Mathematics Exam Paper 18 (E) March 2024 PDF

This Question Paper contains l2 printed pages. (, _ 2\a235q (Section -A, B, C & D) SI.No. 079757 ffi 18 (E) (]\{ARCH,2024) Time : 3 HoursJ...

This Question Paper contains l2 printed pages. (, _ 2\a235q (Section -A, B, C & D) SI.No. 079757 ffi 18 (E) (]\{ARCH,2024) Time : 3 HoursJ fMaximum Marks : 80 Instructions : 1) Write in a clear legible handwriting. 2) This question paper has four Sections A, B, C & D and Question Numbers from 1 to 54. 3) All Sections are compulsory. Internal options are given. 4) The numbers to the right represent the marks of the question. 5) Draw neat diagrarns wherever necessary. 6) Nerv sections should he written in a new page. Write the answers in numerical order. 7) Calculator. digital watch or smart watch is not alrowed. SECTION-A I Answer the follo*ing as per instruction given (Questions : 1 to 24) (l mark each). 124l I Choose the correct option from the question given below (Questions : 1 to 6). (l markeach). 1) For a given pair of linear equations in two variables, if ar * L then equation has a2 b2 solution. tu (A) One (B) Two (C) Three (D) ]rlo solution HUH67 I s-l716 (P.T.O.)  s-1716 2) Ifthetwo roots ofquadratic equation ax' -r bx + c = 0 (a * 0) are real and equal then tu (A) - 4ac 0 (D) b2 -4ac*o 3) For the AF : 4, 10, 16, 22,....... commo{l difference (d) is tll (A) 8 (B) s L@). 6 (D) t2 4) The distance between the points (0, 5) and (-5, 0) is _. tU (A) s qB) sJz (c) zJi tn) 10 5) sec' 0 -tanz 0 - tll (A) 0 L€rx' 1 (c) -1 (D) 2 6) For any data [ - lJ and Z: 25 then M : _. tu a. ,.I/.) 2s (B) -2s (c) s (u) -s Fill in the blanks with correct option as to make the given statement correct : (Questions : 7 to 12). (1 mark each). 7) Z +zJi is a/an number. (rational. irrational, negative integer) 11] (t t__t 4 z\ 8) Thesumofzeroesofquadraticpolynomial 4xz -3x -7 is_. [+'l'gJ tll 9) When a coin is to.s-sed /\ three times, the total number of possible outcomes \ is (4, 6 ,18)i tll -. HUH67 ) 18 (E)  s-1716 10) tan?.cot0 = (-1,0J) tU 11) A circle can have parallel tangents at the most. (1,2,3) IU L2) Median of -2,-3, 0, 1,3,2.7 is _. (-2, t,3) tu r State True or False for statements given below : (Questions : 13 to L6). (1 mark each). 13) H.C.F. of 17,23 and29 is 1 tU ,. t4) Number of zeroes of y = p(r) is 2 from figure given below tU _r x o v '- 15) Ifthepairoflinearequations intwovariables are 2x*3y -12 and3x+2y -l$ thenx*y-s. tU ,-16) The prohability of an impossible event is zero (0). tu HUH67 3 18 (E) (P.TO.)  s-l716 Answer the following in one sentence or one word or number (Questions : 17 to 20). (1 mark each). 17) a,2a,3a, 4a,... is an Arithmetic Pro_eression or not? tu I 18) How many tangents can be drawn to a circle passing through a point lying lirside the circle? IU p ,, 19) A die is thrown once. What is the probabilitv of not gettins number 6? UI 20) Find the mean of First 11 Natural rniumbers. tll Match the pairs : (Questions : 21 to i4). (1 nrerk errr-ir 1. lll A B 21) Base area of hemisphere (a) 2rrlt 22) Volume of a 5 rupee coin (b) ftr' (c) rr'h A B 23) Length of an arc of a sector of angle B (a) nd. 24) Circumference of a circle (b) nr nr0 (c) 180 HUH67 4 18 (E)  s-1716 SECTION - B tr Ansn'er the following briefly with calculation : (Any 9) (Questions : 25 ta 37) (l marks each). U8l ,::ii ,Find the zeroes of the quadratic polynomial x2 + 7x -l 1 0. t21 26) Find a quadratic polynomial whose sum and product of its zeroe, ur. -|44,nO ,L respectively 121 27) Find the roots ofthe quadratic equation *' - 3* - 10 = 0 by factorisation method. 28) Find the 10'h term of the AP : 2. 7. 1:.. t2l 29) Find the sum of the f-rrst 1,000 positive integcrs" lzt 30) Find the distance bet*,een the points (2,3) and (4" i) using distance fonnula. 31) Findthevaluesofyforr,vhichthedistancebetrveenthepoints?(,2,-3)andQ(10,y) is 10 units. l2l 5..r' {Di. scrrr 32) If sin 0 = y5, calculate cos 6 and tanl. \j\ r3i I ', l2l ui:, t"tr t3 '-@*" i: \ ,t g iJq 'trt- i ; -..-( 33) Evaluate: l2l sin 60o cos 30o + sin 3 0o cos 60o HUH67 5 18 (E) (P.To.) g1.  s-1716 34) A tower stands vertically on the ground. From a point on the -eround, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60o. Find the height of the tower. I21 35) 2 cubes each of volume 125 cm3 are joined end to end. Find the volume of the resulting cuboid. tzt 36) A juice seller was seruing his customers using glasses as shown in the figure. The inner diarneter of the cylindrical giass was 5 cm. but the bottom of the glass had a hemispherical raised portion which reduced the capacitl' of the glass. Ifthe height ofa glass was l0 cm. Find the apparent capaciq' ofthe 91ass. ( Use t = 3. 14).t2I Figure 37) Find Median for the classical distribution data when n: 53, l: 60, cf:22, f:7 andh:10. l2l 6 18 (E) HUH67 \ 6 s-1716 a SBCTION.C S l I ,\nsn.er the folprwing questions any 6 from 38 to 46. (9 questions). (3 marks each). e I 38) Solve the follorving pair of linear equations by the substitution method. t3l 2x +3Y =t1 2x-4y=-24 A t 39) Solve the following pair of linear equations by elimination method. t3l 3x-5y-4=0 9x -2y +7 40) Find the sum of the first 40 positiye integers divisible by 7. t3l 11 ) Find the coordinates of a point A. ri.here AB is the diameter of a circle whose.entre is (2. -3) and B(1, 4) l3I lZ) Find the coordinates of the points of trisection of the line segment joining (4, -l) and (-2, -3). t3l 43) Prove that "The lengths of tangents drawn from an external point to a circle are equal. \ o L (rz -- \> \c t3l 441' Trvo concentric circles are of radii 41 cm and 40 cm. Find the length of the chord 7 l of the larger circle which touches the smaller circle. t3l o A HUH67 7 rl 18 (E) (P.TO.) I L "l \  s-1716 45) The following table shows the ages ofthe patients admitJed in a hospital during a year: rA t3] Age (inyears) 5-15 15-25 25-35 35-45 45-55 55-65 Number ofpatients 6 i1 21 23 t4 5 Find the mode of the data given above. 46) A Pigry bank contains hundred 50 p coins, fifly { | 66ins, twenty { 2 coins and ten t 5 coins. If it is equally likely that one ofthe coins wtll fall out when the bank is tumed upside down, what is the probability that the coin r D Will be a 50 p coin? ii) Will not be a { 5 coin? iii) Willbeatlcoin? SECTION - D Answer the following questions any 5 from {7 to 54 (8 Questions) with calculation : (4 marks each). I20l 47) State Basic proportionality theorem and prove it. t4l 48) A girl ofheight 90 cm is walking away from the base of a lamp-post at a speed of l.2mls.Ifthe lamp is 3.6 m above the ground, find the length of her shadorv after 4 seconds. t4l 49) The altitude ofa right triangle is 7 cm less than its base. If the hl,potenuse is 13 cm, find the other trvo sides. t4l HUH67 I 18 (E).6 s-1716 a 50) A manufucturer of TV sets produced 600 sets in the third year and 700 sets in the ]l seventh year. Assuming that the production increases uniformly by a fixed number every year, find : [a] ,) the production in the l't year. ii) the production in the 10'h year. iii) the total production in first 7 years. )n is 51) The table below shows the daily Expenditure on food of25 households in a localtty. t4I l--- ]l Daily Expenditure 100-150 150-200 240-254 250-300 300-350 (in t) Number of 4 5 t2 2 2 Households Find the mean daily Expenditure on food by a suitable method. n :ij 52 ) If the median of the distribution given belorv is 28.5, find the values ofx andy. Class interval Frequency )l 0-10 5 {l 10-20 x cf 20 - 30, 20 er 30-40 l5 {l 40-50 v 50-60 5 11, Total 60 {l HUH67 9 18 (E) (P.TO.) n  s-1716 53) one card is drawn from a well-shuffled deck of 52cards. Find the probability of getting: 141 D A red face card. ,f. ii) The jack of hearts. +. iii) An ace of black colour J- TL t") Not an ace (^s 'L 54) A game of chance consists of spinning an arro\\,r,hich comes to rest pointing at oneofthenumbers r,2,3,4,5,6,7,g(seetheFigure)andtheseareequallylikely outcomes. what is the probabiliry that it wilr point at wl i) 8?t ii) an odd number? g t I -gz i ii) anumbergreaterthan}? g 3 3 a (-,( -L4 ,r) a number less than 9?. €.tt -_ r I +++ HUH67 10 18 (E) ! =