Chapter - 1 REAL NUMBERS

Transcription

1 Chapter - 1 REAL NUMBERS 1. Express 1000 as product of prime factors.. Which prime numbers will be repeatedly multiplied in prime factorization of 00.. Find the digit at units place of 8 n if n is multiple of What are the prime factors of denominator of fraction 7 80? 5. If H.C.F. of two number is 68 and 85 is 17. What is the L.C.M. of two numbers. 6. What is the H.C.F. of 95 and 15? 7. Find the number which when divided by 18 gives the quotient and remainder as 7 and when divided by a number gives the remainder 5 and quotient 9. What is the number? 9. By which smallest irrational number 7 be multiplied so as to get a rational number? 10. What is the product of ( 7 5) and ( 7 5)? 11. Which rational number is equivalent to 0.7? 1. Find the sum of 0. and The rational number when expressed in the form p q is. 14. Which smallest irrational number should be added to ( 5) to get a rational number? 15. Give the fractional form of Which number should be multiplied to ( 5 ) to get a rational number? 17. How much is ? 1 Maths-X (E)

2 18. Simplify : Give the decimal representation of Give the decimal representation of Give the decimal representation of If 7 when written in decimal representation is then 5 7 =. If then What will be the unit s digit of 7 5? 5. Find the digit at unit s place of If unit s digit of 7 is then what will be the unit s digit of 7? 7. Find the digit at unit s place of What will be the unit s digit of 7 1? 9. Which digit you will get at unit s place of 6 18? 0. Simplify : ( ) (5 ) (6 ) (7 ) 1. Simplify : ( 5) (6 ) ( ). Multiplicative inverse of 5 is.. Simplify : ( 7 )( 7 ) ( 7 ) ( 7) Maths-X (E)

3 4. Express as a rational number : (4 )(4 ) ( 5 )( 5 ) 5. If L.C.M. of two numbers 16 & 8 is 11, then what is the H.C.F. of these numbers. 6. Find the square of ( ). 7. Simplify : ( 5)²( 5)² 8. What is the H.C.F. of 15 and 171? 9. If H.C.F. of two numbers 40 and 441 is 1 then find the L.C.M. of these two numbers? 40. H.C.F. and L.C.M. of two numbers are 19 and 80 respectively. If one of the numbers is 95, what is the other number? Maths-X (E)

4 ANSWERS 1. ³ 5³. and ( 5 ) Maths-X (E)

5 Chapter - POLYNOMIALS 1. What is the coefficient of x² in the polynomial p(x) = x³ 15x²+10x?. Find the value of the polynomial p(x) when x =. p(x) = x² 4x + 7. What is the value of f where 7 f x 4 x² x? 4. If f(x) = x² 5x 14, find the value of f(7). 5. Find the zeros of the polynomial x² 15x 4 6. What should be added to the polynomial x² 5x + 4, so that is the zero of the polynomial? 7. Which of the numbers,,, 1 are zeros of the polynomial x² 4? 8. What should be subtracted from the polynomial x² 16x + 0 so that x = 15 is a zero of the polynomial? 9. Find the quotient when x² 7x + 1 is divided by (x ). 10. Find the polynomial whose zeros are and. 11. Find the value of a in the polynomial x² + ax 0 if 5 is the zero of the given polynomial. 1. What will be the remainder if f(x) = x³ + 4x² x + 1 is divided by (x )? 1. If f(x) = x² 7x + 8, find f( ) 14. In the polynomial x² 4x 7, find the sum of two zeros of the polynomial. 15. What is the product of zeros of the polynomial x² 11x + 0? 16. Which quadratic polynomial have its zeros as 1 4 and 4? 17. What is the value of k in the polynomial p(x) = x² + 11x + k if 4 is a zero of the polymnomial? 18. Find both the zeros of the polynomial x² x If (x + ) is a factor of x² + ax + b and a + b = 4 then a = and b =. 5 Maths-X (E)

6 0. What is the quotient if x³ 1 is divided by x² + x + 1? 1. For what value of x both the polynomials x² + 8x + 4 and x² x 6 becomes zero?. From the graph given below find the number of zeros of the polynomial y = f(x).. Find the number of zeros of the polynomial y = f(x) whose graph is given below. 4. How many zeros does the polynomial f(x) = (x 1)(x + 1)(x ) have in all? 5. Find all the zeros of the polynomial f(x) = (x )(x² 9x + 0). 6. Find sum and product of the zeros of the polynomial x² 14x What is the quotient and remainder if x² 8x + 15 is divided by (x )? 8. How many maximum number of zeros a quadratic polynomial can have? 9. If one of the zero of the polynomial p(x) = x² 1x + 40 is 8, which is the other zero? 6 Maths-X (E)

7 0. Find the zeros of the polynomial whose graph is given below : 1. Which are the two zeros of the quadratic polynomial given in figure?. Find the zeros of the polynomial x² 5 = 0. Also give the sum of zeros.. Which quadratic polynomial have the sum and product of roots as 15 and 50? 4. Find the polynomial whose roots are and. 5. What is the sum and product of roots of the cubic polynomial x³ 7x + 6? 6. The three roots of the polynomial (x + 4) (x² 6x + 8) are, and. 7 Maths-X (E)

8 7. Two roots of the polynomial x³ + x² 9x 9 are and. What is the third root? 8. Find the quadratic polynomial whose two roots (zeros) are 5 and Complete the following : Dividend = Divisor x (x 1) is a factor of (x³ + ax² + bx 11) and a b = 6. Find a and b. 41. For what value of a, x = 6 is a zero of the polynomial x² ax 6? 4. Which factor is common in x² 1, x 4 1 and (x 1)²? 4. Find the common zero of (x² + x + 1), (x² 1) and x³ Which is the factor common in 6(x + 1)(x + ) and 9(x³ + 1)? 45. For what value of x, both the polynomials x² x + and x² 6x + 5 becomes zero? 46. For what value of k, x = 4 is a zero of the polynomial x² + kx 1? 47. Which factor is common in x² + 8x + 15 and x² + x 10? 48. Reduce x² 5x 4 x² x 1 to lowest terms. 49. Find the cubic polynomial whose three zeros are 0, 4, If p(x) = x² + 5x +, what is the value of p() + p()? 8 Maths-X (E)

9 (17, ) (, ) (x 4) 10. x² 11. a = k = , (16x² 16x + ) 19. a =, b = 1 0. (x 1) 1. x =. 4 zeros. zeros 4. ANSWERS 5., 4, , 7. quotient (x 5), R = 0 8. Two x =, x = 4 1.,. (5, 5), 0. x² + 15x x² 5 x (0, 6) 6. (, 4, 4) 7. ( 1) 8. x² 6x Quotient, Remainder 40. a = 8, b = 41. a = 5 4. (x 1) (x + 1) 45. x = k = (x + 5) 48. x 4 x x³ 16x Maths-X (E)

10 Chapter - PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 1. How many variables are there in the equation x y + 4 = 0?. The point ( 4, 0) lies on which axis?. For what value of m the system of linear equation has unique solution? x + y = 7 mx + y = 8 4. Find the value of y corresponding to x = in the equation x + y = Find the point on x-axis satisfying the equation x + y = Find the point on y-axis satisfying the equation x 5y = At what point does the line 5x + y = 15 intersects the x-axis? 8. What are the coordinates of points where x 7y = 14 intersects y-axis? 9. What is the y coordinate of the point which lies on the line x + y = 5 and whose x-coordinate is 1? 10. Find x-coordinate of point lying on the line 5x y 7 = 0 corresponding to y =. 11. Find the coordinates of two points which lie on the line x + 7y = Find two solutions of the equation x + y = If C and F denote the temperature of celcius and fahrenhiet scales respectively, 5 then the following relations holds : C ( F ). Find the value of C when F = What type of lines are these : x + y 1 = 0, 6x + 9y + 10 = 0? 15. Give equation of a line which passes through the origin. 16. For what value of K the pair of linear equations has infinite solutions? 4x + y = 1x + y = K 17. How many solutions the following simultaneous linear equations have? 4x + 6y = 9, x + y = If a system of equations is inconsistent, then what type of graph the equations will have? 10 Maths-X (E)

11 19. For what value of a, the pair of linear equations has no solution? x 4y + 7 = 0 ax + y 5 = 0 0. Form an equation of a line so that the point x = 1, y = lies on that line? 1. The line x + = x + 4 is parallel to which axis?. At what point do the lines x y = 0 and x + y = 0 intersects?. What value of p will satisfy the equation px + y = 5 when x =, y = 1? 4. Find the value of x and y from the following simultaneous linear equations. x + y = 7, 5x + 1y = 7 5. What is the value of y satisfying both the equations when x = 1? x y =, 4x y = 5 6. What are the coordinates of the point of intersection of two lines x + y = 0, 5x y = 0? x y 7. What are the points of intersection of the line 0 with x-axis and with a b y-axis? 8. Find coordinates of two points on the line 5x + y = 15 in the graph below : 9. If x = y, x =, and x-axis form the triangle as shown in the graph below, find the coordinates of the three vertices of the triangle. 11 Maths-X (E)

12 0. What is the length of base of triangle formed by the lines x y 1 = 0, x + y = 8 and y-axis in the graph below? x + y = 8 x y 1 = 0 1. If speed of a boat in still water is 5km/hr and speed of stream is 5km/hr, what are the speeds of boat in upstream and downstream?. A person can row downstream 0km in hrs. and upstream 4km in hrs. Find the speed of rowing in still water and the speed of the current?. What is the area of the triangle formed by the lines. x y = 8, 8x + y = 4 and x-axis in the graph below? (0, 8) 4. Find the two digit number if ratio of digits is 1 : and their sum is If ratio of three angles of a triangle is 1 : :, what are the measures of three angles in degrees? 6. If three angles of a triangle are x, x, x + 5, what is the measure of each angle? 7. For rectangular plot having 7 square metre area, find the sides if length is twice the breadth? 8. If one number is thrice the other and their sum is 16, find the numbers. 9. chairs and tables cost Rs.,400. If cost of one chair is Rs. 400, what is the cost of 1 table? 1 Maths-X (E)

13 40. Sum of two numbers is 5 and their difference is 1. Find the two numbers. 41. What should be added to 5 to get the number obtained by reversing the digits? 4. A father is times as old as his son. After 1 years his age will be twice as that of the age of his son. Find their present ages. 4. In ABC, A x, B y and C y 0. If x y = 50, what type of is ABC? 44 Two audio cassettes and three video cassettes cost Rs. 40. But three audio cassettes and two video cassettes cost Rs. 60. Find the price of a pair of an audio and a video cassette. 45. Find the increase in area of a rectangle (15m 1m ) if 7m is added to both sides of a rectangle. 46. A man rowing at the rate of 5km/hr in still water takes thrice as much time to going 40km up the stream as in going 40km down the stream. Find the rate at which the river flows? 47. The sum and difference of ages of Reema and her elder sister are 60 years and 10 years. Find their ages. 48. A number is as much greater than 15 as it is less then 5. Find the number. 49. A man has only 50 paisa coins and 5 paisa coins in his purse. If the ratio of coins is 4 : 5 and amount Rs 1 in all, how many coins of each type does he have? 50. If we add 1 in the numerator of a fraction and subtract 1 from its denominator, the fraction becomes 1. If it is also given that the fraction becomes half when we add 1 to its denominator, then what is the fraction? 1 Maths-X (E)

14 ANSWERS 1.. x-axis. 1 m 4. y = 0 5. (5, 0) 6. (0, ) 7. (, 0) 8. (0, ) 9. y = 10. x = 11. (1, 0) (8, 1) 1. (1, 1)(4, 1) Parallel 15. ax + by = K = 17. No Solution 18. Parallel lines a 4 0. x y = 8 1. y-axis. origin (0, 0). p = 1 4. x = 11, y = 4 5. y = 1 6. (0, 0) 7. (a, 0)(0, b) 8. (, 0), (0, 5) 9. (0, 0), (, 0), (, ) 0. 9 units 1. 0km/hr, 0km/hr. 6km/hr; 4km/hr. 8 sq. units 4. 6 or , 60, , 70, m, 6m 8. 1 and 4 9. Rs , yrs., 1 yrs. 4. Right angled triangle 44. Rs m² km/hr years, 5 years paisa coins = /5 5 paisa coins = 0 14 Maths-X (E)

15 Chapter - 4 QUADRATIC EQUATIONS 1. Is the equation ( 5 x )² 5 0 a quadratic equation?. Determine whether the equation is quadratic or not : x (x + ) + 5 = x² + 9x + 8. What is the degree of the equation x³ 6x² + x 1 = 0? 4. For the quadratic equation x² 5x = 0, which of the two values x =, x = is a solution of the equation? 5. Determine whether the given value of x is solution or not : x² + x 4 = 0; x = 6. What are the two roots of the equation (x + 4) (x 5) = 0? 7. Find two values of x which satisfy the quadratic equation x² 64 = What are the solutions of equation x² + 5x = 0? 9. Solve the quadratic equation : (x )² 5 = Solve the quadratic equation : ax² abx = Find the solutions of quadratic equation : y² y Find the solutions of quadratic equation : 5z² z = What are the solutions of quadratic equation z² + az a² = 0? 14. Find the value of x which satisfies the equation : 15. What are the two roots of x² 7x = 0? 16. Find the value of discriminant in 5x² 0x + 9 = What are the two roots of the equation (x + 5)² 6 = 0? 18. What is the value of D in the equation 9x 15x 4 0? 4 x 4; x 0 x 19. For what value of p the quadratic equation, x² 4x p 0, will have real and equal roots? 0. Write the quadratic equation whose roots are and Maths-X (E)

16 1. When will the two roots b b ² 4 ac a ax² + bx + c = 0 be equal? and b b ² 4 ac a of quadratic equation. Find the value of discriminant of the equation x² x 0. For what value of p the equation px² + 4x + 1 = 0 will have equal roots? 4. What value of x will satisfy the equation x² = (x + 5)(x + )? 5. The length of a hall is 10m more than its breadth. Find the length and breadth of the hall if its area is 600m². 6. If sum of a whole number and its reciprocal is 17 4, what is the number? 7. Difference of the number and its reciprocal is. What is the number? 8. What is the quadratic equation whose one of the roots is 5? 9. Find two consecutive whole numbers, the difference of whose squares is What are the two values of z which satisfy the equation z² + z 8 = 0? 1. What will be the value of discriminant (D) if the given quadratic equation is perfect square?. What is the equation whose roots are and?. What are the nature of roots of the equation (x a) (x b) = 4ab? 4. For what value of p, the equation 4x² + 8x p = 0 will have equal roots? 5. What will be the middle term of the equation whose solutions are 4 and 5? 6. If 1 x² x², what are the values of x? 7. Divide 5 into two parts such that their product is One side of the rectangle exceeds the other side by cm. If the area of rectangle is 180sq.cm., find the two sides of the rectangle. 9. What are the values of p and q if these are the roots of the equation x² + px + q = 0? 16 Maths-X (E)

17 40. If n( n 1) S 78, find n. 41. Find the roots of the equation x² 5 x Find the roots of the equation 4. What is the value of x in 1 y² y 1 0. x 4x x? 44. What is the value of x which satisfies the equation 7 x 1 1? There are three consecutive positive integers such that sum of the square of the first and product of other two, is 9. What are the integers? 46. For what value of k will the equation 5y² 0y + (k 1) = 0 have real and equal roots? 47. Determine the value of p for which the given quadratic equation has real roots : x² + x + p = The product of Ramu s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu s present age. 49. The sum S of n successive odd natural numbers starting from is given by the relation S = n(n + ). Determine n, if the sum is If 4 is a root of the equation x² + px 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k. 17 Maths-X (E)

18 1. Yes. No. 4. x = 5. Yes ANSWERS 17. 1, p = 4 0. x² 7x + 1 = 0 1. b² 4ac = , cm, 15cm 9. p = 1, q = , , , 9. x =, x = 0 or x = b 11. y, 1. 1, 5 a 1. a, 14. x = m, 0m x² 6x + 4 = , , x² 4x + 1 = 0. real and distinct , 4 4 1, 4 45., 4, k = p years 49. n = , x Maths-X (E)

19 Chapter - 5 ARITHMETIC PROGRESSIONS 1. Find the common difference d of the A.P. 10, 8, 6, 4,.... If 7th and 6th terms of an A.P. are 5 and, what is the value of d?. Find the 6th term of an A.P., 5, , 4, 7, 10, 1... is an A.P. Find d. 5. Find the common difference of the A.P. 1,, 5, 8, 11, What is the common difference of the A.P. formed by even numbers? 7. Find the value of 11th term of the A.P., whose first two terms are and If t n 1 then find the series. n 9. If a = 5 and a = 9, then find t Find the nth term of the A.P. 5,, 1, 4, 7, What is the difference between rd and 8th terms of the A.P?, 7, 11, 15, If first term of an A.P. is and 11th term is 4, find the common difference. 1. If 4th and 8th terms of an A.P. are 11 and respectively, find a and d. 14. First term of an A.P. is and 10th term is 8. What is the value of d (common difference) 15. Find the 16th term of an A.P. if a = 15, and d = 16. Find 8th term of an A.P. whose rd term is 5 and common difference is Which term of the A.P., 7, 11, 15,... will be 0 more than its 6th term? 18. How many d s will be added to get 9th term of an A.P. to the first term? 19. Find 4th term from the end of the A.P. 4, 1,, 5, 8, 11, 14, 17, 0, The sum of series in A.P. is 18. If the first term is and the last term is 14 find the number of terms of the series. 1. Find the value of d of the A.P. whose nth term is 9 5n.. If a = 5, d = 1, then which term of the A.P. is zero?. Verify if the sequence a n, where a n = n² 1 is an A.P. or not? 4. Find the sum of first 5 terms of the A.P., 7, Maths-X (E)

20 5. If S n and S n 1 are given, then what is S n S n 1? 6. Find the 10th term of the A.P. 117, 104, 91, 78, If common difference of an A.P. is 5, find the difference of 15th and 11th terms. 8. Is 184 is term of the sequence, 7, 11,...? 9. If 7th term of an A.P. is and 1th term is 6. Find the series. 0. Find the number of terms of the A.P. 5, 9, 1, 17, 1, 5, 9, Find the number of terms of the A.P. 1, 4, 7, 10, If Rajni goes from Rohini to Lajpat Nagar with a speed of 0km/hr by car and after every hour she increases the speed by 5km/hr., then what is the speed of car after 4 hours?. Find the sum of all terms of the A.P Find the sum of first 10 natural numbers. 5. What is the sum of first five multiples of? 6. Find the sum Find the sum of up to n terms. 8. If three consecutive terms of an A.P. are a d, a, a + d and their sum is 54 and d is 7, find the three terms. 9. Find the A.P. if the 15th term is 10 more than the 1th term and first term is Determine the sum of first 10 terms of an A.P. if t = and t 7 =. 41. Determine k so that 8k + 4, 6k, k 7 are three consecutive terms of an A.P. 4. If the sum of first n terms of an A.P. is n² + n, then find its nth term. 4. For the A.P. 9, 14, 19, 4 find t 0 t If 7 th term of an A.P. is zero then what is the relation between 17 th and 7 th term? 45. If the 9 th term of an A.P. is zero, then 9th term is... the 19th term (complete the sentence) 46. A man saved 16,500 in 10 years. In each year after the first he saved 100 more than he did in the preceeding year. How much did he save in the first year? 47. Find the sum of first 100 multiples of Find the sum of the A.P Find the value of k if the k th term of the A.P. 1,, 5, 7... is The sum of n terms of a series is n² + n for all values of n. Find the rd term of the series. 0 Maths-X (E)

21 , 5, 7, n a =, d = th th term. No t n ANSWERS No 9., 7, 1, km/hr n(n + 1) 8. 11, 18, , 10, 15, n Thrice 45. Twice 46. Rs. 1, , Maths-X (E)

22 Chapter - 6 SIMILAR TRIANGLES 1. Select the pair of similar figures. (a) (b) (c) (d). In figures, ABC DEF, find the value of x. A D cm cm 4cm 6cm B 4cm C E x F. In figures PQR XYZ, find the value of Y and Z. X 4. In ABC, PQ BC, find CQ. Y A Z 1.5cm cm B 5. In figures, name the similar triangles. P cm Q C Maths-X (E)

23 6. In figure, ACB ECD, find B. 7. In figures, ABC DEF, find F. D E F 8. In figures, ABC DEF A, find BC EF. D 1.8cm.cm.6cm 6.4cm B C E F 9. In figures, find ar( PQR) ar( LMN) P L cm cm 5cm 5cm Q cm R M 5cm N 10. In figure, AD is bisector of A, find AB AC. A B.5cm D 1.5cm C Maths-X (E)

24 11. In figures, find M. 1. In figure, S PRQ, MN QR. Write the names of similar triangles. P M Q S 1. BAC is an isosceles with AB = AC, AD is the bisector of BAC A N R T. Find BD DC. 14. In figure, PT is bisector of QPR B D, find TR. C.cm 6.6cm 1.cm 15. ABC and DEC are the right triangles with B E 90 ; find BE. 5cm A 1cm 5cm D 4cm 16. In ABC, DE BC and B AD DB C, find AE : AC. E 4 Maths-X (E)

25 17. In figure, PQ MN. If KP 4 PM and QN = 6, find KQ The perimeters of two similar triangles ABC and PQR are 6cm and 4cm respectively. If PQ = 10cm, find AB. 19. In figure, AD : DB = 1 :, AE : EC = 1 : and BF : FC = 1 : 4, find which two lines are parallel. 0. In figure, DE BC. If AD = 5BD and EC = 1.6cm, find AE. 1. In ABC, DE BC. If AD = 6cm, DB = 9cm and AE = 8cm, find AC.. Express x in the terms of a, b and c in the following figure. 5 Maths-X (E)

26 . In figure, ABO DCO. If AB = cm, CD = cm, OC =.8cm and OD =.cm, find OA. D B 4. In figure, P and Q are points on the sides AB and AC respectively of ABC, If PQ = 4cm, find BC. A cm 5 cm A cm.8cm O.cm C cm 8 cm P Q 10 cm B C 5. In figure, AD is the internal bisector of BAC. If AB = 6cm, AC = 4cm and BD =.4cm, find BC. 6. In figure, AX is the bisector of BAC. If AB = cm, AC = 4cm and BC = 5cm, find BX. 7. The lengths of sides of a triangle are 1cm, 16cm and 1cm. The bisector of the greatest angle divides the opposite side into two parts. Find the lengths of these two parts. 8. In a triangle, the internal bisector of angle bisect the opposite side; what type of triangle is this? 9. Two triangles ABC and DEF are similar. If AB = 10cm and DE = 8cm, find the ratio of the areas of ABC and DEF. 6 Maths-X (E)

27 0. In figure, find AD if : CAB ADB cm cm 1. In figure, PR = 6cm and AB QR. Find BP. cm cm cm. In figure, if PQ BC and PR CD, AR = 4cm, AD = 16cm and AQ = cm. Find AB.. A ladder is placed in such a way that its foot is at a distance 5 m from the wall and its top reaches a window 1 m above the ground. Determine the length of the ladder. 4. In figure, BP CF, and DP EF, find AD DE. cm 8cm 5. In figure, point P divides the line segment AB internally. What is the ratio PA : PB? 6. In a trapezium ABCD, AB CD and AB = CD. The diagonals AC and BD meet at O. If the area of AOB is 84 sq.cm., find the area of COD. A D O C B 7 Maths-X (E)

28 7. In figure, DE BC and AD : DB = :. Find ar( ADE) : ar( ABC). 8. AD is a median of a ABC. DE and DF are bisectors of ADB and ADC meeting AB and AC at E and F respectively. If AE = cm, BE = 4cm and AF = 15cm, find FC. 9. In figure, find x if DE BC. 40. In figure, find the value of x. 10cm 8cm 5cm 41. ABC is an isosceles triangle in which C 90. If AC = 6cm, find AB². 4. In figure AB = 8cm, BC = 1cm and AE = 6cm. Find area of the rectangle BCDE. 8cm 1cm 6cm 8 Maths-X (E)

29 4. In an equilateral ABC of side a, what is the height of ABC? 44. A boy goes 15m due east and 0m due north. How far is he from the starting point? 45. The sides of triangle are 5cm, 8cm and 11cm. Determine whether it is a right triangle or not. 46. In figure, find x. cm cm 47. In figure, if AB BD, then find AC CD ABD. cm 48. If ABC DEF, ar( DEF ) 100 cm² and AB 1 DE, then find the area of ABC. 49. In a rhombus ABCD with side 4cm, AC and BD are diagonals bisecting at O. Find the value of AC² + BD². 50. The corresponding altitudes of two similar triangles are 7cm and 8cm respectively. Find the ratio of their areas. 9 Maths-X (E)

30 ANSWERS 1. (a) and (c). 8cm. Y 60, Z cm 5. ABC FDE ½ PQR PTS, PMN 1. 1 : cm cm 16. : cm 19. DE BC 0. 8cm 1. 0cm. ac b c. 4.8cm 4. 1 cm 5. 4cm cm 7. 9cm, 1cm 8. Isosceles cm 1. cm. 1cm. 1 m 4. 1 : 5. : 6. 1 sq.cm : cm 9. x = cm 41. 7cm 4. 10cm² 4. a 44. 5cm 45. No cm cm² cm : 64 0 Maths-X (E)

31 Chapter - 7 CO-ORDINATE GEOMETRY 1. In which quadrant does the point ( 10, ) lie?. (0, ) and (0, 5) are the co-ordinate of two points lying on axis.. Find the distance of a point P(x, y) from the origin (0, 0). 4. What are the co-ordinates of mid-point of line joining the points (6, ) and (4, 8)? 5. What are the co-ordinates of centroid of triangle formed by the points ( 7, 6), (8, 5), (, )? 6. What is the x - coordinates of the point which divides the line joining (1, ) and (, ) in the ratio 4 :? 7. Find the co-ordinates of points which divides line joining ( 4, 0) and (0, 6) in the ratio 1 :. 8. Find the third vertex of a triangle if two of its vertices are ( 1, 4) and (5, ) and centroid is (0, ). 9. The length of the line AB, where A (1, 0) and B (5, ) is units. 10. Find the length of the line AB, where co-ordinates of points A and B are (, 7) and (, 4). 11. What is the distance of the point (8, ) from the origin? 1. Find the centroid of a triangle whose vertices are (, ), ( 1, 0) and (7, 6) 1. What is distance between points (, ) and (1, )? 14. What is the area of triangle ABC, whose vertices are A(x 1, y 1 ), B(x, y ) and C(x, y ) 15. Find the co-ordinates of points dividing the points (, 5) and (7, 9) in the ratio :. 16. Find the distance of the point (0, ) from the mid-point of the line joining (4, 10) and (, ). 17. Point Q lies on the line joining P (, ) and origin in such a way that OP = OQ. What will be the co-ordinates of Q? 18. State which of the two lines is longer (i) line joining (0, 1) and (4, ) or (ii) (1, ) and (6, 4)? 1 Maths-X (E)

32 19. Find the ratio in which the line segement joining (, ) and (5, 6) is divided by x-axis. 0. Find the sum of lengths of the diagonals AC and BD of rectangle ABCD if A(, 0), B(5, ), C(0, 7) and D(, 0). 1. Find the sum of lengths of AB and BC if the coordinates of A, B and C are (1, ), (, ) and (4, 6) respectively.. Find the value of k if the point (0, ) is equidistant from (5, k) and (k, k).. Which of the points (, 4) and ( 4, ) is nearer to the origin? 4. What is the area of triangle formed by the points (, 0), (0, 4), and (0, 0)? 5. Find the co-ordinates of a point, which is at a distance of 1 units from the origin and lies on x-axis. 6. One end of a diameter of a circle is (, ) and the centre is (, 5). What are the co-ordinates of the other end of his diameter? 7. Find the length of median AD of the triangle formed by the points A(0,6), B(8, 0) and C(4, ). 8. Gunjan walks 1m due east and then 5m due north. At what distance is Gunjan from the starting point? 9. The base BC of an equilateral triangle ABC with side 10cm lies along x-axis such that the mid-point of the base is at the origin. Find the co-ordinates of point B. 0. Find the co-ordinates of fourth vertex of the rectangle formed by the points (0, 0), (, 0) and (0, ). 1. Find the value of x such that Q is the mid-point of PR and coordinates of P, Q and R are (6, ), (1, ) and (x, 8) respectively.. The line segment joining the points (, 4) and (1, ) is trisected at the points P and Q. Find the coordinates of P.. Find the value of y if the points A(5, y), B(1, 5), C(, 1) and D(6, ) are the vertices of the square. 4. A(, ) and B(, 1) are two vertices of a ABC whose centroid G has 5 1 co-ordinates,. Find the co-ordinates of the third vertex C of the triangle. 5. What is the area of ABC if points A, B and C are collinear? 6. Find the ratio in which the line-segments joining the points (6, 4) and (1, 7) is divided internally by x-axis. Maths-X (E)

33 7. The three vetices of a rhombus taken in order are (, 1), (, 4) and (, ). Find the fourth vertex. 8. Find the third vertex of a triangle, if two of its vertices are (, 1) and (0, ) and the centroid is at origin. 9. The mid-point of the line segment joining (p, 4) and (, q) is (, 6). Find the value of p. 40. In which ratio is the line joining the points A ( 4, 4) and B(7, 7) divided by (0, 1)? 41. P is the point on x-axis such that its distance from the origin is units. Find the point Q on y-axis such that OP = OQ. 4. The line segment joining the points ( 4, 0) and (0, 6) is divided into four equal parts at P, Q and R. Find the co-ordinates of Q. A(1, 1) 4. In the figure, M is the mid-point of AB. Find the coordintes of B. M(, ) N B 44. Find the value of k if the distance between (k, 5) and (4, 5) is 5. C 45. The points (0, 1), (, 1), (0, ) and (, 1) are the corners of a square. Find the length of its side. C 46. If (p, q) is the mid-point of the line joining the points (5, ) and (, 4), find the value of p + q. 47. In the figure ACBD, is a rhombus. Find the co-ordinates of the point C. B ( a, 0) 48. Find the co-ordinates of the fourth point B such that OABC forms a square and co-ordinates of O, A and C being (0, 0), (, 0) and (0, ). 49. If two vertices of parallelogram are (, ), ( 1, 0) and the diagonals cut at (, 5) find the co-ordinates of other vertices of the parallelogram. 50. Find the co-ordinates of a point on x-axis which is equidistant from (, 5) and (, ). Maths-X (E) D (a, 0) A (0, a)

34 ANSWERS 1. nd Quad.. y. x 4. (5, ) 5. (1, ) y units 17. externally (, ), (, ) 18. (ii) : units units (, 4) 7. (, 1.5) 8. ( 4, 15) units 4. 6sq. units 5. (1, 0) or ( 1, 0) 6. ( 6, 7) units 8. 1m 1. 4, 9. ( 5, 0) 0. (, ) 1. 4 units x y y x y y x y y , 15., units (4, 4) 4 Maths-X (E)

35 5. zero 6. 4 : 7 7. ( 7, ) 8. (. 1) (4 : 7) 41. (0, ) or (0, ) 4. (, ) 4. ( 5, 5) or ( 1) (0, a) 48. (, ) 49. (1, 1), (5, 10) 50. (, 0) 5 Maths-X (E)

36 Chapter - 8 TRIGONOMETRY AND ITS APPLICATIONS 1. If x sin and y cos 1, then find the value of x+y.. If sec (1 sin )(1 sin ) k, then find the value of k.. Find the value of sin 0 sin 70 cos 0 cos If 0 tan tan 45 1, then find the value of 5. Find the value of 0 0 sin 10 sin If cos A, 5 then find the value of tan A sec A. 7. If sina = cosa, then find the value of A. 8. If tan tan(90 ) 0, then find the value of 9. Complete the following:- The angle nearer to altitude is than the angle away from the altitude. 10. In the figure, find the area of ABC in which ABC 90 ACB 45 and BC=8cm. 11. Name the angle of depression in the figure. 6 Maths-X (E)

37 1. If x sec 1 and y tan then find the value of x y. 1. If x cosec and cot, then find the value of x 4 x 1 x 14. If 15. If sin, then find the value of 5 5cos sin 1 tan then find the value of 1sin Find the value of cosec9 0 sec (sin 5 sin 85 ) 17. Find the value of cos 15 cos 5 cos 65 cos Find the value of 0 0 sin 10 sin Find the value of 0 0 cos 67 sin 0. Find the value of tan10 tan 0 tan 70 tan Find the value of 0 0 cosecasec(90 A) cot A tan(90 A). Find the value of sin sin cos cos. If 1 tan and 1 sin, find the value of. 4. If cosec and cot k, then find the value of k. 5. If cos ec, then find the value of (cosec cot ). 7 Maths-X (E)

38 6. If tan 4, then find the value of 1 (tan sec ) Ifsin, then find the value of cos ec cot If cos, then find the value of 8sec tan If 1 sin cos sin cos 4k sin cos, then find the value of k. 0. If 0 0 cos 0 cos (sin 59 sin 1 ) k, then find the value of k. 1. Find the value of tan 5 tan 0 4 tan 85. If cos 0 0 cos k 0 0 sin 70 sin(90 ), then find the value of k.. If tan 4 cot, where 4 and and are acute angles, then find the value of. 4. If 5. If 0 k cos(81 ) sin, then find the value of k. sec A, then find the value of tan A. 6. If cos 1, then find the value of. A B 7. If, A, B and C are the angles of a triangle, then find the value of tan in terms of angle C. 8. If sin cos 4, then find the value of In Fig., ABCD is a rectangle, find AE. 40. In Fig. 4, find the value of CF. 8 Maths-X (E)

39 41. In Fig. 5, find the value of AP + AD. 4. At a point 0m. away from the foot of a tower the angle of elevation of the top of the tower is 60. Find the height of the tower. 4. In Fig. 6, AB AC find. D A 45 60cm Q 60 P B 44. A person standing on the bank of a river observes that the angle of elevation of 0 tree is 60. When he moves 40m away, the angle of elevation becomes what distance is he now standing away from tree? 45. In Fig. 7, find PR At 80m 46. In Fig. 8, find BC. 47. In Fig. 9, find the value of DC. 48. In Fig. 10, two men are on the opposite sides of a tower. If the height of the tower is 60m. Find the distance between them. 49. In Fig. 11, find the value of AB. 50. In Fig. 1, DF is the reflection of building AD in the water. If BC = 10m and AE = 1m. Find DF. m 9 Maths-X (E)

40 ANSWERS cot C greater 10. cm 11. ABC cot cm m m m m ( 1) 50. m Maths-X (E)

41 Chapter - 9 CIRCLE 1. Count the number of tangents in the given figure.. How many lines in this figure are not intersecting the circle at all?. How many tangents are there in all in this figure? 4. Count number of secants in this figure. 41 Maths-X (E)

42 5. How many tangents are there in this figure? 6. How many lines in this figure are touching the circle? 7. Find PR in the given figure. Q P 1cm 5cm O 8. Find OP. S R O 4cm 5cm 9. Find ACB P A Q C 15 O If LOM 105. What is OLN? B L O N M 4 Maths-X (E)

43 11. Find XOY Y O 45 Z 1. Find AB. X 5cm A O C B 1cm 1. Find QOP Q O 40 P 14. Find the perimeter of the quadrilateral ABCD. 8cm R 7cm A B 5cm D 6cm C 15. In the figure if XY=0cm., find perimeter of XLM Y L N X M Z 16. Find perimeter of quadrilateral PQRS. P cm 4cm Q 10cm 5cm S R 4 Maths-X (E)

44 17. Find perimeter of triangle ABC. A 7cm 9cm 18. Find BP. 5cm A B 1cm 1cm C O cm P B 19. Find perimeter of PQR P 7cm cm Q 4cm R 0. BQ, AP and QP are tangents to circle with centre O. Find QOP? B Q O R A 1. What is the similarity between quadrilateral PZXY and a cyclic quadrilateral? P Y X P Z 44 Maths-X (E)

45 . Find radius of the circle. 1 cm cm O. Find OP when RS = 4cm. O 1cm R P S 4cm 4. Find OB when AB = 48cm. A O 7cm B 48cm 5. Find x and y. 6. Find QOP 45 Maths-X (E)

46 7. If PR = 7.5cm, find PS. S Q O P 8. In figure, a point P is 9cm away from the centre of a circle. Find the length of tangent drawn from P to the circle whose radius is 0cm. T 0cm R O 9cm P 9. Find BTQ? P 0. In figure, if PC=CR, then which two sides of a triangle are equal. C A R Q B 1. In figure, a circle touches all the four sides of a quadrilateral. ABCD; then which side of the quadrilateral, is equal to (AR + BT)? S B A R T D C Q. Find the distance between two parallel tangents to a circle whose radius is 5.5cm. 46 Maths-X (E)

47 . In figure, PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B. Then complete the statement : OP is the of AB. P A B O 4. In figure, ABC touches a circle at a point P. If we extend the sides AB and AC, they touch the circle at Q and R respectively. If the perimeter of a triangle is 1cm, find AQ. A B P C Q R A 4cm P Q 1cm 5. Find BC in the given figure. 7cm B R C 6. In the figure, the sides of a quadrilateral ABCD touch a circle at P, Q, R and S. What is (AB + CD) equal to? B A P 7. In the given figure if AB = 11.5cm and DC = 10.5cm find AD+BC. Q D R C S A Q P O B S D R C 47 Maths-X (E)

48 8. In figure AP = 4cm, OA = cm, OB = cm. Find BP. 9. In fig. a chord AB of the larger of the two concentric circles is tangent to the smaller circle at P. If AP = 4.5cm. Find BQ. 40. In figure, if AQ = 5cm, find the perimeter of ABC A Q B P C R 48 Maths-X (E)

49 cm ANSWERS 8. 1cm cm cm 0. PQ = QR cm 1. AB cm 8. 7cm cm cm 19. 8cm sum of opposite angles is cm. 5cm 4. 5cm x 40, y cm. 11cm.. Perpendicular bisector 4. 6cm 5. 15cm. 6. AD+BC 7. cm cm cm cm 49 Maths-X (E)

50 Chapter - 10 GEOMETRICAL CONSTRUCTIONS 1. If for a circle of radius 7cm, a tangent is to be made at a point 5cm away from the centre of the circle. What will be the length of the tangent? ' ' ' 5. In constructing A BC ABC such that BC BC, into how many equal parts is BC divided?. If a line AB = 7cm is divided in ratio : 4 by a point P, find BP. 4. For dividing line PQ in ratio 4 : 7 in how many minimum points will the parallel lines at P and Q be divided into. 5. For dividing a line LM in ratio 5 : into how many parts the arm of acute angle be divided. 6. A PQ R PQ? ' ' PQR is to be constructed to get ' PQ 5 PQ. If PQ = 6cm. What will be 7. A LM N ' ' LMN is to be made such that ' LM 4 LM. If ' LM = 48cm. find LM. 8. In a PQR PQR such that PQ PQ 1. If QR=6cm, what is QR? 9. If a point L is to be located on line YZ such that LY : LZ = :. If YZ = 15cm, what is LZ? 10. ABC ABC such that BC be divided? BC 4 5 BC. Into how many equal parts does the side 11. ABC ABC such that AB AB 7, if BC = 9cm what will be BC? 1. PQR PQR with PQ PQ 5 if QR = 15cm, what will be QR? 50 Maths-X (E)

51 1. If a tangent 8cm long is drawn to a circle of radius 6cm. What will be the distance of the point from the centre? 14. If a line AB = 4cm is divided in the ratio 5 : by the point P. What is AP equal to? 15. If a point P divides a line AB such that AP = 4.5cm and AP : PB = :. What is the length of AB? ANSWERS 1. 4cm.. 4cm cm 7. 6cm 9. 9cm 10. five cm 1. 5cm 1. 10cm cm cm 8. cm 51 Maths-X (E)

52 Chapter - 11 AREAS RELATED TO CIRCLE 1. Find the area of circle whose diameter is 'd'.. What is the area of a sector of a circle of radius r and central angle?. If the circumference and area of a circle are numerically equal then what is the radius of the circle equal to? 4. Two circles having circumference C 1 & C having radii R 1 & R respectively. The circumference C of the third circle of radius R is such that C = C 1 + C then what is R 1 + R equal to? 5. The radius of circle is.5cm. What is the perimeter of the semicircle? ( ) 7 6. The archery target has three concentric circular regions. The diameter of the regions are in the 1 : :. What is the ratio of their areas? 7. The radius of two circles are 1cm and 6cm respectively. What is the radius of the circle which has circumference equal to the sum of the circumference of two circles? 8. The cost of fencing a circular field at the rate of Rs. 10 per meter is Rs What is the radius of the circular field? ( ) 7 9. Find the perimeter of the protactor if its diameter is 14cm. ( ) In the figure, a shaded portion is cut off. Find the area of the remaining portion. ( ) 7 14cm cm 11. The numerical difference between circumference and diameter is 0cm. What is radius of the circle? ( ) 7 5 Maths-X (E)

53 1. A bicycle wheel makes 10 revolutions in moving 880m. Find the diameter of the wheel A wire is in the form of circle of radius 4cm. It is bent into a square. Determine the side of the square Find the area of ring if the radius of the smaller circle is 6cm and radius of the bigger circle is 1cm. 15. Find the area of cirular path of uniform width h surrounding a circular region of radius r. 16. A path of 5m is build round the circular park of radius 15m. Find the area of the path. 7 5m 15m 17. The radii of two circles are 4cm and cm respectively. Find the radius of a circle having area equal to the sum of the areas of the circles Find the area of sector of a circle with radius 6cm and central angle of In the figure find l if O is the centre of the circle and radius is 14cm. 7 14cm A l O 90 B 14cm 5 Maths-X (E)

54 0. In fig. ABC is an equilateral triangle of side 0m. A cow is tied at vertex A by a 10m long rope. What is area the cow can graze in? 1. Find the area of the four blades of same size of radius 0cm and central angle 45 of a circular fan.. Find the perimeter of the shaded region. 4cm cm 6cm 6cm 4cm. Two concentric circles with centre O and radius 7cm. & 14cm. If What is the area of shaded region? 0 AOC 10. A B O 10 D C 54 Maths-X (E)

55 4. Find the perimeter of the shaded portion. 5. Find the circumference of the circle with centre O. Q O 4cm 6. Chord AB subtends an angle of 0 90 at the centre O. Find the area of the minor segment ACBA. 7. The radius of two circles are cm and 4cm and sum of the areas of two circle is equal to the area of third circle. What is the radius of third circle? 8. What is the perimeter of the given plot? R A 7cm O 5cm C 50cm B 14cm 14cm 50cm 0 9. If an arc forms an angle of 90 at the centre of the circle then what is the ratio of its length to the circumference of the circle? 0. What is the area of the largest triangle that can be inscribed in a semi-circle of ra d iu s r cm? 1. A piece of wire 0cm long is bent into an arc of a circle subtending an angle of 60 at the centre then what is the radius of the circle? 55 Maths-X (E)

56 . If an arc form an angle of 7 at the centre of the circle. Find the ratio of its length to its circumference.. The minute hand of a clock is 1cm long. What is the area described by the minute hand between 8:00am to 8:05am? 4. What is the area of the shaded portion in the figure? 6cm 6cm 5. A paper is in the form of a square of side 0cm. Semi-circles are drawn inside the square paper on two sides as diameter. The semicircular portions are cut off. Find the are of remaining paper In the figure, What is the area of the blue ring, if width of each ring is r cm and radius of yellow circle is r cm.? White Black Blue Red Yellow r r r r r 56 Maths-X (E)

57 7. In the figure ABCD is the square of side 5cm. What is the area of the shaded region? A B cm 5 cm D 5 cm C 8. In the figure ABCD and EFGH are the square of sides 6cm and 1cm respectively. Find the area of the shaded region. 1 cm A E F H G 1 cm B 6 cm 9. In the figure find the area of the sector. D 6 cm C ABCD is square kite of side 4cm. What is the area of the shaded portion? 57 Maths-X (E)

58 ANSWERS 1. 4 d 15. h(r + h) m cm 9. 1 : r 17. 5cm 0. r. units 4. R 5. 18cm : 4 : cm 8. 7m 9. 6cm cm m. ( cm ) cm cm. 1 : 5. cm cm² 5. 86cm 6. 5 r cm cm 11. 7cm cm 7. (5 4 )cm 8. (5 ) cm² 1. 8cm 1. 66cm cm or 1 cm cm² cm 9. cm² 40. (16 4 ) cm² 58 Maths-X (E)

59 Chapter - 1 SURFACE AREAS AND VOLUMES 1. What will be the volume of tank whose length is 10m, breadth 8m and height 6m?. How much aluminium sheet is required to make a box with lid of length m, breadth m and height 4m?. What will be the area of four walls of a room of length 1m, breadth 10m and height 9m? 4. An underground water tank is in the form of cube of side 6m. What will be its volume? 5. The volume of cube is 8a, find its edge. 6. Volume of a cube is 1000cm. What will be the length of its edge? 7. The length of a diagonal of a cube is 17.cm. Find the volume of cube. (use 1.7 ) 8. Three cubes of the same metal, whose edges are 6, 8, 10cm are melted and formed into a single cube. Find the diagonal of the single cube. 9. Two cubes each of length 5m edge are joined end to end. What will be the surface area of the resulting cuboid? 10. Find the area of cardboard needed to make a rectangular box 14cm long, 9cm wide and 7cm high. 11. The total surface area of the cube is 16cm.Find its edge. 1. What will be the volume of a cylindrical tank with radius 7cm and height cm.? 1. What is the number of solid spheres of radius 1 cm, which may be formed from a solid sphere of radius cm? 14. If the volume and surface area of a sphere are numerically same, then what is its radius? 15. If height of frustum is 4cm and the radii of two bases are cm and 6cm respectively, find the slant height of the frustum. 16. Volume of right circular cylinder is 448 cm, height of cylinder is 7cm. Find the radius. 59 Maths-X (E)

60 17. If surface area of sphere is 144 cm. What is its radius? 18. If lateral surface area of a cube is 64 cm, what will be its edge? 19. Volume of hemisphere is 18 cubic units, what will be its radius? 0. Curved surface area of a cone is 90 cm. What will be the radius of the cone if its slant height is 90cm? 1. Radius of sphere is 8cm. How many small spheres of radii 4cm can be formed out of it?. Volume of a cuboid is 40 cm. If its lenght is 4cm, breadth is 5cm, find the height of the cuboid.. Five equal cubes, each of side 6cm, are joined end to end. Find the surface area of the resulting cuboid. 4. The area of rhombus is 4 cm and one of its diagonal is 8cm. What is other diagonal of the rhombus? 5. What is the length of the largest rod that can be put in a box of inner dimensions 0cm, 4cm and 18cm? 6. Curved surface area of cylinder is 16 cm. Its radius is 4cm, then find its height circular plates each of equal radius are placed one over the other to form a cylinder. Find the height of the cylinder so formed, thickness of each plate is 1/cm. 8. There are two cones. The lateral surface area of one cone is twice the lateral surface area of second cone. The slant height of second cone is twice the slant height of first cone, find the ratio of their radii. 9. If volume of a solid sphere is 88 cm, find its radius. 0. A cone of height 4cm and radius 8cm is reshaped by a child to form a sphere. Find the radius of the sphere. 1. A well of diameter m is dug 14m deep. Find the volume of the earth dug out.. A largest sphere is carved out of a cube of side 7cm; find the radius.. If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, what would be the ratio of their heights? 4. A right cylindrical vessel is full of water. How many right cones having the same diameter and height as those of the right cylinder will be needed to store that water? 60 Maths-X (E)

61 5. A wooden box of dimensions 8 m 7 m 6 m, is to carry rectangluar boxes of dimension 8 cm 7 cm 6 cm, find the maximum number of boxes that can be carried out in the wooden box. 6. Find the slant height of a cone, if its height is 1cm and radius is 5cm. 7. If the semi-vertical angle of a cone of height cm is 60, find its volume. 8. Find the edge of cube if volume of the cube is equal to the volume of cuboid of dimensions 8 4 cm. 9. The volume of a cylinderical rod is of its cross section. 40. Find the volume of cone of height h and radius r. 980 cm. If its height is 0cm, find the radius 41. Give the condition for which a right circular cylinder closed at both ends, has its total circular area equal to its total curved surface? 4. Find the radius of the largest right circular cone that can be cut out of a cube whose edge is 9cm. 4. The volume of a room is height. 5760m. Its length and width are 4m and 0m, find the 44. The circumference of the circular edge of solid hemispherical ball is 1cm. Find the radius of ball persons took dip in a cuboidal tank which is 80m long and 50m broad. What is the rise in level of water in the tank if the average displacement of water by a person is 0.04m? 46. If the radius and height of a cylinder are in the ratio : 7 and its volume is then what will be its radius? 88m, 47. If a sphere of diameter 1cm is melted and drawn into a wire of diameter 0.cm, find the length of the wire. 48. What is the total surface area of a solid hemisphere of radius R? 49. Cube of sides cm is cut down into cubes of sides 1cm. What is the ratio of surface area of smaller cubes to that of larger cube? 50. In a shower, there is 5cm rainfall. Find in cubic metre the volume of water that falls on hectares of ground. (1 hectare = 10,000 m ) 61 Maths-X (E)

62 1. 480m. 5m. 96m 4. 16m 5. a 6. 10cm cm 8. 1 cm 9. 50m m 11. 6cm 1. 08cm cm 16. 8cm 17. 6cm 18. 4cm cm cm ANSWERS. 79 cm 4. 6cm 5. 0 cm 6. cm 7. 5cm 8. 4 : cm 0. 4cm 1. 44m..5cm. 5 : ,00, cm cm 9. 7cm 40. r h 41. r = h cm 4. 1m 44. 1cm cm or 0.005m 46. m m 48. R² : m³ 6 Maths-X (E)

63 Chapter - 1 STATISTICS AND PROBABILTY 1. What is the mean of n numbers x 1,x, x n?. What is the mean of observations x 1,x, x n with frequencies f 1, f,......,f n?. What is the mean of the data 6, 8, 7,,? 4. The number of children of 10 families of a locality are, 4,, 4,, 0,, 5, 1, 1. What is the mean number of children per family? 5. What is the mean of data x, x +, x + 4, x + 6, x + 8? 6. Find the mean of first five natural numbers For the numbers 9.6, 5.,.5, 1.5, 1.6,.4,.6, 8.4, 10., 10.9 find xi x 8. Find the frequencies:- Marks Below 10 5 Below 0 9 Below 0 17 Below 40 9 Below Number of Students 9. Find the missing frequency p if fi 0 and Class Marks : Frequencies : 6 9 p The mean of 0 numbers is 17. If is added to every number, then find the new mean. 11. If x is the mean of n obeservations x 1,x, , x n then find n i 1. Find the mean of first five prime numbers. ii i1 x x. 6 Maths-X (E)

64 1. The mean of 6, 4, 7, x and 14 is 8. Find x. 14. Find the frequencies of the data:- Marks Above 0 80 Above Above 0 7 Above 0 65 Above Number of Students 15. The mean of 5 numbers is 18. If one number is excluded their mean is 16. Find the excluded number. 16. In the following data what is fi? x f 5 10 p Find the mean of first five odd natural numbers. 18. The scores of two batsmen A and B in five innings of a test series are A : B : Who is the better choice for the man of the series? 19. Find the sum of deviations of the variate values, 4,6, 8, 14 from their mean. 0. The mean of 0 numbers is 5. If each number is divided by 5 then what is the new mean. 1. What is the mean of first five composite numbers?. In the following data what is fixi? x : f : 7 p 8 4 fx : 5 10p The mean of 40 observations was 160.It was detected on rechecking that the value of 165 was wrongly copied as 15 for computing of mean. Find the correct mean. 64 Maths-X (E)