OMT-101 : Preparatory Course in General Mathematics (Revised)

Transcription

1 OMT-101 Bachelor's Preparatory Programme (B.P.P.) (For Non 10+2) Term-End Examination December, 2009 OMT-101 : Preparatory Course in General Mathematics (Revised) Time 120 Minutes Maximum Marks : 50 croti)t144 :,( q 41ruid vrtf94-- ilickq *4-1 (#7111-Era) 7:11171: 120 fit9z 3N-W-d1=1 :50 OMT P.T,O.

2 OMT-101 2

3 General Instructions : Preparatory Course in Mathematics (OMT-101) Questions All questions are compulsory, each of which carries one mark. Each question has four alternatives, one of which is correct. Write the Si. No. of your correct alternatives/answers below the corresponding question number in the answer sheet and then mark the rectangle for the same number in that column. If you find that none of the given alternatives is correct write 0 and mark in column 0. Do not waste time in reading the whole question paper. Go on solving questions one by one. You may come back to the left out questions, if you have time at the end. No Calculators are allowed di r Yi : ii t trITT g iq toto-t( ) # Wrff 3Tri-4P4 t -) i;r7ff -) 3 f9-zrff T-112,1 74It fq--* Trtti -14 -RiivR Tit 314/i.;14)(, 41 chi Ai k fffd 3-'g f r3-fw 31-rTd (t f' Trcr Lit(,7 fen.1,1 Tit t o fi 3 *To g 014 tr--q4 TriTzT Trd r, cik qiq al 14 TITRE ter, ')R1 -s-qm kur -1011c11 t I (iv) 411 (e.4 Tzkrr chi ff t I O MT P.T.O.

4 Which of the following is not a prime number? (1) 2 (2) 19 (3) 1 (4) 67 The HCF of the numbers 6, 30, 42 is : (1) 42 (2) 6 (3) 30 (4) 750 The value of 11 ( 8) is : ( 1 ) 3 (2) 19 (3) 3 (4) = ( 1) 5 (2) 6 (3) 6 (4) 5 The difference of km and km is : (1) km (2) km (3) km (4) km If 200 g of sugar are needed to make 3 cakes, then the amount of sugar needed to make 15 cakes is : (1) 1500 g (2) 1000 g (3) 600 g (4) 3000 g What percent of Rs. 350 is Rs. 50? (1) 14-2 % 7 (2) 7% (3) 70% (4) 14-4 % 7 Which of the following statements is true? There is only one proof for a theorem. Mathematical statements are ambiguous. Mathematics is a not hierarchically structured Mathematical ideas usually grow from concrete situations to abstract ideas. ()MT-101 4

5 9. Which of the following statements is false? Every integer is a rational number. Every integer is a natural number. Every integer is real number. Some integers are natural numbers also Out of the fractions : 5, 3 4, (1) 3, 2 1, , 1-1 the mixed fractions are : (2) 5, 3-4, 2-3, (3) (4) 3-4, 6 12 The Hindu-Arabic numeral for the Roman Numeral XIX is : (1) 29 (2) 20 (3) 21 (4) 19 1 x x = (1) 24 5 (2) 27/i 2 1 (3) 24 (4) Which of the following statement is incorrect? Many lines may pass through a point. Only one line passes through two distinct points. An angle is measure of the space between its arms. A ray is part of a line with one end fixed. 14. The angle of measure 3600" in degrees is : (1) 60 (2) 1 (3) 6 (4) One angle of a right angled triangle is 30. The measures of the other two angles are : (1) 90', 90 (2) 120, 30 (3) 90, 60 (4) 90, 30 OMT P.T.O.

6 The sum of the angles of an octagon is : (1) 180 (2) 360 (3) 900 (4) 1080 How many axes of reflection symmetry does an equilateral triangle have? (2) 2 (3) 3 (4) 4 Which of the following figures have exactly two fold rotational symmetry? (1) circle (2) square (3) rectangle (4) equilateral triangle The number of faces of a tetra hedron is : (1) 4 (2) 3 (3) 6 (4) 8 A carpet costs Rs. 400 per sq.m. The cost of the carpet required to cover the floor of a room measuring 3.75 m by 3 m is : (1) Rs (2) Rs (3) Rs (4) Rs The surface areas of two spheres are in the ratio 1 : 4. The ratio of their volumes is : (1) 1 : 2 (2) 1 : 8 (3) 1 : 4 (4) 1 :16 A field is in the shape of a trapezium whose parallel sides are of measures 25 m and 11 m, and the distance between them is 17 m. Its area is : (1) 360 m2 (2) 350 m2 (3) 306 m2 (4) 612 m2 Where does the point (0, 5) lie? 1st quadrant 3rd quadrant at the intersection of 2nd and 3rd quadrant. at the intersection of 3rd and 4th quadrant. 24. The equation of the line passing through the points ( 4, 4) and the origin is : (1) y = 4x (2) y x = 0 (3) x =4y (4) y = r + 4 OMT-101 6

7 The area of a triangle whose vertices are (5, 0), (3, 3) and (4, 1) is : (1) 2.5 sq. units (2) 7 sq. units (3) 4.5 sq. units (4) 5 sq. units The amount of a sum of Rs. 10,000 invested at 5% simple interest became Rs. 15,000 after some time. Then the time for which the money is invested is : (1) 4 years (2) 12 years (3) 3 years (4) 10 years A shopkeeper sells a Juicer for Rs. 2805, after offering 15% discount on marked price, and then 10% sales tax on the reduced price. The marked price of the Juicer is : (1) Rs (2) Rs (3) Rs (4) Rs The mean of first 10 natural numbers is : (1) 5 (2) 5.5 (3) 6 (4) 4.5 Which of the following is a measure of dispersion? (1) Mean (2) Median (3) Standard deviation (4) Mode Two dice are thrown simultaneously. Then the total number of possible outcomes in terms of the scores on the upper faces of each die is : (1) 12 (2) 6 (3) 36 (4) 30 Which of the following statements is not a method of proof? (1) giving a counter example (2) deductive logic (3) inductive logic (4) identifying a pattern In a survey it is found that 5 men out of every 100 men and 25 women out of every 10,000 women are illiterate. In this village about half the population is male. What is the probability that a person chosen at random from the village will be illiterate? (1) 400 (2) 800 (3) 40 (4) 80 ()MT P.T.O.

8 33. The standard deviation of the data : 3, 6, 6, 7, 8, 8, 8, 9, 10, 15 (1) 2,96 (2) 8.2 (3) 15 (4) (3 ) 5 5 _ (2 ) 1 = (1) ( 3 \ 5 (2) (3) \21 (4) (3/ The sides of a rectangle are 1)in and (V-j- +1) m. Its area will be : (1) 2 sqm (2) 4 sqm (3) 3 sqm (4) 1 sqm Which of the following values of x satisfies the equation 4x 1= -- 7 (1) 2 (2) 3 (3) 3 (4) 2 The number of diagonals of a polygon with n sides is n(n-3). The number of diagonals of a 2 2 hexagon are : (1) 6 (2) 9 (3) 5 (4) 18 The sequence 2, 4, 8, 16,... is : (1) an A.P. (2) a G.P. (3) Fibonacci sequence (4) Sequence of perfect numbers 39. The sum is equal to : (1) 100 (2) 400 (3) 385 (4) ! The value of 2! is : (1) 24 (2) 360 (3) 720 (4) 6 OMT-101 8

9 41. The value of C(12, 3) is : (1) 220 (2) 1320 (3) 10,000 (4) The cube root of 1.01 to three decimal places is : (1) (2) (3) (4) The number of different 4 digit numbers that can be formed by using the numbers 1, 2, 3, 4, 5, 7, 9 without repetition is : (1) 360 (2) 15 (3) 840 (4) 990 The first and third terms of an A.P. are and 6-5 ' respectively. Its common difference is : 1 20 (1) (2) 3 (3) 2-35 (4) 7 The quotient of (x3-1) ± (x 1) is : (1) X2-1 (2) x2 (3) x2 + 1 (4) x2+x+1 Mohini's present age is 25 years more than that of her son, Akhil. After 5 years, Mohini will be twice as old as Akhil. The age of Mohini after 10 years from now will be : (1) 55 years (2) 50 years (3) 20 years (4) 45 years The value of al + l a + + On, when a 0, is : (1) a (2) a + 1 (3) a+ 2 (4) a + 3 The base and hypotenuse of a right angled triangle are 3 cm and 5 cm respectively. Its height is : (1) 6 cm (2) 4 cm (3) 14 cm (4) 16 cm The solid shape we get on rotating a circle about any of its diameters is named as : (1) paraboloid (2) ellipsoid (3) platonic solid (4) sphere 50. The area of cardboard needed to make a cuboidal box of dimensions 10 cm x 11 cm x 14 cm is : (1) 404 sq. cm (2) 808 sq. cm (3) 1540 sq. cm (4) 35 sq. cm - o 0 o - OM'F P.T.O.

10 OMT

11 F-1-11(.114ff 4 A cb-r A E T t? (1) 2 (2) 19 6, 30, 42 'TT HCF tl (1) 42 (2) (-8) t (1) 3 (2) 19 (3) 1 (3) 30 ( 3) 3 (4) 67 (4) 750 (4) = (1) 5 (2) 6 (4) 56- (3) tft * # 411 t (1) ,.T (2) f4h.t (3) :ft (4) ).1t "zffc11 i.kt q-91-k FQ-t 200 T. -4 ch 31-rd'qz11 Tsd t 151 t f rl f1 -cr Atc\kci 8)41? (1) 1500 T. (2) (3) 600 T. (4) 3000 T. 350 T. 50 T. fir i;rf-a7m t? (1) 14-2 % 7 (2) 7% (3) 70% (4) 14-4 % 7 8. _Icr Off-Trr weit? -9-4zr cr-> ti 41ruid 4 2.1"ff '4f-111 ti ifilm tkcn Alum Atr-Td t Trfttrratzr tra fa-qrif f-4--rt'f 4 fam-ftrd F-14-troi6cr 4A chl-i-ter 3R:r-rt? (1) slrltiitt if74-zr 42s111 t1 (2) 1:Ft4 5T t7 1'1 t (3) Tc4T -cpjft.1r-4;4* 4t? t 1 (4) T) tfurfw 7r-f-d Tirrfr t O MT P.T.O.

12 f9.-t 5, 3-4, - 6, 1 1-2' # ? 1 1 (1) 3, 1 2-, (2) - 5, 5 3-1, 4 2-1, (3) D (4) 3 4-, 2-3, 5 tricra 31.-T xix aft (1) 29 (2) 20 (3) 21 (4) 19-1 x x - =? (1) 24 (2) (3) 24 (4) f-p-irc,irkg ct -14 TI9-7,Fr T24-9' 4/Nri t? -) cr) tur q, ti t 31-d7T-31-FIT qztol -) 3-TI-4- VIA t T t I 31'q T 1-) ftzt-d-fereit t " TIN 13T fti-gt : (1) 60 (2) 1 (3) 6 (4) 10 lkch fqv cbt tk^ t Izt:1--* qrlirff -T1 HI LI : (1) 90, 90 (2) 120, 30 (3) 90, 60 (4) 90, 30 T sate11- rcr: (1) 180 (2) 360 (3) 900 (4) W,F4TE 117-d-49 rd (1) 1 (2) 2 (3) 3 (4) 4 OMT

13 18. -F-1i--lioR5ct -{4 f-*-tr 31-r-t-fa. 3 3 t d1 t? (1) co (2) <44 (3) 3-17M (4) - 11:1-4T- ftif (1) 4 -ciqu-bocn cf-)1 Tf.c--n t : (2) 3 (3) 6 (4) 8 -) c( --1-2:1-u 400 T. mid Th-{ * I -) 3.75 f. x 3 It. ITN 4111:17 f,114 c : (1) 4000 T. (2) 4500 T. (3) T. (4) 1125 T "F 3-17M 1 : T 69 T3T11:1M 411 : (1) 1 2 (2) 1 : 8 (3) 1 : 4 (4) 1 : 16 k TE*7{ ct t chi Hi y 25 * at 39-k 41'4 cb1 ci 17 t I 7T-*-r : (1) 360 lt2 (2) 350 1:IF (3) 306 Tft2 (4) 612 -rft2 f (0, 5) --4#.2.M 6)cll t? 3 2P4 -c4q2ltr -fl#r r4q2ti* 7=it *t=ft -clq417-r tr'{ 1?)- 24. fq 31'i (-4, 4) 3-TIT tts-tr4 cgt : (1) y -= 4x (2) y x = 0 (3) x = 4y (4) y=x (5, 0), (3, 3) 3t (4, 1) 71-11# fq.v t : (1) 2.5 (2) 7 (3) 4.5 qrf 5 chiii (4) 5 ci4f OMT P.T.O.

14 10,000 T. 5% Till-4R u! o 11,31 TIT ft-4-qt t I To H144 1T it TrIF 15,000 T. t Wal t I Tf'sql fa---d-4t fm f-447-r fwq-r, Iit? (1) 4 cpi (2) 12 a ti (3) 3 q'ci (4) 10 citi 7T Cchl-iR 31f*---d Tffr % Kz ci-! fm-trff ITT 10% f 1 cf-) 2805 t I 1TR chi 3-ff ---d t : (1) 2000 T. (2) 3000 T. (3) 4000', (4) 3500 T M10-5ITT7 H(Nr3i'l -Tr : ( 1 ) 5 (2) 5.5 (3) 6 (4) 4.5 okact 4 A T1-9---m 51,4-)1 t? (1) Trial (2) 1:r (3) b 01 74(11 (4) > TIPT h t I t c\ LI 7 A---T TrfA -hcich ITT ssil 4 m1 31-r-krn cb) 11-1c1111 4," rth t : (1) 12 (2) 6 (3) 36 (4) 30 f9hrriftg d 4 A T1--i Tri chi fqfq Wit? (1) ii-ct-6q ie-ti1 (2) -( lch (3) 3-TFut--1-T A (4) te4 31 T1*-TuT -4 -zit TIFF, i q r f 7-c-k tff y) ti 31 T"51-F;10,000 -nt--ffra -4 A 25 Trftffl tt i 4ri,4 31-I-q-4 4 oilwr 3Tr4 vts) zrrsr--49* (c,,4 A 1-ir Trzur F-Raf{ titri t : (1) 400 (2) 800 (3) 40 (4) , 6, 6, 7, 8, 8, 8, 9, 10, 15 chi 411-t ch t : (1) 2.96 (2) 8.2 (3) 15 (4) 3 OMT

15 (32)- 5 (25)-1= 1 ( 3)5 2 5 (1) (2) (3) (4) (-3-) 2) 4-{(f +1) 3TPTd chl T *Tn. (1) 2 ail 1:11 (2) 4 col -RI (3) 3 c44 1#. (4) 1-1-f c-1-14 A x :11-9" -.11:ft,TTIT 4x 1= 7 Tfq-E %71 t? 3 (1) 2 (2) 3 (3) 2 (4) 2 11(71-3) n '11714 "4.0 q-e-f % fd%1311 chl 4tsi1 t1 fd-wkrit chl -4(seif tft : 2 (1) 6 (2) 9 ( 3 ) 5 (4) f*T1 2,4, -- 8, 16,... t : (1) (2) (4) (3) t+)01-1r1 49,4413-ff 31-1-*-14 i) J E "F%- '1*.t? (1) 100 (2) 400 (3) 385 (4) ! (1) 24 (2) 360 (3) 720 (4) 6 C(12, 3) : (1) 220 (2) 1320 (3) 10,000 (4) ;FIT(d1.1cI-i1aT-2.TM d cb) t : (1) (2) (3) (4) OMT P.T.O.

16 tiky-ir 1, 2, 3, 4, 5, 7, Ift f*-7 f-49t, T -4F(trf thaq R cciri t? (1) 360 (2) 15 (3) 840 (4) 990 tihldt { t I T{T*--I 3 t: (2) 3 (3) (4) --7--, (x3-1)--(x-1) c f ITTTTCh : (1) X2-1 (2) x2 (3) x 2 +1 (4) x 2 +x+1 Itf -t ct;) q ,t 3Tra flqi I 474 ci tt Att cb ft19 chl TA-11 t,4r J 11 I,44 A 10 c oliq l:ftrgt cht 39 : (1) 55 ci4 (2) (3) 20 -T31 (4) 45 as a Otf tal +1 a +a ±0ach : CO a (2) a +1 (3) a+ 2 (4) a +3 Q,ch ti 4-1 u t f97 chl 3-i1g17 3 'WO TIPT: 3-4:it :ff. t. I 74 I t ( ) 6-4.1t. (2) 4 AIM (3) 14 A.t. (4) 16 Alt. f-*-am-4 T.77 3#1 3Tr*--r-{ 5-1-H t t : (1) t cic-ii (2) t1;*7 (3) 331F- 1-11:t 3 T -q11 (4) 4t 10 x 11 x :A. f-laraff 3-Trft atrtt, a ffi l,4)11-4) > ita 1 4? (1) 404 ci4 t. (2) 808 I (3) 1540 CI It. (4) 35 chi OMT