MOST IMPORTANT QUESTIONS

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1 PART - Centurion Assignment By OP GUPTA INDIRA AWARD WINNER CLASS XII MATHEMATICS MOST IMPORTANT QUESTIONS Without Mathematics, there s nothing you can do Everything around you is Mathematics Everything around you is Numbers! Compiled By : OP Gupta (Math Mentor) Maths (Hons), Elect & Comm Engineering INDIRA Award Winner र ब, न रखन : ज बह न बन त ह, व बह ज त ह और, करन व ल कर ज त ह Hey! After remarkable success in CBSE XII Math Examinations of last four years, (from 05 to 08), we have come up with the Centurion Assignment : Most Important Questions Assignment Sheet again for 09 Board Exams We always strive to serve you better in Math We hope this endeavour of ours shall be of some help for you in achieving your desired goal in the Math Examination of March 8, 09 With Best Wishes - OP Gupta, Math Mentor #Advanced Math Classes, Thana Road, Najafgarh

2 XII Mathematics CENTURION Assignment for CBSE 09 By OP Gupta ( ) SURE SHOT SUCCESS MANTRA FOR CHAMPIONS THE CENTURION ASSIGNMENTS BY OP GUPTA Note that Every Question in the CENTURION ASSIGNMENT has been given with their due Weightage for CBSE XII Math Exam Question of Section A ( Mark question) has been marked as () Question of Section B ( Marks question) has been marked as Question of Section C (4 Marks question) has been marked as Question of Section D (6 Marks question) has been marked as (6) Also, some questions have been marked as (/) or (/4) or : These questions can fall in either Section A/B or Section B/C or in Section C/D respectively Guys, be ready to grab a few delicious sums Here we go!!! Q0 Let A {,,3,,00} Let a relation R be defined on A, given by R {(x, y) : xy is a perfect square} Obtain the equivalence class [] Q0 How many binary operations can be defined on the set {, }? () Q03 Consider the binary operations : R R R and : R R R defined as a b a b and a b a for all a, b R Show that distributes over Does distribute over? Q04 Let X be the set of all singular matrices of the form, where x is a non-zero real no On set X, let * be an operation defined as A*B AB for all A, B X Prove that * is a binary operation Q05 On the set A M(x) : x R 0 of the square matrices of order, find the identity element for the multiplication of matrices as a binary operation Here R 0 denotes the set of all non-zero real numbers Q06 Show that the relation R in the set A of points in a plane given by R = {(P, Q) : Distance of the point P from the origin is same as the distance of point Q from the origin}, is an equivalence relation Q07 Let a relation R on the set of real numbers be defined as (a, b) R ab 0 a, b For all the Math-Gyan, click at : wwwtheopguptacom

3 THE OP GUPTA S ADVANCED MATH CLASSES, Thana Road, Najafgarh Show that R is reflexive and symmetric Is it transitive? Q08 Show that f : R R defined as f (x) [x] is neither one-one nor onto Here [] represents the greatest integer function Q09 Evaluate sin sin 5 cos cos5 () Q0 If cos x cos y, then find the value of x y x y x Q Find the largest and smallest value of f (x) tan, x [0,] x sin (3 x) Q Write the domain of log( x ) () ACHIEVEMENtS CBSE XII (07-8) : Our student PARV JOSHI got Perfect Score of 00 And, 5 other students got scores in 90s with scores such as 98, 96, 95, 94, 93, 9 Students Qualified in JEE Main with Scores like 44, 3, 08, 44 etc Students were Rank Holders in IPU Entrance (BTech) CBSE XII (06-7) : Our students VINAY, MOHIT & AKSHAY got Score of 98 Also, other students got scores in 90s with scores such as 97, 95, 93, 90 Students Qualified in JEE Main Students, VINAY & BHARAT, Qualified for NDA and cleared SSB too Many Students Qualified in IPU Entrance (BTech) FOR DETAILED RESULTS, VISIT AT Q3 Find the domain of the definition of the function f (x) sin x Q4 If x [0,/], then find the value of Q5 If Q6 If Q7 Prove x y z r then, find the value of x x tan sin sin x xy yz zx tan tan tan zr xr yr x y ax bsec tan x c and ay bsec tan y c, then find the value of xy cosec 5 cosec 65 cosec 35 up to n terms tan n n () Exclusively For Math, click at : wwwtheopguptacom M

4 THE OP GUPTA S ADVANCED MATH CLASSES, Thana Road, Najafgarh Q98 A husband and wife appear in an interview for two vacancies in the same post The probabilities of their selection is /4 and /7 respectively What is the probability that (a) both of them will be selected? (b) none of them will be selected? (c) at least one of them will be selected? Q99 A pack of playing cards was found to contain only 5 cards If the first 3 cards, which are examined, are all red, what is the probability that the missing card is black? Q00 A bag I contains 3 white and black marbles, while another bag II contains white and 4 black marbles A bag and a marble out of it is picked at random What is the probability that the marble is white? Hey Scholars! Do you have any Doubt (s) regarding any question (s) in this Centurion Assignment? Please send us an Image of that Question (s) along with your concern via or, write an to theopgupta@gmailcom # Please, keep in mind that we will surely reply to your queries, though it may take some time (as we re very much occupied in Clearing Maths related Doubts of many scholars like you) ## For FREE Sample Papers, please visit Disclaimers All care has been taken while preparing this CENTURION ASSIGNMENT (Part ) Still if you notice any Error (s), please bring it to our notice This Assignment is based on the Sample Paper issued by CBSE for 09 Math Examinations To obtain this sample paper, click at theopguptacom/ in Class section under CBSE Solved Papers (XII) and download (Marking Scheme has also been given there) Or, you can visit directly the link to download this Sample Paper This Assignment is just indicative for CBSE 09 Exam of Math for class XII It doesn t mean to directly reflect the exact questions going to be asked in Math board exam to be held on 8 th March, 09 If any resemblance is found in the Final Paper of CBSE Board, 09 Exams, it may be just due to co-incidence At best we can say, this Centurion Assignment (Part ) is just for the purpose of practice All Rights Reserved with OP Gupta With Best wishes Here s Your Math Mentor OP GUPTA ### ONE TARGET ### 00% EFFORTS FOR 00% MARKS SCORE CENTURY With Century Of Questions!! Exclusively For Math, click at : wwwtheopguptacom M

5 Let s check if you did correct or, need help Answers/ Hints/ Solutions Q0 Let x A such that Rx such that x is a perfect square Clearly, values of x can be, 8, 8, 3, 50 Hence [] = {, 8, 8, 3, 50} 4 Q0 No of binary operations are 6 Q03 Let a, b,c R As a (b c) a b a b and (a b) (a c) a b a c a b That is, a (b c) (a b) (a c) So, distributes over Now a (b c) a b c nd (a b) (a c) a a a a a That is, a (b c) (a b) (a c) So, doesn t distribute over b b Q04 Let A, B b b be elements of set X Then a, b both are non-zero real nos b b ab ab As a, b R 0 Now AB X b b ab ab so, ab R 0 That is, A*B AB X Hence, * is binary operation on X Q05 Let M(a), a R 0 be the identity element in set A Then, M(x)M(a) M(x) M(a)M(x) x R 0 That is, and, ax a x ax ax and, ax ax ax ax By equality of matrices, we get : ax x and, x ax a / / / Therefore, M / / is the identity element Q06 Given that the relation R in the set A of points in a plane given by R = {(P, Q) : Distance of the point P from the origin is same as the distance of point Q from the origin} That is, R = {(P, Q) : OP = OQ, where O is the origin} Reflexivity : Let P A Since OP = OP so, (P, P) R Therefore, R is reflexive Symmetry : Let P,QA Let (P,Q) R So, OP OQ OQ OP (Q, P) R R is symmetric Transitivity : Let P, Q,S A Let (P, Q) R and (Q,S) R So, OP OQ and OQ OS OP OS (P,S) R R is transitive Hence R is equivalence relation Q07 The relation R is defined as (a, b) R ab 0 a, b Reflexive : Let a As a 0 ie, a 0 ie, aa 0 ie, (a,a) R so, R is reflexive Symmetric : Let a, b and let (a,b) R So, ab 0 ie, ba 0 ie, (b,a) R So, R is symmetric For all the Math-Gyan, click at : wwwtheopguptacom

6 XII Mathematics CENTURION Assignment for CBSE 09 By OP Gupta ( ) Q96 Let E : a student selected at random is a girl, E : a student selected at random is a boy, E : a student selected at random will get first division By total probability rule, P(E) P(E )P(E E ) P(E )P(E E ) Q97 Let E : getting doublet on the pair of dice So, E = {(, ), (, ), (3, 3), (4, 4), (5, 5), (6, 6)} so, P(E) p 6/36 /6, q 5/6 No of trials, n = 3 r 3r C r 3r r As P(X r) C (5) Following table represents the Probability distribution : X 0 3 P(X) 5/6 75/6 5/6 / Expectation, E (X) X P(X) Q98 /8, 8/8, 0/8 Q99 Let E : missing card is black, E : missing card is red, and A : 3 cards, which were examined, are red 6 5 C3 C3 P(E ) P(E ), P(A E ), P(A E 5 ) 5 C3 C3 P(A E )P(E ) So, P(E A) P(A E )P(E ) P(A E )P(E ) 3 Q00 Let E : bag I is selected and E : bag II is selected and E : a white marble is drawn So, P(E ) / P(E ) Let A E E, B E E Therefore, required probability, P(E) P(A B) P(A) P(B) [As A and B are mutually exclusive events P(E) P(E E) P(E E) P(E )P(E E ) P(E )P(E E ) 3 7 P(E) Hey Scholars! If you ve ANY DOUBTS in this Assignment, then Please Send us an Image of that Question (s) along with your concern via or, write an to us at theopgupta@gmailcom ### ONE TARGET ### 00% EFFORTS FOR 00% MARKS SCORE CENTURY With Century Of Questions!! Click For All The Math-Gyan at wwwtheopguptacom (FREE Downloads of NCERT Solutions, CBSE Solved Papers etc) Buy Math Books for IIT-JEE, XII and XI by OP Guptt wwwimathematiciacom 30 For all the Math-Gyan, click at : wwwtheopguptacom

CBSE 2018 ANNUAL EXAMINATION DELHI

CBSE 2018 ANNUAL EXAMINATION DELHI CBSE 08 ANNUAL EXAMINATION DELHI (Series SGN Code No 65/ : Delhi Region) Ma Marks : 00 Time Allowed : Hours SECTION A Q0 Find the value of tan cot ( ) Sol 5 5 tan cot ( ) tan tan cot cot 6 6 6 0 a Q0 If