Cosortium of Medical Egieerig ad Detal Colleges of Karataka (COMEDK) Udergraduate Etrace Test(UGET) Maths-0. If the area of the circle 7 7 7 k 0 is sq. uits, the the value of k is As: (b) b) 0 7 K 0 c) 6 d) ± C, r K 7 K A 7 K K 7 8 6 K 0 K -0 K. A ma ruig a race-course otes that the sum of the distaces from the two flag posts from him is alwas 0 metres ad the distace betwee the flag posts is 8 metres. The equatios of the path traced b the ma is give b b) c) d) 9 9 6 9 6 SP S P a a 0 a ae 8 ae b a ( e ) 6 9 9. The umber of commo tagets to the circles 0 ad 6 9 0 is b) c) d) As: (d) C (, ) r C (6, 8) r 6 6 9 C C 6 6 R r < 6 Circle are far apart o of commo tagets
. Equatio of the chord of the circle 6 9 0 bisected at (0, ) is As: ( b) c) d) Required T S (0) () ( 0) - ( ) 9 0 0 6 9 9 0 0. The agle betwee two asmptotes of the hperbola is 6 As: (b) ta - θ ta b) ta - b ta a c) ta - d) - ta - 6. The parametric equatio of a parabola is t, t. The Cartesia equatio of its directri is 0 b) - c) 0 d) 0 t t t 0 r 7. If ab r As: (d) ( ) t ( ) t ( ) ( ) a -a - h -a r ad a. b r the a r b r is equal to 6 b) c) d) a b a b a. b a b - 9 a b r r r 8. The directio cosies of the vector i j k is equal to,, b),, c),, d),,
As: (,, a 9. If,, are the cube roots of uit the ( ) 6 ( 6 ) is equal to 0. If As: ( b) 6 c) 0 d) - ( ( ) ) 6 ( ( ) 6 ) ( (-) ) 6 ( (- ) 6 ) () 6 ( ) 6 6 6 0 the is equal to e 6 log log e b) log e c) d) put t e dt e dt t e dt (t ) ta ( t ) t 6 e e ( d( t) t) 6 ta - e ta ta e e e e log e 8. (si ) d 8 9 9 b) - c) 0 8 d) 0 (odd fuctio). Area of the ellipse is give b 6 sq. uits b) 0 sq uits c) sq uits d) uits As: (b) A ab.. 0
d. The order of the differetial equatio d d b) c) d) Order. The solutio of - e - is d e - c b) e -(-) c c) e -(-) c d) e - c d e d e. d d( ) d e d e - ( - ). d ( ) 0 Itegrate : e ( ) C. If si - p - cos - p q ta - the the value of is equal to q As: (d) si p q pq p p b) p q pq c) p q pq - cos q ta q.ta p ta q ta ta (ta p ta q) ta ta p q.ta - ta pq ta d) p q pq p q pq r r r 6. The uit vector i the directio of the vector a b c is equal to r r a b r r r r r r r r r r c a b c a b c a b c b) c) d) 6 6 Required a b c a b c 6
7. Idetif the false statemet. A o-empt subset H of group G is a subgroup of G if ad ol if for ever a, b H a b - H b) The itersectio of two subgroups of a group G is agai a subgroup c) A group of order three is ot abelia d) If i a group F, (ab) a b a, b G the G is abelia Is false sice ever group of order is abelia. 8. If ta - ta - ta -. upto terms the 7 at 0 ad is equal to d b) - c) 0 d) As: (b) ta - ta ta ( ) ( )( ) ( )( )... whe ta ( )( ) ta ta ( ) ta ( ) ta ( ) ( ) d ( ) d 9. If cot α cot β the 0 cos( α β) cos( α β) is equal to b) c) d) ta α ta β cos( α β) cos( α β) cos α.cos β si α si β cos α. cos β si α.si β cot α.cot β cot α.cot β 0. If is a cube root of uit, the the value of determiat is equal to b) - c) 0 d) As: All aswers wrog c c 0 0 0 - ( - ) 0 - ( - ) - ( - ) -
. If the taget to the curve a at the poit (a, cuts off itercepts α ad β o the coordiate aes where α β 6 the the value of a is equal to b) 6 c) ± 0 d) ± 0 a Diff. w. r. t 6 a d d (a, a a a itercept α 6a 6 itercept 6 a β α β 6 a a 6 a ± 0 6. Legth of the subtaget at (a, o the curve a is equal to 8 b) 8 a c) - 8 a d) 8 a As: Questio is wrog because (a, does ot satisf the give equatio. The fuctio f () 6 is icreasig i the iterval As: ( (-, ) b) (, ) c) [, ) d) (, ] f () 6 f () -6 6 6-6 ( 6) -6 ( ) ( ) > 0 [ for icreasig fuctio] ( ) ( ) < 0 [ < & > -] [ > & < -] - < <. Divide 0 ito two parts such that the product of oe part ad the cube of the other is maimum. The two parts are As: (b) (, 8) b) (, ) c) (0, 0) d) (, 8) Give, 0 () P (0 ) [from ()] P 0 dp 60 d P 0 dp 0 60 two parts are (, ) [ correct aswer is (, ). Amog the give aswers b ot cosiderig the aswer (, ) ca be take as aswer]
. The umber of positive divisors of 896 is b) c) 6 d) 8 We have, 896 7 T ( ( ) ( ) ( ) 6 6. The last digit of 8! 7 9 is b) c) 0 d) As: (d) We have, 8! 0 (mod 0) ad 7 - (mod 0) (7 ). 7 (-). 7 (mod 0) 7 9-7 (mod 0) (mod 0) 8! 7 9 (mod 0) last digit is 7. ( log ) d C b) - c) log d) log As: ( ( ) d ( log )d d C d e 8. If ( ) d e f() the f() is equal to ( ) b) ( ) c) d) ( ) e ( ) d e d ( ) e d ( ) e ce f () c f () / 9. 0 si si t t cos dt t b) As: (d) c) d) / 0 si si t t cos dt t / 0 si t. cos t dt si t cos t Divide Nr. & Dr. b cos t / 0 ta t. sec t dt (ta t) put ta t 0 d ta 0
log 9 0. If 9 log 0 log the is equal to 8 0 b) c) 0 d) - log log 9 9 0 log log log 8 log 8 9 0 8 0 log 8 0 log 0 9. If p.. 7 the p As: (b) b) c) 9 d) 8 8 P 9.. 7...... 9 a dr r ( r). ( ) P P. If α, β, γ are the roots of the equatio 0 the the value of ( - α) ( - β) ( - γ) is b) c) - d) - ( - α) ( - β) ( - γ) (α β γ) (αβ βγ γα) - αβγ -. The middle term i the epasio of ( ) is...( ) b)...( ) -! c) As: (d)...()! d) ( ) ; Middle term t...( )! ( ) C..!. ( )!! ( )( )( ).... (!)(!) [( )( )...][( )( )...] (!)(!). If p (~ qvr) is false the the truth values of p, q, r are T, T, F b) T, F, T c) F, T, T d) F, F, T As: ( Give P (~q v r) is false (~q v r) is false ad p is true q is true, r is false ad p is true ( )( )...!
a. If 9!!7!!! b! where a, b N the the ordered pair (a, b) is (0, 9) b) (0, 7) c) (9, 0) d) (, 0) 9! a!7!!! b!.8.9 6.7.8.9 6.7.8.9 8 9!!! 9!... 6 9! a 9, b 0 9! 6 0 6 9!. 0! 9 0! 6. ta 0 o ta 0 o ta 0 o ta 0 o ta 0 o ta 60 o ta 70 o ta 80 o 0 b) - c) d) As: (d) ta 0 o ta 0 o ta 0 o ta 0 o ta 0 o ta 60 o ta 70 o ta 80 o ta0 0.ta0 0.ta0 0.ta0 0.cot0 0.cot0 0.cot0 0.cot0 0 7. If ta θ m the cos θ m si θ is equal to b) c) m As: (.cosθ m.siθ ta. ta θ ta θ m. θ ta θ m. m m m. m d) m. m m m m ( m ) m 8. b c c a a b If the cos A 7 b) c) As: (b) b c c a a b k b c k, c a k, a b k addig them, (a b c) 6k a b c 8k a 7k, b 6k, c k cos A b c a bc 6k k (0k 9k ) k 60k d) 7 cos A
9. If a cos α i si α, b cos β i si β the As: (d) i si (α - β) b) i si (α β) c) cos (α β) d) cos (α - β) a b cisα cisβ cis( α β) b a cis(α - β) cos (α - β) isi(α - β) a b b a b cos (α _ β) isi (α - β) a a b cos(α - β) b a 0. If log ta the d As: ( sec b) si c) cosec d) sec log ta si cos sec. d ta si. If si ta the d As: (b) cos sec b) c) d) si ta put cosθ θ si ta θ ta si cos θ. If d d a the. b) c) d) 0
Squarig a Diff; 0 - - f f d d d d d. If t t : t t the d d As: (d) dt t ( t) ( t) t ( t) b) ( ( t) t) c) d dt t ( t) d) 0 ( t) ( t) ( t) ( t) d - 0 d d. I the group G {,, 7, } uder the value of 7 - is equal to b) 7 c) d) As: ( Clearl - ( ) 7 7. Which of the followig is a subgroup of the group G {,,,,, 6} uder 7 {, 6, } b) {,, } c) {,, } d) {,, } As: (b) (c) cat be a subgroup as idetit is ot preset (d) cat be a subgroup as 7 6 {,, } ( cat be a subgroup as 7 6 {, 6, } (b) is a subgroup
6. If A, B (adj A) ad C A the 0 C adjb b) - c) d) - As: Wrog optios C adjb A B A B A () () (-) 9 8 GE A Adj A A A A A is equal to 7 7. If A, B 6, X ad AX B the z is equal to z b) - c) - d) As: (d) GE z 7 ------- () z 6 ------- () z ------- () () () z 9 ------- () () (); z 6 ------- () () () z logb a 8. If A the A is equal to loga b As: ( 0 b) log a b c) - d) log b a A log a b. log b a 0 9. If a verte of traigle is (, ) ad the mid poits of two sides through this verte are, ad, the the cetroid of the triagle is give b (, ) b) (, 0) c) (, ) d) (0, ) A (, ) A,, B ( ) C ( )
,,,,, 0 8 0 B (, 0) G (, ) C (, 0) 0. The image of the poit (, ) o the lie 0 0 is (, 8) b) (6, ) c) (6, 8) d) (0, 0) Let the image of (, ) (h, k) The h a h k b k (a a h k h 6 k 8 (h, k) (6, 8) b b ( 0) c). If the sum of the slopes of the lies give b p 8 0 is three times their product the p has the value As: (d) Give, m m m m h b b) c) d) a -h a (-p) p b. lim 0 e b) e c) e d) As: ( lim 0. lim ( ) 0. ( ) e e e. e fo r 0. If f () is cotiuous at 0, the k k for 0 b) c) d) 0
As: (b) f () is cotiuous at 0 lim 0 f () f (o) lim 0 e k 0 lim 0 e k lim 0 (e ) k. k k. The o adjacet verte i the graph is V V V V V V b) V V c) V V d) V V As: (d). si cos cot ta is equal to As: ( 7 8 si [ cos - b) cotta 7 8 c) 7 si cos cot ta si cos cot cot si cos si θ where cos θ d) 7 7 θ 7. 7 8 6. The multiplicative iverse of i is i 8, As: (b) i MI i 8 b), ( i)( i) 9 6 8 i 8 c), 8 d),
(-) c) b) (-) d) 6 As: ( ta si ta si si cos - si - si cos si si si cos cos si si si cos cos si si ( si ) cos ( si ) (si cos ) ( si ) 0 (-) si cos 0 si - si ta (-) ta ta OR ta ta si si ta ( si ) si ( si ) (ta ) 0 si - ta (-) 8. The agle betwee the circles 0 ad 6 6 0 is 6 b) c) As: (d) Usig cosie rule i ΔAPB r AB r - rr cosθ ---- () d) cos - 7 6 P r θ r A B
Here A (-, -), B (, -) r, r 9 6 AB 9 () 6 () () cosθ 0 6 cosθ -7-6 cosθ 7 cosθ θ cos - 7 6 6 9. If a r, b r 7 ad a r r r r b î ĵ 6kˆ the the agle betwee a ad b is b) 6 c) d) As: (b) a r, b r 7, a r r b î ĵ 6kˆ a b a b si θ ^ 9 6.7. siθ. 9.7 siθ 7 7. si θ si θ θ 6 60. The domai of the fuctio f() log(-) As: ( (-, -) b) (-, -] c) (-, ] d) (-, 0) log ( ) is defied if > 0 < (-, -) ----- () is defied if 0 or - ------------- () Reqd domai is the istructio of () & () i.e. (-, -)