STD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0
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1 STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed by the espective co-fctos s its elements will be ) b) c) d) 0. The diection tios of the vecto = 5 i + 7 j 6 k ) ( 5, 7, 6) b) ( 5, 7, 6) c) ( 5, 7, 6) d) ( 5, 7, 6) 4. Sum of the sques of diection sines is ) b) 0 c) - d) 5. If = ( )( ) then = ) 4 b) 5 c) 7 d) 8 6. Sum of the binomil coefficients is ) n b) n c) n d) n If,b, c e in A.P. s well s in G. P. then ) = b c b) b = c c) b c d) = b =c 8. If A, G, H e espectively ithmetic men, geometic men nd hmonic men then ) A > G > H b) A < G > H c) A < G < H d) A > G < H 9. If two cicles touch ech othe etenlly then the distnce between thei centes is ) b) c) d) RAVEENDRAN R, LECTURER IN MATHS, ACHARIYA SIKSHA MANDIR, PUDUCHERRY Pge
2 0. Which of the following point lies in side the cicle + y 4 + y 5 = 0 ) (5, 0 ) b) (-5, 7) c) (9, 0) d) (, ). The vlue of Cos 5 0 is... ) sin 5 0 b ) c) d) sin If the teminl side is colline with the initil side in the opposite diection then the ngle included is ) 0 o b) 90 o c) 80 o d) 70 o. Which of the following is function which is not one-to-one? ) f : R R; b) f : R R; c) f : R {, }; d) f : R R; 4. Identify the coect sttements (i) constnt function is polynomil function (ii) polynomil function is qudtic function (iii) fo line function, invese lwys eists (iv) A constnt function is one-to-one only if the domin is singleton set ) (i) nd (iii) b) (i), (iii) nd (iv) c) (ii) nd (iii) d) (i) nd (iv) 5. equl to ) b) c) d) 6. If y = d y then d ) 6 b) c) d) 7. d ) 4 c b) log 4 c c) 4 c d) c sin 8. sin d ) c cos b) c c sin c ) + c ) d sin RAVEENDRAN R, LECTURER IN MATHS, ACHARIYA SIKSHA MANDIR, PUDUCHERRY Pge
3 9. Thee coins e tossed. The pobbility of getting tlest two heds is ) 8 b) 8 7 c) 8 d) 0. Two events A nd B e independent, then P(A/B) = ) P(A) b) P( A B) c) P(A) = P(B) d) P(A)/P(B) II Answe ny 0 questions, question numbe 0 is compulsoy ( 0 = 0 ). Evlute b bc c c( b) ( b c) b( c ). Find the sum of the vectos i j + k nd i + j 4 k nd lso the modulus of the sum.. Find the 7 th tem of the sequence whose n th tem is ( - ) n+ n n 4. Is the point ( 7, -) lie inside o outside the cicle +y 0 = 0? 5. Pove thtsin cos sin cos ec cos sec 6. Find the domin of the tionl function 7. Diffeentite: 8e + 7 tn + 8. Integte: sin 5 9. An intege is chosen t ndom fom the fist fifty positive integes. Wht is the pobbility tht the intege chosen is pime o multiple of Define Impope Fction of Rtionl Epession with one emple III Answe ny 0 questions, question numbe 40 is compulsoy ( 0 = 0 ). Solve fo if 4 0 RAVEENDRAN R, LECTURER IN MATHS, ACHARIYA SIKSHA MANDIR, PUDUCHERRY Pge
4 . If ABC nd A BC e two tingles nd G, G be thei coesponding centoids, pove tht A A + B B + C C = G G 7. Resolve into ptil fctions 4. Find the sum of 0 th tem to 00 th tem of the seies n 5. Find the dius nd cente of the cicle ( ) ( 5) + (y 7) (y ) =0 n 6. If tn nd tn show tht Solve the ineqution: Integte: e 7 4sec(4 ) tn(4 ) 5 9. A cd is dwn t ndom fom deck of 5 cds. Wht is the pobbility tht the dwn cd is (i) queen o club cd (ii) queen o blck cd 40. Diffeentite: tn IV Answe ll the questions ( 7 5 = 5 ) 4. Pove tht b bc whee, b, c e non zeo el numbes nd b c c hence Evlute the vlue of Pove tht the medins of tingle e concuent. 4. Resolve into ptil fctions ( 9 6)( ) b c b c If, b, c e in H.P., Pove tht b b c RAVEENDRAN R, LECTURER IN MATHS, ACHARIYA SIKSHA MANDIR, PUDUCHERRY Pge 4
5 4. Find the cicles which cuts othogonlly ech of the following cicles : + y + + 7y +4 = 0, + y y + = 0 nd + y - + y + = 0 Find k such tht the eqution + 7y - y - + 7y + k = 0 epesents pi of stight lines. Find the septe equtions of the stight lines nd lso the ngle between them. 44. If tn sin p, tn sin q, nd p > q then show tht p q = 4 pq If A+ B + C=, pove tht sin A - sin B + sin C = 4 cos A sin B cos C 45. Diffeentite sin cos sin cos using quotient ule. dy Find : d cos cos, y sin sin 46. Integte 0 Integte: ( 5) 47. If is el, pove tht the nge of 4 is between 4, A husbnd nd wife ppe in n inteview fo two vcncies in the sme post. The pobbility of husbnds selection is /6 nd tht of wife s selection is /5. Wht is the pobbility tht (i) both of them will be selected (ii) only one of them will be selected (iii) none of them will be selected. ALL THE BEST RAVEENDRAN R, LECTURER IN MATHS, ACHARIYA SIKSHA MANDIR, PUDUCHERRY Pge 5
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