ENJOY MATHEMATICS WITH SUHAAG SIR

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Amberly Stevens
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1 R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) , IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) Pag: SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE PAHLE, WEBSITE PAR BHI... Papr - I. Th locus of th mid-point of th chord of contact of tangnts drawn from points ling on th straight lin 5 to th circl + is ( ) ( ) ( ) ( ) (A) ( ) SUHAG SHORT TRICK TAKE A POINT (0,-)ON LINE It s vr simpl no nd for dtalid solution.. Th total numbr of was in which 5 balls of diffrnt colours can b distributd among prsons so that ach prson gts at last on ball is (A) 75 Concpt mak bundals,,,,. Lt cos, 0, f ( ) IR, 0, thn f is diffrntiabl both at and at diffrntiabl at but not diffrntiabl at not diffrntiabl at but diffrntiabl at diffrntiabl nithr at nor at (B) diffrntiabl at but not diffrntiabl at. Th function f :[ 0,] [, ], dfind b f ( ) , is On-on and onto onto but not on-on on-on but not onto nithr on-on nor onto (B) f ( ) f ( ) ( )( ) f '( ) wav curv f '( ) thn f() If + + a b, + thn a, b a, b a, b a, b (B) + + a b, a a b b + ( ) ( ) a + a b + b + ( ) b + b lim + b b 6. Lt z b a compl numbr such that th imaginar part of z is nonzro and a z + z + is ral. Thn a cannot tak th valu

2 R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) , IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) Pag: SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE PAHLE, WEBSITE PAR BHI... (D) + + a z z Lt z + and givn 0 ( ) ( ) a i + + i + ( ) ( ) a i + a R So, + or sinc 0 z Thus a ( ) / 7. Th llips : E + is inscribd in a rctangl R whos sids ar parallsl to th coordinat as. Anothr llips E passing through th point (0,) circumscribs th rctangl R. Th ccntricit of th llips E is (C) Form figur on vrt of rctangl is (,) Lt E : + a 6 (,0) (0,) (0,) (0,0) (0, ) It passs thorugh (,) a + 6, a or (,) (,0) a Thus a 6( ), a a, 6, or 8. Lt P a ij b a matri and lt Q b ij, whr i + b j a for i, j. If th dtrminant of P ij ij is, thn th dtrminant of th matri Q is 0 (D) SUHAG SHORT TRICKS 0 0 P 0 0, 0 0 So Q Q sc. Th intrgral d quals (for som sc+ tan arbitra constant K) ( ) ( sc tan ) + + K 7 ( sc + tan )

3 R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) , IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) Pag: SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE PAHLE, WEBSITE PAR BHI... ( sc tan ) + + K 7 ( sc + tan ) ( sc tan ) K 7 ( sc + tan ) S + (A,B,D) ( sc tan ) K 7 ( sc + tan ) C 50. Th point P is th intrsction of th straight lin joining th points Q (,,5) and (,, ) R with th plan 5 z. If S is th foot of th prpndicular drawn from th point T (,, ) to QR, thn th lngth of th sgmnt PS is A 5. Lt θ, ϕ [ 0, ] b such that - Rq. Ara θ θ cosθ ( sinϕ ) sin θ tan + cos cosϕ, tan ( θ ) > 0 and < sin θ <. Thn ϕ cannot satisf 0 < ϕ < < ϕ < < ϕ < < ϕ < ANS. A,C,D 5. Lt S b th ara of th rgion nclosd b,, and. S S + Thn S d, 0 S & S 0 5. A ship is fittd with thr ngins E, E and E. Th ngins function indpndntl of ach othr with rspctiv probabilitis, and. For th shop to b oprational at last two of its ngins must function. Lt X dnot th vnt that th ship to b oprational at last two of its ngins must function. Lt X dnot th vnt that th ship is oprational and lt X, X and X dnot rspctivl th vnts that th ngins, E E and E ar functioning. Which of th following is (ar) tru?

4 R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) , IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) Pag: SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE PAHLE, WEBSITE PAR BHI... c P X X 6 7 ] 8 P {Eac tl two ngins of th ship ar functioning 5 P X X 6 [ ] 7 P X X 6 [ ] B,D 5. Tangnts ar drawn to th hprbola, paralll to th straight lin. Th points of contact of th tangnts on th hprbol ar, (, ) (, ) (A,B) Lt P b ( sc θ, tanθ ) tangnt at P scθ tanθ 55. If () satisfis th diffrnt ial quat ion ' tan sc and (0), thn d ( tan )..sc d + tan If d ln sc cos..cos.sc cos d + c.cos d + c.cos + c (0) so c cos.sc '.sc + sc tan 6 ( corrct) + 6 '.. ( wrong ) ( wrong ) ' ' 8 +. ( corrct) (A,D) If () satisfis : ' + d.tan.sc d and (0) 56. Lt f : IR IR b difind as f ( ) +. Th total numbr of points at which f attains ithr a local maimum or a local minimum is (5) f ( ) + + X

5 R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) , IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) Pag: 5 SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE PAHLE, WEBSITE PAR BHI... - ( - )( + ) ( - ) 57. Th valu of 6 + log... Lt... is cosα + cos β + cosγ SUHAG SHORT TRICKS ASSUME ANGLE ALL SAME 0 DEGREE In think Ans is 60. Lt S b th focus th parabola 8 and lt PQ b th common chord of th circl + and th givn parabola. Th ara of th triangl PQS is ANS Lt S b th focus... Put in circl (,) 5 + ± , log + S (,0) 8, 8,.. s (,0), log 6 + ( ) 58. Lt p( ) b a ral polnomial of last dgr which has a local maimum at and a lacal minimum at. If p ( ) 6 and ( ) p, thn p '(0) is s ANS. 5. If a, b and c ar unit vctors satisfing a b + b c + c a, thn a + 5b + 5c a + b a b cosα So, 6 ( cosα + cos β + cosγ )

Objective Mathematics

Objective Mathematics x. Lt 'P' b a point on th curv y and tangnt x drawn at P to th curv has gratst slop in magnitud, thn point 'P' is,, (0, 0),. Th quation of common tangnt to th curvs y = 6 x x and xy = x + is : x y = 8