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Contents • Latest Revised Syllabus for Academic Year (2021-2022) i–iii (Issued by CBSE on 28-07-2021) • CBSE Sample Paper 2021-22 (Basic) with solutions SQP 21-22-1–12 (Issued by CBSE on 02-09-2021) • Objective Questions and Solutions  SQP 20-21-1–4 CBSE Sample Paper 2020-21 (Basic) • Objective Questions and Solutions  SP 2020-1–2 (Basic) CBSE Board 2020 Solved Paper All India • Objective Questions and Solutions  QB 1–14 CBSE Questions Bank 2021 10 Sample Papers with OMR Answer Sheets SP-1–8 • Sample Paper-1 SP-9–16 • Sample Paper-2 SP-17–24 • Sample Paper-3 SP-25–32 • Sample Paper-4 SP-33–40 • Sample Paper-5 SP-41–48 • Sample Paper-6 SP-49–56 • Sample Paper-7 SP-57–64 • Sample Paper-8 SP-65–72 • Sample Paper-9 SP-73–78 • Sample Paper-10 SOLUTIONS TO SAMPLE PAPERS 1-10 S-1–42

Note for Students Dear Aspirants, All sample papers of Disha’s “Super-10 Mock Test”, Class-10, Mathematics are as per latest CBSE SAMPLE PAPER 2021-22 issued by CBSE on 02nd September, 2021 Each SAMPLE PAPER contains Section-A has 20 MCQs , attempt any 16 out of 20 (16×1=16 Marks) Section-B has 20 MCQs , attempt any 16 out of 20 (16×1=16 Marks) Section-C has 10 MCQs based on two Case Studies, attempt any 8 out of 10 (8×1=8 Marks) Marking Scheme • Each question carries 1 mark • There is no negative marking. All SAMPLE PAPERS based on Revised Academic curriculum for the session 2021-22 issued by CBSE on 28th July, 2021 For detailed revised CBSE Syllabus & Latest SAMPLE PAPERS, visit http://www.cbseacademic.nic.in/web_material/CurriculumMain22/termwise/Secondary/Mathematics_ Sec_2021-22.pdf http://www.cbseacademic.nic.in/web_material/SQP/ClassX_2021_22/MathsBasic-SQP.pdf All the best Disha Experts

Latest Revised Syllabus Issued by CBSE on 28-07-2021 for Academic Year (2021-2022) Mathematics (Code no. 041) TERM-I Unit No. Unit Name Marks I Number Systems 06 Internal Assessment II Algebra Total 10 III Coordinate Geometry 06 IV Geometry 06 V Trigonometry 05 VI Mensuration 04 VII Statistics & Probability 03 40 Total 10 50 Unit I: Number Systems 1. Real Number Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.  Euclid’s division lemma, Proofs of irrationality of 2, 3 5 Unit II : Algebra 2. Polynomials Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials only.  Statement and simple problems on division algorithm for polynomials with real coefficients. 3. Pair of Linear Equations in Two Variables Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.  cross multiplication method Unit III : Coordinate Geometry 4. LINES (In two-dimensions) Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).  Area of a triangle. Unit IV : Geometry 5. Triangles Definitions, examples, counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. (i)

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar. 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other. 7. (Motivate) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. 8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. 9. (Motivate) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle. Unit V : Trigonometry 6. Introduction to Trigonometry Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); Values of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios. Trigonometric Identities Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.  Motive the ratios whichever are defined at 0° and 90°. Trigonometric ratios of complementary angles Unit VI : Mensuration 7. Areas Related to Circles Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60° and 90° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)  Area of segment for central angle 120° Unit VII : Statistics and Probability 8. Probability Classical definition of probability. Simple problems on finding the probability of an event. TERM-II Unit No. Unit Name Marks I Algebra (Cont.) 10 II Geometry (Cont.) 09 III Trigonometry (Cont.) 07 IV Mensuration (Cont.) 06 V Statistics & Probability (Cont.) 08 Total 40 10 Internal Assessment 50 Total (ii)

Unit : Algebra 1. Quadratic Equations Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.  Problems on equations reducible to quadratic equations. 2. Arithmetic Progressions Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. application of Arithmetic Progressions in solving daily life problems.  Applications based on sum to n terms of an A.P. Unit : Geometry 3. Circles Tangent to a circle at, point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal. 4. Constructions 1. Division of a line segment in a given ratio (internally). 2. Tangents to a circle from a point outside it.  Construction of a triangle similar to a given triangle. Unit : Trigonometry 5. Some applications of trigonometry Heights and Distances: Angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, 60°. Unit : Mensuration 6. Surface Areas and Volumes 1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.  Frustum of a cone. 2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combina- tion of not more than two different solids be taken). Unit VII : Statistics and Probability 7. Statistics Mean, median and mode of grouped data (bimodal situation and step deviation method for finding the mean to be avoided). Mean by direct method and assumed mean method only.  Cumulative frequency graph. (iii)

CBSE Sample Paper 2021-2022 (Basic) with Solutions Term-1Sample Question Paper Class- X Session- 2021-22 TERM 1 Subject- Mathematics (Basic) Time Allowed: 90 minutes Maximum Marks: 40 General Instructions: 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 questions of 1 mark each. Attempt any 16 questions. 3. Section B consists of 20 questions of 1 mark each. Attempt any 16 questions. 4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 5. There is no negative marking. Q.NO. SECTION A MARKS 1 Section A consists of 20 questions. Any 16 questions are to be attempted 1 2 A box contains cards numbered 6 to 50. A card is drawn at random from the box. The 1 probability that the drawn card has a number which is a perfect square like 4,9….is 3 1 4 (a) 1/45 1 5 (b) 2/15 1 6 (c) 4/45 1 (d) 1/9 7 In a circle of diameter 42cm ,if an arc subtends an angle of 60 ˚ at the centre where 1 ∏=22/7,then the length of the arc is (a) 22/7 cm (b) 11cm (c) 22 cm (d) 44 cm If sinƟ = x and secƟ = y , then tanƟ is (a) xy (b) x/y (c) y/x (d) 1/xy The pair of linear equations y = 0 and y =-5 has (a) One solution (b) Two solutions (c) Infinitely many solutions (d) No solution A fair die is thrown once. The probability of even composite number is (a) 0 (b) 1/3 (c) 3/4 (d) 1 8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be (a) Rs. 750 (b) Rs.600 (c) Rs. 850 (d) Rs. 900 If cosƟ+cos2Ɵ =1,the value of sin2Ɵ+sin4Ɵ is (a) -1 (b) 0 (c) 1 (d) 2

SQP 21-22-2 Mathematics 1 8 23 The decimal representation of 23 × 52 will be 1 (a) Terminating 1 1 (b) Non-terminating (c) Non-terminating and repeating (d) Non-terminating and non-repeating 9 The LCM of 23X32 and 22X33 is (a) 23 (b) 33 (c) 23X33 (d) 22X32 10 The HCF of two numbers is 18 and their product is 12960. Their LCM will be (a) 420 (b) 600 (c) 720 (d) 800 11 In the given figure, DE II BC. Which of the following is true? (a) ������������ ====������������������������������������������������������+���������������������������������++��������������������������������������������������������������������������������� (b) (c) ������������ (d) ������������ ������������ ������������ 12 The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6) 1 internally in the ratio 2:1 are (a) (2,4) (b) (4,6) (c) (4,2) (d) (3,5) 13 The prime factorisation of 3825 is 1 (a) 3x52x21 (b) 32x52x35 (c) 32x52x17 (d) 32x25x17 14 In the figure given below, AD=4cm,BD=3cm and CB=12 cm, then cotƟ equals 1 (a) 3/4 (b) 5/12 (c) 4/3 (d) 12/5

CBSE Sample Paper 2021-2022 SQP 21-22-3 15 If ABCD is a rectangle , find the values of x and y 1 (a) X=10,y=2 (b) X=12,y=8 (c) X=2,y=10 (d) X=20,y=0 16 In an isosceles triangle ABC, if AC=BC and AB2=2AC2, then the measure of angle C will be 1 (a) 30˚ (b) 45˚ (c) 60˚ (d) 90˚ 17 If -1 is a zero of the polynomial p(x)=x2-7x-8 , then the other zero is 1 (a) -8 (b) -7 (c) 1 (d) 8 18 In a throw of a pair of dice, the probability of the same number on each die is 1 (a) 1/6 (b) 1/3 (c) 1/2 (d) 5/6 19 The mid-point of (3p,4) and (-2,2q) is (2,6) . Find the value of p+q 1 (a) 5 1 (b) 6 (c) 7 (d) 8 20 147 The decimal expansion of 120 will terminate after how many places of decimals? (a) 1 (b) 2 (c) 3 (d) 4 SECTION B Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 21 The perimeter of a semicircular protractor whose radius is ‘r’ is 1 (a) π + 2r (b) π + r (c) πr (d) πr + 2r 22 If P (E) denotes the probability of an event E, then 1 (a) 0< P(E) ⩽1 (b) 0 < P(E) < 1 (c) 0 ≤ P(E) ≤1 (d) 0 ⩽P(E) <1

SQP 21-22-4 Mathematics 23 In ∆ABC, ˂B=90˚ and BD ꓕ AC. If AC = 9cm and AD = 3 cm then BD is equal to 1 (a) 2√2 cm (b) 3√2 cm (c) 2√3 cm (d) 3√3 cm 24 The pair of linear equations 3x+5y=3 and 6x+ky=8 do not have a solution if 1 (a) K=5 (b) K=10 (c) k≠10 (d) k≠5 25 If the circumference of a circle increases from 2∏ to 4∏ then its area _____ the original 1 area (a) Half (b) Double (c) Three times (d) Four times 26 Given that sinƟ=a/b ,then tanƟ is equal to 1 ������������ 1 (a) √������������2+������������������������2 (b) √������������2������−������ ������������2 (c) √������������2���������−��� ������������2 (d) √������������2−������������2 27 If x = 2sin2Ɵ and y = 2cos2Ɵ+1 then x+y is (a) 3 (b) 2 (c) 1 (d) 1/2 28 If the difference between the circumference and the radius of a circle is 37cm ,∏=22/7, the 1 circumference (in cm) of the circle is (a) 154 (b) 44 (c) 14 (d) 7 29 The least number that is divisible by all the numbers from 1 to 10 (both inclusive) 1 (a) 100 (b) 1000 (c) 2520 (d) 5040 30 Three bells ring at intervals of 4, 7 and 14 minutes. All three rang at 6 AM. When will they 1 ring together again? (a) 6:07 AM (b) 6:14 AM (c) 6:28 AM (d) 6:25 AM 31 What is the age of father, if the sum of the ages of a father and his son in years is 65 and 1 twice the difference of their ages in years is 50? (a) 40 years (b) 45 years (c) 55 years (d) 65 years 1 32 What is the value of (tanƟ cosecƟ)2-(sinƟ secƟ)2 (a) -1 (b) 0 (c) 1 (d) 2

CBSE Sample Paper 2021-2022 SQP 21-22-5 33 The perimeters of two similar triangles are 26 cm and 39 cm.The ratio of their areas will be 1 (a) 2:3 (b) 6:9 (c) 4:6 (d) 4:9 34 There are 20 vehicles-cars and motorcycles in a parking area. If there are 56 wheels 1 together, how many cars are there? (a) 8 (b) 10 (c) 12 (d) 20 35 A man goes 15m due west and then 8m due north. How far is he from the starting point? 1 (a) 7m (b) 10m (c) 17m (d) 23m 36 What is the length of an altitude of an equilateral triangle of side 8cm? 1 (a) 2√3 cm (b) 3√3 cm (c) 4√3 cm (d) 5√3 cm 37 If the letters of the word RAMANUJAN are put in a box and one letter is drawn at random. 1 The probability that the letter is A is (a) 3/5 (b) 1/2 (c) 3/7 (d) 1/3 38 Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor 1 arc. (a) 90˚ (b) 60˚ (c) 45˚ (d) 30˚ 39 A vertical stick 20m long casts a shadow 10m long on the ground. At the same time a tower 1 casts a shadow 50m long. What is the height of the tower? (a) 30m (b) 50m (c) 80m (d) 100m 40 What is the solution of the pair of linear equations 37x+43y=123, 43x+37y=117? 1 (a) x = 2,y = 1 (b) x = -1,y = 2 (c) x = -2,y = 1 (d) x = 1,y = 2 SECTION C Case study based questions Section C consists of 10 questions of 1 mark each. Any 8 questions are to be attempted. Case Study -1 Pacific Ring of Fire

SQP 21-22-6 Mathematics The Pacific Ring of Fire is a major area in the basin of the Pacific Ocean where many earthquakes and volcanic eruptions occur. In a large horseshoe shape, it is associated with a nearly continuous series of oceanic trenches, volcanic arcs, and volcanic belts and plate movements. https://commons.wikimedia.org/wiki/File:Pacifick%C3%BD_ohniv%C3%BD_kruh.png Fault Lines Large faults within the Earth's crust result from the action of plate tectonic forces, with the largest forming the boundaries between the plates. Energy release associated with rapid movement on active faults is the cause of most earthquakes. https://commons.wikimedia.org/wiki/File:Faults6.png Positions of some countries in the Pacific ring of fire is shown in the square grid below. Based on the given information, answer the questions NO. 41-45

CBSE Sample Paper 2021-2022 SQP 21-22-7 1 41 The distance between the point Country A and Country B is (a) 4 units 1 (b) 5 units (c) 6 units (d) 7 units 42 Find a relation between x and y such that the point (x,y) is equidistant from the Country C and Country D (a) x-y = 2 (b) x+y = 2 (c) 2x-y = 0 (d) 2x+y = 2 43 The fault line 3x + y – 9 = 0 divides the line joining the Country P(1, 3) and 1 Country Q(2, 7) internally in the ratio (a) 3 : 4 (b) 3 : 2 (c) 2 : 3 (d) 4 : 3 44 The distance of the Country M from the x-axis is 1 (a) 1 units 1 (b) 2 units (c) 3 units (d) 5 units 45 What are the co-ordinates of the Country lying on the mid-point of Country A and Country D? (a) (1, 3) (b) (2, 9/2) (c) (4, 5/2) (d) (9/2, 2) Case Study -2 ROLLER COASTER POLYNOMIALS Polynomials are everywhere. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them. Since, polynomials are used to describe curves of various types engineers use polynomials to graph the curves of roller coasters. https://images.app.goo.gl/WfcM1aRTHjjqtyT27 Based on the given information, answer the questions NO. 46-50. 1 46 If the Roller Coaster is represented by the following graph y=p(x) , then name the type of the polynomial it traces.

SQP 21-22-8 Mathematics (a) Linear 1 (b) Quadratic (c) Cubic (d) Bi-quadratic 47 The Roller Coasters are represented by the following graphs y=p(x). Which Roller Coaster has more than three distinct zeroes? (a) (b) (c )

CBSE Sample Paper 2021-2022 SQP 21-22-9 (d) 48 If the Roller Coaster is represented by the cubic polynomial t(x)= px3+qx2+rx+s ,then which of the 1 following is always true (a) s≠0 (b) r≠0 (c) q≠0 (d) p≠0 49 1 If the path traced by the Roller Coaster is represented by the above graph y=p(x), find the 1 number of zeroes? (a) 0 (b) 1 (c) 2 (d) 3 50 If the path traced by the Roller Coaster is represented by the above graph y=p(x), find its zeroes? (a) -3, -6, -1 (b) 2, -6, -1 (c) -3, -1, 2 (d) 3, 1, -2

SQP 21-22-10 Mathematics Marking Scheme Class- X Session- 2021-22 TERM 1 Subject- Mathematics (Basic) Q. CORRECT HINTS/SOLUTION N. OPTION 1 (d) P(perfect Square)=5/45=1/9 2 (c) length of the arc= Ɵ /360˚ (2πr)=(60˚/360˚)x2x(22/7)x21=22cm 3 (a) TanƟ = sinƟ/cosƟ = sinƟxsecƟ = xy 4 (d) The lines are parallel hence No solution 5 (b) P(even composite no) =2/6=1/3 6 (a) Let the cost of one chair=Rs. x Let the cost of one table=Rs. y 8x+5y=10500 5x+3y=6450 Solving the above equations Cost of each chair= x= Rs. 750 7 (c) CosƟ=I-cos2Ɵ=sin2Ɵ Therefore Sin2Ɵ+sin4Ɵ=cosƟ+cos2Ɵ=1 8 (a) Terminating 9 (c ) 23x33 10 (c) 1st No. x 2nd No. = HCF X LCM 12960=18 X LCM LCM=720 11 (c) AE/AC=DE/BC=a/a+b=x/y X=ay/(a+b) 12 (d) (2x4+1x1)/3 , (2x6+1x3)/3 =(3,5) 13 (c) 3825=32x52x17 14 (d) AB2=AD2+BD2 AB=5cm AC2=AB2+CB2 AC=13 cm Cot ������������=CB/AB=12/5 15 (a) x+y=12 X-y=8 Solving the above equations X=10,y=2 16 (d) AB2=AC2+AC2 =AC2+BC2 Hence, angle C=90° 17 (d) Let the zeroes be a and b Then, a=-1 , a+b=-(-7)/1 Hence, b=7+1=8 18 (a) P(same no on each die)=6/36=1/6 19 (b) (2,6)=((3p-2)/2, (4+2q)/2) 3p-2=4, 4+2q=12 P=2, q = 4 hence p+q = 6 20 (c ) 147/120= 49/40=49/23x5

CBSE Sample Paper 2021-2022 SQP 21-22-11 21 (d ) Three decimal places Perimeter of protractor=Circumference of semi-circle + 2 x radius =πr+2r 22 (c) 0≤ P( E) ≤1 23 (b) 24 (b ) CD/BD=BD/AD 25 (d ) BD2=CDXAD=6X3 BD=3√2 cm 26 (d) 3/6=5/k ⇒K=10 27 (a) 28 (b) C1/C2=2πr/2πR 29 (c) 2π/4π=2πr/2πR 30 ( c) 31 (b) r/R=1/2 A1/A2=πr2/πR2=(r/R)2=(1/2)2=1/4 32 ( c) 33 ( d) A2=4A1 sinƟ=a/b H2=P2+B2 b2=a2+B2 B=√(b2-a2) tanƟ=P/B=a/√(b2-a2) x+y=2sin2Ɵ+2cos2Ɵ+1 =2(sin2Ɵ+ cos2Ɵ)+1 =2+1=3 2πr- r=37 r{2x(22/7)-1}=37 r=37x7/37 r=7 circumference=2x(22/7)x7=44cm 1=1 2=2×1 3=3×1 4=2×2 5=5×1 6=2×3 7=7×1 8=2×2×2 9=3×3 10 = 2 × 5 So, LCM of these numbers = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520 Hence, least number divisible by all the numbers from 1 to 10 is 2520 LCM 0f 4,7,14=28 Bells will they ring together again at 6:28 AM Let age of Father=x Years Let age of son = y years x+y = 65 2(x-y)=50 Solving the above equations Father’s Age =x = 45 years (tanƟcosecƟ)2-(sinƟsecƟ)2 =tan2Ɵcosec2Ɵ-sin2Ɵsec2Ɵ =(sin2Ɵ/cos2Ɵ)x1/ sin2Ɵ - sin2Ɵx1/cos2Ɵ =(1- sin2Ɵ)/ cos2Ɵ= cos2Ɵ/ cos2Ɵ =1 A1/A2=(P1/P2)2=(26/39)2

SQP 21-22-12 Mathematics 34 (a ) A1/A2=(2/3)2=4/9 35 ( c) Let no of Cars=x 36 ( c) 37 (d) Let no of motorcycles=y 38 ( b) X+y=20 39 ( d) 4x+2y=56 40 (d) Solving the above equations No of cars=x=8 41 ( b) H2=P2+B2 42 (a) H2=152+82 H=17m 43 (a ) (altitude)2=(side)2-(side/2)2 44 ( c) =82-42= 64-16 =48 45 (b) Altitude=4√3 cm 46 (c) P=3/9=1/3 47 (d ) Ɵ/360˚xπr2=1/6x πr2 48 ( d) 49 (d) Ɵ=60˚ 50 ( c) Height of Vertical stick/Shadow of vertical stick=height of tower/shadow of tower 20/10=Height of tower/50 Height of tower=100 m 37x+43y=123 ____(1) 43x+37y=117 ____(2) Adding (1) and (2) X+y=3 ______(3) Subtracting (2) from (1) -x+y=1..............(4) Adding (3) and (4), 2y=4 y=2 ⇒ x=1 ∴ solution is x=1 and y=2 AB=√{(4-1)2+(0-4)2} =√(32+42) AB=5 units (x-7)2+(y-1)2=(x-3)2+(y-5)2 X2+49-14x+y2+1-2y=x2+9-6x+y2+25-10y Simplifying x-y=2 3x + y – 9 = 0 Let R divide the line in ratio k:1 R( 2k+1/k+1, 7k+3/k+1) 3(2k+1/k+1)+( 7k+3/k+1)-9=0 4k-3=0 K=3/4 3:4 Distance of M from X-axis=√(2-2)2+(0-3)2=√9=3units ( (1+3)/2 , (4+5)/2) = (4/2, 9/2) = (2, 9/2) Cubic Four Zeroes as the curve intersects the x-axis at 4 points p≠0 3 Zeroes as the curve intersects the x-axis at 3 points -3,-1,2

Objective Questions and Solutions CBSE Sample Paper 2020-2021 SECTION-I OR What type of straight lines will be represented by the Section I has 12 questions of 1 mark each. system of equations 2x + 3y = 5 and 4x + 6y = 7? 1. Express 156 as the product of primes. 11. A bag contains 3 red balls and 5 black balls. A ball is 2. Write a quadratic polynomial, sum of whose zeroes is 2 drawn at random from the bag. What is the probability that the ball drawn is red? and product is –8. 3. Given that HCF (96,404) is 4, find the LCM (96,404). OR A die is thrown once. What is the probability of getting a OR prime number? State the fundamental Theorem ofArithmetic. 4. On comparing the ratios of the coefficients, find out whether 12. Probability of an event E + Probability of the event E the pair of equations x – 2y = 0 and 3x + 4y – 20 = 0 is (not E) is, ______. consistent or inconsistent. 5. If a and b are co-prime numbers, then find the HCF (a, b). SECTION-II 6. Find the area of a sector of a circle with radius 6 cm if The case study based questions are compulsory. Attempt any angle of the sector is 60°. æ Take p = 22 ö 4 sub-parts of question. Each question carries 1 mark. èç 7 ÷ø 13. Class X students of a secondary school in Krishnagar OR have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on A horse tied to a pole with 28m long rope. Find the the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. perimeter of the field where the horse can graze. The students are to sow seeds of flowering plants on the remaining area of the plot. æ Take p = 22 ö èç 7 ø÷ BC 7. In the given fig. DE || BC, ÐADE = 70° and ÐBAC = 50°, P then angle ÐBCA = ______. R A DE BC Q OR A 1 2 3 4 5 6 7 8 910 D In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC? Considering A as origin, answer question (i) to (v). A (i) Considering A as the origin, what are the coordinates DE of A? BC (a) (0, 1) (b) (1, 0) 8. The cost of fencing a circular field at the rate of ` 24 per (c) (0, 0) (d) (–1, –1) metre is ` 5280. Find the radius of the field. 9. If the perimeter and the area of a circle are numerically (ii) What are the coordinates of P? equal, then find the radius of the circle. (a) (4, 6) (b) (6, 4) 10. For what values of p does the pair of equations 4x + py + (c) (4, 5) (d) (5, 4) 8 = 0 and 2x + 2y + 2 = 0 has unique solution? (iii) What are the coordinates of R? (a) (6, 5) (b) (5, 6) (c) (6, 0) (d) (7, 4) (iv) What are the coordinates of D? (a) (16, 0) (b) (0, 0) (c) (0, 16) (d) (16, 1)

SQP 20-21-2 Mathematics (v) What are the coordinate of P if D is taken as the (v) What is the area of the kite, formed by two origin? perpendicular sticks of length 6 cm and 8 cm? (a) 48 cm2 (b) 14 cm2 (a) (12, 2) (b) (–12, 6) (c) 24 cm2 (d) 96 cm2 (c) (12, 3) (d) (6, 10) 14. 15. Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below. y 6 5 4 3 2 1 Rahul is studying in X standard. He is making a kite to fly –6 –5 –4 –3 –2 –1–1 12345678 –2 it on a Sunday. Few questions came to his mind while –3 –4 making the kite. Give answer to his questions by looking –5 at the figure. (i) Rahul tied the sticks at what angles to each other? (a) 30° (b) 60° (c) 90° (d) 45° (ii) Which is the correct similarity criteria applicable for (i) Name the shape in which the wire is bent smaller triangles at the upper part of this kite? (a) spiral (b) ellipse (a) RHS (b) SAS (c) linear (d) parabola (c) SSA (d) AAS (ii) How many zeroes are there for the polynomial (shape (iii) Sides of two similar triangles are in the ratio 4 : 9. of the wire)? Corresponding medians of these triangles are in the (a) 2 (b) 3 ratio. (c) 1 (d) 0 (a) 2 : 3 (b) 4 : 9 (iii) The zeroes of the polynomial are (c) 81 : 16 (d) 16 : 81 (a) –1, 5 (b) –1, 3 (iv) In a triangle, if square of one side is equal to the sum (c) 3, 5 (d) – 4, 2 of the squares of the other two sides, then the angle (iv) What will be the expression of the polynomial? opposite the first side is a right angle. This theorem (a) x2 + 2x – 3 (b) x2 – 2x + 3 is called as, (c) x2 – 2x – 3 (d) x2 + 2x + 3 (a) Pythagoras theorem (v) What is the value of the polynomial if x = –1? (b) Thales theorem (a) 6 (b) –18 (c) Converse of Thales theorem (c) 18 (d) 0 (d) Converse of Pythagoras theorem

CBSE Sample Paper 2020-2021 SQP 20-21-3 1. 156 = 22 × 3 × 13 So, AD ¹ AE 2. Quadratic polynomial is given by x2 – (a + b) x + ab BD EC = x2 – 2x – 8 Hence, By converse of Thale's Theorem, DE is not parallel Here a + b = 2 ab = – 8 to BC. 3. HCF × LCM = Product of two numbers 8. Length of the fence of the circular field = Total cost Rate LCM (96, 404) = 96´ 404 = 96 ´ 404 HCF(96, 404) 4 = ` 5280 = 220m LCM = 9696 ` 24/metre OR So, length of fence = Circumference of the field Every composite number can be expressed (factorised) 2pr = 220 as a product of primes and this factorisation is unique, apart from the order in which the factors occur. r= 220 4. Given equations are x – 2y = 0 2p 3x + 4y – 20 = 0 So, r = 220 ×7 = 35 m 2× 22 1 ¹ -2 3 4 9. Given Perimeter = Area (Numerically) 2pr = pr2 a1 b1 As, a2 ¹ b2 is one condition for consistency. r = 2 units Therefore, the pair of equations is consistent. 10. Let equations a, x + b, y + c1 = 0 and a2x + b2y + c2 = 0 5. 1, HCF of co-prime numbers is always 1. then a1 b1 is the condition for the given pair of æ q ö 2 a2 ¹ b2 çè 360° ÷ø 6. Given angle is q = 60°, Area of sector = pr equations to have unique solution. A = 60° ´ 22 ´ (6)2 4 ¹ p 360° 7 2 2 1 22 p¹4 6 7 A = ´ ´ 36 = 18.86 cm2 Therefore, for all real values of p except 4, the given pair OR of equationsn will have a unique solution. Horse can graze in the field which is a circle of radius 28 OR cm. Here, a1 = 2 = 1 a2 4 2 So, required perimeter = 2pr = 2.p(28) cm =2´ 22 ´ (28) cm = 176 cm b1 = 3 = 1 and c1 = 5 7 b2 6 2 c2 7 7. By converse of Thale's theorem DE || BC 1 1 5 2 2 7 ÐADE = ÐABC = 70° (Corresponding angles) = ¹ Given ÐBAC = 50° ÐABC + ÐBAC + ÐBCA = 180° (Angle sum prop. of a1 = b1 ¹ c1 is the condition for which the given system triangles) a2 b2 c2 70° + 50° + ÐBCA = 180° ÐBCA = 180° – 120° = 60° of equations will represent parallel lines. OR So, the given system of linear equations will represent a EC = AC – AE = (7 – 3.5) cm = 3.5 cm pair of parallel lines. AD = 2 and AE = 3.5 = 1 11. In the bag number of red balls = 3, Number of black balls BD 3 EC 3.5 1 =5 Total number of balls = 5 + 3 = 8

SQP 20-21-4 Mathematics Probability of red balls = 3 14. (i) (c) 90° 8 (ii) (b) SAS (iii) (b) 4 : 9, Ratio of sides of similar triangles = Ratio of OR corresponding medians (iv) (d) Converse of Pythagoras theorem Total number of possible outcomes (1, 2, 3, 4, 5, 6) = 6 (v) (a) 48 cm2 There are 3 prime numbers = 2, 3, 5. 15. (i) (d) parabola (ii) (a) 2, Graph cuts at two distinct point on x-axis So, probability of getting a prime number is 3 = 1 (iii) (b) –1, 3, Points at where y-coordinate becomes zero 6 2 (iv) (c) x2 – 2x – 3 (v) (d) 0,As, x2 – 2x – 3 = (–1)2 – 2 (–1) – 3 = 1 + 2 – 3 = 0 12. 1 13. (i) (c) (0, 0) (Q A is origin) (ii) (a) (4, 6) (iii) (a) (6, 5) (iv) (a) (16, 0) (v) (b) (–12, 6)

Objective Questions and Solutions Basic Solved Paper 2020 (All India) SECTION-A Question numbers 1 to 9 carry 1 mark each. Choice the correct option in question numbers 1 to 6. 1. The probability of an impossible event is (a) 1 (b) 1 (c) not defined (d) 0 2 2. If (3, –6) is the mid-point of the line segment joining (0, 0) and (x, y), then the point (x, y) is (a) (–3, 6) (b) (6, –6) (c) (6, –12) (d) æ 3 , -3 ö÷ø èç 2 3. 8 cot2A – 8 cosec2 A is equal to (a) 8 (b) 1 (c) –8 (d) - 1 8 8 4. The point on x-axis which divides the line segment joining (2, 3) and (6, –9) in the ratio 1 : 3 is (a) (4, –3) (b) (6, 0) (c) (3, 0) (d) (0, 3) 5. If a pair of linear equations is consistent, then the lines represented by them are (a) parallel (b) intersecting or coincident (c) always coincident (d) always intersecting 6. 120 can be expressed as a product of its prime factors as (a) 5 × 8 × 3 (b) 15 × 23 (c) 10 × 22 × 3 (d) 5 × 23 × 3 Fill in the blanks in question numbers 7 to 8. 7. If 2 is a zero of the polynomial ax2 – 2x, then the value of ‘a’ is ____________. 8. All squares are _____________ . (congruent/similar). Answer the following question number 9. 9. A dice is thrown once. If getting a six, is a success, then find the probability of a failure.

SP 2020-2 Mathematics 1. (d) 0 2. (c) 0 + x = 3, 0 + y = -6 2 2 x = 6, y = –12 (x, y) = (6, –12) 3. (c) 8(cot2A – cosec2A) = 8 × (–1) = –8 4. (c) Required point = æ 1´ 6 + 3 ´ 2 , 0 ö = æ 12 , 0 ö = (3, 0) èç 1 + 3 ø÷ çè 4 ÷ø 5. (b) Intersecting or coincident 6. (d) 5 × 23 × 3 7. 2 is a zero of ax2 – 2x then, a(2)2 – 2 × 2 = 0 4a = 4 Þ a = 1 8. similar 9. Probability of getting a success = P(getting a six) = 1 6 \\ Probability of failure = 1 – P (getting a six) =1- 1 = 5 . 6 6

Objective Questions and Solutions CBSE Questions Bank-2021 Directions : Study the given case/study and answer the following questions. Case Study To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections-section A and section B of grade X. There are 32 students in section A and 36 students in section B. [From CBSE Question Bank-2021] 1. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 288 (d) 272 2. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is (a) 2 (b) 4 (c) 6 (d) 8 3. 36 can be expressed as a product of its primes as (a) 22 × 32 (b) 21 × 33 (c) 23 × 31 (d) 20 × 30 4. 7× 11 × 13 × 15 + 15 is a (a) Prime number (b) Composite number (c) Neither prime nor composite (d) None of the above 5. If p and q are positive integers such that p = ab2 and q = a2b, where a, b areprime numbers, then the LCM (p, q) is (b) a2b2 (c) a3b2 (d) a3b3 (a) ab Case Study-II A seminar is being conducted by an Educational Organisation, where theparticipants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. [From CBSE Question Bank-2021]

QB-2 Mathematics 6. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants thatcan accommodated in each room are (a) 14 (b) 12 (c) 16 (d) 18 7. What is the minimum number of rooms required during the event? (a) 11 (b) 31 (c) 41 (d) 21 8. The LCM of 60, 84 and 108 is (a) 3780 (b) 3680 (c) 4780 (d) 4680 9. The product of HCF and LCM of 60,84 and 108 is (a) 55360 (b) 35360 (c) 45500 (d) 45360 10. 108 can be expressed as a product of its primes as (a) 23 × 32 (b) 23 × 33 (c) 22 × 32 (d) 22 × 33 Case Study-III A Mathematics exhibition is being conducted in your school and one of your friendsis making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience. x 5 2783 253 y 11 z   [From CBSE Question Bank-2021] Observe the following factor tree and answer the following: 11. What will be the value of x? (a) 15005 (b) 13915 (c) 56920 (d) 17429 12. What will be the value of y? (a) 23 (b) 22 (c) 11 (d) 19 13. What will be the value of z? (a) 22 (b) 23 (c) 17 (d) 19 14. According to Fundamental Theorem of Arithmetic 13915 is a (a) Composite number (b) Prime number (c) Neither prime nor composite (d) Even number 15. The prime factorisation of 13915 is (a) 5 × 113 × 132 (b) 5 × 113 × 232 (c) 5 × 112 × 23 (d) 5 × 112 × 132 Case Study-IV The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.  

CBSE Questions Bank-2021 QB-3   [From CBSE Question Bank-2021] 16. In the standard form of quadratic polynomial, ax2 + bx + c, a, b and c are (a) All are real numbers. (b) All are rational numbers. (c) ‘a’ is a non zero real number and b and c are any real numbers. (d) All are integers. 17. If the roots of the quadratic polynomial are equal, where the discriminant D = b2 – 4ac, then (a) D > 0 (b) D < 0 (c) D ≥ 0 (d) D = 0 18. If a and 1 are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is α (a) 4 (b) 1 –1 (d) 2 4 (c) 4 19. The graph of x2 + 1 = 0 (b) Touches x-axis at a point. (a) Intersects x-axis at two distinct points. (d) Either touches or intersects x-axis. (c) Neither touches nor intersects x-axis. 20. If the sum of the roots is –p and product of the roots is – 1, then the quadratic polynomial is p (a) k  – px2 + x + 1 (b) k  px2 – x –1 (c) k  x2 + px – 1 (d) k  x2 – px + 1 p  p       p  p  Case Study-V An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial. TRIKONASANA ADHOMUKHA SAVASANA   ADHO MUKHA SVANA [From CBSE Question Bank-2021] 21. The shape of the poses shown is (a) Spiral (b) Ellipse (c) Linear (d) Parabola (d) a > 0 22. The graph of parabola opens downwards, if__________. (a) a ≥ 0 (b) a = 0 (c) a < 0

QB-4 Mathematics 23. In the graph, how many zeroes are there for the polynomial? –2 4 –8 (a) 0 (b) 1 (c) 2 (d) 3 (d) 2, –8 24. The two zeroes in the above shown graph are (a) 2, 4 (b) –2, 4 (c) –8, 4 25. The zeroes of the quadratic polynomial 4 3x2 + 5x – 2 3 are (a) 23 , 3 (b) – 23 , 43 (c) 2 ,– 3 (d) – 23 , − 43 4 3 4 Case Study-VI Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial. v = 8.552 m/s 3 θ = 51.89° R = 7.239 m 1 h = 3.048 m 2 4 26. The shape of the path traced shown is [From CBSE Question Bank-2021] (d) Parabola (a) Spiral (b) Ellipse (c) Linear (d) a ≥ 0 27. The graph of parabola opens upwards, if____________. (a) a = 0 (b) a < 0 (c) a > 0 28. Observe the following graph and answer 6 –4 –3 –2 –1 2 1234 –2 –6 In the above graph, how many zeroes are there for the polynomial? (a) 0 (b) 1 (c) 2 (d) 3

CBSE Questions Bank-2021 QB-5 29. The three zeroes in the above shown graph are (a) 2, 3, –1 (b) –2, 3, 1 (c) –3, –1, 2 (d) –2, –3, –1 (d) x3 + 2x2 + 5x + 6 30. What will be the expression of the polynomial? (c) x3 + 2x2 + 5x − 6 (a) x3 + 2x2 − 5x − 6 (b) x3 + 2x2 − 5x + 6 Case Study-VII A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks. Type of Question Marks given for correct answer Marks deducted for wrong answer True/False 1 0.25 [From CBSE Question Bank-2021] 31. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly? 32. How many questions did he guess? 33. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got? 34. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks? Case Study-VIII Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq.m. x 2y 5m Bath Kitchen Bedroom 1 room 2m Living Room 5m Bedroom 2 15 m [From CBSE Question Bank-2021] Based on the above information, answer the following questions: 35. Form the pair of linear equations in two variables from this situation. 36. Find the length of the outer boundary of the layout. 37. Find the area of each bedroom and kitchen in the layout. 38. Find the area of living room in the layout. 39. Find the cost of laying tiles in kitchen at the rate of ` 50 per sq.m Case Study-IX It is common that Governments revise travel fares from time to time based on various factors such as inflation ( a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, rickshaws, taxis, radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations. Name of the city Distance travelled (km) Amount paid (`) City A 10 75 15 110 City B 8 91 14 145

QB-6 Mathematics Situation 1: In city A, for a journey of 10 km, the charge paid is ` 75 and for a journey of 15 km, the charge paid is ` 110. Situation 2: In a city B, for a journey of 8 km, the charge paid is ` 91 and for a journey of 14km, the charge paid is ` 145. [From CBSE Question Bank-2021] Refer situation 1 40. If the fixed charges of auto rickshaw be ` x and the running charges be ` y km/hr, the pair of linear equations representing the situation is (a) x + 10y = 110, x + 15y = 75 (b) x + 10y = 75, x + 15y = 110 (c) 10x + y = 110, 15x + y = 75 (d) 10x + y = 75, 15x + y = 110 41. A person travels a distance of 50km. The amount he has to pay is (a) ` 155 (b) ` 255 (c) ` 355 (d) ` 455 Refer situation 2 42. What will a person have to pay for travelling a distance of 30km? (a) ` 185 (b) ` 289 (c) ` 275 (d) ` 305 43. The graph of lines representing the conditions are: (situation 2) Y (20, 25) Y 25 25 20 20 15 15 (a) 10 (30, 5) (b) 10 (0, 10) (20, 10) 5 (0, 5) 5 (12.5, 0) X¢––550 5 10 15 20 25 30 35 X X¢––550 5 10 15 20 25 30 35 X –10 Y¢ –1Y0¢ (5, –10) (25, –10) 50 45 40 Y 25 35 20 30 15 (15, 15) 10 (35, 10) 25 (d) 5 (0, 10) (c) 20 15 (11, 10) (19, 9) (47, 7) X¢––550 5 10 15 20 25 30 35 X (15, –5) 10 (5, 10) –10 Y¢ 5 (27, 8) 0 5 10 15 20 25 30 35 40 45 50 55 Case Study-X In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag. [From CBSE Question Bank 2021]

CBSE Questions Bank-2021 QB-7 D C G R 2 1 A 1 2 3 4 5 6 7 8 9 10 44. Find the position of green flag (a) (2, 25) (b) (2, 0.25) (c) (25, 2) (d) (0, –25) 45. Find the position of red flag (a) (8, 0) (b) (20, 8) (c) (8, 20) (d) (8, 0.2) 46. What is the distance between both the flags? (a) √41 (b) √11 (c) √61 (d) √51 47. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? (a) (5, 22.5) (b) (10, 22) (c) (2, 8.5) (d) (2.5, 20) 48. If Joy has to post a flag at one-fourth distance from green flag ,in the line segment joining the green and red flags, then where should he post his flag? (a) (3.5, 24) (b) (0.5, 12.5) (c) (2.25, 8.5) (d) (25, 20) Case Study-XI Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground. [From CBSE Question Bank-2021] Vijay's House Tower Ajay's House 49. What is the height of the tower? (a) 20m (b) 50m (c) 100m (d) 200m 50. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m? (a) 75m (b) 50m (c) 45m (d) 60m 51. What is the height of Ajay’s house? (a) 30m (b) 40m (c) 50m (d) 20m 52. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house? (a) 16m (b) 32m (c) 20m (d) 8m 53. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house? (a) 15m (b) 32m (c) 16m (d) 8m

QB-8 Mathematics Case Study-XII Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below. To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12m, connecting C to point D at a distance of 40m from point C and the connecting D to the point A which is are a distance of 30m from D such the ∠ADC=90° . [From CBSE Question Bank-2021] B 12 m AC 30 m 40 m D 54. Which property of geometry will be used to find the distance AC? (a) Similarity of triangles (b) Thales Theorem (c) Pythagoras Theorem (d) Area of similar triangles 55. What is the distance AC? (a) 50m (b) 12m (c) 100m (d) 70m (d) (21, 20, 28) 56. Which is the following does not form a Pythagoras triplet? (d) 100m (d) 22m (a) (7, 24, 25) (b) (15, 8, 17) (c) (5, 12, 13) 57. Find the length AB? (a) 12m (b) 38m (c) 50m (c) 82m 58. Find the length of the rope used. (a) 120m (b) 70m In ∆ABC, right angled at B Case Study-XIII C 3cm A B [From CBSE Question Bank-2021] AB + AC = 9 cm and BC = 3cm. 59. The value of cot C is (a) 34 (b) 14 (c) 45 (d) None of these 60. The value of sec C is (a) 43 (b) 53 (c) 13 (d) None of these 61. sin2C + cos2C = (b) 1 (c) –1 (d) None of these (a) 0

CBSE Questions Bank-2021 QB-9 Case Study-XIV Pookalam is the flower bed or flower pattern designed during Onam in Kerala. 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. [From CBSE Question Bank-2021] A AB B C DC I II Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure. Design II: This Pookalam is made with 9 circular design each of radius 7cm. Refer Design I: 62. The side of equilateral triangle is (c) 48 cm (d) 64 cm (a) 12√3 cm (b) 32√3 cm 63. The altitude of the equilateral triangle is (a) 8 cm (b) 12 cm (c) 48 cm (d) 52 cm Refer Design II: 64. The area of square is (a) 1264 cm2 (b) 1764 cm2 (c) 1830 cm2 (d) 1944 cm2 65. Area of each circular design is (a) 124 cm2 (b) 132 cm2 (c) 144 cm2 (d) 154 cm2 66. Area of the remaining portion of the square ABCD is (a) 378 cm2 (b) 260 cm2 (c) 340 cm2 (d) 278 cm2 Case Study-XV A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully. [From CBSE Question Bank-2021] AB Design A: Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts. Design B: Brooch b is made two colours-Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.

QB-10 Mathematics Refer to Design A 67. The total length of silver wire required is (a) 180 mm (b) 200 mm (c) 250 mm (d) 280 mm 68. The area of each sector of the brooch is (a) 44 mm2 (b) 52 mm2 (c) 77 mm2 (d) 68 mm2 Refer to Design B 69. The circumference of outer part (golden) is (a) 48.49 mm (b) 82.2 mm (c) 72.50 mm (d) 62.86 mm 70. The difference of areas of golden and silver parts is (a) 18 p (b) 44 p (c) 51 p (d) 64 p 71. A boy is playing with brooch B. He makes revolution with it along its edge.How many complete revolutions must it take to cover 80 p mm ? (a) 2 (b) 3 (c) 4 (d) 5 Case Study-XVI On a weekend Rani was playing cards with her family. The deck has 52 cards. If her brother drew one card . [From CBSE Question Bank-2021] 72. Find the probability of getting a king of red colour. (a) 216 (b) 1 (c) 512 (d) 14 13 73. Find the probability of getting a face card. (a) 216 (b) 1 (c) 123 (d) 133 13 74. Find the probability of getting a jack of hearts. (a) 216 (b) 1 (c) 532 (d) 236 52 75. Find the probability of getting a red face card. (a) 236 (b) 1 (c) 512 (d) 14 13 76. Find the probability of getting a spade. (a) 216 (b) 1 (c) 216 (d) 14 13

CBSE Questions Bank-2021 QB-11 Case Study-XVII Rahul and Ravi planned to play Business (board game) in which they were supposed to use two dice. [From CBSE Question Bank-2021] 77. Ravi got first chance to roll the dice. What is the probability that he got thesum of the two numbers appearing on the top face of the dice is 8? (a) 216 (b) 5 (c) 118 (d) 0 36 78. 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 (c) 118 (d) 0 36 79. 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 (c) 118 (d) 0 36 80. 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) 95 (b) 5 (c) 16 (d) 0 36 81. 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 (c) 118 (d) 158 36 1. (c) For getting least number of books, 3. (a) 36 is expressed as prime taking LCM of 32, 36 36 = 2 × 2 × 3 × 3 = 22 × 32 4. (b) 7 × 11 × 13 × 15 + 15 4 32, 36 ⇒ 15 (7 × 11 × 13 + 1) 8 8, 9 so given no. is a composite number. 9 1, 9 5. (b) Given a, b are prime number. So LCM of p, q, where p = ab2, q = a2b 1, 1 p = a × b × b ⇒ 4 × 8 × 9 = 288 q = a × b × a 2. (b) HCF of 32, 36 is a × b × b × a ⇒ a2b2 6. (b) For maximum number of participants, taking HCF of 4 32, 36 8, 9 60, 84 and 108 = 4 12 60, 84, 108 5, 7, 9 = 12

QB-12 Mathematics 7. (d) Minimum number of rooms required are −=5 ± 25 + 4 × 4 3 × 2 3 −5 ±11 83 83 5 + 7 + 9 = 21 = 8. (a) LCM of 60, 84, 108 is 12 × 5 × 7 × 9 = 3780 ⇒ −2 , 3 9. (d) Product is = 12 × 3780 = 45360 3 4 10. (d) 108 = 2 × 2 × 3 × 3 × 3 = 22 × 33 11. (b) x = 5 × 2783 = 13915 26. (d) Parabola 12. (c) y = 253) 2783( = 11 27. (c) If a > 0, Graph of parabola looks like 13. (b) z = 11) 253( = 23 14. (a) Composite number having more than 2 factors. 28. (d) Here graph cuts x-axis at 3 points 15. (c) Prime factorisation of 13915 = so it has three zeros. 29. (c) Observing the graph we find –3, –1, 2 as zeros. 5 13915 30. (a) Given zeros are –3, –1, 2, then 11 2783 11 253 Expression is (x – (–3)) (x – (–1)) (x – 2) 23 23 = (x + 3)(x + 1)(x – 2) 1 = x3 + 2x2 – 5x – 6 ⇒ 5 × 11 × 11 × 23 x3 – (Sum of zeros)x2 + (Sum of zeros taking two at ⇒ 5 × 112 × 23 16. (c) a ≠ 0, a, b, c are real numbers a time)x – (Product of zeros) x3 – (– 3 – 1 + 2) x2 + ((–3)(–1) + (–1)(2) + (2)(–3)) 17. (d) For roots are equal b2 – 4ac = 0 x – (–3)(–1)(2) or D = 0 x3 + 2x2 + (3 – 2 – 6)x – 6 x3 + 2x2 – 5x – 6 Sol. (31-34): 1 8. ( b) Fαo.rα1v=aluace of(Pk,roduct of roots = c ) Let x be number of known questions and y be number of a questions cheating by the student. 8k Here, x + y = 120 12 1= x − 1 y =90 4 or k = 4 19. (c) For x2 + 1 = 0 On solving these two equations roots are not real. We have, x = 96 and y = 24 So, graph of x2 + 1 = 0, neither touches nor intersects x-axis. 31. No. of correct questions are 96 20. (c) We know, for a quadratic polynomial 32. He guessed 24 questions. k(x2 – (Sum of roots) x + Product of roots) k(x2 – (–p) + (–1/p)) 33. Marks = 80 – 1 of 40 = 70 k (x2 + p – 1/p) 4 34. Here, x + y = 120 ...(i) 21. (d) Parabola. 1 4 22. (c) a < 0, Graphs look like x − y =95 ...(ii) open downwards On solving (i) & (ii) x = 100 23. (c) According to graph, there are two zeros 35. Given area of two bedrooms and a kitchen is 95 sq m. one at (–2) and 2nd at 4, –2 24. (b) –2, 4 2 × Area of bedroom + Area of kitchen = 95 25. (b) For zeros D = −b ± b2 − 4ac 2 × 5 x + 5y = 95 2a or 2x + y = 19 ...(i) Here, a = 4 3, b = 5, c = −2 3 and x + 2 + y = 15 or x + y = 13 ...(ii)

CBSE Questions Bank-2021 QB-13 36. Length of outer boundary = 12 + 15 + 12 +15 = 54 m AB = BC ⇒ 20 = 12 PQ QR 100 QR 37. On solving x + y = 13 2x + y = 19 ⇒ QR = 60 51. (b) Q DABC ~ DXYZ x = 6m, y = 7m Area of a bedroom = 5x = 5 × 6 = 30 sq m ∴ AB = BC ⇒ 20 = 10 XY YZ XY 20 Area of kitchen = 5y = 5 × 7 = 35 sq m 38. Area of living room = 9 × 5 + 2 × 15 = 75 sq m ⇒ XY = 40 39. Total cost of laying tiles in the kitchen = ` 50 × 35 = ` 1750 52. (a) Let QR = 40 m, PQ = 100 m and XY = 40 m 40. (b) Given, fixed charges of auto rickshaw be ` x and ∴ PQ = QR ⇒ 100 = 40 running charges be ` y km/hr, so representing situation XY YZ 40 YZ 1 x + 10y = 75 ⇒ YZ = 16 m. x + 15y = 110 53. (d) Let QR = 40m, PQ =100m and AB = 20 m 41. (c) On solving x + 10y = 75 ∵ AB = BC ⇒ 20 = BC PQ QR 100 40  x + 15y = 110 we get x = 5 km, ⇒ BC = 8 m.  y = ` 7/km 54. (c) Pythagoras theorem 55. (a) AC2 = 302 + 402 = 2500 ⇒ AC = 50m Charges to go 50 km. 56. (d) (21, 20, 28) [Q 282 ≠ (21)2 + (20)2] x + 50y = 5 + 50 × 7 = ` 355 42. (b) To cover 30 km distance, 57. (b) AB = 50 – 12 = 38m x + 30y = 19 + 30 × 9 = 289 58. (c) 82m 43. (c) Sol. (59-61): 44. (a) (2, 25) ∵ x =2, y =14 ×100 =25 In ∆ABC, by Pythagoras theorem, AC2 = AB2 + BC2 ⇒ AB = 4 cm. ∵ x =8, y =15 ×100 =20 AC = 5 cm. 45. (c) (8, 20) 59. (a) cot C = BC = 3 AB 4 AC 5 46. (c) (8 − 2)2 + (25 − 20)2 = 36 + 25 = 61 60. (b) sec C = BC = 3  8 + 2 25 + 20 61. (b) sin C = 4 , cos C = 3  2 2  5 + cos2 C 47. (a) , = (5, 22.5) 5 4 2 3 2 L.H.S = sin2 C = 5   5  +  48. (a)  2 + 5 , 25 + 22.5  = (3.5, 24) = 16 + 9 =1 = R.H.S  2 2  25 49. (c) Q DABC ~ DPQR Sol. (62-66) A ∴ AB = BC ⇒ 20 = 10 PQ QR PQ 50 ⇒ PQ = 100 O 32 cm \\ Height of the tower = 100 m 30° BD 50. (d) Let BC = 12 m and PQ = 100 m C

QB-14 Mathematics 62. (b) cos 30° = BD 71. (c) Number of revolution 32 = Distance BD = 16 3 cm. Outer circumference side BC = 32 3 cm = 82=00ππ 4. 63. (c) AD = AB2 − BD2 5=22 1 26 = (32 3)2 − (16 3)2 72. (a) P(king of red colour=) = 48 cm 73. (d) P(getting a face card=) 15=22 3 13 64. (b) Side of square = 6 × 7 = 42 cm. 74. (b) P(getting a jack of hearts) = 1 Area of square = 42 × 42 = 1764 cm2 52 65. (d) Area of each circular 75. (a) P(getting a red face card) = 3 26 22 = p(7)2 = 7 × 49 = 154 cm2 76. (d) P(getting a spade=) 15=32 1 4 66. (a) Area of remaining portion = 1764 – 9 × 154 = 378 cm2 77. (b) Sum of the two numbers appearing on the top face of dice is 8. 67. (b) Here r = 14 mm (2, 6), (3, 5), (4, 4) (5, 3), (6, 2) Length of silverwire \\ Required probability = 5 36 = 2pr + 8r =2× 22 × 14 + 8 × 14 = 200 mm 78. (d) Since, the sum of two numbers appearing on the top 7 face of dice cannot be 13. 68. (c) Area of each sector So, required probability = 0. = 1 × 22 × 14 × 14 = 77 mm2 79. (a) Since, the pair of number whose sum is less than 0 or 8 7 equal to 12 in a pair of dice is 36. 69. (d) Circumference of inner part = 44 mm \\ Required probabilit=y 33=66 1 ⇒2× 22 × r = 44 7 ⇒ r = 7 mm 80. (c) Since, the pair of numbers on the top of dice whose outer radius = 7 + 3 = 10 mm sum is 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) , (6, 1) outer circumference \\ Required probabilit=y 3=66 1 22 5 6 = 2 × 7 × 10 = 62.86 mm 81. (d) 18 70. (c) Difference of areas 22 = 7 ( 102 – 72) = 51 p mm2

Sample Paper 1 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. Two numbers are in the ratio of 15 : 11. If their H.C.F. is 13, then numbers will be (a) 195 and 143 (b) 190 and 140 (c) 185 and 163 (d) 185 and 143 2. Put suitable word in the sentence below: 35 has ..................... decimal expansion. 50 (a) Terminating (b) Non-terminating (c) Recurring (d) Repeating 3. Which of the following is true? (a) π is equal to 22 7 (b) The only real numbers are rational numbers (c) Every non-terminating decimal can be written as a periodic decimal (d) 0.21 lies between 0.2 and 0.3 4. A polynomial of degree 7 is divided by a polynomial of degree 4. Degree of the quotient is (a) less than 3 (b) 3 (c) more than 3 (d) more than 5 5. If 1 is zero of polynomial p(x) = ax2 – 3(a – 1)x – 1, find a. (a) 1 (b) 2 (c) –2 (d) 3

SP-2 Mathematics 6. Two isosceles triangles have their corresponding angles equal and their areas are in the ratio 25 : 36. The ratio of their corresponding height is (a) 25 : 35 (b) 36 : 25 (c) 5 : 6 (d) 6 : 5 7. Two dice are thrown at a time, then find the probability that the difference of the numbers shown on the dice is 1. (a) 136 (b) 158 (c) 376 (d) 178 8. The coordinates of the point which is reflection of point (–3, 5) in x-axis are (a) (3, 5) (b) (3, –5) (c) (–3, –5) (d) (–3, 5) 9. In the given figure, AD is the bisector of ∠A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, determine AC A 6 cm B 4 cm D 3 cm C (a) 4.5 cm (b) 3.5 cm (c) 4.8 cm (d) 3.2 cm 10. If b tan θ = a, the value of a sin θ − b cos θ is a sin θ + b cos θ a−b a+b (a) a2 + b2 (b) a2 + b2 a2 + b2 a2 − b2 (c) a2 − b2 (d) a2 + b2 11. If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father? (a) 45 years (b) 40 years (c) 50 years (d) 55 years 12. If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1, then the value of y is (a) 4 (b) 3 (c) 2 (d) 1 13. If x = p sec q and y = q tan q, then (b) x2q2 – y2p2 = pq (d) x2q2 – y2p2 = p2q2 (a) x2 – y2 = p2q2z 1 (c) x2q2 – y2p2 = p2q2 14. If f (x) = 2x3 – 6x + 4x – 5 and g(x) = 3x2 – 9, then the value of f (1) + g(–2) is (a) –3 (b) –2 (c) 3 (d) 2 15. A book containing 100 pages is opened at random. Find the probability that a doublet page is found. (a) 285 (b) 1090 (c) 1070 (d) 11010 16. sin2q + cosec2q is always (a) greater than 1 (b) less than 1 (c) greater than or equal to 2 (d) equal to 2

Sample Paper-1 SP-3 17. Points A and B are 90 km. apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction, they meet in 9 hrs and if they go in opposite directions, they meet in 9/7 hrs. Find their speeds. (a) 40 km/hr, 30 km/hr (b) 10 km/hr, 20 km/hr (c) 20 km/hr, 30km/hr (d) 50 km/hr, 40km/hr 18. The two consecutive odd positive integers, the sum of whose squares is 290 are (a) 9, 11 (b) 11, 13 (c) 13, 15 (d) 15, 17 19. Determine the value of k for which the following system of equations becomes consistent : 7x – y = 5, 21x – 3y = k. (a) k = 15 (b) k = 11 (c) k = 4 (d) k  11 2 20. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then find the greater number. (a) 111 (b) 137 (c) 37 (d) 311 SECTION-B Section B consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 21. ABCD is a square. F is the mid-point of A B, BE is one-third of BC. If the area of the ∆FBE is 108 sq. cm find the length AC.   (a) 36 2 cm (b) 37 2 cm   (c) 36 2 cm (d) (36)2 cm 22. A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street. E D 15m 15m 9 m 12 m A CB (a) 21 m (b) 18 m (c) 22 m (d) 12 m 23. The graphs of the equations x – y = 2 and kx + y = 3, where k is a constant, intersect at the point (x, y) in the first quadrant, if and only if k is (a) equal to – 1 (b) greater than – 1 (c) less than 3/2 (d) lying between – 1 and 3/2 24. If 0 < x ≤ π , then sin x + cosec x ≥ 2 (a) 0 (b) 1 (c) 2 (d) 3

SP-4 Mathematics 25. If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2sin 3θ – 3 tan 3θ is equal to (a) sin2θ (b) 12 (c) 13 (d) 0 26. Which among the following is correct? (a) The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides. (b) The areas of two similar triangles are in the ratio of the corresponding altitudes. (c) The ratio of area of two similar triangles are in the ratio of the corresponding medians. (d) If the areas of two similar triangles are equal, then the triangles are congruent. 27. If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 represents coincident lines, which of the conditions holds true? (a) b = 2a (b) a = 2b (c) 2a + b = 0 (d) a + 2b = 0 28. Solve the following system of linear equations : 2 (ax – by) + (a + 4b) = 0 (b) x = –1/2, y = 2 2 (bx + ay) + (b – 4a) = 0 (a) x = 0, y = 1 (c) x = 1, y = 2 (d) x = 1/2, y = –1/2 29. Find a and b if x + 1 and x + 2 are factors of p (x) = x3 + 3x2 − 2αx + β (a) 3, –1 (b) –1, 0 (c) 0, –3 (d) 5, 6 30. If one zero of the quadratic polynomial 2x2 – 8x – m is 5 , then the other zero is 2 (a) 23 (b) – 32 (c) 23 (d) −215 31. If x = 2 and x = 0 are roots of the polynomials f (x) = 2x3 – 5x2 + ax + b. Then values of a and b respectively are (a) 2, 0 (b) 1, 2 (c) – 1, 1 (d) 0, 3 32. If cos A = , find the value of 9 cot2A – 1. (a) 1 (b) 16 (c) 1665 (d) 0 65 33. Which of the following statement is false? (a) All isosceles triangles are similar. (b) All equilateral triangles are similar. (c) All circles are similar. (d) None of the above 34. If one root of the equation px2 – 14x + 8 = 0 is six times the other, then p is equal to (a) 2 (b) 3 (c) 1 (d) none of these 35. Determine the values of a and b for which the following system of linear equations has infinitely many solutions: 3x – (a + 1) y = 2b – 1, 5x + (1 – 2a) y = 3b (a) a = 8, b = 5 (b) a = 4, b = 6 (c) a = 7, b = 1 (d) a = 5, b = 3 36. If sin θ = a2 − b2 , then find cosec θ + cot θ. a2 + b2 (a) a +a b (b) bb +− aa (c) aa+2b (d) aa +− bb

Sample Paper-1 SP-5 37. Degree of polynomial y3 − 2 y2 − 3y + 1 is 2 1 (b) 2 (c) 3 3 (a) 2 (d) 2 38. Solve the following system of equations ax + by = c; bx – ay = c =(a) x a=2 +a b2 , y b (b) =x 1a=, y 1 a2 + b2 b =(c) x (=a2+abb)2 , y 2ab (d) x = c(a+ b) , y= − c(a− b) (a− b)2 a2 + b2 a2 + b2 39. The decimal expansion of 21 is : 45 (a) terminating (b) non-terminating and repeating (c) non-terminating and non-repeating (d) none of these 40. Find the value of a if (sin A + cosec A)2 + (cos A + sec A)2 = a + tan2A + cot2A (a) 5 (b) 4 (c) 0 (d) 7 SECTION-C Case Study Based Questions: Section C consists of 10 quesions of 1 mark each. Any 8 quesions are to be attempted. Q 41. - Q 45 are based on case study-I Case Study-I HCF of natural numbers is the largest factor which is common to all the number and LCM of natural numbers is the smallest natural number which is multiple of all the numbers. 41. If p and q are two co-prime natural numbers, then their HCF is equal to (a) p (b) q (c) 1 (d) pq 42. The LCM and HCF of two rational numbers are equal, then the numbers must be (a) prime (b) co-prime (c) composite (d) equal 43. If two positive integers a and b are expressible in the form a = pq2 and b = p3q; p, q being prime number, then LCM (a, b) is (a) pq (b) p3q3 (c) p3q2 (d) p2q2 44. The largest number which divides 285 and 1249 leaving remainders 9 and 7 respectively, is (a) 46 (b) 6 (c) 12 (d) 138 45. The largest number which exactly divides 2011and 2623 leaving remainders 9 and 5 respectively is (a) 11 (b) 22 (c) 154 (d) 13 Q 46 - Q 50 are based on case study-II Case Study-II An honest person invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. He received yearly interest of 130, but if he had interchanged amounts invested, he would have received 4 more as interest. If x be the amount invested at the rate of 12% and y be the amount invested at the rate of 10%, then answer the following questions.

SP-6 Mathematics 10x +12 y 46. What is the yearly interest in terms of x and y ? (d) 100 (d) 5 x + 6 y = 6500 12x +10 y (b) 12 x + 10 y (c) 10 x + 12 y (d) 5 x + 6 y = 6300 (a) 100 (d) x – y = 700 47. Find the equation corresponding to yearly received interest of `130. (a) 12 x + 10 y = 130 (b) 12 x + 10 y = 13000 (c) 6 x + 5 y = 6500 48. Find the equation corresponding to x and y when invested amount is interchanged. (a) 5 x + 6 y = 6700 (b) 6 x + 5 y = 6700 (c) 6 x + 5 y = 6300 49. Which of the following is true for x and y ? (c) x – y = 100 (a) x + y = 120 (b) x + y = 1200 50. How much amount did he invest at different rates ? (b) x = ` 500, y = ` 700 (a) x = ` 500, y = ` 200 (d) x = ` 400, y = ` 300 (c) x = ` 100, y = ` 500

OMR ANSWER SHEET Sample Paper No –  Use Blue / Black Ball pen only.  Please do not make any atray marks on the answer sheet.  Rough work must not be done on the answer sheet.  Darken one circle deeply for each question in the OMR Answer sheet, as faintly darkend / half darkened circle might by rejected. Start time : ____________________ End time ____________________ Time taken ____________________ 1. Name (in Block Letters) 2. Date of Exam SECTION-A 17. a    b    c    d 18. a    b    c    d 3. Candidate’s Signature 9. a    b    c    d 19. a    b    c    d 10. a    b    c    d 20. a    b    c    d 1. a    b    c    d 11. a    b    c    d 2. a    b    c    d 12. a    b    c    d 37. a    b    c    d 3. a    b    c    d 13. a    b    c    d 38. a    b    c    d 4. a    b    c    d 14. a    b    c    d 39. a    b    c    d 5. a    b    c    d 15. a    b    c    d 40. a    b    c    d 6. a    b    c    d 16. a    b    c    d 7. a    b    c    d 49. a    b    c    d 8. a    b    c    d SECTION-B 50. a    b    c    d 21. a    b    c    d 29. a    b    c    d 22. a    b    c    d 30. a    b    c    d 23. a    b    c    d 31. a    b    c    d 24. a    b    c    d 32. a    b    c    d 25. a    b    c    d 33. a    b    c    d 26. a    b    c    d 34. a    b    c    d 27. a    b    c    d 35. a    b    c    d 28. a    b    c    d 36. a    b    c    d 41. a    b    c    d SECTION-C 42. a    b    c    d 43. a    b    c    d 45. a    b    c    d 44. a    b    c    d 46. a    b    c    d 47. a    b    c    d 48. a    b    c    d No. of Qns. Attempted Correct Incorrect Marks

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Sample Paper 2 Time : 90 Minutes Max Marks : 40 General Instructions 1. The question paper contains three parts A, B and C. 2. Section A consists of 20 quesions of 1 mark each. Any 16 quesitons are to be attempted. 3. Section B consists of 20 quersions of 1 mark each. Any 16 quesions are to be attempted. 4. Section C consists of 10 quesions based two Case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION-A Section A consists of 20 questions of 1 mark each. Any 16 quesions are to be attempted. 1. Solve cos θ + cosceocsθθ−1= 2, θ < 90º cosec θ +1 (a) 0° (b) 30° (c) 45° (d) 60° 2. is equal to tan 2θ + cosec2θ tan2 θ−1 sec2θ−cosec2θ (a) 0 (b) 2 (c) 2 sin 2 1 cos2 θ (d) 1 θ− sin2 θ − cos2 θ 3. If 5q and 4q are acute angles satisfying sin 5q = cos 4q, then 2sin 3q – 3 tan 3q is equal to (a) sin2q (b) 1 (c) 1 (d) 0 2 3 4. Determine the value of k for which the following system of equations becomes consistent : 7x – y = 5, 21x – 3y = k. (a) k = 15 (b) k = 11 (c) k = 4 (d) k  11 2 5. A railway half -ticket costs half the full fare but the reservation charges are the same on a half ticket as on full ticket. One reserved first class ticket from station A to station B costs ` 2125. Also, one reserved first class ticket and one reserved half first class ticket from A to B costs ` 3200. Find the full fare from station A to B and also the reservation charges for a ticket. (a) ` 1100, ` 15 (b) ` 2100, ` 25 (c) ` 1000, ` 25 (d) ` 2000, ` 40 6. Mrs. Vidya bought a piece of cloth as shown in the figure. The portion of the cloth that is not coloured consists of 6 identical semi-circles. 42 cm

SP-10 Mathematics Find the area of the coloured portion. (a) 144 cm2 (b) 126 cm2 (c) 195 cm2 (d) 243 cm2 7. A factory has 120 workers in January, 90 of them are female workers. In February, another 15 male workers were employed. A worker is then picked at random. Calculate the probability of picking a female worker. (a) 3 (b) 94 (c) 2 (d) 1 4 3 2 8. When 2256 is divided by 17, then remainder would be (a) 1 (b) 16 (c) 14 (d) None of these 9. In the given figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into 2 parts, equal in area. The ratio of PA : AB = A PQ (a) 1 : 1 B (c) C (b) ( 2 −1) : 2 1: 2 (d) ( 2 −1) :1 10. The figure given shows two identical semi-circles cut out from a piece of coloured paper. Find the area of the remaining piece of paper (Use π = 22 ) 7 15 cm 4 cm 20 cm 7 cm (a) 296.1 cm2 (b) 265.4 cm2 (c) 221.5 cm2 (d) 201.7 cm2 11. In what ratio does the point (–2, 3) divide the line-segment joining the points (–3, 5) and (4, –9) ? (a) 2 : 3 (b) 1 : 6 (c) 6 : 1 (d) 2:1 12. A box contains a number of marbles with serial number 18 to 38. A marble is picked at a random. Find the probability that it is a multiple of 3. (a) 53 (b) 270 (c) 3 (d) 13 4 13. The area of a right angled triangle is 40 sq. cm. and its perimeter is 40 cm. The length of its hypotenuse is (a) 16 cm (b) 18 cm (c) 17 cm (d) Data insufficient 14. The sum of exponents of prime factors in the prime-factorisation of 196 is (a) 3 (b) 4 (c) 5 (d) 2 15. A drain cover is made from a square metal plate of side 40 cm having 441 holes of diameter 1 cm each drilled in it. Find the area of the remaining square plate. (a) 1250.5 cm2 (b) 1253.5 cm2 (c) 1240.2 cm2 (d) 1260.2 cm2