May 2011 - Career Point
May 2011 - Career Point May 2011 - Career Point
17. Ifsin 3θcos 2θ2–147137= 0Then no. of values of θ in [0, 2π].18. Minimum value ofy = (sin x + cosec x) 2 + (cos x + sec x) 2 ∀ x ∈ R is.19. If sin –1 (sin 5) > x 2 – 4x then number of possibleintegral values of x will be.20. Find no. of solution of x for e x cot x = 1 wherex ∈ (0, 2π).21. In ∆ABC if angles A, B, C are in A. P. & ∠Aexceeds lowest angle by 30º & D divides BC∠BAD1internally in 1 : 3 then = . Find k∠CADk22. The number of solution ofcos(2sin –1 (cot(tan –1 (sec(6cosec –1 x))))) + 1 = 0where x > 0 is23. Circumcentre is at origin & a ≤ sin A. P(x, y) lie1inside the circumcircle & k = , then least8 | xy |integer value of k can be.PREFIXESPrefix Symbol Powers of 10deciSub multipliesd 10 –1centi c 10 –2milli m 10 –3micro µ 10 –6nano n 10 –9pico p 10 –12femto f 10 –15atto a 10 –18zepto z 10 –21yocto y 10 –24Multiplesdeca da 10 1hecto h 10 2kilo k 10 3mega (or million) M 10 6giga (or billion) G 10 9tera (or trillion) T 10 12peta P 10 15exa E 10 18zetta Z 10 21Yotta Y 10 24Facts on the SunThe Milky Way galaxy is home to Planet Earth andis energized by the enormous ball of energy, theSun. This big star is much closer to us than themillions of stars that twinkle in the night sky and itsupports life with the heat generated.The quest to know the space or void that surroundsthe planet and the celestial bodies that intrigue manby their shimmer and movements have led scientiststo delve deep into the study of the universe, with thesupport of harnessed technology. Research revealsthat the Sun is average in size and features,compared to the million others that just appearsmall in the night sky due to their proximity toearth. The Sun is the center of our galaxy and ismade up of hot gases that comprise elements likecalcium, hydrogen, helium, sodium, iron andmagnesium.The Sun is a big star that simply looks small in thesky because it is approximately 93 million miles or150 million km away. While the Earth is about 13thousand kilometers across, the sun is 1.4 millionkilometers and the difference in size between theEarth and the Sun is better understood with thecalculation that it would take more than a millionEarths to fill the Sun, if possible! Considering that abeam of sunlight takes approximately 8 minutes toreach us, scientists have calculated that it wouldtake man about a hundred and seventy six years toreach the sun; this is in conjunction to the speeds weallow ourselves on the planet.Although actually weighing the Sun with a scale isimpossible, scientists compute its weight with theunderstanding that it contains the same materialmass that is weighable in our solar system. Certaincomparisons and the updated study that the Sun isover 300,000 times heavier than Earth, defines anapproximate gravitational pull and the weightincrease factor. The Sun has no solid surface! TheSun is estimated to be more than four billion yearsold. In comparison to the time frame within whichearliest evidence of life forms on the planet havebeen recorded, the Big Bang seemed to have takenplace much, much earlier. And, the Sun is notexpected to change in form or size at least another 5billion years.Once the hydrogen exhausts, or burns out, scientistsexpect this Center of the Galaxy to enter a newphase of existence, burning out the heliumcomponent next. The burning of helium will resultin the expansion of the star to nearly 100 times itscurrent size! The prediction and study reveals thatthe resultant Red Giant will then collapse into asmaller White Dwarf!XtraEdge for IIT-JEE 60 MAY 2011
XtraEdge for IIT-JEE 61 MAY 2011
- Page 11 and 12: 60 cmK 1 K 2VB5. A solid sphere of
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- Page 16 and 17: Physics Challenging ProblemsSet # 1
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- Page 42 and 43: Students' ForumExpert’s Solution
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- Page 52 and 53: 6. Choose the INCORRECT statement f
- Page 54 and 55: 7. If the equation 3x 4 - 16x 3 + 3
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- Page 58 and 59: 17. A stone is projected from level
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- Page 74 and 75: 40. A block is moving on an incline
- Page 76 and 77: MATHEMATICSSECTION - ISingle Correc
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- Page 88 and 89: Ans.[D]m 1 = 0.01 kgvH = 5mm 2 = 0.
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XtraEdge for IIT-JEE 61 MAY <strong>2011</strong>
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