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XB KENDRIYA VIDYALAYA SANGATHAN, CHENNAI REGION HALF YEARLY EXAMINATION 2022-2023 CLASS: XI - TIME: 3 HOURS MAXIMUM MARKS :80 MATHEMATICS General Instructions: 1.This question paper contains- five sections A,B,C,D and E. Each section is compulsory. However, there are internal choices in some questions. 2.SectionA has 18 MCQs and 02 Assertion-Reason based questions of I mark cach. 3.Section B has 5 Very Short Answer (VSA)type questions of 2 marks each. 4.Section C has 6 Short Answer (SA)- type questions of 3 marks each. 5.Section D has 4 Long Answer (LA)- t pe 6.Section E has 3 source based /case based/ questions of 5marks each. passage based/ integrated units of assessment ( 4marks each ) with subparts. SECTION-A (18 x 1= 18) (Multiple Choice Questions) 1.If A={ 1,2, {3,4),5 }, then (a) 3 EA (b) 4 A( ) { 3,4} CA({3,4) e A 2.IfAand B are any two sets, then (a) 0 An (A UB) is equal to A (b)B (d)AnB 3. The set A= {x: x is a positive prime numbers< 10} in the roster form is (a) { 1,2,3,5,7) (d) None of these. (b) {1,3,5,7,9 2,3,5,7 4.1fA and B (a) A- B are anytwo sets ,then A n (AnB) A-BC is equal to (c)AnB (d) none ofthese. 5.Iffx)= |x], then Rr is equal to (a) R 0, 0) (b) (-0o,0] (d)none of these 6.If f( x) axt b, where a and b are integers ,f(-1) =-5 and f( 3) =3 , thenthe values of a and b respectively (a)-3 and 1 7. if fx)=x, then ftx) +f (a). 2x3 (c) 0 and 2 (6) 2 and -3 Ad)2 and3. isequal to (c).0 (d). 1 8. The domain of the function fis given by 1( x+2x+1 X) x-6 (a)R-3,2) R-(-3,2 (c)R-[-2,3] OThe value of sin (45+0) cos (45-0) is (d)R-(-2,3). - (a)2 cos (b) 2 sin 0 (c)1 (d)0 (c) 2-V3 (d)2/3. (foJThe value of tan 75- cot 75 is equal to (a)1 (b) 2+ V3 (11, The circular measure of an angle of 7*30 is () (d) none of these. 12 Ifx.y ER and (x+3y)+4i =2+ (2x-y) i. Then (x, y) (a)( 0,2) (6) (2,0) 13.Ifn is any (a) i ()2,2) (d) (0,0) integer, then i"+ int1 + int2 + in+3 is equal to -i (d) (c) 14.)Real part of (-cos6)+i sin a)-cos 0. Cui is (b) (c)2 (d)tan6. (15 cose +i sin@) 2 is equal to (a) cos 20+i sin20 (b) sin20 +i cos20 (c)cos 20-isin20 16. Ifn C12 a 20 n (d)none of these Cs, then n is equal to (b) 12 17.The number of words that O n e 124? (c)620 can be formed (d) 8 by using the letters the word MATHEMATICS a) 11! 11! (b)21+21+2 11 2 ( d) none of these. )) 18. The number of al 0,1,2,3,4 is Cay S Ps five-digit numbers that can be formed by using the (b)s s (c) 4x 4 P4 digits (d) 4x 5 Assertion- Reason Based Questions In the following Reason R. questions, a statement of assertion (A) is followed Choose the correct answer out by a statement o of the following choices. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and Rare true and R is not the correct explanation of A. (c)A is true but R is false. (d)A is false but Ris true. 19.Let A={1,2,3,4),B-={1,5,9,11,15,16}, f={ (1,5),(2,9).(3,1),4,5),(2,11)} Assertion:( A) fis a relation from A to B(Definition of relation) Reason:(R) fis a function from A to B (Definition of function) 20. Assertion: (A) +3i)3 +(-26)i 27 Reason:(R) (at b)3 =a3 +3ab +3ab2+ b3, i=-1, 13=-I SECTION-B Thissection comprises very short answer type- questions ( VSA) of 2 marks each. 21.Let U- (1.2,3,4,5,6,7,8,9 ), A= { 1,2,34) B= ( 2,4,6,8), C= ( 3,4,5.6} Find (i) (AUC) 22.Findthe domain and (ii) (B-C)C. range of the following relation R-{ (x,y): X, y E N and x+y=10 } 23)1fin two circles, arcs of the same length subtend angles 60 and 75 at the centre, find theratio of their radii. the value nd quadrant. of other five trioonometric functions , second Xhes n ifsin x 25) Find the multiplicative inverse of V -2 SECTION-C Section 0. 4Let comprises short answer tvpe -questions A-{ a, b}, B-( a, b, c)Is Ac 0f 3 marks ( SA ) B?Find AUB? each. pu b 1203 C-A.-7 5 27.Let At 1,2) ,B-=( 1,2,3,4), C={ 56} and D-( 5,6,7,8), verify that tio &1,3/8 eiy Showthat if Ac B,then C-B c )AX(Bn c) =(A XB) n (AXC) i,2,3,43 ii) AXC is a subset of B XD. 28.Prove that cos x =32 cos x-48 cos xt 18 cos X-l1 ex ,) , 27 t3 o4) (2,) &s) (2,2) 3,3) 214) Cus) (25) (2,63 29.1f(xtiy)" =utiv then show that 4 ( x y ) (OR) RAS HS Ifatib 2x241 prove that a? 43 +h2-+12 (2x2+1)2 C 4i)2 30.Solve for real x, 2x-1, r-2)@-) (OR) Find all pairs of consecutive even integers both of which are larger(2 than x2412 5 such that their sum is less than 23. GO Lnse thve HDetemine n if 2n C3 n C2 =12 :1 , 42 3+ X4 2 # 23 (OR) 2.x2 23 Find r if5 P, =2x 6Pr. 1 The paina ad C681 (o A nis section S2.Draw SECTION-D comprises Long answer tvne questions( LA) of 5 marks each appropriate Venn Diagram for each of the followIng OaUB) Gi)ACnB (ii) (A oR)s iv) Ae UB .Verify the 33.Find D.A sin.cos.and tan if sinx,x in tv De-Morgan's Laws. quadrant il. Solution of 9% acid is to be diluted by adding 3% acid solution to it. than 5% but less than7%.If there is 460 litres of 9%, The resulting solution, how of 3% xture is to be more many litres solution will have to added? D.A Committee of 7 has to be formed from 9boys antd 4 be done when the committee consists of d)exactly 3 girls? i) at least 3 girls? girls. Tn how many ways can tnis (iii) at most 3girls? SECTION-E Thissection comprises of 3 case- study / passage based questions of 4 marks each case study questions have 4 sub-parts each part 1 mark. - The 36.Let fand g be real function defined by fx) =vx-1 and g(x) 3-2x. Based on the above information, answer the following questions. = G)Domain offis (a) (1,co) (b) [1,co) (c) (-co0,1) (d) (-0, 1] i)Domain of is 9 (a)R- (b) R (C)R- (d)R- ii) Domain of ftg is (a) R (b)R-(1,0o) (c)[ 1,00) (d)R-1) Giv) Domain of is R- (b) R (C) R-1) (d)[1,o) 3/.Marks obtained by Radhika in quarterly and halfyearly the above are o0 and 70 respectively. Based on examination information, answer questions. ) in the annual Maximum marks, she should get of at least 70 marks is (ii) Maximum in the annual marks, she should get the following to have an average ( d) 90. (c) 75 ( b ) 85 (a) 80 examination of mathematics examination to have an average of at most 75 marks is (a) 85 (d)80. (c)95 (b) 90 (11) Range of marks in annual examination, so that the average mark is at least 60 and at most 70 is (a) [60,70] (c )[50,70] (b) [50,80] (d) [60,80]. (1V)if average of at least 60 marks is considered pass, then minimum marks she need to score in annual exam to pass is (a) 60 (d)50. (c)70 (b)65 38.The letters of the word "COMPUTER" are arranged in all possible ways. Based on the above information answer the following questions. i) The total number of words with or without meaning that can be formed is (a)8Cs (b) 8P (c)2 x8Ps (d) 8 x7 C7 (i)The number of words in which vowels occupy odd places is (a)4Ps x5! (b)3! 5! (c)4C3 X3! (ii)The number of words in which vowels occurs (a) 6! (b) 3!5! (d ) 4P3 X4!. together is (c) 316! (d) 5!. (v)The number of words starting with C and end with R is (a) 2! 6! (b)5! x 2 (c)5! x 3! 6 (d)6!.
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