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If x=\left(16^{3}+17^{3}+18^{3}+19^{3} \right) , then x divided by 70 leaves a remainder of what? ...
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What is the sum of all the factors of factorial 30? ...
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Evaluate: \lim_{x\rightarrow 0} \frac{tan^{-1}x}{sin^{-1}x} ...
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Find the condition that the straight line cx-by+b^{2}=0 may touch the circle x^{2}+y^{2}=ax+by and find the point of contact. ...
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A 40 kg mass hanging at the end of a rope of length l oscillates in a vertical plane with an angular amplitude \theta _{0} . What is the tension in the rope, when it makes an angle \theta with the vertical ? If the breaking s ...
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{\color{red} 17^{14}>31^{11}-\mathit{Prove...}} ...
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Does anybody know whether this new centre of 'Adudine' is a good one for the correspondence course or rankers study materials or the classroom coaching? Any idea? ...
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Find out the remainder of 19^{92}/92 ...
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Solve :- \int \left(a-x \right)\left(b-x \right)\left(c-x \right)...............\left(z-x \right)dx ...
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Two steel balls freely drop onto an elastic plate, the first one from a height of \small \mathit{h}_{1} =44cm and the second from a height \small \mathit{h_{2}} =11cm but after time \small \tau measured from the instant the f ...
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If α≠β and atanα + btanβ = (a+b)tan(α+β)/2, show that, cosα/cosβ = a/b ...
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If a ,b and c are unit vectors,then show that 0≤ \left|\vec{a}-\vec{b} \right|^{2}+\left|\vec{b}-\vec{c} \right|^{2}+\left|\vec{c}-\vec{a} \right|^{2}\leq 9 \left|\vec{a}-\vec{b} \right|^{2}+\left|\vec{b}-\vec{c} \right|^{2 ...
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Point A moves uniformly with velocity 'v' so that the vector 'v' is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity u<v. At the initial moment of time v perpendicular to u a ...
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