CET MOCK TEST If a,b,c are p, q and r terms repectively of a G.P., then (q-r)loga+(r-p)logb+(p-q)logc= a)0 b) 1 c)-1 d)abc

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Owen Barton
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1 CET MOCK TEST 5 SUB:MATHEMATICS MARKS:60 TOTAL DURATION MARKS FOR ASWERING:70MINUTES th th th 0. If a,b,c are p, q ad r terms repectively of a G.P., the (q-r)loga+(r-p)logb+(p-q)logc= a)0 b) c)- d)abc 0. Epress the recurrig decimal as a ratioal fractio. a)68/495 b)66/433 c)67/495 d)68/ The value of is a)3 b) c) 4 d)5 ( + )! 04. is divisible by! ( ) a)4 b)5 c)6 d)7 05. Total umber of ways of givig at least oe coi out of three 5 paise ad two 50 paise cois to a beggar is a)3 b) c) d)35 th 06. term of + is 3 a)78 b)78 c)78 d)

2 07. R is the set of real umbers f:r R defied by f()=, the f is a) oto fuctio b)oe-oe fuctio c)ito fucio d) ot a fuctio. 08. The egatio of the propositio:" It is cloudy or it is raiig" a)it is cloudy ad it is raiig b)it is cloudy ad it is ot raiig c)it is ot cloudy ad it is ot raiig d) It is ot cloudy ad it is raiig. 09. Oe ed of a lie segmet is (5,3), the midpoit is (7,). Fid the other co-ordiates of the other ed. a)(9,-) b)(9,0) c)(9,) d)(9,) 0. Fid the equatio to the locus of a poit which moves at a costat distace of 5 uits from a fied poit (,-3) a) + y 4+ 6y = 0 b) + y y 4 = 0 c) + y 4 6y+ = 0 d) y 4+ 6y = 0.Fid the orthocetre of the triagle formed by the vertices A(5,-),B(-,) ad C(,4) a)(-, ) b)(-,- ) c) (, ) d)(-,- ) If slope of oe of the lies a + hy + by = 0 is three times the other the it is a) 3h = ab b)3h = 4 ab c)h = 3 ab d)h = ab! 3. The agles of a triagle are ia.p. The ratio of the umber of r! r! degrees i the least to the umber of radias i the greatest is 60: π. Fid the agles i degrees. 0 0 a)30,60, 90 b)45,60,90 c)60,90,0 d)30,60, If si θ =.si( θ+ α) the (-).ta( θ+ α) = a).ta α b)(+).ta α c)(-).ta α d).(+ta α) ( )

3 5. Solve the triagle give that b=, c= 3 +, A = 30 a)a=, B = 45, C = 05 b)a=, B= 60, C = b) a=, B = 45, C = 60 d) a=, B = 30, C = A cycle graph cosists a)two cycle of vertices c)oly vertices b) a sigle cycle of vertices d)multiple cycle of vertices π / θ 7.lim = cot θ π θ a) b) c)0 d) lim = a)e b)e c)e d)e Fid the last digit i 3 a)4 b)8 c)9 d) 0.For ay positive odd iteger, ( ) is divisible by a) 6 but ot by b) but ot by 4 c) 4 d) 5. If A=, B= & C = fid X such that A+B+X=3C a) b) c) d) π π π π cos si cos cos. 4 = π π π π cos si si si a)9/6 b)3/4 c)3/6 d)/6

4 cos( α + β) -si( α+ β) cosβ 3. The determiat si α cos α siβ -cos α si α cosβ is idepedet of a) α b) β c) α ad β d)either α or β 4. If A= 3 the characterstic roots of A are: a)-5,,, b)5,-, c)5,-,- d)5,, 5. I the multiplicative group whose elemets are the cube roots of uity,amely { ωω },,, the iverse of the elemet ωis a) b) ω c)/ ω d) ω { } 6. I the group G= 0,,,3,4,5 uder additio modulo 6,(3+5 ) a) 0 b) c) d)3 { } 7. The set G= 0,,,3,4,5 with operatio of additio modulo 6 is a group. Which of the followig is a subgroup of G? { } { } { } { } a) 0,3 b),4 c),3 d),3 is r r 8. The projectio of a = (,,) o b = (4, 4,7) is a)9/ b)9/8 c)9/9 d)9/7 r r θ 9.If a ad b are uit vectors ad θ is the agle betwee them,si = r r rr r r r r a b ab. a) a b b) a+ b c) r r d) r r ab ab 3. If a, a, a..., a is a A.P. with commo differece d the 3 d d d + + is + aa + aa 3 + a a ( ) d d d a a a) b) ta c) ta d) ta a + a + a a + aa a + a ta ta ta...ta equal to 3+ 3.cos si =, is 4 the 3 a) b) 6 c)/ d) 3 /

5 4 6 (si + si + si... + ) loge 33. If e satisfies the equatio 9+ 8 = 0, the the value of cos π,0 p p is... cos + si a) ( 3 + ) b) ( 3 ) c) ( 3) d) ( 5 + ) 34. If (cos θ +isi θ)(cos θ+isi θ)...(cos θ+isi θ)=, the the value of θ is mπ 4mπ mπ a)4m π, m z b),m z c),m z d),m z ) ( + ) ( + ) ( + ) 35.If ω( ) is a cube root of uity,the +i+ ω i ω - - equals ω -i -i+ ω- - a)0 b) c)i d) ω + y + c = a + y + c by = 36. The circles whose equatios are ad 0 will touch oe aother eterally if a) + = b) + = c) + = d) - - = b c a c a b a b c b c a 37. If the circles 6 0, 0 itersect orthogoally, + y + + ky+ = + y + ky+ k = the k is a) or -3/ b)- or -3/ c) or 3/ d)- or 3/ 38. The focus of the parabola y y+ = 0 is a)(/4,0) b)(,) c)(3/4,) d)(5/4,) y 39. The ecetricity of a ellipse + = whose latus rectum is half of its major ais is a b 3 3 a) b) c) d) The equatio of the chord of the hyperbola 5 6 = 400 which is bisected at the y poit (6,) is a)6-75y=48 b)75-6y=48 c)5-4y=400 d)67+5y=396 ta + sec 4.. If f()=, the f '() is ta sec + a)sec(ta-sec) b)sec(sec-ta) c)sec(sec+ta) d)ta(ta-sec)

6 4. If y=cos3.cos4, the y is π π π π a) 7 cos 7 cos b) 7 cos 7 si π π π π c) 7 cos cos + c) 7si 7 cos Derivative of sec... at =/ is wrt a) b)4 c) d)- dy λ 44. If siy=.si(a+y) ad =. the λ is d + cosa a)si a b)cosa c) 0 d) -sia 45. If y=si(msi ), the (- ) y y + m y is a) b)- c)0 d) 46. The poit o the curve y=6- where the taget is parallel to -ais is a)(0,0) b)(,8) c)(6,0) d)(3,9) If 47. the subormal at ay poit o y=a is of costat legth, the the value of is a)/ b) c) d)- 48. The agle of itersectio of the curves y=4- & y = is π a) / b)ta (4 / 3) c)ta (4 / 7) d) π 49.The sides of a equilateral triagle are icreasig at the. rate of cm/sec.the rate at which the area is icreases whe the side is 0cm.is a) 3sq.uits/sec b )0 sq. uits /sec c )0 3 sq. uits /sec 0 d ) sq. uits /sec The. Maimum value of log = a) log b)0 c)/ e d )

7 5. cos cot = + ) + b) ) si cot + + c) + c d) + c a c b c 5. If + si d = 4 cos( a + b) + c. the the value of a & b is π π a), b), c), d), 4 3cos+ si 53. If d = f ( ) + log(4si + 5cos ) + c, the f()= 4si + 5cos a) b) c) d) e ( + log ) 54. d = e log a) + c b) e ( + log ) + c c) e log + c d) e log + c 55. d = a)- b)0 c) d)4 π /4 56. If I = ta θ. dθ, the I + I = a) / 4 b)/5 c)/6 d)/7 57. For which of the followig values of m, is the area of the regio bouded by the curve y=- ad the lie y=m equals 9/? a)-4,0 b)-,3 c),3 d)-,4,

8 58. Area of the curve +y =a is a) πa b)πa c)4πa d) πa 59.Degree of the differetial equatio: 3/ dy d y + = 5 is 3 d d a) b) c)3 d)4 dy 60. The solutio of = cos( y) is d y y y y a)y+cot +c b)+cot +c c)+ta + c d)y-cot + c

JEE(Advanced) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 20 th MAY, 2018)

JEE(Advanced) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 20 th MAY, 2018) JEE(Advaced) 08 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 0 th MAY, 08) PART- : JEE(Advaced) 08/Paper- SECTION. For ay positive iteger, defie ƒ : (0, ) as ƒ () j ta j j for all (0, ). (Here, the iverse