Transcription of ANSWERS
1 EXERCISE1.(i) {2}(ii) {0, 1}(iii) {1, p}2.(i) {0, 1, 1}(ii) 113 (iii){}3,2 , 2 , 3 3. {1, 2, 22, 23, ..2P 1,(2p 1}4.(i) true (ii) false (iii) true (iv)True7.( i){2, 4, 6, 8, .. , 98}(ii)(1,4, 9, 16, 25, 36, 49, 64, 81,}8.(i){4, 8, 12}(ii){7, 8, 9}(iii)13, 1,22 (iv){0, 1, 2}9.(i){4, 5, 6, ..10}(ii){5}(iii){1, 2, 3, 4, 5} T = {10}24.(i) 2 (ii) 3 (iii) 3 (iv) (a) 3300 (b) 400028.(i) 6, (ii) 3, (iii) 9, (iv) 1, (v) 2, (vi) 6, (vii) 30, (viii) 2029. EXEMPLAR PROBLEMS [1,2] n (B) B 48.{ , {1}, {2}, {1, 2}49.{0, 1, 2, 3, 4, 5, 6, 8}50.(i) {1,5, 9, 10 } (ii) { 1, 2,3, 5, 6, 7, 9, 10 } 52.(i) (b) (ii) (c) (iii) (a) (iv) (f) (v) (d) (vi) (e) EXERCISE1.(i){( 1, 1), ( 1, 3), (2, 1), (2, 3), (3, 1), (3, 3)}(ii){(1, 1), (1, 2), (1, 3), (3, 1), (3, 2), (3, 3)}(iii){(1, 1), (1, 3), (3, 1), (3, 3)}(iv){( 1, 1), ( 1, 2), ( 1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}2.))
2 {(0, 1), (0, 2), (1, 1), (1, 2), (2, 1), (2, 2)}3.(i){(0, 3), (1, 3)}(ii){(0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1,5)}4.(i)113a= and b = 23 (ii) a = 0 and b = 25.(i){(1, 4), (2, 3), (3, 2), (4, 1) }(ii){(1, 1), (1, 2), (1,3),(2, 1), (2, 2), (3, 1)}(iii){ (4, 5), (5, 4), (5, 5)} of R = {0, 3, 4, 5} = Range of of R1 = [ 5, 5 ] and Range of R1 = [ 3, 17 ] = {(0, 8), (8, 0) (0, 8), ( 8, 0)} of R3= R and range of R3 = R+ {0}10.(i) h is not a function(ii) f is a function(iii) g is a function (iv) s is afunction(v) t is a constant function11.(a) 6(b)13644(c)13(d)t2 _ 4 (e) t + 512.(a)x = 4(b)x > 413.(i)(f + g) x = x2 + 2x + 2(ii)(f g)x = 2x x218/04/18 ANSWERS 305(iii) ( f g) x = 2x3 + x3 + 2x + 1(iv)fg x = 2211xx++14.(i)f = {( 1, 0), (0, 1), (3, 28), (7, 344), (9, 730)} = 1 , , ===== 2 , = = = = = 117.
3 (i)R {2n : n Z}(ii)R+(iii)R(iv)R { 1, 1}(v)R {4}18.(i)[32, )(ii)( , 1](iii)[ 0 , )(iv)[ 2, 4] , 32( )4 , 222 , 23xxf xxx < = < 21.(i)(f + g) x = x+ x(ii)(f g ) x = x x(iii)(fg) x = 32x(iv)1fxgx = of f = (5, ) and Range of f = R+ {2, 3, 4, 5}37.(a) (iii) (b) (iv) (c) (ii) (d) (i) coscos 2xx18/04/18306 EXEMPLAR PROBLEMS 1+15. = n + ( 1)n 44 16. = 2n + 74 17. = 2n 3 18. = 5,3 3 19.,,6 4 2x = 111722 + 4 = + [4 3(a2 1)2] , 22a 2 Axx +65. 1366.[ 3, 3] (a) (iv) (b) (i) (c) (ii) (d) (iii)18/04/18 ANSWERS (n) : 2n < (n) : 1 + 2 + 3 + .. + n = (1)2n n+ 1 + i3.(0, 2) (1, 0) 2 , 0 ,33 ,22ii 22. 2 i23. 552 cossin1212i + 25.]
4 (i)()()222212abzz++(ii) 15(iii) 2 (iv) 0 (v) 12 2i (vi)1z (vii) 0(viii)6 and 0(ix) a circle(x) 23 + 2i26.(i)F(ii)F(iii)T(iv)T(v)T(vi)T(vii)F (viii)F27.(a) (v),(b) (iii), (c) (i),(d) (iv),(e) (ii),(f) (vi),(g) (viii) and(h) (vii)18/04/18308 EXEMPLAR PROBLEMS (1)41aa++31. 23 + 2 2.[0,1] [3,4]3.(, 5 ) ( 3, 3) [5, )4.[ 4, 2][2, 6] 22,33 than and than 230 litres but less than 920 104 F and 113 F11. 41 8 km and 10 , 3248,0,0xyxyxy+ + ,4,5,5,0,0xyxyxyxy+ + (i) F(ii)F (iii)T (iv)F(v) T(vi)F(vii)T(viii)F18/04/18 ANSWERS 309 (ix) T(x)F(xi)T(xii)F(xiii)F(xiv)T (xv) (i) (ii) (iii)>(iv)>(v) >(vi)>(vii) < , >(viii) . , ( 2)! 3 !nrr = 20. !(6!)22.(a) 11C4 (b) 6C2 5C2 (c) 6C4 + 5C423.(i) 14C9 (ii) (20C5 20C6)25.]
5 (i) 21, (ii) 441 (iii) = ,51, (a) (ii)(b) (iii) and(c) (i)61.(a) (iii)(b) (i)(c) (iv),(d) (ii)62.(a) (iv)(b) (iii)(c) (ii),(d) (i)63.(a) (i)(b) (iii)(c) (iv),(d) (ii)64.(a) (iii)(b) (i)(c) (ii) = 33. 194. 3003 (310) (25)18/04/18310 EXEMPLAR PROBLEMS MATHEMATICS5. (i) 252 (ii) 171898x; 192116x 6. 252 7. 1365 8. 5532252y x9. r = = 917. 175418.(C)19.(A)20.(C)21. (D)22.(B)23.(B)24.(C) 26. ()1 (2)2nn++ = 1229. 112027a C14 a56 term33. 8080 , Rs days6. 3420 72511. (i) 4n3 + 9n2 + 6n (ii) 6r term + last (a) (iii) (b) (i) (c) (ii)36.(a) (iii) (b) (i) (c) (ii)(d) (iv) + y + 1 = 4y + 3 = or 120 18/04/18 ANSWERS 3114.
6 X + y = 7 or 168xy+ =5.(3, 1), ( 7, 11) 3x 2 +3 = + 4y + 3 = =, b = 5y + 60 = 011. 3xy+ = 7y 12 = (1, 1) or 75 20y + 96 = 4y + 6 = 0 and 4x 3y + 1 = 020.(0, 2 + 5 32) (1, 2) + y + 1 = y 7 = 0, x + 3y 9 = (x2 + y2) 83 x + 64 y + 182 = x2 y2 = p2 (x2 + y2) (a) (iii)(b) (i) and(c) (ii)58.(a) (iv)(b) (iii)(c) (i),(d) (ii)59.(a) (iii)(b) (i)(c) (iv),(d) (ii) + y2 2ax 2ay + a2 = 03.,2 2a b 18/04/18312 EXEMPLAR PROBLEMS + y2 2x 4y + 1 = + y2 + 4x + 4y + 4 = 07.(1, 2) + y2 2x + 4y 20 = + y2 6x + 12y 15 = = 45and foci (4, 0) and ( 4, 0) += (2, 4) , (2, 4) cossina + 8y = = y2 = =. + y2 2x + 2y = + y2 4x 10y + 25 = 025.(x 3)2 + (y + 1)2 = + y2 18x 16y + 120 = + y2 8x 6y + 16 = 028.
7 (a) y2 = 12x 36,(b) x2 = 32 8y, (c)4x2 + 4xy + y2 + 4x + 32y + 16 = + 4y2 36x = + 5y2 = 18032. (a) 15x2 y2 = 15 (b) 9x2 7y2 + 343 = 0, (c) y2 x2 = (x 3)2 + (y + 4)2 = 24513 + y2 46x + 22y = + 25, += + 4xy + y2 + 4x + 32y + 16 = 13664yx= and (0, 10).47.(C)48.(C)49.(C)50.(C)18/04/18 ANSWERS EXERCISE2.(i) 1st octant (ii) 4th octant (iii) viiith octant (iv) vth octant (v) 2nd octant(vi) 3rd octant (vii) viiith octant (viii) vith octant3.(i) (3,0,0), (0,4,0), (0,0,2) (ii) ( 5, 0, 0), (0,3,0), (0,0,7) (iii) (4,0,0), (0, 3, 0),(0,0,5)4.(i) (3,4,0), (0,4,5), (3,0,5) (ii) ( 5, 3, 0),(0,3,7), ( 5, 0, 7) (iii) (4, 3, 0),(0, 3, 5), (4, 0, 5) (2, 4, 16)11.( 2, 2, 1)12.(1, 1, 2)13.( 3, 4, 7), (7, 2, 5) and ( 3, 12, 17)14.(4, 7, 6)15.(4, 5, 1), (3, 2, 1) = 2, b = 8, c = 13,, 92 2 :1 are (3,4,5), ( 1,6, 7), (1,2,3) and centroid is (1,4,13 ) :3 externally21.
8 (2,0,0), (2,2,0), (0,2,0), (0,2,2) (0,0,2) (2,0,2), (0,0,0), (2,2,2) cordinates (0, y, z) = 041. (0, 0, z) = 0 , y = cordinates44.(y, z cordinates) = 5 or 349.(1, 1, 2)50.(a) (iii) (b) (i) (c) (ii) (d) (vi) (e) (iv) (f) (v) (g) (viii)(h) (vii) (i) (x) (j) (ix)18/04/18314 EXEMPLAR PROBLEMS ()32522a+ = xxx++ 3xxx+ sec5sec3 tan3xxxx+++ tan secxx33.()22255 40 155 79xxxx+ cos5sec sin1sinxxxx++35.()cos ec2 cot2xxxx36.()() ()()22cot sincos2 cosaxxqxp qxaxec x+++37.()2cossincosbcx adx dbc dx+++ cos 2x18/04/18 ANSWERS 31539.()()()22 7 30 43 35xxx+ sin 2 sin 2xxxxx+ 2 cos 24xx42.()()22 2ax baxbx c+++43.()2 2 sin1xx+44.()2 adbccx d+ sinxxx47.()sectan1x xx+ 49. = = 33m= EXERCISE1.(i)to (v) and (viii) to (x) are (i)p : Number 7 is prime(ii)p : Chennai is in Indiaq : Number 7 is oddq : Chennai is capital of Tamil Nadu (iii)p : 100 is divisble by 3(iv)p : Chandigarh is capital of Haryanaq : 100 is divisible by 11q : Chandigarh is the capital of : 100 is divisible by 518/04/18316 EXEMPLAR PROBLEMS MATHEMATICS(v) p :7is a rational number(vi)p : 0 is less than every positive integerq : 7is an irrational numberq : 0 is less than every negative integer(vii)p : plants use sunlight for photosynthesisq : plants use water for photosynthesisr : plants use carbondioxide for photosynthesis(viii)p : two lines in a plane intersect at one pointq : two lines in a plane are parallel(ix)p : a rectangle is a quadrilateralq : a rectangle is a 5- sided (i)Compound statement is true and its component statements are :p.
9 57 is divisible by 2 and q : 57 is divisble by 3(ii)component statement is true and its component statements are :p : 24 is multiple of 4 and q : 24 is multiple of 6(iii)component statement is false and is component statements arep : All living things have two eyesq : All living things have two legs(iv)component statement is true and its component statements are :p : 2 is an number ; q : 2 is a prime number4.(i)The number 17 is not prime (ii) 2 + 7 6 (iii) Violet are not blue(iv)5 is not a rational number (v) 2 is a prime number (vi)There exists a real number which is not an irrational number(vii)Cow has not four legs (viii) A leap year has not 366 days (ix)There exist similar triangles which are not congruent(x)Area of a circle is not same as the perimeter of the circle5.(i)p q where p : Rahul passed in Hndi; q : Rahul passed in English(ii)p q where p : x is even integer ; q : y is even integer(iii)p q r where p : 2 is factor of 12; q : 3 is factor of 12; r : 6 is factorof 12(iv) p q where p : x is an odd integer.
10 Q : x +1 is an odd integer(v)p q where p : a number is divisible by 2, q : it is divisibe by 3(vi)p q where p : x = 2 is a root of 3x2 x 10 = 0, q : x = 3 is a root of3x2 x 10 = 018/04/18 ANSWERS 317(vii)p q where p : student can take Hindi as an optional paper and q :student can take English as an optional (i)It is false that all rational numbers are real and complex(ii)It is false that all real numbers are rational or irrational(iii)x = 2 is not a root of the quadratic equation x2 5x + 6 = 0 or x = 3 is nota root of the quadratic equation x2 5x + 6 = 0(iv)A triangle has neither 3-sides nor 4-sides(v)35 is not a prime number and it is not a complex number(vi)It is false that all prime integers are either even or odd(vii)x is not equal to x and it not eqaul to x(viii)6 is not divisible by 2 or it is not divisible by (i)If the number is odd number then its square is odd number(ii)If you take the dinner then you will get sweet dish(iii)If you will not study then you will fail(iv)If an integer is divisible by 5 then its unit digits are 0 or 5(v)If the number is prime then its square is not prime(vi)
