MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1

Size: px
Start display at page:

Download "MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1"

Transcription

1 CBSE - X MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 3/ Series RLH Please check that this question paper contains 6 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 34 questions. Please write down the serial number of the question before attempting it. MATHEMATICS Time allowed : 3 hours Maximum Marks : 80 General Instructions: i) All questions are compulsory. ii) The question paper consists of 34 questions divided in four sections: A,B,C and D. Section A comprise 0 questions of mark each, Section B comprise 8 questions of marks each, Section C comprise 0 questions of 3 marks each, and Section D comprise 6 questions of 4 marks each. iii) Question numbers to 0 in Section A are multiple choice questions where you have to select one correct option out of the given four. iv) There is no overall choice. However, internal choice has been provided in question of two marks, 3 questions of three marks each and questions of four marks each. You have to attempt only of the alternative in all such questions. v) Use of calculator is not permitted.

2 SECTION - A Question number to 0 carry marks each is (a) an integer (b) a rational number (c) a natural number (d) an irrational number. If am bl, then the system of equations ax + by c, lx + my n (a) has a unique solution (b) has no solution (c) has infinitely many solution (d) may or may not have a solution 3. The length of the hypotenuse of an isosceles right triangle whose one side is 4 cm is (a) cm (b) 8 cm (c) 8 cm (d) cm 4. A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is (a) x 9 (b) x + 9 (c) x + 3 (d) x 3 5. The median of a given frequency distribution is found graphically with the help of (a) Histogram (b) Frequency polygon (c) Ogive (d) Standard deviation 6. If the system of equations x + 3y 5, 4x + ky 0 has infinitely many solutions, then k (a) (b) ½ (c) 3 (d) 6 7. The HCF of 95 and 5, is (a) 57 (b) (c) 9 (d) (sec A + tan A) ( sin A) (a) sec A (b) sin A (c) cosec A (d) cos A 9. In Fig. 4.4, the measures of D and F are respectively (a) 50 o, 40 o (b) 0 o, 30 o (c) 40 o, 50 o (d) 30 o, 0 o A D B C 7 E 5 F

3 if 8 tan x 5, then sin x cos x is equal to (a) 8 7 (b) 7 7 (c) 7 (d) 7 7 SECTION - B Question number to 8 carry marks each.. Find the mode of following distribution : Height (in cm) No. of Plants Check whether x + 3x + is a factor of 3x 4 + 5x 3-7x + x Check whether 6 n can end with the digit 0 for any natural number n? 4. If ST QR. Find PS. R cm Q 3cm T S 3cm 5. If sin (A+B) cos (A-B) A and B. 3 and A,B (A > B) are acute angles, find the values of 5. If A, B, C are the interior angles of ABC, then prove that cos A B sin C. 6. Find the L.M.C and H.C.F. of 5, 8, 45 by the prime factorisation method. P 7. Prove that is an irrational number. 8. Solve the following system of equations by using the method of crossmultiplication : x y 3 0 4x + y 3 0

4 SECTION - C Question numbers 9 to 8 carry 3 marks each. 9. Prove that 5 is irrational Calculate the area of PQR, where OP 6 cm, 8 cm and QR 6 cm. QPR P 90 O P 6 cm. For any positive integer n, prove that n 3 - n is divisible by 6.. Prove that one and only one out of n, n + or n + 4 is divisible by 3, where n is any positive integer. Q 6 cm R 8 cm. If and are the zeros of the quadratic polynomial f(x) kx² + 4x + 4 such that ² + ² 4, find the values of k. A 3. ABC is right angled at B. AD and CE are the two medians drawn from A and C respectively. If AC 5cm, AD 3 5 cm, E find the length of CE. B D C 4. The distribution below gives the weight of 30 students of a class. Find the median weight of students. Weight (in Kg.) No. of Students The mean of the following frequency distribution in 5. Determine the value of P: Class Frequency P 6

5 If tan 3, evaluate sin cos cos ² sin ² 6. x takes three hours more than y to walk 30 km. But if x doubles his speed, he is ahead of y by hours. Find their speed of walking. 7. Without using trigonometric tables evaluate : cos58 cos38 cosec5 3 sin3 tan5tan60tan75 sincos(90 )cos cos sin(90 )sin Prove that : cos sin 0. sec(90 ) cos ec(90 ) 8. In the figure given below, if PQR PRQ. Prove that PQS TQR. QR QT and QS PR P T Q S R SECTION - D Question numbers 9 to 34 carry 4 marks each. 9. (cosec A sin A) (sec A cos A) tan A + cot A 30. Obtain all other zeroes of x 4-6x 3 + 3x + 3x -, if two of it s zeroes are and. 30. In trapezium ABCD, AB DC, DC AB. EF AB where E and F lie on BC and AD respectively such that BE 4. Diagonal DB intersects EF at G.Prove that EC 3 7EF AB.

6 3. In fig, DE BC and AD : DB 5: 4, A Find Area( DEF) Area( CFB). D E 4 5 F B C 3. women and 5 men together can finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by woman alone to finish the work, and also that taken by man alone. 33. Solve the equations graphically : x + y y + x 4 What is the area of triangle formed by the two lines and x - axis. 34. The following table gives production yield per hectare of wheat of 00 farms of a village. Production yield (in kg/ha) Number of farms Change the distribution to a more than type distribution, and draw its ogive. Use Euclid s division lemma to show that the cube of any positive integer is of the form 9m, 9m + or 9m + 8 for some integer m. All the Best

7 CBSE X Date : MODEL ANSWER PAPER Time : 3 hrs. Any method mathematically correct should be given full credit of marks. SECTION - A. (b) a rational number. (a) a b 3. (b) 8 cm 4. (a) x 9 5. (c) Ogive 6. (d) 6 7. (c) 9 8. (d) cos A 9. (b) 0 o, 30 o 0. (d) 7 7 MT EDUCARE LTD. SUBJECT : MATHEMATICS SUMMATIVE ASSESSMENT - SECTION - B. Given, x 60, f, f 0 6, f 8, h 0 f f 0 Mode l + f f0 f h Marks : 90. On dividing 3x 4 + 5x 3-7x + x + by x + 3x + x + 3x + ) 3x 4 + 5x 3-7x + x + (3x - 4x + 3x 4 + 9x 3 + 3x x 3-0x + x + - 4x 3 - x - 4x x + 6x + x + 6x

8 Reminder is 0 hence x + 3x + is a factor of 3x 4 + 5x 3-7x + x If 6 n ends with digit zero, then it will be divisible by 5, i.e., the prime factorisation of 6 n. must contain the prime number 5. This is not possible because 6 n ( 3) n n 3 n This shows that the only prime factorisation of 6 n are and 3 by uniqueness fundamental theorem of Arithmetic, there are no other primes in the factorisation of 6 n. So there is no natural number n for which 6 n ends with digit zero. 4. In PRQ, we have ST QR PS PT QS RT PS 3 3 PS 9 cm 4.5 cm R cm T 3cm P S Q 3cm 5. sin (A + B) A + B 60 3 sin 60...(i) and cos (A - B) 3 cos 30 A - B (ii) On adding (i) (ii), We get A 90 i.e., A 45 Putting the value of A in eq. (i), we get B 5 5. A + B + C 80 A + B 80 - C L.H.S. cos A B 80 C cos

9 cos C 90 sin C So, H.C.F. 3 L.C.M Let us assume that is a rational number p q 7 3 p q - 5 Since p and q are integers 3 p-5q 7q p-5q 7q is a rational number 3 is rational But we know that 3 is irrational. our assumption is wrong, is irrational. 8. The given system of equation is x y 3 0 4x + y 3 0 By cross- multiplication, we get x 3 3 y

10 x 3 3 -y x 3 3 -y 6 4 x -y x 6 6 and y 6 6 Hence, the solution of the given system of equations is x, y. SECTION - C Question numbers 5 to 4 carry 3 marks each. 9. Suppose 5 is rational. 3 5 p, q 0 3 q 3q 6p 5, q q 0 3q 6p 5 is irrational while is rational abd an irrational number can q never be equal to a rational number. Thus our assumption is wrong. Hence 5 is irrational In P, P 90 so by Pythagoras theorem, According to question PR PO + OP 6 sm, 8 cm and QR 6 cm PR PR 0 PR 0 In the right triangled QPR by Pythagoras theorem, QR PQ + PR PQ Hence PQ m Q O 6 cm P 6 cm 8 cm R

11 ar ( PQR) PR PQ PR PQ cm. n 3 - n n(n - ) n(n + ) (n - ) (n - ) n(n + ) product of three consecutive positive integers. Now, we have to show that the product of three consecutive positive integers is divisible by 6.Let a, a +, a + by any three consecutive integers a. Let a, a +, a + by any three consecutive integers. Case I. If a 3q. a(a + ) ( a + ) 3q(3q + ) (3q + ) 3q (even number, say r) 6qr, (Product of two consecutive integers (3q + ) and (3q + ) is an even integer which is divisible by 6.) Case II. If a 3q + a(a + ) ( a + ) (3q + ) (3q + ) (3q + 3) (even number, say r) (3) (q + ) 6 (rq + r ), which is divisible by 6. Case III. If a 3q +. a(a + ) ( a + ) (3q + ) (3q + 3) (3q + 4) multiple of 6 for every q 6r (say), which is divisible by 6. Hence, the product of three consecutive integers is divisible by 6.. We Know that any positive integer is of the form 3q, 3q + or 3q + for some integer q. Case I : when n 3q, n 3q + 0 n is divisible by 3 n + 3q + n + is not divisible by 3. and n + 4 3q + 4 3(q + ) + n + 4 is not divisible by 3. Case II : when n 3q +, n 3q + n is divisible by 3 n + (3q + ) + 3(q + ) + 0 Here remainder is zero, so (n + ) is divisible by 3 and n + 4 (3q + ) + 4 3(q + ) + (n + 4 ) is not divisible by 3.

12 Case III : when n 3q +. n 3q + is not divisible by 3 n + (3q + ) + 3(q + ) + n + is not divisible by 3 and n + 4 (3q + ) + 4 3(q + ) + 0 Here remainder is zero, so (n + 4) is divisible by 3. Thus, we conclude that one and only one out of n, n + and n + 4 is divisible by 3.. Since a and b are the zeros of the quadratic polynomial f(x) kx² + 4x k and 4 k Now, ² + ² 4 ()² 4 4 k 4 k 4 6 k² 8 k 4 6 8k 4k² 3k² + k 0 3k (k+) (k+) 0 (k+) (3k ) 0 k+ 0 or, k 3 Hence, k or, k 3 3. By pythagoras theorem, In ABD, AB + BD AD AC - BC + BD AD 3. AC - AD BC -BD 3 5 In BEC, 5 - CE - BE - BD

13 CE - AB BC CE - 4 (AB + BC ) CE CE CE 5 cm 4. Weight ( in kg.) No. of students c.f l f c.f n 30 n 5 4. C.I x i n c. f. Medain l + h f f i p 6 f i 44 + p f i x i p 70 f i x i p

14 fixi Mean fi p 44 p 5. We have, sin cos cos ² sin ² p 44 p P p 0 P 60 P 6 sincos cos ² cos ² sin² cos ² tan tan ² Let speed of x be p km/h and speed of y be q km/h Time taken by x 30 p Time taken by y 30 q By question, p q (i) If Speed of x is doubled it becomes p, then p q...(ii) Let p a, q b

15 a 30b + 3 0a - 0b a - b 0...(iii) and (ii) is 5a b 5a - 30b 5a - 0b 3 a - b 0 Now (iii) - (iv) given, b 0 5 q 5 q 5km/hr From (iii), we get a p 0...(iv) p km/h cos58 ) cos38 cosec5 sin(90 58 ) sin(90 38 )cosec sin3 tan5 tan60 tan75 sin3 tan5 3cot(90 75 ) sin 3 sin 5 cos ec 5 3 sin 3 tan5 3 cot5 3 sin5 sin5 tan5 3 tan

16 sin cos (90 )cos cos sin(90 )sin L.H.S cos sin sec (90 ) cos ec (90 ) sinsincos cos sin(90 )sin cos sin cosec cos ec(90 ) sin cos cos sin cos sin /sin /cos cos sin sin 3 cos cos 3 sin cos sin (sin cos sin + cos sin cos sin cos R.H.S. 8. Given, QR QT QS PR PQR PRQ PQ PR T From (), QR QT QS PQ QS PQ QR QT In PQS and TQR, Q is common and QS QP QR QT By SAS, PQS TQR. SECTION D Q S R 9. L.H.S (cosec A sin A) (sec A cos A) sin A cos A sin A cos A sin A cos A sin A cos A R.H.S. cos A sin A sin A cos A cos A. sin A... () tan A + cot A

17 sin A cos A + cos A sin A sin A+ cos A cos A-sin A cos A.sin A sin A + cos A cos A.sinA... ()... ( sin A cos A ) From () and (), L.H.S. R.H.S. 30. Two zeroes are and One factor is x x + i.e., x - ) x 4-6x 3 + 3x + 3x - (x - 3x + x 4 - x x 3 + 4x + 3x -6x 3 + 3x + - 4x - 4x Another factor is x - 3x + 0 (x - ) ( x - ) 0 x + and + Hence, other zeroes are and. 30. In trapezium ABCD, AB DC and DC AB. Also In trapezium ABCD, EF AB CD BE 4 EC 3 AF BE 4 FD BC 3

18 In BGE and BDC, As BE EC 4 3 B B BEG BCD BGE BDC EG BE CD BC EC 3 BE 4 EC 3 BE 4 ECBE 7 BE 4 BC 7 BE 4 BE 4 BC 7 EG 4 CD 7 F A G B 4 E 3 EG 4 7 CD D C Similarly DGF DBA DF FG DA AG FG 3 AB 7 FG 3 7 AB AF 4 BE FD 7 BD EC 3 BC 7 Adding (i) and (ii), we get EG + FG 4 7 CD AB EF 4 7 (AB) AB 8 7 AB AB 7 AB 7EF AB.

20 Work done by man in one day y According to the first condition, According to the second condition, x + 5 y 3 4 x + 6 y 3 Substitute x p & y q eq n (i) and eq n (ii) reduce to, p + 5q 4 3p + 6q 3 8p + 0q 9p + 8q... (ii) 8p 0q p 0 q... (i) 8 Substituting eq n (i) in eq n (ii) Substituting q 36 in eqn (i), 9 0 q q p q + 8q p q + 44q 8 36q q 36 Resubstituting for p and q. p p x q y 8 x 36 y x 8 y 36 Woman would take 8 days to complete the work alone and a Man will take 36 days to complete the work alone.

21 x + y x y Table of this equation (i) is...(i) x 0 y 0 - y - x 4 y Table of this equation (ii) is x 4...(ii) x 0 4 y 3 4 Ar (ABC) BC AO cm 34. Production yield Number of Production yield Cumulative Points to be (in kg/ha.) farms Frequency plotted or more than (50, 00) or more than (55, 98) or more than (60, 90) or more than (65, 78) or more than (70, 54) or more than 75 6 (75, 6)

22 Y 0 SCALE : X-axis, cm 5 kg/ha Y-axis, cm 0 farms 00 (50, 00) (55, 98) 90 (60, 90) 80 (65, 78) (70, 54) No. of farms (75, 6) X X Production yield (in kg/ha) Y Points are (0, ), (40, 6), (60, 34), (80, 40); (00, 50) 34. Let x be any positive integer and b 3 Applying Euclid s Division Algorithm x 3q + r where 0 < r < 3

23 The possible remainders are 0,, x 3q or 3q + or 3q + i) If x 3q x 3 (3q)³ 7q³ 9(3q³) 9m for some integer m, where m 3q³ ii) If x 3q + x³ (3q + )³ (3q) 3 + 3(3q)²() + 3(3q) ()² + ()³ [ since (a +b) ³ a³ + 3a²b + 3ab² + b³] 7q 3 + 7q + 9q + 9q(3q² + 3q + ) + 9m + for some integer m, where m q (3q² + 3q + ) iii) If x 3q + x 3 (3q + ) 3 (3q) 3 + 3(3q)² () + 3(3q) ()² + () 3 [ since (a + b)³ a³ + 3a²b + 3ab² + b³] 7q q + 36q + 8 9q(3q² + 6q + 4) + 8 9m + 8 for some integer m, where m q (3q² + 6q + 4) cube of any positive integer is either of the form 9m, 9m + or 9m + 8

MT EDUCARE LTD. SUMMATIVE ASSESSMENT Roll No. Code No. 31/1

CBSE - X MT EDUCARE LTD. SUMMATIVE ASSESSMENT - 03-4 Roll No. Code No. 3/ Series RLH Please check that this question paper contains 6 printed pages. Code number given on the right hand side of the question

CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1:If sin α = 1 2, then the value of 4 cos3 α 3 cos α is (a)0 (b)1 (c) 1 (d)2 Question 2: If cos 2θ = sin(θ 12 ), where2θ and (θ 12 ) are both acute

KENDRIYA VIDYALAYA GILL NAGAR CHENNAI -96 SUMMATIVE ASSESSMENT TERM I MODEL QUESTION PAPER TIME: 3 HOURS MAXIMUM MARKS: 90

KENDRIYA VIDYALAYA GILL NAGAR CHENNAI -96 SUMMATIVE ASSESSMENT TERM I MODEL QUESTION PAPER CLASS X MATHEMATICS TIME: 3 HOURS MAXIMUM MARKS: 90 General Instructions: 1. All Questions are compulsory. 2.

Sample Question Paper Mathematics First Term (SA - I) Class X. Time: 3 to 3 ½ hours

Sample Question Paper Mathematics First Term (SA - I) Class X Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided

Mathematics. Mock Paper. With. Blue Print of Original Paper. on Latest Pattern. Solution Visits:

10 th CBSE{SA I} Mathematics Mock Paper With Blue Print of Original Paper on Latest Pattern Solution Visits: www.pioneermathematics.com/latest_updates www.pioneermathematics.com S.C.O. - 36, Sector 40

Time: 3 Hrs. M.M. 90

Class: X Subject: Mathematics Topic: SA1 No. of Questions: 34 Time: 3 Hrs. M.M. 90 General Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four

KENDRIYA VIDYALAYA SANGATHAN, ERNAKULAM REGION

KENDRIYA VIDYALAYA SANGATHAN, ERNAKULAM REGION SUMMATIVE ASSESSMENT-1 :1-13 (Question Paper) TIME: 3 hrs Class-1 : Mathematics MaxMarks=9 Total No Pages: 6 GENERAL INSTRUCTIONS (i) All questions are compulsory

Paper: 03 Class-X-Math: Summative Assessment - I

1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm

CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1: In figure, AB = 5 3 cm, DC = 4cm, BD = 3cm, then tan θ is (a) (b) (c) (d) 1 3 2 3 4 3 5 3 Question 2: In figure, what values of x will make DE

Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-I, September-01 only. This question paper

Paper: 02 Class-X-Math: Summative Assessment - I

1 P a g e Paper: 02 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] The relation connecting the measures of central tendencies is [Marks:1]

CBSE MATHEMATICS (SET-2)_2019

CBSE 09 MATHEMATICS (SET-) (Solutions). OC AB (AB is tangent to the smaller circle) In OBC a b CB CB a b CB a b AB CB (Perpendicular from the centre bisects the chord) AB a b. In PQS PQ 4 (By Pythagoras

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 05 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

Important Instructions for the School Principal. (Not to be printed with the question paper) Note:

Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-I, September-01 only. This question paper

SAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80

SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

ANSWER KEY & SOLUTIONS

PRE-HALFYEARLY ASSESSMENT- [P-H-A MATHS SYLLABUS] ANSWER KEY & SOLUTIONS General Instructions:. The question paper comprises of four sections, A, B, C & D.. All questions are compulsory. 3. Section A Q

I, SUMMATIVE ASSESSMENT I, / MATHEMATICS X / Class X

I, 015-16 SUMMATIVE ASSESSMENT I, 015-16 / MATHEMATICS X / Class X : hours 90 Time Allowed: hours Maximum Marks: 90 JMYCH7I 1.. 1 1 6 10 11.. General Instructions: 1. All questions are compulsory.. The

[Class-X] MATHEMATICS SESSION:

[Class-X] MTHEMTICS SESSION:017-18 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,

2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term.

CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of

SUMMATIVE ASSESSMENT I, IX / Class IX

I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS - IX - IX IX / Class IX MA-0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions:

CBSE Board Class X Mathematics

CBSE Board Class X Mathematics Time: 3 hrs Total Marks: 80 General Instructions: 1. All questions are compulsory.. The question paper consists of 30 questions divided into four sections A, B, C, and D.

CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80

CBSE Class X Mathematics Board Paper 2019 All India Set 3 Time: 3 hours Total Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 03 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

Time Allowed : 3 hours Maximum Marks : 90. jsuniltutorial

6KN77NA I, 0 SUMMATIVE ASSESSMENT I, 0 / MATHEMATICS X / Class X 90 Time Allowed : hours Maximum Marks : 90 General Instructions: All questions are compulsory. - 8 0 6 0 The question paper consists of

SUMMATIVE ASSESSMENT I, 2012 / MATHEMATICS. X / Class X

I, 0 SUMMATIVE ASSESSMENT I, 0 MA-0 / MATHEMATICS X / Class X 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 4 8 6 0 0 4 (iii) 8 (iv) (v) 4 General Instructions: (i) All questions are compulsory.

Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-202 only. This question paper

1 / 23

CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

MODEL TEST PAPER 9 FIRST TERM (SA-I) MATHEMATICS (With Answers)

MODEL TEST PAPER 9 FIRST TERM (SA-I) MATHEMATICS (With Answers) CLASS X llme Allowed, : 3 to 3% Hours] LMaximum Marks : 80 General Instructions : (i) All are compulsory. (ii) The question paper consists

Visit For All NCERT Solutions, CSBE Sample papers, Question, papers, Notes For Class 6 to 12

SUMMATIVE-ASSESSMENT-1 1-16 SUBJECT MATHEMATICS CLASS-X zzdr-13 Time allowed: 3 hours Maximum Marks: 9 General Instructions: 1. All questions are compulsory. The question paper consists of 31 questions

CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four

CBSE Sample Question Paper 1 ( )

CBSE Sample Question Paper (07-8 Time: Hours Maximum Marks: 80 General Instructions: (i All questions are compulsory. (ii The question paper consists of 0 questions divided into four sections A, B, C and

Marking Scheme. Mathematics Class X ( ) Section A

Marking Scheme Mathematics Class X (017-18) Section A S.No. Answer Marks 1. Non terminating repeating decimal expansion.. k ±4 3. a 11 5 4. (0, 5) 5. 9 : 49 6. 5 Section B 7. LCM (p, q) a 3 b 3 HCF (p,

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 06 (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Unit

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.

Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32 SAMPLE PAPER TEST 03 (2018-19) (ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions are compulsory.

Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-I, September-01 only. This question paper

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 03 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

Class-IX CBSE Latest Pattern Sample Paper {Mathematics}

Class-IX CBSE Latest Pattern Sample Paper {Mathematics} Term-I Examination (SA I) Time: 3hours Max. Marks: 90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of

MODEL QUESTION PAPERS WITH ANSWERS SET 1

MTHEMTICS MODEL QUESTION PPERS WITH NSWERS SET 1 Finish Line & Beyond CLSS X Time llowed: 3 Hrs Max. Marks : 80 General Instructions: (1) ll questions are compulsory. (2) The question paper consists of

ANSWER KEY MATHS P-SA- 1st (FULL SA-1 SYLLABUS) Std. X

ANSWER KEY MATHS P-SA- 1st (FULL SA-1 SYLLABUS) Std. X General Instructions: 1. The question aer comrises of four sections, A, B, C & D.. All questions are comulsory. 3. Section A Q 1 to 4 are 1 mark each

1 / 23

CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper

CBSE Class IX Mathematics Term 1. Time: 3 hours Total Marks: 90. Section A

CBSE sample papers, Question papers, Notes for Class 6 to 1 CBSE Class IX Mathematics Term 1 Time: 3 hours Total Marks: 90 General Instructions: 1. All questions are compulsory.. The question paper consists

SAMPLE QUESTION PAPER 11 Class-X ( ) Mathematics

SAMPLE QUESTION PAPER 11 Class-X (2017 18) Mathematics GENERAL INSTRUCTIONS (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B,C and D. (iii)

MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS)

MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS) SECTION A 1x4=4 1. Find the number of zeros in the following fig. 2. 3. If 4cotA = 3, find tan A. 4. If the less than type ogive and the more than type ogive

CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four sections

DAV Public School, Jharsuguda

DAV Public School, Jharsuguda QUESTIONS BANK CLASS-X Term-I Real Number (1Mark) 1.The LCM of two numbers is 760 and their product is 6080. Find their HCF. 2. Is it possible for the LCM and HCF of numbers

SUMMATIVE ASSESSMENT I (011) Lakdfyr ijh{kk&i MATHEMATICS / xf.kr Class X / & X 60018 Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.Vs : 80 General Instructions: (i) All questions are compulsory.

Class X Mathematics Sample Question Paper Time allowed: 3 Hours Max. Marks: 80. Section-A

Class X Mathematics Sample Question Paper 08-9 Time allowed: Hours Max. Marks: 80 General Instructions:. All the questions are compulsory.. The questions paper consists of 0 questions divided into sections

SAMPLE QUESTION PAPER Class-X ( ) Mathematics. Time allowed: 3 Hours Max. Marks: 80

SAMPLE QUESTION PAPER Class-X (017 18) Mathematics Time allowed: 3 Hours Max. Marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided

SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)

1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x

ICSE Solved Paper, 2018

ICSE Solved Paper, 018 Class-X Mathematics (Maximum Marks : 80) (Time allowed : Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32. SECTION A Questions 1 to 6 carry 1 mark each.

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER TEST 09 (2018-19) (SAMPLE ANSWERS) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : X DURATION : 3 HRS General Instruction: (i) All questions

1 / 23

CBSE-XII-07 EXAMINATION CBSE-X-00 EXAMINATION MATHEMATICS Series: LRH/ Paper & Solution Code: 30// Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

Q4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and.

SUMMATIVE ASSESSMENT 1 (2013 2014) CLASS IX (SET I) SUBJECT : MATHEMATICS Time: 3 hours M.M. : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions

CCE RR. ( / English Version ) ( / New Syllabus ) ( / Regular Repeater )

CCE RR 1 81-E : 81-E Code No. : 81-E CCE RR Subject : MATHEMATICS ( / English Version ) ( / New Syllabus ) ( / Regular Repeater ) General Instructions : i) The Question-cum-Answer Booklet consists of objective

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 08 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

FIITJEE SUBJECT:MATHEMATICS (CBSE) CLASS 10 SOLUTION

FIITJEE SUBJECT:MTHEMTICS (CBSE) CLSS 10 SOLUTION 1. SECTION 99 551 44 55 44111 44 11 4 0 HCF of 55 and 99 is 11 11 55 441 11 55 (99 551) 11 55 99 55 11 55 99 So m =. cubic polynomial with zeros -, - and

CBSE 10th Mathematics 2013 Unsolved Paper Summative Assessment - I

Perfect solution to all problems Tips, Tricks, General Knowledge, Current Affairs, Latest Sample, Previous Year, Practice Papers with solutions. CBSE 10th Mathematics 2013 Unsolved Paper Summative Assessment

9 th CBSE Mega Test - II

9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A

DESIGN OF THE QUESTION PAPER

SET-II DESIGN OF THE QUESTION PAPER MATHEMATICS CLASS IX Time : 3 Hours Maximum Marks : 80 The weightage or the distribution of marks over different dimensions of the question paper shall be as follows:

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F SESSING ENDING EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA

MATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION - A

MATHEMATICS Time allowed : 3 hours Maximum Marks : 100 GENERAL INSTRUCTIONS : 1. All questions are compulsory 2. The question paper consists of 30 questions divided into four sections - A, B, C and D.

'R'nze Allowed : 3 to 3% Hours] LMaximum Marks : 80

MODEL TEST PAPER 6 FIRST TERM (SA-I) MATHEMATICS (With ~nszuers) CLASS X 'R'nze Allowed : 3 to 3% Hours] LMaximum Marks : 80 General Instructions : (i) All questions are compulsory. (ii) The question paper

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 09 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32 SAMPLE PAPER 02 (2018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-) MATHEMATICS CLASS IX Time: 3 to 3 1 hours Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory.. The question paper is divided into four sections

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 07 (017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I ( marks) SA II (3 marks) LA (4 marks) Total Unit Total

Blue print Chapters 1mark 2marks 3marks 4marks total

PRE-BOARD SAMPLE PAPER 2018-19 CLASS-X BLUEPRINT Blue print Chapters 1mark 2marks 3marks 4marks total real numbers 1 1 5 Polynomials 1 1 4 Linear equations 1 1 6 quadratic equation 1 1 6 A.P. 1 4 Triangles

[Maxin~um Marks : 80 General Instructions :

llme Albwed : S to 3% Hoursl MODEL TEST PAPER 4 FIRST TERM (SA-I) MATHEMATICS (With Answers) CLASS X [Maxin~um Marks : 80 General Instructions : (i) All questions are compulsory. (ii) The question paper

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 FOR HALF YEARLY EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I (2 marks) SA

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 FOR HALF YEARLY EXAM (017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR HALF YEARLY EXAM: CLASS IX Chapter VSA (1 mark) SA I ( marks) SA II

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

( )( ) PR PQ = QR. Mathematics Class X TOPPER SAMPLE PAPER-1 SOLUTIONS. HCF x LCM = Product of the 2 numbers 126 x LCM = 252 x 378

Mathematics Class X TOPPER SAMPLE PAPER- SOLUTIONS Ans HCF x LCM Product of the numbers 6 x LCM 5 x 378 LCM 756 ( Mark) Ans The zeroes are, 4 p( x) x + x 4 x 3x 4 ( Mark) Ans3 For intersecting lines: a

Model Answer Paper 24(24 1) 2 12

ICSE X SUBJECT : MATHEMATICS Marks : 80 Exam No. : MT/ICSE/Semi Prelim II- Set-B-00 Model Answer Paper Time : ½ hrs. SECTION I (40 Marks) A. (a) Maturity value ` 0,000 No. of months (n) 4 months Rate of

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

() Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A.

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX Time allowed: hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper consists of

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 04 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

CBSE 10th Maths 2016 Unsolved Paper Summative Assessment - I

Perfect solution to all problems Tips, Tricks, General Knowledge, Current Affairs, Latest Sample, Previous Year, Practice Papers with solutions. CBSE 10th Maths 2016 Unsolved Paper Summative Assessment

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has

Similarity of Triangle

Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 32

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD 3 SAMPLE PAPER 01 FOR PERIODIC TEST II EXAM (018-19) SUBJECT: MATHEMATICS(041) BLUE PRINT FOR PERIODIC TEST II EXAM: CLASS IX Chapter VSA (1 mark) SA I (

Geometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS

SUMMATIVE ASSESSMENT I (011) Lakdfyr ijh{kk&i MATHEMATICS / xf.kr Class X / & X 560033 Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.Vs : 80 General Instructions: (i) All questions are

TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions

CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)

DESIGN OF THE QUESTION PAPER Mathematics Class X

SET-I DESIGN OF THE QUESTION PAPER Mathematics Class X Time : 3 Hours Maximum Marks : 80 Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage

SOLUTIONS 10th Mathematics Solution Sample paper -01

SOLUTIONS 0th Mathematics Solution Sample paper -0 Sample Question Paper 6 SECTION A. The smallest prime number and smallest composite number is. Required HCF (, ).. y...(i) and + y...(ii) Adding both

SOLUTIONS SECTION A SECTION B

SOLUTIONS SECTION A 1. C (1). A (1) 3. B (1) 4. B (1) 5. C (1) 6. B (1) 7. A (1) 8. D (1) SECTION B 9. 3 3 + 7 = 3 3 7 3 3 7 3 3 + 7 6 3 7 = 7 7 6 3 7 3 3 7 0 10 = = 10. To find: (-1)³ + (7)³ + (5)³ Since

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO

DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO T.B.C. : P-AQNA-L-ZNGU Serial No.- TEST BOOKLET MATHEMATICS Test Booklet Series Time Allowed : Two Hours and Thirty Minutes Maximum Marks : 00

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *7560400886* ADDITIONAL MATHEMATICS 0606/22 Paper 2 May/June 2011 2 hours

DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80

DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content

Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =

Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain

Revision Question Bank

Revision Question Bank Triangles 1. In the given figure, find the values of x and y. Since, AB = AC C = B [angles opposite to the equal sides are equal] x = 50 Also, the sum of all angles of a triangle

TA0DV2S I, 2013 SUMMATIVE ASSESSMENT I, 2013 / MATHEMATICS IX / Class IX

TA0DVS I, 0 SUMMATIVE ASSESSMENT I, 0 / MATHEMATICS IX / Class IX 90 Time Allowed : hours Maximum Marks : 90 General Instructions: All questions are compulsory. 6 0 The question paper consists of questions

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00

SUMMATIVE ASSESSMENT I (2011) Lakdfyr ijh{kk&i. MATHEMATICS / xf.kr Class X / & X. Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.

For more sample papers visit : www.4ono.com SUMMATIVE ASSESSMENT I (20) Lakdfyr ijh{kk&i MATHEMATICS / xf.kr Class X / & X 600 Time allowed : 3 hours Maximum Marks : 80 fu/kkzfjr le; % 3?k.Vs : 80 General