Objective Mathematics

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Alan Stanley
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1 6. If si () + cos () =, the is equal to :. If < <, the umber of solutios of equatio ta ( ) ta ( ) ta ( ) ta ( ) 5. If 0 to :. If si si ta, the is equal 5 cos ta ta ta cot ta ta ta... terms 7 is equal to ta ( ), the is equal to :. A root of the quadratic equatio ta ta Sum of ifiite series : cot () cot (8) cot (8) cot ()... is equal to : Which oe of t he followig is equivalet to? ta ( ) cos 5 si 5 ta ta 9. The pricipal value of si (si 0) cos (cos 5) Complete solutio set of, si cos, The value of si ta cos ta 5,. If si si ( ), the,,, 5 7 [ 9 ] Mathematics for JEE-0

2 Iverse Trigoometric Fuctios. If cot cot y cot z, the ( + y + z) y z y z y + yz + z. The value of cos y z y z 6 cos 9. The value of si (si) cos (cos) is equal to : If si... cos..., for 0, the equals to : / /. If,, ta 6 the value of the summatio ta si ta 5 cos 5. If = ta ; si, where (0, ), the ( + ) is equal to : 0. If,, the value of the epressio si cos(cos (cos ) si (si )) is equal to :. Complete solutio set of ta (si ),,, {0} (, ) {0} 6. cos cos( cot ( )) is equal to : 8 7. The maimum value of (sec ) (cosec ) 8. Rage of, f ( ) si ta sec, 6. The value of si si If,, the cos cos ta cos cos, 0 [ 0 ] Mathematics for JEE-0

3 5. If 0,, t he the value of summatio ta ta ta (cot ) ta (cot ) 0 C passes through origi ad have costat slope of sg(e). all poits o C are equidistat from origi. C bouds a regio of square uit area. C bouds a regio of coordiate aes. square uits with 6. Let si( cos { cot( ta )}) 0, the possible values of ' ' ca be : sg( ) 7. Let the equatio si ( ) 0 is havig at least oe real solutio, the possible values of ' ' ca be : ta (ta ) cos (cos ) si (si ) cosec (cosec 7) 8. Let the system of equatios cos (si y) ad (si y) cos be cosistet, where 6 R, the : Least positive itegral value of is. Greatest positive itegral value of k, where k =, is 7. Possible umber of itegral values of are. Least positive itegral value of is. Followig questios are assertio ad reasoig type questios. Each of these questios cotais two statemets, Statemet (Assertio) ad Statemet (Reaso). Each of these questios has four alterative aswers, oly oe of them is the correct aswer. Select the correct aswer from the give optios : Both Statemet ad Statemet are true ad Statemet is the correct eplaatio of Statemet. Both Statemet ad Statemet are true but Statemet is ot the correct eplaatio of Statemet. Statemet is true but Statemet is false. Statemet is false but Statemet is true.. Statemet : Sum of the ifiite series : 9 9 S cot () cot cot cot... 8 is equal to Statemet : If S r ta, r r the 9. If [ ] represets the greatest iteger just less tha or equal to, the solutio set of the equatio cot ta 0 cotais : 5, cot,, ta [si, si ] 0. Let P(, y ) satisfy the equatio cos ( ay) cos ( y) cos ( b) 0. If a = 0 ad b = the P lies o curve C. For curve C which of the followig statemets are correct : S ta, ad hece lim S.. Let cot si p cos(ta ( )) q ta cos cos(cot ( )), ad the Statemet : p + q = 0 Statemet : p ( ) ad q ( ). [ ] Mathematics for JEE-0

4 Iverse Trigoometric Fuctios. Statemet : If cos cot si, where [.] represets the greatest iteger fuctio, the ehaustive set of values of '' is (cot, ] Statemet : si 0.. Cosider the ordered pairs (, y) satisfyig the coditios y cos = 0 ad y = si (si ). Statemet : If [, ], the four ordered pairs of (, y) eist Statemet : y = cos ad y = 0 itersects at four distict poits. o 5. Cosider a triagle ABC, where B 90, ad M ta a c ta b c a b. M Statemet : Value of cot Statemet : Value of M is 5º. [ ] Mathematics for JEE-0

5 Comprehesio passage () ( Questios No. - ) Cosider the fuctios f ( ) si ad g () = ( ) + k for all R, where ' k' is a parameter. O the basis of defiitios of f () ad g () aswer the followig questios.. If [.] represets the greatest iteger fuctio, ad, are the maimum ad miimum values respectively of y = [ f ()], the ( ) is equal to : 7. If the equatio f () g() = 0 is havig at least oe real solutio the complete set of values of k,,, (, ). Number of values of satisfyig the equatio (ta ) f ( ) f ( ) (ta ) is/are : 0 Comprehesio passage () ( Questios No. -6 ) Let P ad Q be the positive itegral ordered pairs of (, y ), where < y, which satisfy the equatio y ta ( ) cos si. y 0 O y plae if OP < OQ, where 'O' is origi, the aswer the followig questios. 5. Let poits 'P' ad 'Q' be (a, b) ad (c, d) respectively, where f :[ a, c] [ b, d] is liear fuctio which is surjective i ature, the f () ca be : Diametric legth of circle passig through 'P' ad 'Q' ad orthogoal to + y = 0, Let ta, the the least iteger just r r greater tha the value of cot is equal to Let the equatio p (si ) (cos ) is 8 havig real solutio of, where p I, the total umber of possible values of p are... cos (cos ) log, 9. If the umber of solutios of ' ' is/are Let u ta ta cos v (u + v) is equal to... ta ta ( ) cos, ad the value of. Let poits 'R' ad 'S' be the reflectio of 'P' ad 'Q' respectively about the lie mirror y = 0, the area (i square uits) of the quadrilateral PRSQ is equal to : [ ] Mathematics for JEE-0

6 Iverse Trigoometric Fuctios. Match the followig colums (I) ad (II). Colum (I) Colum (II) If ta () is a solutio of the equatio (p) ta 0 sec 0, the value of ca be (q) 0 7 If cot, the value of ca be (r) Value of ta (ta ) + si (si ) is (s) Maimum value of. Match the followig colums (I) ad (II) Colum (I) If (, 0), the value of If 7 5( ).sec is less tha (t) 5 ( ) ta cos (p) 0 Colum (II),, the value of si si ( ) (q) If (, e), the value of ta cot ( ) If (, ), the value of ta ta (r) (s) (t) [ ] Mathematics for JEE-0

7 E (a, c, d) 7. (a, b, d) 8. (b, c, d) 9. (a, b, d) 0. (b, d) E ( ) 8. ( 7 ) 9. ( 8 ) 0. ( 8 ). p, r, t. p r, s, t q p r r, s, t q [ 5 ] Mathematics for JEE-0

Objective Mathematics

Objective Mathematics . If sum of '' terms of a sequece is give by S Tr ( )( ), the 4 5 67 r (d) 4 9 r is equal to : T. Let a, b, c be distict o-zero real umbers such that a, b, c are i harmoic progressio ad a, b, c are i arithmetic