MH CET 2018 (QUESTION WITH ANSWER)

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Darcy Hart
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tn - in sec - in I - log. In ABC, with usul nottions, if,, c re in A.P. () 3 C A cos + cos ( ) + 3 3.

1 ( P C M ) MH CET 8 (QUESTION WITH ANSWER). /.sec () + log () - log (3) + log () Ans. () - log MATHS () 3 c + c C C A cos + cos c + cosc + + cosa ( + cosc ) + + cosa c c ( + + ) c / / I tn - in sec - in I - log. In ABC, with usul nottions, if,, c re in A.P. () 3 C A cos + cos ( ) If e ( ) y sin - cos, e sin + cos then t () () (3) is () 3 c (3) 3 () Ans () d ( ) e cos + sin + e e sin - cos sin

2 ( P C M ) d ( ) e cos - sin + e e sin + cos cos / d e cos cot d / d e sin cot. The numer of solution of sin + sin 3 + sin 5 in the intervl () () 3 (3) () 5 (sin + sin5) + sin3 sin3 cos + sin3 sin3 (cos + ) sin3 nd cos + cos or or, 3 sin3 hve 3 solutions cos - hve solutions., 3 is 5. If tn - + tn - 3, then () - () 3 (3) 6 () - - tn + tn tn ; > ( + ) - ( + ) (6 - ) ( + ) -; Mtri A 5 then the vlue of 7 3A3 + 3A3 + 33A33 is () () 3 (3) - () -3 3A3 + 3A3 + 33A33 A A (7 - ) (7 - ) + 3( - ) A - 7. The contrpositive of the sttement : If the wether is fine then my friends will come nd we go for picnic.

3 3 ( P C M ) Ans. () () The wether is fine ut my friends will not come or we do not go for picnic. () If my friends do not come or we do not go for picnic then wether will not e fine. (3) If the wether is not fine then my friends will not come or we do not go for picnic. () The wether is not fine ut my friends will come nd we go for picnic. ( ) p q r ( ( )) contrpositive q r p ( V ) q r p If my friends do not come or we do not go for picnic then wether will not e fine. 8. If f ( ) the vlue of lies in () R () (-, -) (3) (, ) () (-, ) f is incresing function on + + ( + ) - ( ) - + ( + ) ( + ) f' f () > (- + ) > s + is lwys positive + < ( - ) ( + ) < (-, ). If X ( n - 3n - : n N) nd Y Ans. () {(n - ) : n N}, then X Y () X () Y (3) φ () {} X { n - 3n - : n N} X {( + 3) n - 3n - : n N} 3 n n - X + 3 n + +! n n n - n ( n ) 3 - X 3 n ( n - ) n ! 6 X ( n - ) n +...! Y {(n - ) : n N} X X (OR) Y Y X Put n,, 3,, 5, 6, in X nd Y X {,, 5, } Y {,, 8, 7, 36, 5, 5, 63 } X X Y Y X. The sttement pttern p ( p q ) Ans. () () A tutology () A contrdiction (3) Equivlent to p q () Equivlent to p q ( ) p p q F q is

4 ( P C M ) F y - Contrdiction.. If () 3 () k, + 8 then the vlue of k is 3. P ( t ) (- t, t ) -, P(t) (-, ) sin cos () sec + log sec + tn + c (3) 3 () sec tn + c (3) sec + log sec - tn + c () k + k + ( 3 ) tn - ( 3 ) 3 tn - 3 k 3k k 3 k. The Crtesin co-ordintes of the point on the prol y -6, whose prmeter is re () (-, ) () (, -) (3) (-, -) () (-, ). If () sec + log cosec - cot + c I sin cos sin + cos I sin cos sin I + cos sin cos sin cos I sec tn + cosec I sec + in cosec - cot + c y log then y () y () - y (3) - y () y t ; y -6 - y + y

5 5 ( P C M ) n n - y y d y k then nd y y 5. If f : R - {} R is function defined y f () R () R - {} (3) R - {} () R - {-, } f Rf : R - {} -, then rnge is - ( - ) ( + ) ( - ) ; D : R - {} f 7. The order of the differentil eqution of ll prols, whose ltus rectum is nd is prllel to the is, is () One () Four (3) Three () Two Eqution of prol (y - k) ( - h) hve two ritrry constnts h nd k Order 6. If plnes r p i - j + k + 3 nd r i - p j - k - 5 include ngle 3 (), -3 () -, 3 (3) -3 () 3 then the vlue of p is P + P - cos 3 P + 5 P + 5 3P - P + 5 P + 5 6P P - 6P + (P - 3) 3 P 3 8. If lines Ans. () - y - z - y - k nd z 3 intersect the vlue of k is () () (3) 5 () 7 - y + z - 3

6 6 ( P C M ) - 3 y - k z k k (-5) - (k + ) (-) () - + k + k k. If line mkes ngles nd 6 with the positive directions of X nd Z es respectively then the ngle mde y the line with positive Y - is is () 5 () 6 (3) 35 () cos β - cos α - cos γ - cos ( ) cos (6 ) cos β ± β 35 : eternlly is () () (3) 3 5 () 3 + n m - e - n n n 5. cos. cos. cos 3 cos 7 () () (3) Ans. () - () - cos cos cos 3 cos cos 7 cos cos cos 3 cos 7. L nd M re two points with position vectors - nd + respectively. the position vector of the point N which divides the line segment LM in the rtio. If plnes - cy - z, c - y + z pss through stright line then + + c () - c () c - (3) - c

7 7 ( P C M ) () c () {,, 3} () {,, 3, } (3) {,, 3,, 5, 6} () {, 3, 5} X {,, 3,, 5, 6} -c - c - - ( - ) + c(-c - ) - (c + ) - - c - c - c - - c c - c + + c 3. The point of intersection of lines represented y - y + + 3y - is () (, ) () (, ) 3 (3) -, - y + + 3y - (), + hy + y + yz + fy + c 3, h, -, g, f, c P, -, - -. A die is rolled. If X denotes the numer of positive divisors of the outcome then the rnge of the rndom vrile X is 5. A die is thrown four times. The proility Ans. () of getting perfect squre in t lest one throw is () 6 8 (3) 3 8 n P 6 3 q 6 3 () 65 8 () 58 8 X Numer on die is perfect squre 6 P(X ) C P(X ) - P (X ) If the line y - 5 touches to the curve Ans. () 3 y + t the point (, 3) then 7 + () () (3) - () 3 y + y 3( ) (,3) (3)() slope of tngent (3) Given tngent y 5 m + c m (, 3) lies on curve y 3 +

8 8 ( P C M ) 3 (3) () () + (-7) 7. The sides of rectngle re given y Ans. () ± nd y ±. Then eqution of the circle pssing through the vertices of the rectngle is () + y () + y + (3) + y - () ( - ) + ( y - ) + Eqn. of circle ( - ) ( + ) + ( y - )( y + ) - + y - + y + f log f + log f + log To e min f ( ) + log log e - - e e lso f f e > e / e f ( ) isminimum - - f log e e e e e. If X B (n,p)with n, p. then E(X ) () (). (3) 3.6 () 8. X ~ B( n, p); n, p. q.6e(x )? V(X) npq E(X) np V(X)..6. lso E(X). V(X) E(X ) - (E(X)). + E(X) E(X) The minimum vlue of the function f log is () Ans. () (3) e - e () -e () e 3. The generl solution of differentil eqution cos( + y) is + y () tn y + c + y () tn + c

9 ( P C M ) Ans. () + y (3) cot y + c + y () cot + c Let + y V + dv dv - dv - cos V dv + cos V dv V cos dv V cos V sec dv + C V tn + C + y tn + C + y tn + C + y tn + C / + y tn + C 8! n (S)!3! 6! n (A)! n(a) 6!/! 6! 3! P(A) n(s) 8!/! 3! 8! 3 6!/6 3 P (A) 8 7 6! 8 3. The sum of the first terms of the series Ans. () is () ( -) 8 (3) - () ( -) () ( -) S ( ) n S ( ) -(++...) n n - S n - n - n - S n - - S - -- S - S S ( -) 3. Letters in the word HU LU LU LU re rerrnged. The proility of ll three L eing together is () 3 (3) 3 38 () 5 () If A, B, C re the ngle ABC then cot A. cot B + cot B.cot C. cot A () () (3) () - Ans. () A + B + C

10 ( P C M ) A + B - C cot(a + B) cot( - C) cot A cot B- -cot C cot A+cot B Cot A cot B -cot A cot C cot B cot C Cot A cot B + cot B cot C + cot A cot C - 3. If Asin (B ) + C then A+ B 6 -,, c 3 () () c c (3) 3 I 35. -(3 ) 3 I sin + C A+B + 3 Ans. () e + sin + sin () e tn + C (3) e + tn + C I e () 3 sin cos cos + I e (tn + sec ) I e tn + C () e + tn + C () e tn + C + + c - c c c + c c - c c c + - c c c cos c sin ( 3) sin 37. If points P(, 5, ), Q(3, y, ) nd R(5, 8, ) re colliner, then the vlue of + y is 36. If,, c re mutully perpendiculr vectors hving mgnitude,, 3 respectively then + + c - c () () 6 (3) () 8 () - () 3 (3) 5 () drs of PQ y c

11 ( P C M ) drs of PR c - - s P - Q - R colliner y nd y - - y + y If the slope of one of the lines given y + hy + y is two lines the other then () 8h () 8h (3) 8h () 8h Ans. () + hy + y m m -h + m... m... m m..(3) Put (3) in () -h 3 m m -h 3 Put (3) in () m m ( m ) -h 3 8h. 3. The eqution of the line pssing through the point (-3, ) nd isecting the ngle etween co-ordinte es is () + y + () - + y + (3) - y + () + y + 5 Ans. () (y - ) -( + 3) (y - ) y y +. The negtion of the sttement : Getting ove 5% mrks is necessry condition for Hem to get the dmission in good college. () Hem gets ove 5% mrks ut she does not get the dmission condition for Hem to get the dmission in good college." () Hem does not get ove 5% mrks nd she gets dmission in good college. (3) If Hem does not get ove 5% mrks then she will not get the dmission in good college. () Hem does not get ove 5% mrks or she gets the dmission in good college. Ans. () ( ) p q p q Hem gets ove 5% mrks ut she does not get dmission in good college.. If f ( ) + α for + α + + β for < is continuous t nd f

12 ( P C M ) f then α + β is () 3 () 8 5 (3) 5 8 () 3 lim + α lim + + β α + β... + α ; f f + α + α 7 α β α + β If y (tn - ) then Ans. () d y ( ) ( ) () () (3) () y (tn - ) - tn ( ) ( + ) ( + ) tn - ( ) d y ( ) ( ) d y ( ) ( ) ( ) 3. The line 5 + y - coincides with one of the lines given y 5 + y - ky - y + then the vlue of k is () - () 3 (3) () -3 As y is scent in given eqution first line is 5 + y - nd second is + c (5 + y - ) ( + c) 5 + 5c + y + cy - - c 5 + y + (5c - ) + cy - c Given eqution 5 + y - ky - y + ; c - -k 5c -k 5 (-) K 3. If A - then (A - 5A) A - () (3) Ans. () 3 - () () (A - 5A) A - A A - 5A A - A - 5I The eqution of line pssing through (3, -, ) nd perpendiculr to the lines

13 3 ( P C M ) r i + j - k + i - j + k λ nd r i + j - 3 k + i - j + k µ is () () (3) () + 3 y + z y z 3-3 y + z y z 3 i j k - - i - 3 j - k - drs of line - -3 c - or 3 c - 3 y + z - Eqution of line 3 6. A coin is tossed three times. If X denotes the solute difference etween the numer of heds nd the numer of tils then P(X ) () (3) 6 () 3 () P(X ) 8 7. If sin + cos -, then tn 3 6 () 3 () - 3 (3) 3 3 sin + cos 3 3 cos +sin () - 3 sin + 3 cos 3 cos + sin sin - 3 cos tn The re of the region ounded y y, Ans. () y, y nd the y-is lying in the first qudrnt is squre units. () 3 () 8 3 (3) 3 () H H H 3H nd T H H T H nd T n(h) n(t) H T H H nd T n(h) n(t) H T T H nd T n(h) n(t) T H H H nd T n(h) n(t) T H T T nd H n(h) n(t) T T H T nd H n(h) n(t) T T T 3T A 3/ y A 3 / y

14 ( P C M ) 8 A (8 -) (7) y e. If f - cos t, then vlue of f () is () 3, for is continuous () 5 (3) () 3 e f () lim - cos e - - cos lim + lim z + y ZA 6 + ZB ZC Zm t 6 nd y The mimum vlue of + y suject to 3 + 5y 6 nd 5 + 3y 3,, y is () ().5 (3) () 7.33 Ans. () 3 + 5y 6 (i) y 3 (ii) y y 6y

Lesson-5 ELLIPSE 2 1 = 0

Lesson-5 ELLIPSE 2 1 = 0 Lesson-5 ELLIPSE. An ellipse is the locus of point which moves in plne such tht its distnce from fied point (known s the focus) is e (< ), times its distnce from fied stright line (known s the directri).