SENIOR INTER MATHS 2A IMPORTANT QUESTION BANK By Srigayatri

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1 VaithaTV GUIDE educatio & areer Page No. SENIOR INTER MATHS A IMPORTANT QUESTION BANK By Srigayatri MATHEMATIS IIA BLUE PRINT S.NO TOPI NAME NUMBER OF TOTAL VSAQ(M) SAQ(M) LAQ(7M) Quadratic Equatios - 6 Theory of Equatios - 9 Matrices Permutatios ad ombiatios - 5 Biomial theorem Partial Fractios Epoetial ad Logarithemic series Probability 9 Radom Variables ad Probability Distributios - 9 TOTAL NO.OF QUESTIONS S.NO TOPI NAME QUESTION BANK ANALYSIS LAQ SAQ *** ** * *** ** * VSAQ TOTAL Quadratic Equatios Theory of Equatios Matrices Permutatios ad ombiatios Biomial theorem Partial Fractios Epoetial ad Logarithmic series Probability Radom Variables ad Probability Distributios SUB TOTAL TOTAL

2 VaithaTV GUIDE educatio & areer Page No. LONG ANSWER QUESTIONS THEORY OF EQUATIONS ***. Solve = 0 (Model of 005) ***. Solve = 0. (Model of 005) ***. Give that the roots of + p + q + r = 0 are i i) A.P. show that p pq + r = 0(march09,may 08) ii) G.P. show that p r = q (Mar 0) iii) H.P. show that q = r ( pq r) ***. Solve the equatio = 0, give that they have multiple roots. ***5. Solve = 0, give that oe root is equal to half the sum of the remaiig roots. (Mar 05) ***6. Solve the equatio = 0 give that the roots are i G.P. (March 07) ***7. Solve = 0, give that the rootes are i the A.P. **8. Solve = 0, give that it has two pairs of equal roots (Mar 0) **9. Solve = 0 give that two roots have the same absolute value, but are opposite i sig. *0. Solve = 0, give that the product of two of its roots is. *. Trasfor + + = 0 ito oe i which the coefficiet of secod highest power of is zero ad also fid its trasformed equatio. MATRIES ***. If a b c A a b c = a b c is a o-sigular matri, the show that A is ivertible ad A = adja det A (Mar 07) ***. Show that b + c c + a a + b a b c c + a a + b b + c = b c a a + b b + c c + a c a b (Oct 96) ***. If a a + a b b + b = 0 c c + c ad a b c a b c 0 the show that abc = - (Mar 0) a b c bc a c b b c a = c ac b a = ***5. Show that ( a + b + c abc) c a b b a ab c (Apr 0) ***6. Solve the followig simultaeous liear equatios by usig ramer s rule, Matri iversio ad Gauss -Jorda method (i) + y + 5z = 8, y + 8z =, 5 y + 7z = 0 (Mar 08) + + =, + 5y + 7z = 5, + y z = 0 (March 07, 09) (ii) y z 9

3 Page No. VaithaTV GUIDE educatio & areer ***7. Eamie whether the followig system of equatios is cosistet or icosistet. If cosistet fid the complete solutios. i) + y + z =, + 5y z =, + 7 y 7z = 5 ii) y z, y z, y z iii) + y + z = 6, y + z =, y z 9 ***8. Show that + + = + = + = (Ju 0) + = (March 05) b b = ( a b)( b c)( c a)( ab + bc + ca) a c a c (Mar 09) **9. By usig Gaus-Jorda method, show that the followig system has o solutio + y z = 0, + y + z = 5, + 6y 7z = **0. Show that **. Show that a b c a a b b c a b = ( a + b + c) c c c a b b + c c + a a + b = + + a b b c c a a b c abc a b c (May 07, Mar 08) a a + b c + a a + b b b + c = **. Show that ( a + b)( b + c)( c + a) c + a c + b c *. If *. If A = A = the show that T A = A (Mar 09) ad A 6A + 9A I = 0 (Mar 0) BI-NOMIAL THEOREM ***5. If the coefficiet of 0 i the epasio of a + b is equal to the coefficiet of 0 i the epasio of a b fid the relatio betwee a ad b, whe a ad b are real umbers. (Model of Mar 07) ***6. For r = 0,,,..., prove that c. c + cc + c c c c = c ad hece deduce that i) co c c c c o r r+ r+ r + r = ii) c c + c c + c c + + c c = c 0 + ***7. Suppose that is a atural umber ad I, F are itegral part ad fractioal part of ( 7 + ). The show that i) I is a odd iteger ii) (I+F) (-F) =

4 VaithaTV GUIDE educatio & areer ***8. If is a positive iteger ad is ay o zero real umber, the prove that + ( ) ( ) + co + c + c + c c = + + (Ju 05) ***9. If the d, rd ad th terms i the epasio of ( a + ) are respectively, 0, 70, 080 fid a,,. (May 06) ***0. If the coefficiets of th r, ( r + ) th ad ( r + ) d terms i the epasio of ( + ) are i ***. If A.P. the show that ( r + ) + r = 0 (Mar 08) = the prove that 9 + = (Mar 09) ***. Fid the sum of the series (Model of Mar 06) ( ) ( )( ) **. Show that for ay o-zero ratioal umber, ( + ) ( + )( + ) = (Mar 9) **. If the coefficiets of cosecutive terms i the epasio of ( + ) are a, a, a, a respectively. The show that a a a + = a + a a + a a + a (Mar 07) **5. Usig biomial theorem prove that 50 9 is divisible by 9 for all positive itegers. **6. State ad prove Biomial theorem for positive itegral ide. (Mar 09) **7. Fid the sum of the ifiite series 6 (March 005) PROBABILITY ***8. State ad prove additio theorem o probability. (Ju 05, Mar 07, May 07, Mar 06) ***9. Defie coditioal probability. State ad prove the multiplicatio theorem o probabiity. ***0. State ad prove Baye s theorem. (Ju 05, Mar 09) ***. Three boes umbered I, II, III cotai the balls as follows. oe bo is radomly selected ad a ball is draw from it. If the ball is red the fid the probability that it is from bo II. **. If oe ticket is radomly selected from the tickets umbered to 0, the fid the probability that the umber o the ticket is. (Mar 08) i) a multiple of 5 or 7 ii) a multiple of or 5 Page No.

5 VaithaTV GUIDE educatio & areer **. I a bo cotaig 5 bulbs, 5 are defective. If 5 bulbs are selected at radom from the bo. Fid the probability of the evet that i) oe of them is defective ii) oly oe of them is defective iii) atleast oe of them is defective. **. I a eperimet of drawig a card at radom from a pack, the evet of gettig a spade is deoted by A ad gettig a pictured card (kig, quee or jack) is deoted by B. Fid the probabilities of A, B, A B, A B, **5. Three boes B, B ad B cotai balls with differet colours as show below A die is throw, B is chose if either or turs up. B is chose if (or) turs up ad B is chose if 5 (or) 6 turs up. Havig choose a bo i this way, a ball is choose at radom from this bo. If the ball draw is foud to be red, fid the probability that it is from bo B **6. Defie coditioal probability. Bag B cotais white ad black balls. Bag B cotais white ad black balls. A bag is draw at radom ad a ball is chose at radom from it. What is the pobability that the ball draw is white? *7. Two persos A ad B are rollig a die o the coditio that the perso who gets first will wi the game. If A starts the game, the fid the probabilities of A ad B respectively to wi the game. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS ***8. A radom variable X has the followig probability distributios. fid (i) k (ii) mea ad (iii) variace of (Model of May 07) ***9. The rage of a radom variable X is { 0,, } give that P( X = 0) = c P( X = ) = c 0c P( X = ) = 5c (i) fid the value of c (ii) P( X < ), P( < X ) ad P ( 0 < X ) (Mar 05) ***50. Oe i 9 ships is likely to be wrecked whe they are set o sail, whe 6 ships are o sail. Fid the probability for (i) atleast oe will arrive safely (ii) eactly three will arrive safely (Mar 07) ***5. If the differece betwee the mea ad the variace of a biomial variate is 5 9 the fid the probability for the evet of successes whe the eperimet is coducted 5 times. Page No. 5

6 Page No. 6 VaithaTV GUIDE educatio & areer ***5. A radom variable X has the followig probability distributio fid (i) k value (ii) the meas of X ad (iii) P( 0< X< 5) (March 009) ***5. I the eperimet of tossig a coi times, if the variable X, deotes the umber of heads ad P(X=), P(X=5) ad P(X=6) are i A.P. Fid **5. Fid the probability of guessig atleast 6 out of 0 of aswers i (i) true or false type eamiatio (ii) multiple choice with four possible aswers. ( k + ) *55. If X is a radom variable with probability distributio P( X = k) =, k = 0,,... the fid. *56. A radom variable X has the followig probability distributio. Fid k ad mea, variace of X. k (March 06) SHORT ANSWER QUESTIONS QUADRATI EQUATIONS ***. Let a, b, c R ad a 0. The the roots of a + b + c = 0 are o real comple umbers if ad oly if a + b + c ad a have same the sig R. ***. Let a, b, c R ad a 0 such that the equatio a + b + c = 0 has real roots α ad β with α < β the. i) for α < < β, a + b + c ad a have opposite sigs ii) for < α or > β, a + b + c ad a have the same sig. ***. If the epressio p + ***. If is real, prove that takes all real values for R, the fid the limits for p lies betwee ***5. If is real, show that the value of the epressio ad 9. (Mar 07) + (Mar 06, May 06) ad. (May 07, Mar 08) + 7 do ot lie betwee **6. Prove that + + ( + )( + ) does ot lie betwee ad if is real. (Mar 05) *7. If is real, fid the maimum ad miimum values of the epressio (Jue 05)

7 Page No. 7 VaithaTV GUIDE educatio & areer ***8. If MATRIES cosθ siθ A = siθ cosθ the show that for all positive itegers, cos θ si θ A = si θ cos θ (Nov 98) π cos θ cosθ siθ cos φ cosφ siφ ***9. If θ φ =, the show that 0 = cosθ siθ si θ cosφ siφ si φ (Mar 0) a a a + + a + a + = ***0. Show that ( a ) (Mar 07) ***. Show that y + z y z + y = yz z z + y **. I f A = the for ay iteger show that + A = **. Fid the value of, if 9 6 = (Mar 06) **. Show that A = 0 is o- sigular ad fid A (Mar 05,08) a b b = **5. Show that ( a b)( b c)( c a) c a c (March 005) *6. 0 If I = 0 ad 0 E = 0 0 the show that ( ) ai + be = a I + a be (Ju 05) *7. Show that the determiat of skew-symmetric matri of order is always zero *8. If A ad B are ivertible the show that AB is also ivertible ad ( AB) = B A (Ju 0) *9. Solve the followig system of homogeous equatios. + y z = 0 y z = 0 0 y z + + = *0. For ay matri. A prove that A ca be uiquely epressed as a sum of a symmetric matri ad a skew symmetric matri.

8 VaithaTV GUIDE educatio & areer PERMUTATIONS & OMBINATIONS ***. Fid the umber of ways of permutig the letters of the word PITURE so that (i) all vowels come together (ii) o two vowels come together ***. Fid the umber of ways of seatig 5 Idias, Americas ad Russias at a roud table so that (i) all Idias are sit together (ii) persos of same atioality sit together ***. Fid the umber of ways of arragig 6 red roses ad yellow roses of differet sizes ito a garlad. I how may of them (i) all the yellow roses are together (ii) o two yellow roses are together ***. How may ways ca the letters of the word BANANA be arraged so that (i) all the A s are cometogether (ii) o two A s come together ***5. Simplify + (8 r ) 5 r= 0 ***6. Fid the umber of ways of selectig a cricket team of players from 7 batsme ad 6 bowlers such that there will be atleast 5 bowlers (Mar 05) ***7. If the letters of the word MASTER are permuted i all possible ways ad the words thus formed are arraged i the dictioary order. The fid the rak of the word (i) REMAST (Mar 08) (ii) MASTER (Mar 07,09, May 06,07) ***8. If the letters of word PRISON are permuted i all possible ways ad the words thus formed are arraged i dictioary order.the fid the rak of the word (i) SIPRON ( mar 05) (ii) PRISON ***9. Fid the umber of ways of formig a committee of 5 members out of 6 Idias ad 5 Americas so that always the Idias will be i majority i the committee. (Mar 08, 09)..5...( ) = {..5...( )} ***0. Prove that (May 08) ***. Fid the umber of ways of arragig 6 boys ad 6 girls i a row. I how may of these arragemets. (i) all the girls are together. (ii) o two girls are together (iii) boys ad girls come alterately? **. Fid the umber of -digit eve umbers that ca be formed usig the digits 0,, 5, 7, 8 whe repetio is allowed ladies i the committee. (i) all the girls are together. (ii) o two girls are together (iii) boys ad girls come alterately? **. Fid the umber of ways of arragig 6 boys ad 6 girls aroud a circular table so that (i) all the girls sit together. (ii) o two girls sit together. (iii) boys ad girls sit alterately. **. Fid the sum of all digited umbers that ca be formed usig the digits,,, 5, 6 without repetitio **5. Fid the umber of ways of formig a committee of 5 persos from a group of 5 Idias ad Russias such that there are at least Idias i the committee **6. Fid the umber of digited umbers that ca be formed by usig the digits,,,, 5, 6 that are divisible by (i) (ii) whe repetatio are allowed. Page No. 8

9 VaithaTV GUIDE educatio & areer *7. Fid the umber of letter words that ca be formed usig the letters of the word RAMANA *8. If the letters of the word EAMET are permuted i all possible ways ad if the words thus formed are araged i dictioary order fid the rak of the word EAMET *9. Out of 7 gets, 5 ladies how may 6 member committees ca be formed, such that there will be atleast ladies i the committee. (Mar 06) *0. How may ways ca the letters of the word ENGINEERING be arraged so that N s come together but E s do ot cometogether. Page No. 9 Resolve ito partial fractios ***. ( + )( ) PARTIAL FRATIONS ***. ( + )( + ) (Mar 05,07,09) ***. Fid the coefficiet of i the power series epasios of specifyig the regio i which the epasio is valid. ***. (i) (ii) ( )( + )( ) ( a)( b)( c) ***5. Resolve ito partial fractios + **6. ( )( + ) ( ) (March 06) *7. ( )( + ) *8. + ( + + ) 8 *9. ( + ) EXPONENTIAL AND LOGARITHMI SERIES ***50. Show that =! 5! 7! e + + +!!! e ***5. Show that = ( ) ***5. Fid the sum of the series !!! ***5. Show that 5... log = e

10 VaithaTV GUIDE educatio & areer **5. Show that = e!!! **55. Fid the sum of the ifiite series **56. Show that = loge *57. Show that !! 6! = loge (Mar 09) *58. Sum the series usig d method.!!!! 5! PROBABILITY ***59. Fid the probability of drawig a Ace or a spade from a well shuffled pack of 5 playig cards. ***60. A, B, are three horses i a race. The probabiity of A to wi the race is twice that of B, ad probability of B is twice that of. What are the probabilities of A, B ad to wi the race. (Mar 07) ***6. The probability that Australia wis a match agaist Idia i a cricket game is give to be. If Idia ad Australia play matches what is the probability that i) Austraia will loose all the matches ii) Australia will wi atleast oe match. ***6. A problem i calculus is give to two studets A ad B whose chaces of solvig it are ad. Fid the probability of the problem beig solved if both of them try idepedetly. ( Mar 05) **6. If two umbers are selected radomly from 0 cosecutive atural umbers, fid the probabiity that the sum of the two umbers is i) a eve umber ii) a odd umber ( Mar 07) **6. If A ad B are idepedet evets of a radom eperimet the show that A ad B are also idepedet. **65. A speaks truth i 75% of the cases ad B i 80% cases. What is the probability that their statemets about a icidet do ot match **66. The probability for a cotractor to get a road cotract is ad to get a buildig cotract is 5 9. The probability to get atleast oe cotract is. Fid the probability 5 that he gets both the cotracts. **67. A bag cotais two rupee cois, 7 oe rupee cois ad half a rupee cois. If three cois are selected at radom, the fid the probability that (i) the sum of three cois is maimum (ii) the sum of three cois is miimum (iii) each coi is of differet value **68. The probabilities of three evets A,B, a re such that P(A)=0., P(B)=0., P()= 0.8, P( A B) = 0.08, P( A ) = 0.8, P( A B ) = 0.09ad p( A B ) Show that P( B ) lies i the iterval [ ] Page No. 0 0.,0.8.

11 Page No. VaithaTV GUIDE educatio & areer *69. If A, B, are three evets the show that P ( A B ) = P( A) + P ( B) + P( ) P( A B) P ( B ) P( A) + P( A B ). *70. A pair of dice are rolled what is the probability that they sum to 7 give that either die shows a? *7. If P is a probability fuctio the show that for ay two evets A ad B P( A B) P( A) P( A B) P( A) + P( B) VERY SHORT ANSWER QUESTIONS QUADRATI EQUATIONS. For what values of m the equatio ( m + ) + ( m + ) + m + 8 = 0 has equal roots. (Mar 0). If the equatio 5 m( 8) = 0 has equal roots fid the value of m. (Mar 0, May 08). If = 0 ad a + 5 = 0 have a commo root the fid a.. If α, β are the roots of the equatios a + bc + c = 0 fid the value of α + β (Mar 08, 09) 5. If α ad β are the roots of the equatio a + bc + c = 0 the fid the value of α β (i) β + α (ii) α β 7 + α 7 β 6. α + β If α, β are the roots of a + b + c = 0 the fid the value of α + β 7. Fid the Quadratic equatio whose roots are ± 5i (Mar 07) 8. Fid the Quadratic equatio whose roots are p q p + q, ( p + q) ( p ± q) p q (Mar 06) 9. Fid the chages i the sig of the epressio 5 + ad fid their etreme value. 0. If + b + c = 0 ad + c + b = 0 ( b c) have a commo root, the show that b + c + = 0 (March 005). Fid the quadratic equatio the sum of whose roots is oe ad sum of the squares of the roots is. (March 007) THEORY OF EQUATIONS. Fid the Quotiet ad remaider whe is divided by 7 +. Fid the polyomial equatio whose roots are the squares of the roots of = 0. If,,α are the roots of = 0 the fid α. 5. If α, β,are the roots of = 0, the fid α ad β. ( Mar 08) 6. Fid the trasformed equatio whose roots are the egatives of the roots of = 0.

12 Page No. VaithaTV GUIDE educatio & areer 7. Fid the equatio whose roots are reciprocals of the roots of = 0 8. If α, β, γ are the roots of the equatios + = 0 fid the equatio whose roots are times the roots of give equatio.. (Jue 05, March 09) 9. If α, β ad γ are the roots of + = 0 the fid i) α β ii) α β + αβ 0. Form the equatio whose roots are ±, ± i. ( Mar 07) MATRIES. Defie trace of a matri ad fid the trace of A, if A = 0. If A = is a symmetric matri, fid ( Mar 05). If 0 0 A = 5 6 ad det A = 5, the fid ( Mar 0, 07). If ω is a comple (o - real) cube root of uity, the show that ω ω ω ω ω = 0 ω cosα siα 5. Fid the adjoit ad the iverse of the matri siα cosα ( Mar 09) 6. 8 If A = B = 7 ad X + A = B the fid X ( Mar 95) 7. If A = k ad A = 0 fid the value of k (Mar 05) 8. Defie symmetric matri ad skew-symmetric matri (Mar 05, Jue 05, May 07) 9. If 0 A = is a skew-symmetric matri, fid the value of (Model Mar 09) 0. If cosα siα A = siα cosα the show that AA = A A = I ( Mar 07). Defie scalar matri, give a eample

13 VaithaTV GUIDE educatio & areer. y 8 5 If = z + 6 a, fid, y, z ad a. i 0 If A = 0 i, fid A ( Mar 08). Fid the rak of each of the followig matrices i) ( Mar 08) ii) iii) 5 iv) 0 5. ostruct a X matri whose elemets are give by 6. If Page No. aij i j = (March 06) A = 5 the fid T A + A ad T AA (March 007 ) 7. If P + 5. P = P r fid r 5 PERMUTATIONS & OMBINATIONS 8. Fid the umber of ways of arragig the letters of the word (i) PERMUTATION (ii) INTERMEDIATE (iii) INDEPENDENE ( Mar 09) (iv) MATHEMATIS (Mar 06) 9. If = 500 ad = 0 fid ad r Pr r 0. If = fid r (Mar 08) r+ r 5. If p = 680 the fid (Mar 06). Fid the umber of positive divisors of 080. If p = 0 fid (March 05, 09). Fid the umber of ways of arragig the letters of the word TRIANGLE so that the relative positios of the vowels ad cosoats are ot disturbed 5. Fid the umber of letter words that ca be formed usig the letters of the word PISTON i which at least oe letter is repeated. 6. Fid the umber of bijectios from a set A cotaiig 7 elemets o to itself. 7. Fid the umber of ways of arragig boys ad girls aroud a circle so that all the girls together 8. Fid the umber of ways of selectig vowels ad cosoats from the letters of the word EQUATION 9. Fid the umber of differet chais that ca be prepared usig 7 differet coloured beeds. ( Mar 08) 50. There are 5 copies each of differet books. Fid the umber of ways arragig these books i a shelf i a sigle row

14 Page No. VaithaTV GUIDE educatio & areer 5. Fid the umber of ijectios from set A cotaig elemets i to a set B cotaiig 6elemets 5. How may umbers ca be formed usig all the digits,,,,,, such that eve digits always occupy eve places 5. Fid the umber of 5 letter words that ca be formed usig the letters of the word NATURE, that begi with N whe repetitio is allowed. 5. Fid the value of If c = c7, the fid 9c (Mar 06) 56. If a set A has twelve elemets, the fid the umber of subsets of A havig elemets. (Mar 07) BI-NOMIAL THEOREM 57. Fid the umber of terms i the epasio of (i) ( a + b + c) 7 ( Mar 05) (ii) a b Fid the set of values of for which ( ) 7 is valid. ( Mar 08) 59. Fid the approimate value of i) 5 ii) Fid the umerically greatest term(s) i the epasio of ( 5 y) whe ad = 7 9 =, y = 7 6. If c r is the largest biomial coefficiet i the epasio of ( + ) fid the value of c r. 6. Fid the coefficiet of 7 i the epasio of (Mar 06, 09) 6. Fid the middle terms i the epasio of i) y 7 6. Prove that c 5c 8 c... ( ) c ( ) = ii) a + b 65. Fid the term idepedet of i the epasio of Prove that c 0 + c + c + 8 c c = ( Mar 07) 67. Fid the 8 th term of Fid the middle term or terms of the epasio Fid the umerically greatest term i the epasio of ( ) 0 whe (Jue 05) =. (Mar 05)

15 VaithaTV GUIDE educatio & areer EXPONENTIAL AND LOGARITHMI SERIES 70. y y y If y = the show that = y !!! (Mar 05, 07) 7. Fid the sum of series log e log9 e + log7 e log 8 e +... (Mar 06) 7. Fid the coefficiet of (i) i the series epasio of e + ( ii) i e + (Mar 05, 08) !!!! 7. Fid the sum of the ifiite series If < < ad y 75. Fid the sum of the ifiite series = the show that Page No. 5 = y+ y + y + y +...!!! (Mar 005, 007) ( Mar 08)....5 PROBABILITY 76. Fid the probability that a o-leap year cotais i) 5 Sudaysii) 5 Sudays oly. (Mar 00, 009) 77. If A ad B are idepedet evets with P( A ) = 0., P( B ) = 0.5, the fid i) P( A / B ), P(B/A) ii) P( A B), P( A B) ( Mar 06, 08) 78. If A ad B are two evets with P( A B) = 0.65, P( A B) = 0.5. The fid the value of P ( A) P ( B) +. (Mar 05) 79. Defie i) mutually eclusive evets ii) idepedet evets 80. Two fair dice are rolled, what is the probability that the sum o the faces of the two dice is 0. (March 006) 8. Fid the probability of obtaiig two tails ad oe head whe cois are tossed. 8. Fid the probability that particular persos ever sit together, whe persos sit i a row at radom. 8. Fid the probability of throwig a total score of 7 with dice. 8. For ay two evets A ad B show that P ( A B) P ( A B) P ( A) P ( B) 85. If P( A) =, P( B) = y, P( A B) z = the fid P ( A B) = + (Mar 05). 86. Two dice are throw. The fid the probability of gettig the same umber o both the faces. (Jue 05) 87. Fid the probability of gettig two heads ad two tails whe four cois are tossed at a time. (Mar 008) RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 88. A poisso variable satisfies P( X = ) = P( X = ) fid P( X = 5) 89. The mea ad variace of a biomial distributio are ad respectively. Fid P( X ) ( Mar 08) 90. If X is poisso variate such that P( X = 0) = P( X = ) = k the show that k e = (Mar 05)

16 VaithaTV GUIDE educatio & areer Page No I a biomial distributio radom variable X has mea 5 ad variace 5. Fid the distributio. (Jue 05) 9. If the mea ad variace of a biomial variable X are. ad. respectively, fid P( < X ) ( May 06) 9. For a biomial distributio with mea 6 ad variace, fid the first two terms of the distributio. 9. I a city 0 accidets takes place i a spa of 50 days, assumig that the umber of accidets follows the poisso distributio, fid the probability that there will be three or more accidets i a day. 95. The probability distributio of a radom variable X fid the value of k ad the mea of X. (March 007)

Assignment ( ) Class-XI. = iii. v. A B= A B '

Assignment ( ) Class-XI. = iii. v. A B= A B ' Assigmet (8-9) Class-XI. Proe that: ( A B)' = A' B ' i A ( BAC) = ( A B) ( A C) ii A ( B C) = ( A B) ( A C) iv. A B= A B= φ v. A B= A B ' v A B B ' A'. A relatio R is dified o the set z of itegers as: