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CBSE Class 10 Sample / Model Paper 2024 : : PERIODIC TEST 1 MATHS CLASS 10

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DELHI PRIVATE SCHOOL - DUBAI tf~l\ UNIT TEST I (2024-2025) UT1 XMA MN 2024-25 MATHS ~ MAX MARKS: 45 marks UU I.\J\I TIME: 90 mins GRADE-X General Instructions: 1. This Question Paper has 6 Sections A-F. 2. Section A has 6 MCQs carrying 1 mark each. 3. Section B has 4 questions carrying 02 marks each. 4. Section C has 4 questions carrying 03 marks each. 5. Section D has 2 questions carrying 05 marks each. 6. Section E has 1 case based integrated units of assessment 04 mark, with sub- parts of the values of 1, 1 and 2 marks each respectively. 7. Section F has 1 questionfor RAC carrying 5 marks. 8. All Questions are compulsory. Howeve1 , an internal choice in 1 Question of 2 marks, 1 Question of 3 marks, 1 Question of 5 marks has been provided. An internal choice has been provided in the 2 marks Question of Section E . 9. Draw neat figures wherever required. s. Question Marks No. 1 SECTION A (Section A consists of 6 questions of 1 mark each) If two positive integers a and b are written as a = x3 y2 and b = xy3, where x and y are prime numbers, then the HCF (a, b) is: (a) xy 2 (b) xy2 (c) x3 y 3 1 (d) x2 y2 Which of the following is not the graph of a quadratic polynomial? 1 Page 1 of 5 I y (b) X'-u X X' ( '' y y (d) X' I i\ -X \ ( r- I\ X' ( Y' 4 X Y' (b) 5 (c) 7 (b)l2.12p m 1 (d) 18 (c) 12.11 pm (d) none of these The two zeros in the below shown graph are y I ; . I ~-: ;t . ~ . . -3 X' ::_.:i ,;; l .'.I (a) 2,4 6 I Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for the first time? (a) 12.20 pm 5 V The value of k for which the lines 5x + 7y = 3 and 15x + 2 ly = k coincide is: (a) 9 ! -X Y' (c) 3 " I Y' t I y (a) ~.. -1 _ ~ :0 I .: . . ~ ...... . . :- .\; ::c:2. ' . - :'/ ~.\~: :. (b) -2,4 ' _5' .. , .:: .:: 3 :, J .. ..... 1 . X i _/ ..... . ( c) -8,4 (d) 2,-8 In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices. Assertion (A): For no value of n, where n is a natural number, the number 6 ends with the digit zero. Page 2 of 5 1 Reason (R): For a number to end with digit zero, its prime factors should have 2 and 5. I (a) Both A and Rare true and R is the correct explanatio n of A. (b) Both A and R are true but R is not the correct explanatio n of A. ( c) A is true but R is false. ( d) A is false but R is true. SECTION B (Section B consists of 4 questions of 2 marks each) 2 The HCF of 2472, 1284 and a third number N is 12. If their LCM is 2 3 x 32 x 5 x 103 x 107, then find the number N. 7 '( 8 9 \ 10 (OR) OR Find HCF and LCM of 404 and 96 and verify that HCF x LCM = Product of the two given numbers 2 2 If a and ~ are the zeros of a polynomia l f(x) = px - 2x + 3p and a+ ~ = a~, then find the value ofp. 2 Ram is walking along the line joining ( 1, 4) and (0, 6). Rahim is walking along the line joining (3 , 4) and (1, 0). Represent the above situation graphically and find the point where the lines cross each other. 2 Do the equations 4x + 3y- 1 = 5 and 12x + 9y = 15 represent a pair of coincident lines? Justify your answer. 2 SECTION C (Section C consists of lb uestions of 3 marks each) 11 12 Given that 2 is an irrational, prove that (5 + 3 2) is an irrational. 3 2 If one zero of the quadratic polynomia l (k2 + k) x + 68x + 6k is reciprocal of the other, find k. 3 (OR) -~~,3 3 If sum of the zeroes of 5x2 + (p + q + r) x + pqr is zero, then find p + q + 13 3 r3. Given the linear equation 2x + 3y- 12 = 0, write another linear equation in these variables, such that. geometrica l representa tion of the pair so formed is (i) (ii) (iii) 3 Parallel Lines Coinciden t Lines Intersectin g lines I ij l Page 3 of S !r ./ ,. 14 15 Find the zeroes of the polynomial {3 x2 + IOx+ 7'13.A lso verify the relati onshi p betwe en the zeroes and their coefficients. 3 SECTION D Section D consists of one uestion of 5 marks Three sets of English, Hindi and Mathematics books have to be stack ed in such a way that all the books are stored topic wise, and the heigh t of each stack is the same . The numb er of Engli sh books is 96, the numb er of Hindi books is 240 and the numb er of Math emati cs books is 336. Assuming that the books are of the same thick ness, determ ine the numb er of stacks of English, Hindi and Math emati cs books . Find the total numb er of stacks . 5 (OR) Find the greate st numb er that will divide 445,572 and 699 leaving remai nders 4, 5 and 6 respectively. Justify 16 17 Draw the graph s of the equations x - y + 1 = 0 and 3x + 2y -12 = 0. Deter mine the coord inates of the vertices of the triangle formed by these lines and the x-axi s, and find the area of the triangular region formed. 5 5 SECTION E (Case Study carries 4 marks) Case stud - based uestions are com ulsor . A Math emati cs Exhibition is being conducted in your School and one of your friends is makin g a mode l of a factor tree.He has some diffic ulty and asks for your help in comp leting a quiz for the audience.Observe the follow ing factor tree and answ er the follow ing: l 1 2 (i) What will be the value of x? ii) iii) What will be the value of y? What will be the value of z? OR (OR) Write the prime factorization of 13915 2 iii) Page 4 of 5 18 SEC TION F (RAC , Carries 5 marks) 1980 from Sriha rikot a Rang e (SHA R), SL V-3 was succe ssful ly launc hed on July 18, , thereby maki ng India the sixth mem ber when Rohi ni satell ite, RS-I , was place d in orbit V-3 empl oyed an open loop guida nce of an exclu sive club of space -farin g nations. SL le in flight along a pre-d eterm ined (with store d pitch progr amm e) to steer the vehic 3 proje ct show ed the way to trajec tory. The succe ssful culm inatio n of the SLVV), Polar Satellite Laun ch Vehi cle Adva nced Laun ch vehic le proje cts vehicle (ASL ch Vehi cle (GSL V). (PSL V) and the Geos ynch ronou s Satellite Laun Mars missi on, starts work ing on the Rahu l, study ing Grad e X who is inspired by ISRO When he has been cond uctin g the maki ng mode l of rocke t on his school project. ath of the rocke t with respe ct to heigh t exper imen t, he plots the graph for the trajectory/p of the rocke t from the groun d level and time. ! I I - I - I Y ~ I~ != i I /' : - / I I ~ I I \ I ; ; -... I I It \ 0 --- I \ \ ~v L , i I - I ..... " Im> -~ - ~ \ l I I ~ ! .n,7 l uf-lit 1 - ' r : -- ing quest ions. Base d on the abov e information, answer the follow the height of the rocket above the (i) What will be the shape of the graph representing whic h repre sent the ground and write the polyn omia l in stand ard form trajectory/Path of the rocket? . (ii) Find the numb er of zeroe s of the graph given attain ed durin g the expe rimen t t (iii) What is the maxi mum height that his rocke based on the given graph ? exper imen t from the top of one (iv) Suppose assum e that he is doing the same the rocke t is repre sente d by building and the graph of the trajectory/path of 2 h(t) = 24t2 -4lt + 12. h(t) = 24t2 -4It + 12. Find the zeroes of the graph s Page 5 of s

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