May 2011 - Career Point

X Y Z W01234567890123456789⎧2[x] –{ x}, If x < 017. Let f (x) = ⎨, where {x} and⎩[x]+ 3{ x}, If x ≥ 0[x] are the fractional part and greatest integer of xrespectively. The number of solutions of theequation f (x) – x = {x} ∀ x ∈ [– 8, 8] are.18. If f (x) = lim h ⎛ sin( x + 1/ h)⎟ ⎞πl n⎜; 0 < x < ,h→∞⎝ sin x ⎠2then number of points where f (x) is discontinuousis.19. If set of value of 'p' for which the equation–1 2xsin + px = 0 has exactly three solutions is21+x(l, m) then 8m – l is.20. If the equation 2|x – 2| – |x + 1| + x = k, has infinitesolutions then the value of k is.⎡⎤⎢ n⎥21. The value of ⎢2 1lim ⎥⎢∑, where [.]n→∞n ⎛ 2r⎞⎥r=1⎢ 1+cos⎜⎟⎥⎣⎝ n ⎠⎦represents greatest integer function, is.0123456789012345678922. The greatest value of the functionlog(4 +10 )23. From a point on the curve(cos 2 θ – 6 sinθ cosθ + 3 sin 2 θ + 2) is.y = sin –1 x + cos –1 – x a tangent is drawn to thecurve g(x) = x + cos x + 2π – 1. Then sum of itsintercepts on coordinate axes is.WHAT ARE EARTHQUAKES?Earthquakes like hurricanes are not only superdestructive forces but continue to remain a mysteryin terms of how to predict and anticipate them. Tounderstand the level of destruction associated withearthquakes you really need to look at someexamples of the past.If we go back to the 27th July 1976 in Tangshan,China, a huge earthquake racked up an officialdeath toll of 255,000 people. In addition to this anestimated 690,000 were also injured, wholefamilies, industries and areas were wiped out in theblink of a second. The scale of destruction is hard toimagine but earthquakes of all scales continue tohappen all the time.So what exactly are they ? Well the earths outerlayer is made up of a thin crust divided into anumber of plates. The edges of these plates arereferred to as boundaries and it’s at theseboundaries that the plates collide, slide and rubagainst each other. Over time when the pressure atthe plate edges gets too much, something has togive which results in the sudden and often violenttremblings we know as earthquakes.The strength of an earthquake is measured using amachine called a seismograph. It records thetrembling of the ground and scientists are able tomeasure the exact power of the quake via a scaleknown as the richter scale. The numbers range from1-10 with 1 being a minor earthquake (happenmultiple times per day and in most case we don’teven feel them) and 7-10 being the stronger quakes(happen around once every 10-20 years). There’s alot to learn about earthquakes so hopefully we’llrelease some more cool facts in the coming months.XtraEdge for IIT-JEE 53 MAY 2011