QUESTION_BANK_CLASS_X

2. (a) raise the issue of the absence of an Amul milk booth (b) establish an Amul milk booth (c) open a temporary milk booth (d) make you aware about the opening of milk booth ANSWER: (a) raise the issue of the absence of an Amul milk booth 3. (a) suffer with (b) face many problems (c) get tired (d) become worried ANSWER: (b) face many problems 4. (a) arrange for milk products (b) purchase milk (c) get their daily stock of milk and milk products (d) get the needed amount of grocery and household items ANSWER: (c) get their daily stock of milk and milk products 5. (a) Amul authorities are sensitised (b) people look into the matter (c) authorities can know about (d) people become sensitive ANSWER: (a) Amul authorities are sensitized

LETTER OF COMPLAINT Q4. Your houses are not safe. Thefts are on the increase. Even properly locked houses are being plundered. Choose the most appropriate option to complete the letter you have written to the Deputy Commissioner of Police for increasing patrolling at night in your locality. You are Sumit Mittal residing at B/24, Shyam Nagar, Gurgram. B/24, Shyam Nagar Gurgram 26th August ,2021 The Deputy Commissioner of Police Gurgaon Subject: (a)…………………………………………………………………………………………………….. Sir (b) ………………………………………………………………………………………………………….. ours has become a theft prone area. (c)……………………………………………………………………….. and they are being plundered. A day before yesterday burglars broke open the door of my uncle's house and ran away with a huge booty. The police station is at a distance of 3 km from our locality. Fifteen days ago, (d)……………………………………………………………………………………………….. that some unknown persons had entered a house but the authorities reached very late and by that time the thieves had fled from the scene rendering the owner almost a pauper. (e)……………………………………………………………………… and increase the hours of patrolling also. Moreover, I request you to call a meeting of the area residents and make them understand the necessity of appointing day and night guards by the RWA. Your prompt action would certainly help in reducing thefts. Yours faithfully Sumit Mittal (a) Suggest a suitable subject for this letter. (i) Thefts are on the increase. (ii) Increasing threat of theft in Shyam Nagar. (iii) necessity of appointing day and night guards by the RWA. (iv) to call a meeting of the area residents. Ans (ii) Increasing threat of theft in Shyam Nagar. (b) Choose the most suitable sentence to begin the body of the letter. (i) I wish to draw our attention to the increasing number of theft in our locality. (ii) I will draw your attention to the increasing number of thefts in our locality. (iii) I wish to draw your attention to the increasing number of thefts in our locality. (iv) I wish the thieves would draw our attention to the increasing number of thefts. Ans (iii) I wish to draw your attention to the increasing number of thefts in our locality. (c)……………………………………………………………………….. and they are being plundered.

Complete it. (i) Even properly locked houses are not safe (ii) Though properly locked houses are not safe (iii) As properly locked houses are safe (iv) Properly locked houses are safe Ans (i) Even properly locked houses are not safe (d)………………………………………………………….. that some unknown people had entered a house. (i) a residence will inform the police (ii) a resident is informing the police (iii) a resident has informed the police (iv) a resident did inform the police Ans (iv) a resident did inform the police (e)…………………………………………………… and increase the hours of patrolling also. (i) We requested you to depute more policemen for patrolling (ii) We request you to depute more policemen for patrolling (iii) We have requested you to depute more policeman for patrolling (iv) We request you to be deputed for patrolling Ans (ii) We request you to depute more policemen for patrolling

MATHS

INTRODUCTION TO TRIGONOMETRY 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is: a 12/7 b 24/7 c 20/7 d 7/24 Answer: b 24/7 2. 1 – cos2A is equal to: a sin2A b tan2A c 1 – sin2A d sec2A Answer: a sin2A 3. If cos X = a/b, then sin X is equal to: a (b2-a2)/b b b−a/b c √(b2-a2)/b d √b−a/b Answer: c √(b2-a2)/b 4.The value of sin 60° cos 30° + sin 30° cos 60° is: a0 b1 c2 d4 Answer: b 1 5.sin 2A = 2 sin A is true when A = a 30° b 45° c 0° d 60° Answer: c 0° 6. If ∆ABC is right angled at C, then the value of cos(A+B )is a0 b1 c 1/2 d √3/2 Answer: a 0 7. If cos 2α = ½ ,then α is a 150 b 300 c 600 d 00 Answer: b 300

8. In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is (a) 0 (b) 1 (c) – 1 (d) 2 Answer b 1 9. Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is: (a)30 (b)45 (c)75 (d)60 Answer (c) 75 10. If angle A is acute and cos A = 8/17 then cot A is : (a) 8/15 (b) 17/8 (c) 15/8 (d) 17/15 Answer (a) 8/15 11. If cosec A = 5/4 ,then cot A = (a) ) 4/5 (b) 50/40 (c) 3/4 (d) 4/3 Answer (c) 3/4 12.The value of 2 tan245°+ cos230° − sin260° is (a) 0 (b) 1 (c) -2 (d) 2 Answer (d) 2

13. 13. If α + β = 90° and α = 2β then cos α equal: (a) 1 (b) zero (c) 1/2 (d) 2 Answer (c) ½ 14. In the given figure, if AB = 14 cm, BD = 10 cm and DC = 8 cm, then the value of tan B is a) 4/3 b) 14/3 c) 11/3 d) 9/12 Answer a)4/3 15. Reciprocal of sin A is ————- a. cosec A b. sec A c. cot A d.Tan a Answer a cosec A 16.The values of the trigonometric ratios of an angle ———— with the lengths of the sides of the triangle, if the angle remains the same. a. vary b. Do not vary c. None of these D. Both Answer b. do not vary 17. The value of sin A or cos A never exceeds ————

a. One b. Two c. Three d Four Answer a One 18. Ratios of sides of a right triangle with respect to its acute angles are knownas ————– a. Trigonometric Identities b. Trigonometric Ratios c. Trigonometry d. trigonometry formula Answer b Trigonometric Ratios 19. If tan A = 4/3 and sin A = 4/5 then cos A = —————– a. 4/5 b. 3/5 c. ¾ d.9/11 Answer b 3/5 20. The value of sec A or cosec A is always —————- a. Less than or equal to one b. Greater than or equal to one c. Equal to one d. Negative Answer b. Greater than or equal to one

CHAPTER 3 - LINEAR EQUATIONS IN TWO VARIABLES. 1.One equation of a pair of dependent linear equations is -5x+7y=2 .The second equation can be (a)10x-14y-4=0 (b) -10x+14y+4=0 (c) 10x-14y-4=0 (d) -10x+14y-4=0 Answer (d) 2.The pair of equations y=0 and y=-7 has (a)one solution (b)two solutions (c)no solution (d)infinitely many solutions Answer (c) 3.The pair of equations ax+2y=7 and 3x+by=16 represent parallel lines if (a)a=b (b)3a=2b (c)ab=6 (d)2a=3b Answer (c) 4.The pair of equations ax+by+c=0 and dx+ey+c=0 represent the equations with infinitely many solutions if (a)ad=be (b)ae=bd (c)ab=de (d)ac=de Answer (b) 5. A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22

(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0 Answer (d) 6. Rs.4900 was divided among a group of 150 children. If each girl gets Rs.50 and each boy gets Rs.25 then, the number of boys in the group is: (a) 100 (b) 102 (c) 104 (d) 105 Answer (c) 7. A boat is rowed downstream at 15.5 km/h and upstream at 8.5 km/h. The speed of the stream is: (a) 3.5 km/h (b) 5.75 km/h (c) 6.5 km/h (d) 7 km/h Answer (a) 8.The area of the triangular region, in the following figure, bounded by the lines 2x-y=1 and x+2y=13 and Y-axis is (a) 11.25 sq.units (b) 9.75 sq.units (c) 16.25 sq,units (d) 18.75 sq.units Answer (a)

9. \"Ravi is 10 years older than Rehan. Five years ago, one-seventh of Ravi's age was equal to one-fifth of Rehan's age.\" If Rehan's age be 'x' years and Ravi's age be 'y' years, which of the following pair of linear equations is describing it algebraically? (a) x - y = 10 and 7x - 5y + 10 = 0 (b) y -x = 10 and 5y -7x + 10 = 0 (c) x + y = 10 and 7x + 5y - 10 = 0 (d) x - y = -10 and 7y - 5x + 10 = 0 Answer (b) 10. The coordinates of the vertices of region bounded by lines 3x - y = 5; x+ 2y = 4 and Y-axis are: (a) A(2,0); B(5,0) and C(1,2) (b) A(2,0); B(-5,0) and C(1,2) (c) A(0,2); B(0,-5) and C(2,1) (d) A(0,2); B(0,5) and C(2,1) Answer (c) 11.The value(s) of 'k' for which the following pair of linear equations will represent a pair of intersecting lines graphically is/are: 3x - 4y + 7 = 0 kx - 8y = 5 (a) k = 6 (b) k ≠ 6

(c) any real number (d) any real number except 6 Answer (d) 12. The solution of the following system of linear equations in two variables is: 55x + 67y = 311; 67x + 55y = 299 (a) (2, 3) (b) (3, 2) (c) (-2,3) (d) (3, -2) Answer (b) 13. If (x, y) is a solution of the following pair of linear equations in two variables, then the value of expression (√ is: x + 2y = 4 and 3x - y = 5 (a) 2 (b) 3 (c) 4 (d) √ Answer (a) 14. In the following figure ABCD is a cyclic quadrilateral, the sum of degree measures of ∠A and ∠D is: (SOURCE: Fig. 3.7, Exercise 3.7, Chapter 3, PAIR of LINEAR EQUATIONS in TWO VARIABLES, NCERT, Class X) (a) 120° (b) 180° (c) 230°

(d) 250° Answer (c) 15. Out of the following linear equations in two variables, the two representing a pair of parallel lines graphically are: 3x - 4y = 6 3x + 4y = 6 6x + 8y = 12 6x - 8y + 6 = 0 (a) 3x - 4y = 6 and 6x + 8y = 12 (b) 3x - 4y = 6 and 6x - 8y + 6 = 0 (c) 6x + 8y = 12 and 3x + 4y = 6 (d) 6x - 8y + 6 = 0 and 3x + 4y = 6 Answer (b) 16. All solutions of the linear equation 2x + 3y = 7 are also the solutions of equation (a) 5x + 6y = 13 (b) 4x + 6y = 11 (c) 6x + 9y = 7 (d) 6x + 9y = 21 Answer (d) Case Study Questions(Question number 17 &18) 17. CASE STUDY 1

Mathematics teacher of a school took the standard 10 students to see the painting exhibition which was held at ART COLLEGE OF EDUCATION, Bangalore. It is the part of art integration of Mathematics. Students were eager to see the above painting. The teacher explained that the above painting is based on concept of a pair of linear equations of two variables 1.If the speed of the boat is 5 km/hr and the speed of stream is 2 km/hr, what is the speed of the boat Downstream? a) 5km/hr b) 2km/hr c) 7km/hr d) 3km/hr 2.If the speed of boat is 5 km/hr and speed of stream is 2 km/hr. What is the speed of the boat in Upstream? a) 5km/hr b) 2km/hr c) 7km/hr d) 3km/hr 3. If the boat goes 21 km downstream, What is the time required to cover it? a) 5 hrs b) 2 hrs c) 7 hrs d) 3 hrs 4.A boat goes 12 km Up stream. What is the time required to cover it? a) 4 hrs b) 2 hrs c) 6hrs d) 3 hrs 5.If speed of boat and stream be x km/hr and y km/hr respectively. What is the distance covered by the boat down steam in ‗t‘hours? a) t(x-y)km b) t(x+y)km c) 2t(x-y)km d) 2t(x+y)km Answers 1.(c) 2.(d) 3.(d) 4.(a) 5.(b) 18. In a city, the two main roads cross each other at right angles as shown below. At their intersection, there is a statue of Mahatma Gandhi. Taking that statue as the origin and the two roads represent X-axis and Y- axis. A railway line crosses the city intersects the two cross roads as shown below. At all the points of intersection of the railway track with the two roads, namely A, B, C and D barriers are created. The region enclosed by the two tracks and the two cross-roads represented by the X-axis and Y-axis is to be cleaned by the Local Municipal Authorities and the triangular region OAB is beautified by growing Grass.

Observing the above graph and taking 1unit = 1km as scale factor, answer the following questions: 1. Which of the following pair of linear equations represent the two parallel tracks of the railway line? a) x-2y-4=0 and 2x + 4y - 12 = 0 b) x +2y-4=0 and 2x + 4y +12 = 0 c) 2x + 4y -12 = 0 and x +2y-4=0 d) 2x + 4y + 12 = 0 and x-2y-4=0 2. The coordinates of the points A and B are a) (0,4) and (2,0) b) (4,0) and (0,2) c) (0,4) and (0,2) d) (4,0) and (2,0) 3. The coordinates of the points C and D are a) (0,6) and (3,0) b) (0,6) and (0,3) c) (6,0) and (0,3) d) (6,0) and (3,0) 4. The area to be covered by Green Grass is: a) 4 square km b) 5 square km c) 9 square km d) 10 square km 5. The amount of area to be cleaned is: a) 4 square km b) 5 square km c) 9 square km d) 10 square km Answers 1.(c) 2.(b) 3.(c) 4.(a) 5.(b) Assertion - Reasoning (Question number 19 & 20)

DIRECTION: Following questions consist of two statements – Assertion (A) and Reason (R). Answer these questions selecting the appropriate option given below: 19. Assertion (A) : The value of k for which the system of linear equations kx+2y+1=0 and 6x+4y-5=0 has a unique solution is 3. Reason (R):The system of linear equations a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂ = 0 has a unique solution if (a) Both A and R are correct; R is the correct explanation of A. (b) Both A and R are correct; R is not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect. Answer (d) 20. Assertion (A):A pair of linear equations has no solution (s) if it represented by intersecting lines graphically. Reason (R) : If the pair of lines are intersecting, then the pair has unique solution and is called consistent pair of equations. (a) Both A and R are correct; R is the correct explanation of A. (b) Both A and R are correct; R is not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect. Answer (d)

CHAPTER 7 - COORDINATE GEOMETRY Multiple Choice Questions: 1. If the centroid of △ABC in which A(a,b), B(b,c) and C(c,a) is at the origin, then the value of a³ + b³ + c³ is: (a) abc (b) 2abc (c) 3abc (d) 0 Answer: (c) 3abc 2. The ratio in which P ( , ) divides the line segment joining the points A ( , ) and B(2,-5) is : (a) 1:5 (b) 5:1 (c) 1:4 (d) 4:1 Answer: (a) 1:5 3. If A(5,2), B(2,-2) and C(-2,t) are the vertices of a right angled triangle with ∠B = 90⁰ , then the value of t is: (a) -1 (b) 1 (c) -2 (d) 2 Answer: (b) 1 4. The point (-1,2) divides the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4, then the value of x² + y² is : (a) 27 (b) 28 (c) 29 (d) 30 Answer: (c) 29 5. The point which lies on the perpendicular bisector of the line segment joining the points A(-3,-5) and B(3,5) is: (a) (-3,0) (b) (5,0) (c) (5,-5) (d) (0,0) Answer: (d) (0,0) 6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is: (a) 12 units (b) 11 units (c) 5units (d) (7 + √5)units Answer:(a) 12 units 7. The points (-4, 0), (4, 0), (0, 3) are the vertices of a: (а) Right triangle (b) Isosceles triangle (c) Equilateral triangle (d) Scalene triangle Answer: (b) Isosceles triangle 8. If the distance between the points (4, p) and (1, 0) is 5units , then the value of p is: (a) 4 only (b) 0 (c) – 4 only (d) 4, - 4 Answer: (d) 4, - 4 9.The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a:

(a)Square (b) Rhombus (c) Rectangle (d) Trapezium Answer: (c) Rectangle 10. The point which divides the line segment joining the points (7, –6) and (3, 4) in the ratio 1 : 2 lies in the: (a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant Answer: (d) IV quadrant 11. The endpoint A of a line segment AB is (3 , -1). If midpoint of AB is (5,7) then the coordinates of the point B are: (a) (7,13) (b) (7,15) (c) (4,3) (d) (4,4) Answer: (b) (7,15) 12. Points P,Q,R(in this order) divide the line joining the points A(-2,2) and B(2,8) into four equal parts. The coordinates of the point Q are: (a) (-1,7/2) (b) (1,13/2) (c) (0,5) (d) (5,1/2) Answer: (c) (0,5) 13.The points (-2,-1),(a,0),(4,b),(1,2) are the vertices of a parallelogram taken in order , then the values of a and b are: (a) a = 1,b = 3 (b) a = 3 , b = 1 (c) a = 1 , b = 1 (d) a = 0 , b = 4 Answer: (a) a = 1 , b = 3 14. A (5,-1) , B (-3,-2) and C (-1,8) are the vertices of ∆ ABC . The median from A meets BC at D ,then the coordinates of the point D are: (a) (-4,6) (b) (2,7/2) (c) (1,-3/2) (d) (-2,3) Answer: (d) (-2,3) 15. The coordinates of point A , where AB is the diameter of a circle whose centre is (1,3) and B is (5,4),are: (a) (-3,2) (b) (4,-9) (c) (2,-3) (d) (1/2,-2) Answer: (a) (-3,2) Case study based questions: 16.PLANNING A CITY Chandigarh is the best planned city in India, with architecture which is world renowned , and a quality of life , which is unparalleled. It is rightly called THE CITY BEAUTIFUL.

A locality in Chandigarh has two straight roads perpendicular to each other. There are 5 lanes parallel to road 1. Each lane has 8 houses as shown in the figure. Dhruv lives in 8th house of 4th lane and Anish lives in 2nd house of the 2nd lane. (i) The shortest distance (in units) between the houses of Dhruv and Anish is: (a) 2√10 (b) 5√10 (c) 6√10 (d)7√10 Answer: (a) 2√10 units (ii) If Shivam lives exactly halfway between the houses of Dhruv and Anish then Shivam lives in: (a) 3rd house of the 3rd lane (b) 5th house of the 5th lane (c) 3rd house of the 5th lane (d) 5th house of the 3rd lane Answer: (d) 5th house of the 3rd lane (iii) The distance of the point C from the y-axis is: (a) 2 units (b) 4 units (c) 8 units (d) 12 units Answer: (c) 8 units (iv) The points equidistant from B are: (a) E and F (b) F and D (c) A and D (d) E and D Answer: (b) F and D 17.CONNECTING PEOPLE The poles are being installed by the company to lay optical fibre cables. The Reliance Jio Company has installed three utility poles A, B and C in Rajnagar Society. Despite these three poles, some parts of the

society are facing the problem of low speed in Wi-Fi connections. So, the company decides to have one more pole D to boost Wi-Fi signals which can be modelled as a coordinate system given below. On the basis of the above information, answer the following questions: (i) The position of the pole C is: (a) (4,5) (b) (5,4) (c) (6,5) (d) (5,6) Answer: (b) ( 5,4 ) (ii) The distance of the pole B from the corner O of the park is: (a) 6√2 units (b) 3√2 units (c) 6√3 units (d) 3√3 units Answer: (a) 6√2 units (iii) The position of the fourth pole D so that the four points A, B, C and D form a parallelogram will be: (a) (5, 2) (b) (1, 5) (c) (1, 4) (d) (2, 5) Answer: (b) ( 1, 5 ) (iv) The midpoint of the line segment joining the points B and D is: (a) (10,11) (b) (11,5) (c) (7/2,11/2) (d) (5,11/2) Answer: (c) (7/2,11/2) 18.NATIONAL SPORTS DAY National Sports day is celebrated to honour the national sports teams and sports traditions of the countries.

In a sports day celebration Ram and Shyam are standing at points A and B whose coordinates are given by (2,-2) and (4,8) respectively. The teacher asked Madhav to fix the flag at the mid point X of the line segment joining the points A and B. On the basis of the information given, answer the following questions (i) The distance between the points A and B is : (a) √ units (b) √ units (c) √ units (d) √ units Answer: (a) √ units (ii) The coordinates of the point X are: (a) ( - 3,3) (b) (3, - 3) (c) (3,3) (d) (-3,-3) Answer: (c) (3,3) (iii) The coordinates of the point P such that AP: PB= 2:1 are: (a) ( ) (b) ( ) (c) ( ) (d) ( ) Answer: (b) ( ) (iv) The ratio in which X divides AB is: (a) 2:1 (b)1:1 (c) (d) Answer: (b) 1:1 19.SPREADING AWARENESS Pollution is the introduction of harmful material into the environment . Pollutants can be natural or man made. A school started a campaign to spread awareness about pollution. Students of Class X prepared triangular banners whose vertices are A(1,1),B(6,1) and C(3,7) Answer the given questions (i) The distance AB is: (a) 7 units (b) 5 units (c) 3 units (d) 2 units

Answer: (b) 5 units (ii) The coordinates of the point P dividing AC in the ratio 2:3 are: (a) ( ) (b) ( ) (c) ( ) (d) ( ) Answer: (a) ( ) (iii) A string is to be attached at the mid point X of AB . The coordinates of point X are: (a) ( ) (b) ( ) (c) ( ) (d) ( ) Answer: (c) ( ) (iv) Name the type of triangle formed. (a) Right angled (b) Equilateral (c) Isosceles (d) Scalene Answer: (d) Scalene 20.MORNING WALK Starting your day with a morning walk ,whether it be around your local park,or a beach,can provide your mind and body with many health benefits . Two friends Jai and Rohit went for a morning walk in their society park PQRS. PQRS is a square park of side ‗b' units. If P lies at the origin , sides PQ and PS lie along x - axis and y - axis respectively. (i)The coordinates of the vertex R of the square PQRS are: (a) (0,b) (b) (b,0) (c) (0,0) (d) (b,b) Answer: (d) ( b,b ) (ii)The coordinates of the point of intersection of the diagonals of the square PQRS are: (a) (2b,2b) (b) (b/2,b/2) (c) (1,1) (d) (b,b) Answer: (b) ( b/2,b/2 ) (iii)Length of the diagonal PR is:

(a) 2√ units (b) units (c) b√ units (d) √ units Answer: (c) √ units (iv)If b = 4 units ,the coordinates of point A on the side PQ which divides PQ internally in the ratio 1: 3 are: (a) (1,0) (b) (3,3) (c) (3,0) (d) (1,1) Answer: (a) ( 1,0 ) 21. What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2 Answer: (a) 3,2 22. If a + b = 1 ,and the ordered pair (a, b) satisfies the equation 2x + y = , then it also satisfies (a) 2x + y (b) 3x + 4y = 3 (c) x + 2y = (d) 2x + 4y = Answer: (c) x + 2y = 23. Find x and y , given that + = -1 , – = 4 (a) a and b (b) a and –b (c) -a and b (d) -a and –b Answer: (b) a and –b 24. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Then what is the speed of the stream? (a) 3km/hr (b) 5km/hr (c) 6km/hr (d) 7km/hr Answer: (a) 3km/hr 25. For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8 Answer: (d) k = 8

26. Equation + = 2 is reduced in linear equation as 5p + q = 2. Then the values of p and q respectively are (a) , (b) , (c) x-1 , y - 2 (d) x + 1 , y + 2 Answer: (a) , 27. The 2 digit number which becomes (5/6)th of itself when its digits are reversed. The difference in the digits of the number being 1, then the two digits number is (a) 45 (b) 54 (c) 36 (d) None of these Answer: (b) 54 28. The pair of equations 3x + y = 81 , 81x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1 Answer: (d) x = 2 , y = 1 29. The ratio of the areas of the two triangles formed by the lines representing the equations 2x + y = 6 and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4 Answer: (c) 4 : 1 Assertion and Reason based Questions In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false (d) Assertion (A) is false but reason (R) is true 30. Assertion : The value of q = if x = 3, y = 1 is the solution of the line 2x + y – q2 – 3 = 0 Reason : The solution of the line will satisfy the equation of the line. Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) 31. Assertion : If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.

Reason : If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations. Answer: (d) Assertion (A) is false but reason (R) is true 32. Assertion : The linear equations x – 2y – 3 = 0 and 3x + 4y – 20 = 0 have exactly one solution. Reason : The linear equations 2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 have a unique solution. Answer : (c) Assertion (A) is true but reason (R) is false 33. Assertion : 3x + 4y + 5 = 0 and 6x + ky + 9 = 0 represent parallel lines if k = 8. Reason : a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 represent parallel lines if a1 / a2 = b1 / b2 c1 / c2 Answer : (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) 34. The value of m obtained on solving equations : 2n + m =2n – m = √ is a) 1/4 b) 0 c) 1/2 d) 3/4 Answer: (b) 0 35. The pair of equation x = 4 and y = 3 graphically represents lines which are a) Parallel b) Intersecting at ( 3,4) c) Coincident d) Intersecting at ( 4,3) Answer: (d) intersecting at (4 , 3) 36 One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be a) 4x + 6y = 18 b) 4x - 6y = - 18 c) -4x – 6y = 18 d) None of these Answer: (b) 4x – 6y = -18 37 The value of x and y which satisfy the equations : √ x+ √ y =0 and √ x+ √ y =0 is a) x=1,y=0 b) x=0,y=0 c) x=1,y=1 d) x=0,y=1 Answer: (b) x=0 ,y=0 38. The coordinates of the points where 2x + 5y – 10 =0 meets y axis is a) (0 , 2) b) (0 , -2) c) (2 , 2) d) (-2 , -2)

Answer: (a) (0 , 2) 39 If lines corresponding to given linear equations are coincident, the solutionof the given equations is: a) Unique solution b) Two solutions c) Infintely many solutions d) No solution Answer: ( c) Infinitely many solutions 40 If = = in the system of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions Statement 3 : The equations satisfying the condition are parallel Which of the above statements are true ? a) S1 only b) S1 and S2 c) S1 and S3 d) S2 only Answer: (d) S2 only

Chapter – Area Related to Circles Question Type – MCQs CASE STUDY Pookalam is the flower bed or flower pattern designed during Onam in Kerla. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below . Observe these carefully. Fig- I Fig - II Design I : This design is made with a circle of radius 32cm leaving an equilateral triangle ABC in the middle as shown in the given figure. Design II: This Pokalam is made with 9 circular designs each of radius 7cm. Refer Design I: Q1. The side of equilateral triangle is (a) 12√ cm (b) 32√ cm (c) 48 cm (d) 64 cm Ans: (b) 32√ cm Q2 The altitude of the equilateral triangle is (a) 8 cm (b) 12 cm (c) 48 cm (d) 52 cm Ans:(c) 48 cm Refer Design II Q3

The area of square is (a) 1264 sq. cm (b) 1764 sq. cm (c) 1830 sq. cm (d) 1944 sq. cm Ans: (b) 1764 sq. cm Q4 Area of each circular design is (a) 124 sq. cm (b) 132 sq. cm (c) 144 sq. cm (d) 154 sq. cm Ans: (d) 154 sq. cm Q5 Area of remaining portion of the square ABCD is (a) 378 sq. cm (b) 260 sq. cm (c) 340 sq. cm (d) 278 sq. cm Ans: (a) 378 sq. cm Q6 If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the area of the path is (a) 1450 m2 (b) 1576 m2 (c) 1694 m2 (d) 3368 m2 Ans: (c) 1694 m2 Q7 The area of the circle that can be inscribed in a square of side 6 cm is (a) 36 π cm2 (b) 18 π cm2 (c) 12 π cm2 (d) 9 π cm2 Ans: (d) 9 π cm2 Q8 In a circle of radius 14 cm, an arc subtends an angle of 45O at the centre, then the area of the sector is (a) 71 cm2

(b) 76 cm2 (c) 77 cm2 (d) 154 cm2 Ans: (c) 77 cm2 Q9 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (a) 22:7 (b) 14:11 (c) 7:22 (d) 11:14 Ans: (b) 14:11 Q10 What is the perimeter of the sector with radius 10.5 cm and sector angle 60º? (a) 48 cm (b) 96 cm (c) 64 cm (d) 32 cm Ans: (d) 32 cm Q11 If diameter of a wheel is 1.26 m, what the distance covered in 500 revolutions? (a) 1.38 km (b) 4.64 km (c) 2.46 km (d) 1.98 km Ans: (d) 1.98 km Q12 A thin wire is in the shape of a circle of radius 77 cm. It is bent into a square. What is the side of the square? (a) 168 cm (b) 242 cm (c) 121 cm (d) 336 cm Ans: (c) 121 cm Q13

What is the area of the corresponding major sector of a circle of radius 28 cm and the central angle 45o? (a) 4312 cm2 (b) 2156 cm2 (c) 1256 cm2 (d) 3412 cm2 Ans: (b) 2156 cm2 Q14 In the given figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is (a) 11 cm (b) 18 cm (c) 25 cm (d) 36 cm Ans: (c) 25 cm Q15 In the given figure, AB is the diameter where AP = 12 cm and PB = 16 cm. If the value of π is taken 3, what is the perimeter of the shaded region? (a) 58 cm (b) 116 cm (c) 29 cm (d) 156 cm Ans: (a) 58cm Q16 If the radius of a circle is doubled, what about its area?

(a) Area is 2 times (b) Area is 4 times (c) Area is half (d) does not change Ans: (b) Area is 4 times Q17 In given fig., O is the centre of a circle. If the area of the sector OAPB is 5/36 times the area of the circle, what is the value of x (a) 50° (b) 60° (c) 70° (d) 80° Ans: (a) 50° The following questions consists of 2 statements – Assertion (A) and Reason (R). Answer these questions selecting the appropriate option given below: (a) Both A and R are true and R is the correct explanation for A (b) Both A and R are true and R is not the correct explanation for A (c) A is true but R is false (d) A is false but R is true Q18 Assertion (A): The area covered by 21cm long minute hand in 20 minutes is 462 sq. cm. Reason (R): Area of circle is . Ans: (b) Both A and R are true and R is not the correct explanation for A. Q19 Assertion: (A): The area of the largest triangle that is inscribed in a semi- circle of diameter 2r unit is 2 sq. units. Reason (R): Angle is a semi- circle is a right angle. Ans: (d) A is false but R is true. Q20 Assertion (A): A wheel of radius 0.25m make 7000 revolutions to travel a distance of 11 Km.

Reason (R): To find the number of revolutions, divide the total distance by the circumference of the circle. Ans: (a) Both A and R are true and R is the correct explanation for A

Maths : Ch Linear Equations in Two variables Q1. What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2 Answer: (a) 3,2 Q2. If a + b = 1 ,and the ordered pair (a, b) satisfies the equation 2x + y = , then it also satisfies (a) 2x + y (b) 3x + 4y = 3 (c) x + 2y = (d) 2x + 4y = Answer: (c) x + 2y = Q3. Find x and y , given that + = -1 , – = 4 (a) a and b (b) a and –b (c) -a and b (d) -a and –b Answer: (b) a and –b Q4. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Then what is the speed of the stream? (a) 3km/hr (b) 5km/hr (c) 6km/hr (d) 7km/hr Answer: (a) 3km/hr Q5. For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8 Answer: (d) k = 8 Q6. Equation + = 2 is reduced in linear equation as 5p + q = 2. Then the values of p and q respectively are (a) , (b) , (c) x-1 , y - 2

(d) x + 1 , y + 2 Answer: (a) , Q7. The 2 digit number which becomes (5/6)th of itself when its digits are reversed. The difference in the digits of the number being 1, then the two digits number is (a) 45 (b) 54 (c) 36 (d) None of these Answer: (b) 54 Q8. The pair of equations 3x + y = 81 , 81x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1 Answer: (d) x = 2 , y = 1 Q9. The ratio of the areas of the two triangles formed by the lines representing the equations 2x + y = 6 and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4 Answer: (c) 4 : 1 Assertion and Reason based Questions In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) (c) Assertion (A) is true but reason (R) is false (d) Assertion (A) is false but reason (R) is true Q10. Assertion : The value of q = if x = 3, y = 1 is the solution of the line 2x + y – q2 – 3 = 0 Reason : The solution of the line will satisfy the equation of the line. Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) Q11. Assertion : If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution. Reason : If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations. Answer: (d) Assertion (A) is false but reason (R) is true Q12. Assertion : The linear equations x – 2y – 3 = 0 and 3x + 4y – 20 = 0 have exactly one solution. Reason : The linear equations 2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 have a unique solution.

Answer : (c) Assertion (A) is true but reason (R) is false Q13. Assertion : 3x + 4y + 5 = 0 and 6x + ky + 9 = 0 represent parallel lines if k = 8. Reason : a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 represent parallel lines if a1 / a2 = b1 / b2 c1 / c2 Answer : (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) Q14. The value of m obtained on solving equations : 2n + m =2n – m = √ is a) 1/4 b) 0 c) 1/2 d) 3/4 Answer: (b) 0 Q15. The pair of equation x = 4 and y = 3 graphically represents lines which are e) Parallel f) Intersecting at ( 3,4) g) Coincident h) Intersecting at ( 4,3) Answer: (d) intersecting at (4 , 3) Q16 One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be e) 4x + 6y = 18 f) 4x - 6y = - 18 g) -4x – 6y = 18 h) None of these Answer: (b) 4x – 6y = -18 Q17 The value of x and y which satisfy the equations : √ x+ √ y =0 and √ x+ √ y =0 is e) x=1,y=0 f) x=0,y=0 g) x=1,y=1 h) x=0,y=1 Answer: (b) x=0 ,y=0 Q18. The coordinates of the points where 2x + 5y – 10 =0 meets y axis is e) (0 , 2) f) (0 , -2) g) (2 , 2) h) (-2 , -2) Answer: (a) (0 , 2) Q 19 If lines corresponding to given linear equations are coincident, the solutionof the given equations is: e) Unique solution f) Two solutions

g) Infintely many solutions h) No solution Answer: ( c) Infinitely many solutions Q 20 If = = in the system of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions Statement 3 : The equations satisfying the condition are parallel Which of the above statements are true ? e) S1 only f) S1 and S2 g) S1 and S3 h) S2 only Answer: (d) S2 only

TOPIC – PROBABILITY 1. A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4. a. 3/25 b. 2/25 c. 1/25 d. 13/50 Ans : 2/25 2. All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is face card. a. 2/23 b. 7/44 c. 3/23 d. 4/25 Ans: 3/23 3. A dice is thrown once, what is the probability of getting a prime number? a. 1/3 b. 6/25 c. 1/2 d. 1/4 Ans: 1/2 4. Probability of a sure event is a. -1 b. 1 c. 0 d. 2 Ans: 1 5. Two dice are thrown together. Find the probability that the sum of the numbers obtained is even a. 1/4 b. 1/6 c. 1/3 d. 1/2

Ans:1/2 6. A square of side 5cm is drawn in the interior of another square of side 10cm and shaded as shown in the figure. A point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded part. a. 1/5 b. 1/4 c. 1/9 d. 1/2 Ans:1/4 7. Geeta has a cubical block with one word written on each face. Come, to, learn, go, to, serve. The block is thrown. What is the probability of getting ‗to‘? a. 1/3 b. -5/6 c. 3/8 d. 0 Ans:1/3 8. A ship is reported to reach somewhere in the region as shown in figure. What is the probability that the ship reach in the shaded region. a. 11/67 b. 13/81 c. 1/77 d. 11/113 Ans:1/77 9. In a village fair, Gopal set up a stall of game consisting of spinning an arrow which comes to rest pointing at one of the regions 1, 2 or 3. Find the probability of outcome 1.

a. 1/3 b. 1/2 c. 1/4 d. 1/6 Ans:1/2 10. If a number x is chosen at random from the numbers -2, -1, 0 1, 2. What is the probability that x2 < 2? a. 2/5 b. 3/5 c. 1/4 d. 4/7 Ans:3/5 11. The given figure shows the top view of an open square box that is divided into 6 components with walls of equal height. Each of rectangles D,E,F has twice the area of the squares A,B and C. When a marble is dropped into the box at random, it falls into one of the compartments. what is the probability that it will fall into compartment F? AD BE CF A. 3/9 B. 2/9 C. 3/7 D. 4/9 Ans:2/9 12. What is the probability of a non -occurrence of an event that is certain to happen? a. 0 b. 1 c. -1 d. 2 Ans:0

13. Nine playing cards are numbered 2 to 10. A card is selected at random. What is the probability that the card will be an odd number? a. 1/9 b. 2/9 c. 4/9 d. 3/7 Ans: 4/9 14. In the accompanying diagram a fair spinner is placed at the Centre O of the circle. Diameter AOB and radius OC divides the circle into three regions X, Y and Z. If LBOC = 450, what is the probability that the spinner will hand in the region X? A. 3/8 B. 2/3 C. 1/4 D. 3/5 Ans: 3/8 15. Find the probability that a leap year selected at random will contain 53 Sundays. a. 1/7 b. 2/7 c. 5/7 d. 4/7 Ans: 2/7 16. CASE STUDY On a weekend Anisha was playing cards with her family .The deck has 52 cards. If her brother drew one card.

1. Find the probability of getting a king of red color. A. 1/26 B. 1/13 C. 1/52 D. 1/4 2. Find the probability of getting a face card. A. 1/26 B. 1/13 C. 2/13 D. 3/13 3. Find the probability of getting a jack of hearts. A. 1/26 B. 1/52 C. 3/52 D. 3/26 4. Find the probability of getting a red face card. A. 3/26 B. 1/13 C. 1/52 D. 1/4 5. Find the probability of getting a spade. A. 1/26 B. 1/13 C. 1/52 D. 1/4 Ans:1)1/26 2)3/13 3)1/52 4)3/26 5)1/4 17. CASE STUDY Rahul and Ravi planned to play Business (board game) in which they were supposed to use two dice. 1. Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8? a. 1/26

b. 5/36 c. 1/18 d. 0 2. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13? a. 1 b. 5/36 c. 1/18 d. 0 3. Now it was Ravi‘s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12? a. 1 b. 5/36 c. 1/18 d. 0 4. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7? a. 5/9 b. 5/36 c. 1/6 d. 0 5. Now it was Ravi‘s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8? a. 1 b. 5/36 c. 1/18 d. 5/18 Ans: 1) 5/36 2)0 3)1 4)1/6 5)5/18 18. Ramesh chooses a data at random in April for a party. Calculate the probability that he chooses a Saturday. a. 3/15 b. 2/15 c. 8/17 d. 4/16 Ans: 2/15 19. The probability that a man can hit a target is 2/3. The probability that he misses the target is …….. a. 1/2

b. 1/4 c. 1/3 d. 3/4 Ans: 1/3 20. In a family of 3 children, probability of having at least one boy is: a. 7/8 b. 1/8 c. 5/8 d. 3/8 Ans: 7/8

POLYNOMIALS 1. The degree of the polynomial, x4 – x2 +2 is (a) 2 (b) 4 (c) 1 (d) 0 Answer: (b) 4 2. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial is: (a) Intersects x-axis (b) Intersects y-axis (c) Intersects y-axis or x-axis (d) None of the above Answer: (a) Intersects x-axis 3. The number of polynomials having zeroes as -2 and 5 is: (a) 1 (b) 2 (c) 3 (d) More than 3 Answer: (d) More than 3 4. Zeroes of p(x) = x2-27 are: (a) ±9√3 (b) ±3√3 (c) ±7√3 (d) None of the above Answer: (b) ±3√3 5. If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is (a) 10 (b) –10 (c) 5 (d) –5 Answer: (b) -10 6. The zeroes of the quadratic polynomial x2 + 99x + 127 are (a) both positive (b) both negative (c) one positive and one negative

(d) both equal Answer: (b) both negative 7. The maximum number of zeroes that a polynomial of degree 4 can have is (a) One (b) Two (c) Three (d) Four Answer: (d) Four 8. The graph of the polynomial p(x) = 3x – 2 is a straight line which intersects the x-axis at exactly one point namely (a) (−2/3, 0) (b) (0, −2/3) (c) (2/3, 0) (d)( 2/3, −2/3) Answer: (c) ( 2/3, 0) 9. In fig. given below, the number of zeroes of the polynomial f(x) is a) 1 (b) 2 (c) 3 (d) None Answer: (c) 3 10. The graph of the polynomial ax² + bx + c is an upward parabola if (a) a > 0 (b) a < 0 (b) a = 0 (d) None Answer: (a) a > 0 11. If α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is (a) 0 (b) 4 (c) -4 (d) 16 Answer: (a) 0 12. If α and 1/α are the zeroes of the polynomial ax² + bx + c, then value of c is (a) 0

(b) a (c) -a (d) 1 Answer: (b) a 13. Dividend is equal to (a) divisor × quotient + remainder (b) divisior × quotient (c) divisior × quotient – remainder (d) divisor × quotient × remainder Answer: (a) divisor × quotient + remainder 14. If -√5 and √5 are the roots of the quadratic polynomial. Find the quadratic polynomial. (a) x-5 (b) (x-5)(x+5) (c) x2 – 5 (d) x2 – 25 Answer: (c) x2 – 5 15. If α , β are the zeroes of f(x) = px2 – 2x + 3p and α + β = αβ then the value of p is: (a) 1/3 (b) -2/3 (c) 2/3 (d) -1/3 Answer: (c) 2/3 16. If ‗α ‘ and ‗β ‘ are the zeroes of a quadratic polynomial x2− 5x + b and α − β = 1, then the value of ‗b‘ is (a) – 5 (b) 6 (c) 5 (d) – 6 Answer: (b) 6 17. What value/s can x take in the expression k(x – 10) (x + 10) = 0 where k is any real number. (a) 100, -100 (b) Infinitely many (c) Depends on value of k (d) 10, -10

Answer: (d) 10, -10 18. The value of quadratic polynomial f (x) = 2x2– 3x- 2 at x = -2 is …… (a) 12 (b) 15 (c) -12 (d) 16 Answer: (a) 12 19. If α and β are the zeroes of the polynomial 5x2 – 7x + 2, then sum of their reciprocals is: (a) 14/25 (b) 7/5 (c) 2/5 (d) 7/2 Answer: (d) 7/2 20. Two Friends Rubina and Shruti were given a polynomial by their maths teacher . The polynomial was p(x) = x2 – 5x +6. i. Which of the following is the correct identification of the polynomial: a) Rubina says it‘s a linear polynomial. b) Shruti calls it a quadratic polynomial. c) Both calls it a trinomial. d) Both b) and c) are correct. ii. Solution of this polynomial is : a) x =2 , x = -3 b) x =2 , x = 3 c) x = -2 , x = -3 d) x =-2 , x = 3 iii Value of polynomial when x = -1 is: a) 12 b) 13 c) 14 d) -12 iv. Value of p(3) + p(1) =

a) 0 b) 1 c) 2 d) 3 Answer:i d ii b iii a iv c

TOPIC: SIMILAR TRIANGLES 1. O is a point on side PQ of a APQR such that PO = QO = RO, then (a) RS² = PR × QR (b) PR² + QR² = PQ² (c) QR² = QO² + RO² (d) PO² + RO² = PR² Answer: (b) PR² + QR² = PQ² 2. In || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to (a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm Answer: (c) 4.5 cm 3. In a square of side 10 cm, its diagonal is equal to (a) 15 cm (b) 10√2 cm (c) 20 cm (d) 12 cm Answer: (b) 10√2 cm 4. In a rhombus if d1 = 16 cm, d2 = 12 cm, then the length of the side of the rhombus is (a) 8 cm (b) 9 cm (c) 10 cm (d) 12 cm Answer: (c) 10 cm 5. In the adjoining figure, if ∠BAC = 90° and AD ⊥ BC,then (а) BD.CD = BC² (b) AB.AC = BC² (c) BD.CD = AD² (d) AB.AC = AD² Answer: (c) BD.CD = AD² 6. D and E are respectively the points on the sides AB and AC of a triangle ABC such thatAD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is (a) 2.5 (b) 3 (c) 5 (d) 6 Answer: (b) 3 7. If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF then which of the following is not true? (a) BC.EF = AC.FD (b) AB.EF = AC.DE (c) BC.DE = AB.EF (d) BC.DE = AB.FD Answer: (c) BC.DE = AB.EF

8. In given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm,then (a) DE || BC (b) DF || AC (c) EF || AB (d) none of these Answer: (c) EF || AB 9. Match the column: (A) AA similarity criterion 1. In and ÆB = ÆC = PQ PR 2. In and (B) SSS similarity criterion A= = (C) BPT 3. In and ÆB = ÆC = BC (D) SAS similarity criterion PQ PR QR 4. In , DE ÆD = ÆE BD CE (a) 1 → A, 2 → B, 3 → C, 4→ D (b) 1 → D, 2 → A, 3 → B, 4 → C (c) 1 → B, 2 → A, 3 → C, 4 → D (d) 1 → C, 2 → B, 3 → D, 4 → A. Answer: (b) 1 → D, 2 → A, 3 → B, 4 → C 10. Sides of two similar triangles are in the ratio 3 : 7. Areas of these triangles are in the ratio(a) 9 : 35 (b) 9 : 49 (c) 49 : 9 (d) 9 : 42 Answer: (b) 9 : 49 11. Sides of triangles are (i) 3 cm, 4 cm, 6 cm. (ii) 4 cm, 5 cm, 6 cm. (iii) 7 cm, 24 cm, 25 cm (iv) 5 cm, 12 cm, 14 cm. Which of these is right triangle?