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HOLY CHILD SCHOOL, KALNA Pre-Board Examination (2024 - 25) Subject - Mathematics Class - X Maximum Marks: 80 Time allowed: Three hours Answers tothis paper must be written on the paper provided separately. Candidates are allowed an additional 15 minutes for only reading the paper. They must NOT start writing during this time. B Attempt allquestions from Section Aand any four questions from Section adjucent to the rest and Allworking, including rough work, should be done on thesame sheet as, of the answer. Omission of essential working willresult inloss of marks. The intended marks for questions or parts of questions are given in brackets [J. Mathematicaltables and graph paper are provided SECTION - A(40marks) (Attempt all questions from this Section) Question-] Choose the correct answer to the question from the given options: [15] )lmatrix P isof order 2x 1and matrix Qis order 1x 2 and I is the Identity matrix of order 2, then which of it is Not possible b) QPI a) PQI d) QP c) PQ ii) Bishakhpur hased an article for l680 including 12% GST. Then amount of SGST paid is a) ? 90 b) 100.80 c) 180 d) 201.60 i) Inthe given figure, if z0BD= 25 , then ZBCD will be a) 80 b) 100 c) 110 iv) The mean proportional between 3V3 and 9V3 is c) 2V3 b) 6V3 a) 3 d) 115 d) 9 250 D v) The roots of the quadratic equation 2x + 8x =1 are a) Real, Distinct and irrational b) Real, Equal and rational ) Imaginary d) Real, Equal and irrational Page 1 of 6 vi) Meghadrideposited 800 per month for 1 years in a recurring deposit account for which thebank navs 6% p.a , then the interest received by him is a) 684 b) 468 d) c)?648 864 vii) Maximum and minimum value of xfor the ineauation 11x -4<15x + 43 13x+14,XE2 a) 5 and- 2 b) 2 and d) - 2 and 5 c) 5 and -1 5 viii) The first negative terms of AP: 105, 101, 97, a) -4 b) -3 d) 1 c)-2 ix) A(1,4), B(4, 1)and C(x, 4) are the verices of AABC. Ifthecentroid is G(4, 3), then xis equal to a) 1 b) 2 d) 9 c) 7 x) Abox contain 25 balls bearing numbers 1, 2,3,........s. A ballis drawn at random, then the probability that the mumber7 on the ball is a perfect square is 9 c a) b) 25 20 d) xi) Assertion(A): If the length of shadow of aperson is equal to his height, then the angle of elevation of the sun is 45 Reason(R): For any right angled triangle sin = Perpendicular Hypotenuse explanation of (A) (a) Both Assertion (A) and Reason(R) are true and (R) is the correct correct explanation of (A) (b) Both Assertion (A) and Reason(R) are true but (R) is the not (c) Assertion(A) is true but Reason (R) is false (d) Assertion (A) is false but Reason (R) is true (x+ 2) is xii) The remainder when 3x +x-3x +14 is divided by d) 10 c) 2 b) 1 a) 0 diameter is? its curved surface area is 880 cm', then its xi) If the volume of a cylinder is 6160 cm' and d) 28 cm c) 21 cm b) 14 cm a) 7 cm xiv) Statement 1: -1, 3, 9, 27,........is in Geometric Progression(G. P). Progression(G. P) cannot be l. Statement 2: The common ratio of Geometric Which of the following is true? a) b) c) d) Only 1 Only 2 Both l and 2 Neither 1nor 2 premium xv) Calculate the amount required to invest in 400, Rs.20 shares available at 50% b)10000 d) 14000 c) 12000 a) 8000 Page 2 of 6 Question-2 Find the order of matrix Xand hence find matrix X. (a) Given (b) Aman deposit Rs.1600 per nmonth in arecuring deposit account for 3years. If he receives Rs.64704 at the time of maturity,Find () Interest received on Maturity (i) Rate of interest paid by bank. (c) From the given igure find (i) ZACE (i) angle subtended by arc AE at the centre. C ? B I10 \D 1309 [4+4+4| E Question-3 (a) Case-Study: Aship is sailing very close to the lighthouse antd a right-angled triangle is formed by the light house, line joining the ship to the base of the lighthouse and the line joining the ship to the top of the lighthouse. At aparticular instant, the hypotenuse ofthe right-angled triangle so formed is 4m more than thrice the shortest side and the third side is lm less than the hypotenuse. (i) Taking the shortest side as x m, form a quadratic equation of the given situation. (ii) Identify thenature of roots of the quadratic equation so formed. (ii) Find the length of the shortest side of the right-angled triangle formed. (b) Aarivbought medicines costing 1050.with GST @8% and a laptop bag costing 2500 at a discount of 10% with GST @12%. ()Calculate the total amount of GST paid (ii) Total bill amount which Aariv has to pay. (c) Use2mn Graph paper for this question (Take lcm = lunit on both axis). (i) Plot point P(-4, 4) and Q(2, 2) (ii) (i ) (iv) Reflect P and Q in the origin to P' and Q'. Give geomerical name of the figure PQP'Q and find its area, (v) Find the equation of the line PP'. Find the slope of the line PP'., [4+4+5] xER 2)+ + 4(r 2(x-)-1s4(+i)< (c) (3+3+4) (0) =|2 A chosen (3+3+4) lamp (3+3+4)cach0. the 120-125 vertical their letter shares 10 to 4 factorisc Rohitof + premium perpendicular 2y find graph: the kXmarket, 10 a then that of 0 X# ; when Hence bottom line the a probability Rohan, metres). at 115-120 share from p.a available are the k. 16 and of 6%than in Mode -4). =0 to x 6 nearest value 2xparallel find savingspaying top 2x 6the alphabet. post 5 D(2, shares morc + the estimate B , + Find the 2y 41. line: in lamp and x their100company 500 of 110-115 and find is be 4 + questions) marks) depression 'ACROPOLIS'. 4x number 18 term origin English 1) the to and invest A +(k+3), and is 6x+x-5 C(4, are when income and = most data a through answers 0 5Xrcal 8), B) 40 to p.a in = of building FOUR middle of 4 grouped order Rohit letters + ( a y),B(S, + paying16% 105-110 annual angle B on 2y passing)x x: respectively. (A all SECTIONword 1 in ANY than 13 for whose sct + 10 and the the (Note: kx following solution account Rohit's 4k solve more A(x, AC between (Attempt linesline ( building, of First company A.P + question. post where diagonal letters proportion, +9x (ii) Demat RS000 of If the the 60 distance of equation 20%. lamp A. the100-105 which and Consonant the terms plot high 2x' of parallelogram 8 a a invested = thisof of in of Co-ordinate the and opencd Histogram of expression B 45m30 completely. Equation from for the factor 25 sum discount of for and horizontal of be incquation ofk all properties chosen a to height paper (in find Rohan lbs) Weight (ii) certain Rohan No.of students of found value a of top Hence a is Vowel a a sum Graph (x+2) Construct whileat Investment. is is (i) (ii) theare (i) (ii) and vesteaa the available the letter ABCD Using (a) Find the From Solve Findother. Rohit 20% Find: postFind (i) Use Ouestion-6 Ouestion-7 Question-5 Question-4 If A is (a) (b) (c) (a) (c) (b) (a) (b) diameter. Z0Tp PR with(iv) circle ZSTP the(ii) to ZSQR tangent S the(ii) are ZSPR QT (i) andfind ST 64 , figure = zPRS given theGiven In (c) R (3+3+4) 640 P distributed the andthe be cmget to 3 will is is It conewh0 ice-cream. cachchildren real has 0 = 1) (8k+ + 4)x the (80, 160) 720 workers C.f. + of (2k with radius of 152) number + filled the (79 k)x (60,14O) is If following: the cm tops. (4 find (50,124) equation 8 hemispherical height 100y (40, / then and cm, quadratic answer cm 9 is 9 withice-cream and radius the cones below that of so cqual the container given k, of in of height and equal roots. Ogive children value cvlindrical maximum the 1Ce-cream. the among Study Find Ouestion-8 A (b) (a) (c) ofNo. (30, 62)o 8 (20, 327 30 20 () day (3+3+4) the Find random, 2, 3 OR at wage drawn per Rs.60 (iii) Perfect square Quartile Wages is is ball wage Lower A standard 3,.........,20. (iii) wage the if Median under-paid1, is: from ball2 of theMultiple numbered on number (i) (ii) workers are who 20 A box contain that the probability number Prime (i) of workers balls 2010.12 number No.of (iTotal iv (a) Ouestion-9 4 (b) In the given figure, BF and CE are two chords produced to meet externally at A. If AB =1Sem, AE 9cmand AF= 12cm, Find (i) AC(ii) Ar(AABC): Ar(AAEF) E A B (a) Use Geometrical instruments for this question: () (ii) Construct AABC, BC = 5cm and AB = AC=7cm Construct locus of points equidistant from B and C. (ii) (iv) Construct locus of points which moves such that it is always 2cm from point A. Mark point Pwhich satisfies condition (ii) and (ii). Hence construct a circle passing through P, B and C. (3+3+4) Ouestion-10 (a) Find the sum of first 34 terms of the A.P, aj, az, az,a4. if it is known that a, t a_ t a10 + a1s t az0 + azs t a30 t a34 = 1000 (b) Prove the identity:Vtan?0 + cot20 + 2 = sece cosece (c) Case-Study: Adventure camps are the perfect place for the students topractice decision making for themselves without parents and teachers guiding their every move. Some students of Holy Child School reached for adventure at Jim Corbett National Park. At camp, the waiter served some students with a welcome drink in a cylindrical glass and some students in a hemispherical cup whose dimension are shown below. After that they went for ajungle trek. The jungle trek was enjoyable but tiring. As the dusk fell, it was time to take shelter. Each group of 4students was given a canvas area 551 m. Each group had to make a conical tent to accommodate all four students. It is assumed that 1 m'of canvas may be wasted for cutting and stitching. The radius of the tent needs to be 7m. = d= 7cm 8cm d= 7cm 7m r= h Based on the above information, Answer the following questions: Find the volume of the cylindrical glass. (1) Find the volume of the hemispherical cup. (i) Findthe heightof the conical tent. (i) Find the amount of air spaceavailable for each student inside theconical tent. (iv) ****** ****** *******************k * * ** ** * ND%* * * ** * ** (3+3+4)
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