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SAMPLE QUESTION PAPER - 2, Class – X, Session -2021-22 (TERM 1), , Time Allowed: 90 minutes, , Subject- Mathematics, , 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. Any 16 questions are to be attempted, 3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted, 4. Section C consists of 10 questions based on 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 questions are to be attempted., 2, , 1. Find the zeros of the polynomial 6𝑥 − 3 − 7𝑥., (a.) -4, 3/2, , (b.) 3/2, -1/3, , (c.) − 2, 2, , [1 mark], (d.) 2 3, 2/ 3, , 2. There is a circular path around a sports field. Sonia takes 18 minutes to drive one, round of the field, while Ravi takes 12 minutes for the same. Suppose they both start, at the same point and at the same time and go in the same direction. After how many, minutes will they meet again at the starting point?, , [1 mark], , (a.) After 36 minutes (b.) After 38 minutes (c.) After 46 minutes (d.) After 48 minutes, 3. Assertion: Two coincident rails are represented by equations x+2y–4=0 and, 2x+4y–12=0., Reason : The graphic representation of the equations x+2y–4=0 and 2x+4y–12=0, depicts two parallel lines., (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., , [1 mark]

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(c.) A is true but R is false., (d.) A is false but R is true., 4. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a :, (a.) Square, , (b.) Rectangle, , (c.) Rhombus, , [1 mark], , (d.) Trapezium, , 5. All circles are _____________., (a.) Congruent, , [1 mark], , (b.) Non-congruent, , (c.) Similar, , (d.) Not similar, , 0, , 6. If 𝑐𝑜𝑠 9α = 𝑠𝑖𝑛 α and 9α < 90 , then the value of 𝑡𝑎𝑛 5α is ____., [1 mark], (a.) 1/ 3, , (b.) 3, , (c.) 1, , (d.) 0, , 7. If 𝑠𝑒𝑐 θ + 𝑡𝑎𝑛 θ = 𝑝 then find 𝑠𝑒𝑐 θ in terms of 𝑝., (a.), , 1, 2, , (𝑝 +, , 1, 𝑝, , 1, , 1, , (b.) 2 (𝑝 − 𝑝 ), , ), , [1 mark], 2, , (c.), , 𝑝 −1, , (d.), , 2, , 𝑝 +1, , -9, 2, , 8. Two circles touch each other externally. The sum of their areas is 130Π 𝑐𝑚 and the, distance between their centres is 14 cm. Find the radii of the circles., (a.) 2 cm, 9 cm, , (b.) 4 cm, 7 cm, , (c.) 3 cm, 9 cm, , [1 mark], , (d.) 3 cm, 11 cm, , 9. An event having only one outcome of the random experiment is called a/an ______., [1 mark], (a.) Elementary event, , (b.) Compound event, , 10. Find the greatest number which divides 304 to leave a remainder of 4 and which also, divides 298 to leave a remainder of 4., (a.) 7, , (b.) 8, , [1 mark], (c.) 5, , (d.) 6

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2, , 11. Assertion: If both zeroes of the quadratic polynomial 𝑥 − 2𝑘𝑥 are equal in magnitude, but opposite in sign then the value of k is 2., , [1 mark], 2, , Reason: Sum of zeroes of a quadratic polynomial 𝑎𝑥 + 𝑏𝑥 + 𝑐 is -b/a., (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false., (d.) A is false but R is true., 12. The pair of equations x = a and y = b graphically represent lines which are:, (a.) Parallel, , (b.) Intersecting at (b,a), , (c.) Coincident, , [1 mark], , (d.) Intersecting at (a, b), , 13. What is the distance between two points 𝑃(𝑥1, 𝑦1) and 𝑄(𝑥2, 𝑦2) ?, , [1 mark], , 2, , 2, , (b.), , (𝑥2 + 𝑥1) + (𝑦2 + 𝑦1), , 2, , 2, , (d.), , (𝑥2 + 𝑥1) − (𝑦2 + 𝑦1), , (a.), , (𝑥2 − 𝑥1) + (𝑦2 − 𝑦1), , (c.), , (𝑥2 − 𝑥1) − (𝑦2 − 𝑦1), , 2, , 2, , 2, , 2, , 14. A and B are respectively the points on the sides PQ and PR of a triangle PQR such that, PQ = 12.5 cm, PA = 5 cm, BR = 6 cm, and PB = 4 cm. Find the relation between AB and, QR., , [1 mark], , (a.) AB = QR, , (b.) AB || QR, , 0, , (c.) 2AB = QR, , (d.) AB is not Parallel to QR, , 0, , 15. 𝑠𝑖𝑛 (45 + θ) − 𝑐𝑜𝑠 (45 − θ) is equal to _____., (a.) 2 𝑐𝑜𝑠 θ, , (b.) 0, , (c.) 2 𝑠𝑖𝑛 θ, , [1 mark], (d.) 1, , 16. The area of the sector of a circle of radius 10.5 cm is 69.3 sq cm . Find the central angle, of the sector.(In degrees), 0, , (a.) 69, , 0, , (b.) 66, , [1 mark], 0, , (c.) 72, , (d.) None of the above, , 17. If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability, that the digit is even is (a.) 4/9, , (b.) 5/9, , [1 mark], (c.) 1/9, , (d.) 2/3

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18. Determine the number nearest to 110000 but greater than 100000 which is exactly, divisible by each of 8, 15 and 21., (a.) 109,200, , [1 mark], , (b.) 109,020, , 19. On comparing the ratios, , 𝑎1, 𝑎2, , ,, , 𝑏1, 𝑏2, , and, , (c.) 109002, 𝑐1, 𝑐2, , (d.) 110800, , , find out whether the lines representing a pair, , of linear equations are consistent or inconsistent: 2x – 3y = 8 ; 4x – 6y = 9, (a.) Consistent, , (b.) Inconsistent, , (c.) Semiconsistent, , [1 mark], , (d.) None of these, , 20. The point which divides the line segment joining the points (7,-6) and (3,4) in ratio 1:2, internally lies in the:, (a.) I quadrant, , [1 mark], (b.) II quadrant, , (c.) III quadrant, , (d.) IV quadrant, , SECTION B, Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted., 1. If in two triangles, corresponding angles are equal, then their corresponding sides are, in the _______ ratio and the two triangles are _________., , [1 mark], , (a.) Equal, similar (b.) Unequal, similar (c.) Equal, dissimilar (d.) Unequal, dissimilar, 2. Evaluate, , 0, , 𝑐𝑜𝑠 45, , [1 mark], , 0, , 𝑠𝑒𝑐 30 + 𝑐𝑜𝑠𝑒𝑐 30, , 3 2− 6, 8, , .(a.), , 0, , (b.), , 3− 6, 8, , (c.), , 2− 6, 8, , (d.), , 3 2− 6, 4, , 3. If θis the angle (in degrees) of a sector of a circle of radius r, then the area of the, sector is?, , (a.), , 2, , π𝑟 θ, 360, , [1 mark], , (b.), , 2, , π𝑟 θ, 180, , (c.), , 2π𝑟θ, 360, , (d.), , 2π𝑟θ, 180, , 4. Find the probability of getting a tail when a coin is tossed., (a.) 0, , (b.) 0.5, , (c.) 1, , [1 mark], (d.) 0.25

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5. Without actually performing the long division, state whether 64/255 will have a, terminating decimal expansion or a non-terminating repeating decimal expansion., [1 mark], (a.) Terminating, , (b.) Non Terminating, , 6. Two rails are represented by the equations x + y = 14 ; x - y = 4. Where will the rails, cross each other?, (a.) x = 9, y = 9, , [1 mark], (b.) x = 7, y = 7, , (c.) x = 9, y = 5, , (d.) x = 6, y = 8, , 7. Find a relation between x and y such that the point (x,y) is equidistant from the point, (3,6) and (–3,4)., (a.) x+3y+5=0, , [1 mark], (b.) 3x+y-5=0, , (c.) 3x-y+5=0, , (d.) x-3y+5=0, , 8. In the above figure, if angle A = angle C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4, cm, then find the lengths of PD and CD., , [1 mark], (a.) 5 cm, 7 cm, , (b.) 5 cm, 2 cm, , (c.) 4 cm, 6 cm, , (d.) 4 cm, 7 cm, , 9. The area of the largest triangle that can be inscribed in a semicircle of radius r units, is?, , [1 mark], 2, , (a.) 𝑟 sq.units, , (b.), , 2, , 𝑟, 2, , 2, , 2, , sq.units, , (c.) 2𝑟 sq.units, , (d.) 2𝑟 sq.units, , 10. If the rational number a/b has a terminating decimal expansion, what is the condition, to be satisfied by b, where m and n are some non-negative integers?, 𝑚, , 𝑛, , (a.) 𝑏 = 2 × 5, , 𝑚, , 𝑛, , (b.) 𝑏 = 3 × 5, , 𝑚, , 𝑛, , (c.) 𝑏 = 2 × 2, , [1 mark], 𝑚, , 𝑛, , (d.) 𝑏 = 2 × 4

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11. Assertion: Aftab tells his daughter, “Seven years ago, I was seven times as old as you, were then. Also, three years from now, I shall be three times as old as you will be.”, Hence, 42 and 8 are the ages (in years) of Aftab and his daughter, respectively., Reason: In the substitution method, a pair of the linear equation gets transformed, into one linear equation with only one variable, which can then easily be solved., [1 mark], (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false., (d.) A is false but R is true., 12. Find the distance between the points (-5,7) and (-1,3)., (a.) 2 2, , (b.) 3 2, , [1 mark], , (c.) 2, , (d.) 4 2, , 13. In the above fig, ABC and AMP are two right triangles, right-angled at B and M, respectively. Then CA/PA = __________ ?, , [1 mark], (a.) BC/MP, , (b.) BC/AP, , (c.) AC/AP, , (d.) None of these, , 14. Assertion: Let x be a rational number whose decimal expansion terminates. Then x, can be expressed in the form, p/q where p and q are coprime, and the prime, 𝑛, , 𝑚, , factorization of q is of the form 2 × 5 , where n, m are non-negative integers., Reason: The decimal expansion of the rational number x in the form p/q terminates., [1 mark], (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false.

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(d.) A is false but R is true., 15. Assertion: To solve a pair of linear equations by elimination method, like x – 6 = −6 and, x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right, side of the equation., Reason: In the elimination method, when the coefficients of one variable are, opposites you add the equations to eliminate a variable and when the coefficients of, one variable are equal you subtract the equations to eliminate a variable., , [1 mark], , (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false., (d.) A is false but R is true., 16. The points A (–1, 0), B (3, 1), C (2, 2), and D (–2, 1) are the vertices of a parallelogram., State true or false., , [1 mark], , (a.) True, , (b. ) False, 0, , 17. Evaluate, , .(a.), , 0, , 0, , 𝑠𝑖𝑛 30 + 𝑡𝑎𝑛 45 − 𝑐𝑜𝑠𝑒𝑐 60, 0, , 0, , [1 mark], , 0, , 𝑠𝑒𝑐 30 + 𝑐𝑜𝑠 60 + 𝑐𝑜𝑡 45, , 43−24 3, 11, , (b.), , 41−24 3, 11, , 18. Assertion: The solution of equations, , (c.), 5, 𝑥−1, , +, , 1, 𝑦−2, , 43− 3, 11, , = 2 and, , (d.), 6, 𝑥−1, , −, , 3, 𝑦−2, , 40−24 3, 10, , = 1 is 4 and 3., , Reason: After reducing the equations to a pair of linear equations, it can be evaluated, by the most common algebraic methods like substitution or elimination to find the, solution of the given equations., (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false., (d.) A is false but R is true., , [1 mark]

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19. If the lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, find the length, of the sides of the rhombus., (a.) 11 cm, , [1 mark], , (b.) 10 cm, , (c.) 20 cm, , (d.) 25cm, , 20. Assertion: An equation 5x +7 =0 is not a linear equation in two variables., Reason: An equation that can be written as ax + by + c=0 that has a and b as non-zero, real values, is called a linear equation in two variables., , [1 mark], , (a.) Both A and R are true and R is the correct explanation of A., (b.) Both A and R are true but R is not the correct explanation of A., (c.) A is true but R is false., (d.) A is false but R is true., , 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 - Mr. Colin is a Navy officer who is tasked with planning a coup on the enemy at a, certain date. Currently he is inspecting the area standing on top of the cliff. Agent Dev is on a, chopper in the sky. When Mr. Colin looks down below the cliff towards the sea, he has, Bhawani and Amar in boats positioned to get a good vantage point. Bhawani's boat is behind, Amar's boat. Following angles have been measured :, From Colin to Bhawani : 30°, From Dev to Colin : 60°, From Amar to Colin : 60°, Find the answers to the following questions, assuming that the height of the hill is h.

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1., , Which of the following is a pair of angle of elevation?, ◦, , ◦, , (a) (∠𝑎 , ∠𝑒 ), , ◦, , ◦, , ◦, , (b) (∠𝑏 , ∠𝑒 ), , [1 mark], ◦, , (c.)(∠𝑐 , ∠𝑑 ), , ◦, , ◦, , ◦, , ◦, , (d)(∠𝑎 , ∠𝑓 ), , 2. Which of the following is a pair of angles of depression?, ◦, , ◦, , (a) (∠𝑎 , ∠𝑒 ), , ◦, , ◦, , ◦, , (b) (∠𝑏 , ∠𝑒 ), , ◦, , (c.)(∠𝑐 , ∠𝑑 ), , [1 mark], (d)(∠𝑎 , ∠𝑓 ), , 3. If the angle of elevation of Amar to Colin is 60°, what is the distance of Amar's boat, from the base of the hill ?, , (a), , 3, 2, , ℎ, , (b), , [1 mark], ℎ, 3, , (c.), , 2ℎ, , (d) 3ℎ, , 3, , 4. If the angle of depression of Colin to Bhawani is 30°, what is the distance of Amar's, boat from the Bhawani's boat?, , (a), , 3, 2, , ℎ, , (b), , ℎ, 3, , [1 mark], , (c.), , 2ℎ, , (d) 3ℎ, , 3, , 5. If the angle of depression from Dev to Colin is 60°, what is the height of Dev from the, base of the hill?, (a) h, , [1 mark], (b) 2h, , (c.) 3h, , (d) 4h, , Case Study 2 - Janice, a class 10 student was studying the concept of probability. She saw, her father playing cards one day and asked him to explain it to her. He told her, it consists of

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52 cards which are divided into 4 suits of 13 cards each spades, hearts, diamonds and clubs., Clubs and spades are of black colour, while hearts and diamonds are of red colour. The cards, in each suit are ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2. Kings, queens and jacks are, called face cards. She then randomly draws a card from a well shuffled deck of cards., On the basis of the above information, answer the following questions., , 1., , What is the probability that the card drawn is a red king?, (a), , 2, 52, , (b), , 4, 52, , (c.), , 8, 52, , [1 mark], (d) None of these, , 2. What is the probability that the card drawn is a black jack?, (a), , 2, 52, , (b), , 4, 52, , (c.), , 8, 52, , (d) None of these, , 3. What is the probability that the card drawn is a queen?, (a), , 2, 52, , (b), , 4, 52, , (c.), , 8, 52, , [1 mark], (d) None of these, , 4. What is the probability that the card drawn is a red ace?, (a), , 2, 52, , (b), , 4, 52, , (c.), , 8, 52, , [1 mark], (d) None of these, , 5. What is the probability that the card drawn is a black ace?, (a), , 2, 52, , (b), , 4, 52, , (c.), , 8, 52, , [1 mark], , (d) None of these, , x-x-x- End of Question Paper -x-x-x, , [1 mark]

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SAMPLE QUESTION PAPER - 2, Class – X, Session -2021-22 (TERM 1), , Time Allowed: 90 minutes, , Subject- Mathematics, , Maximum Marks: 40, ANSWER KEY, , Section A, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., , B, A, D, B, C, C, A, D, A, D, D, D, A, B, B, C, A, A, B, D, , Section B, 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., , A, A, A, B, B, C, B, B, A, A, D, D, A, B, D, A, A, D, B, A, , Section C, 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., , B, C, B, C, C, A, A, B, A, A