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If a) x1 + x2 + ...................+x1007 =(2014)2 b) x1 /(x1 +1)=x2 /(x2 +3)=.....................=x1007 /(x1007 +2013) then x253 =? ...
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If f :N→N such that f(f(x))=3x; Then find f(2013) ...
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If f :N→N such that f(f(x))=3x; Then find f(2013) ...
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*Image* Try to apply some other method than maxima minima(if you can). ...
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*Image* A solid iron sphere of radius=1m is just submerged in a water tank. A point source of light is kept vertically above its center at a distance 1m from the water surface. Find the area of the sphere's shadow. Refractive ...
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For x ε (0, π/2) and sin x = 1/3, if \sum_{n=0}^{\infty }\frac{sin(nx)}{3^{n}}=\frac{a+b\sqrt{b}}{c} then find the value of (a + b + c), where a, b, c are positive integers. ...
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If the equation ax3+3bx2+3cx+d=0 has two equal roots,show that it must be equal to bc-ad/2(ac-b2) . ...
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Two particles ,1 and 2, move with constant velocities v1 and v2 . At the initial moment their radius vectors are r1 and r2 . How must these four vectors be interrelated for the particles to collide ? ...
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A ball is dropped on a floor from a height of 2.0m. After the collision it rises upto a height of 1.5m. Assume that 40% of the mechanical energy lost goes as thermal energy into the ball. Calculate the rise in the temperature ...
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If sin A,sin B,sin C are in A.P. prove that the altitudes are in H.P . ...
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*Image* Alpha=12*10-6 ...
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3.nc0-8.nC1+13.nC2-18.nC3.......... upto (n+1) terms =? ...
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Find the coefficient of xr in the following- (x+2)n+(x+2)n-1(x+1)+(x+2)n-2(x+2)2+.....+(x+1)n ...
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Radium(Atomic no. 87 and mass no.221) is a radioactive substance having half life of 4 days.Find the probability that a nucleus undergoes decay after two half lives. A.1 B.1/2 C.3/4 D.1/4 ...
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The value of i log(x – i) + i2+i3 log(x +i) + i4( 2 tan-1x), x> 0 is (A) 0 (B) 1 (C) 2 (D) 3 ...
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Solid Cylinder, rolls over horizontal surface Find the max value of v which still permits it to roll over incline plane without a jump, sliding is absent. *Image* ...
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\hspace{-16}\bf{(1)\;\;}$ Total no. of real solution in $\bf{2^x = x^2}$\\\\\\ $\bf{(2)\;\;}$ Total no. of real solution in $\bf{2^x = 1+x^2}$\\\\\\ $\bf{(3)\;\;}$ Total no. of real solution in $\bf{2^x+3^x+4^x+5^x = 10x+4}$\ ...
