two of zeroes are 5 and The sum of two numbers is 15, if the sum of their reciprocals is 3, find the numbers Solve the following system of linear equations graphically: x 3y 17 = 0 and 4x + y 13 = 0. Shade the region bounded by the above lines and x-axis. 5. An AP consists of 50 terms of which 3rd term is 1 and the last term is 106. Find the 9th term. OR Find the sum of all multiples of 7 lying between 500 and The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

16 7. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and B = 90. BD is the perpendicular from B on AC. The circle through B, C, and D is drawn. Construct the tangents from A to this circle. 8. Find the ratio in which the line segment joining A(1, 5) and B( 4, 5) is divided by the x-axis. Also find the coordinates of the point of division. ORFind the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, 1), (, 1) and (0, 3). Find the ratio of this area to the area of the given triangle. 9. Write the following frequency distribution as less than type and more than type cumulative frequency distribution. Also find the median C.I Frequency A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.