PLEASURE TEST SERIES (XI) - 07 By O.P. Gupta (For stuffs on Math, click at theopgupta.com)

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1 A Cmpilatin By : OP Gupta ) Fr mre stuffs n Maths, please visit : wwwtheopguptacm Time Allwed : 80 Minutes Max Marks : 00 SECTION A Questin numbers 0 t 0 carry mark each x x 5 Q0 Find the dmain f the functin f (x) x 5x Q0 Describe the sample space : A card is drawn frm a deck f 5 playing cards and its clur is nted OR Describe the sample space : A cin is tssed thrice and number f heads is recrded Q0 If 7 th arithmetic mean f and is 5 Hw many means can be inserted between them? Q0 Write the value f tan 75 SECTION B Questin numbers 05 t carry marks each Q05 Write the sum f the real and imaginary part f i i OR Find the value f i i Q06 (i) Write the truth value f : Tw and three when multiplied gives five (ii) Write the negatin f : Mumbai is a metr-city Q07 Write the value f k fr which the line (k )x ( k )y + k 7k + 6 = 0 is parallel t x-axis OR Fr what value f k are the pints (8, ), (, k) and (, 5) cllinear? Q08 Draw the arrw diagram f the relatin R defined n set A, by R = {(x, x + 5) : xa}, where A = {0, x,,, 0} OR Find the range f the functin f (x) x Q09 If A = {, 5, 7, 9, }, B = {7, 9,, }, C = {,, 5} and D = {5, 7}; find A (B D) Q0 Find the equatin f the lines which cut ff intercepts n the axes whse sum and prduct are and 6 respectively Q Slve : x + ix + = 0 Als find the sum f rts f the equatin Q Slve : tanθ + tan θ + tanθ tanθ = SECTION C Questin numbers t carry marks each Q Slve graphically : 5x y 0, x y, x y, x 0, y 0 Q Express 07 as a ratinal number (r qutient f tw integers) Q5 Draw the graph f the functin f (x) = x + x + Write its dmain OR Let f = {(, ), (, ), (0, ),(, )} be a functin defined n Z as f (x) = m x + n, s t m and n are real cnstants Write the values f m + n Hence draw the graph f f (x) Q6 Find the S D f the fllwing data : CI f Q7 Find the equatin f an ellipse whse ne vertex is lcated at (6, 0) and ne f the fcus is lcated at (, 0) Q8 Prve by the principle f mathematical inductin that fr all n N : n 5 57 (n )(n ) n Q9 In a twn f 0000 families, it was fund that 0% families buy newspaper A, 0% buy newspaper B and 0% buy newspaper C Als 5% families buy newspapers A and B, % buy B and C and % buy A and C If % families buy all the three newspapers, find the number f families which buy the PLEASURE TEST SERIES (XI) - 07 By OP Gupta (Fr stuffs n Math, click at thepguptacm)

2 PTS-07 By OP Gupta (M ) newspaper (a) A nly (b) B nly (c) nne f A, B and C Why d yu think that the students shuld read newspaper? OR Shw that fr any sets A and B, (a) A A B A B (b) A B A A B Q0 A cmmittee f persns is t be cnstituted frm a grup f men and wmen In hw many ways can this be dne? Hw many f these cmmittees wuld cnsist f ne men and wmen? OR Find the number f different 8 letter arrangements that can be made frm the letters f the wrd DAUGHTER s that (a) all vwels ccur tgether (b) all vwels d nt ccur tgether Q Find the crdinates f the pint in xy-plane which is equidistant frm the pints A(, 0, ), B(0,, ) and C(0, 0, ) Q If 6 th, 7 th, 8 th and 9 th n terms in the binmial expansin f (x + y) are respectively a, b, c and d then, b ac a shw that c bd c Q One side f a rectangle lies alng the line whse equatin is x + 7y + 5 = 0 Tw f its vertices are (, ) and (, ) Find the equatin f ther three sides SECTION D Questin numbers t 9 carry 6 marks each Q Prve that : cs A cs(60 A) cs(60 A) csa OR Find the value f ct Q5 A beam is supprted at its ends by supprts which are metres apart Since the lad is cncentrated at its centre, there is a deflectin f cm at the centre and the deflected beam is in the shape f a parabla Hw far frm the centre is the deflectin cm? 5(n ) Q6 Prve that the middle term in the expansin f x,x 0 is n x n! Q7 Let the p th and q th terms f an arithmetic prgressin be x and y respectively Shw that the sum f (p + q) terms is : p q x y x + y p q OR Find the sum t n terms f the series : ( ) ( ) upt n terms Q8 The number lck f a suitcase has wheels, each labelled with ten digits ie, frm 0 t 9 The lck pens with a sequence f fur digits with n repeats What is the prbability f a persn getting the right sequence t pen the suitcase? x, if x Q9 Shw that limf (x) des nt exist fr f (x) (x ) x, if x x OR Using first principle methd, differentiate f (x) w r t x x n PLEASURE TEST SERIES (XI) - 07 By OP Gupta (Fr stuffs n Math, click at thepguptacm)

3 PTS-07 By OP Gupta (M ) HINTS & ANSWERS fr PTS XI 07 SECTION A Q0 This functin is defined if x 5x 0 (x )(x ) 0 x and x Dmain = x R {, } Q0 As the pack f playing cards have tw types f card red card and black card S, sample space = {Red, Black} OR As the n f heads in three tsses f a cin may be either 0 heads, head, heads r heads S, sample space fr this experiment is {0,,, } Q0 As 7 th 0 AM is 5 means, a + 7 d = 5 ie, n n n 9 Q0 tan 5 tan 0 tan 75 tan(5 0 ) tan 5 tan 0 SECTION B i i i i i i Q05 Let z z i i i i i S, sum f real and imaginary part f z OR i i i i ( ) Q06 (i) F (ii) Mumbai is nt a metr-city Q07 As the line (k )x ( k )y + k 7k + 6 = 0 is parallel t x-axis s, its slpe will be 0 k Nw 0 k k OR Let the pints be A(8, ), B(, k) and C(, 5) If A, B and C are cllinear then, slpe f AB must be equal t the slpe f BC Nw k 5 k 8 k 5 5k 6k k Q08 Here R = {(0, 5), (, 6), (, 7), (, 8), (, 9), (5, 0)} Arrw Diagram is shwn belw : A R A OR Dmain : R, Range : R Q09 We have B D = {7,9,,,5,7} S, A (B D) = {7,9,} Q0 x y 6 = 0, x y + 6 = 0 PLEASURE TEST SERIES (XI) - 07 By OP Gupta (Fr stuffs n Math, click at thepguptacm)

4 PTS-07 By OP Gupta (M ) Q Rts are 0 i, 0 i Als the sum f rts 0 i 0 i 0 i Q π (n+ ), n Z 9 SECTION C Q (x ) (x ) x, x Q5 Dmain : Set f real numbers Here f (x) (x ) (x ), x (x ) (x ) x, x Take three cases as (i) x (ii) x (iii) x and sketch the graph yurself OR Here m =, n = / S, m + n = 5/ Functin is, f (x) = x Sketch the graph yurself Q6 67 Q7 x y 6 0 Q9 %, %, 0% 5 Q0 C, C C OR 6!!, 8! 6!! Q (,, 0) Q x + 7y =, 7x y =, 7x y + 5 = 0 SECTION D Q LHS : cs A cs(60 A) cs(60 A) cs A cs(60 A)cs(60 A) cs A cs(60 A 60 A) cs(60 A 60 A) cs A cs0 cs A cs A ( cs A ) cs A cs A cs A cs A csa RHS OR cs cs cs cs Let y ct sin sin cs sin cs cs cs cs sin sin 6 y 6 6 sin sin sin cs cs sin y PLEASURE TEST SERIES (XI) - 07 By OP Gupta (Fr stuffs n Math, click at thepguptacm)

5 PTS-07 By OP Gupta (M ) 5 6 y 6 y 6 n(n ) (n ) Q5 6 m Q7 OR Q8 Q9 See Mathematicia Vl by OP Gupta (Example) OR See Mathematicia Vl by OP Gupta (Example) 500 PLEASURE TEST SERIES (XI) - 07 By OP Gupta (Fr stuffs n Math, click at thepguptacm)