1ya richa rite..........cud u give d solutions also???? coz i hav a doubt in 7.........and try 6 and 9 sldo hehe ;)
THIS IS SERIOUSLY NOT FOR IITJEE practice.....THEY ARE 2222222 EASY............ ONLY FOR CBSE sure shot QUESTIONS...
Please other guys dont scold me for these easy questions..
1. Find the principal value of tan-1(tan7∩/6)+cot-1cot7∩/6.....
2.Evaluate...o∫∩/2(x+sinx)dx/(1+cosx)...
3.Two tailors A and B earn Rs.150 and Rs. 200 per day respectively. A can stich 6 shirts and 4 pants per day whike B can stich 10 shirts and 4 pants per day. How many days shall each work if it desired to produce atleast 60 shirts and 32 pants at a minimum labour cost?? GRAPHICALLY..........
Solve these yaar u cud be sure of 11 marks in d next board paper..
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61 Answers
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1=o∫∩/2(x+sinx)dx/(1+cosx)...
=o∫∩/2(x)dx/(1+cosx)+o∫∩/2(sinx)dx/(1+cosx)...
=o∫∩/2(x)dx/(2cos2x/2)-1∫0dt/(1+t)...{t=sinx}
=1/2o∫∩/2(x)sec2(x/2)dx/+o∫1dt/(1+t)...
=1/2([2xtan(x/2)]0π/2-20∫π/2tan(x/2)dx/2+[log|1+t|]01
its easy now integral tanx=log|sinx|
11wat is use of writing ques[7]
akhnd yaar dimag aur nahin chal raha cbse mein to beda garg ho gaya
please post some more easy but conceptual ques and do tell that integration
11nahin maine kya different kiya tha MR AKAND in#28
which shorter method u were talking about???
1MR MS..........if it was just sec2x in d numerator then ur method is the best.....but it is xsec2x in ur method....... uske baad kya karega???? and look at prateek's method???? usse chota hoga kya???? BOL..
11TERI BAINS KI AANKH
maiine bhi to integeration by parts hi use karne ko hi kaha tha[16]
1TERI BHAINS KAA WO.......main bola urs was correct BUT long....just look at d size of prateek's answer dude.....
1next CBSE question........
4. If the sum of two unit vectors is a unit vector, Prove that the magnitude of their difference is √3.
5.If a and b(bar) are position vectors of points A and B respectively, then find the position vector of points of trisection of AB.
1next.......6 . 7. 8. questions 7 8 are veryyyyyyy easyyyyyy
one more awesum wala....
9.
11@akand #43
YAAR TU TO CHA GAYA
MAYHS MEIN SIZE KO DEKTA HAI[3]
MATHEMATICIANS HAASENGE[3]
WAISE NICE JOKE[3]
1haha....MS.........har question kaa hazaaron tarilke hote hai BUT we need the best one and d smartest and easiest one ok??? and NOW stop blabbering and do the other questions..
1only for practice for CBSE math integrations......................
easy ones...............NO need for solutions only practice ........for ur benefit..........
if u want to answer ........then answer 3,4,8,13,18,22,23,29.........they are good......PS...21 is already done in d forum and is a very good question
11Q9
to prove sinθ/2=1/2|a^-b^|
|a-b|2=a2+b2-2a.b
=2-2cosθ
=2(1-cosθ)
=>4sin2θ/2=|a^-b^|2
=>2sinθ/2=|a-b|
=>sinθ/2=1/2|a^ -b^|
HENCE PROVED
1-c (vectr) is the resultant of a n b as they cant be cllinear n thus sm is solved
116)
i am not writing arrows on the top of vectors 4 convenience
(aXb)2
=|a|2|b|2sin2θ
=a2b2-a2b2cos2θ
=(a.a)(b.b)-(a.b)(a.b)
=RHS
1excellent manipal..............thnx anyways.....this was eating my head.u r a genius dude...
16.\frac{5}{6}(\frac{6x-2+2-2}{1+2x+3x^{2}})\frac{5}{6}\int (\frac{6x+2}{1+2x+3x^{2}})-\frac{20}{6}\int \frac{1}{1+2x+3x^{2}}
In first take denominator as t u get derivative in numerator.
in second make the denominator perfect square.
1nice one ankit.....u cau just have written.......
d(den.)/dx=A(num.)+B......thts all.......hehe
1k 10............
PROVE
(cos31°+sin31°)/(cos31°-sin31°)=tan76°..........