Three people go for a morning walk together. Their steps measure 60 cm, 84 cm and 96 cm respectively. What is the minimum distance each of them will cover before they meet again assuming that their walking speed is same?
For a positive integer ^@ k, ^@ we write ^@ (1 + x)(1 + 2x)(1 + 3x) \ldots (1 + kx) = a_0 + a_1 x + a_2 x^2 + \ldots + a_k x^k,\space \space^@ where ^@ a_0, a_1, \ldots a_k ^@ are the coefficients of the polynomial. Find the smallest possible value of ^@ k ^@ if ^@ a_0 + a_1 + a_2 + \ldots + a_{ k-1 } ^@ is divisible by ^@ 2563. ^@
The sum of the 6th element and the 14th element of an arithmetic progression is -216. The sum of the 8th and the 16th element is -268. What is the value of the 30th term?
^@ABC^@ is right triangle right angled at ^@C^@. If ^@p^@ is the length of the perpendicular from ^@C^@ to ^@AB^@ and ^@a^@, ^@b^@, ^@c^@ have the usual meaning, then ^@\dfrac{1}{ a^2 } + \dfrac{1}{ b^2 } = ^@
Point ^@P^@ divides the line segment joining the points ^@A(14, 35)^@ and ^@B(28, 21)^@ such that ^@AP = \dfrac{ 4 }{ 7 } AB^@. If ^@ P ^@ lies on the line ^@2x - y + k = 0^@, find the value of ^@k^@.
In the given figure, ^@ PQ ^@ is a chord of a circle with centre ^@ O ^@ and ^@ PT ^@ is a tangent at point ^@ P ^@. If ^@\angle QPT ^@ = ^@ 66^\circ ^@, find ^@ \angle PRQ ^@.
The perimeters of the ends of the frustum of a cone are ^@7.04 \space cm^@ and ^@9.68 \space cm^@. If the height of the frustum is ^@31 \space cm^@, find its find its volume (Take ^@\pi = \dfrac { 22 } { 7 }^@).
Faces of a cube are marked with A,B,C,D,E and F. Two views of the cube are as shown below, if face A is opposite to face F, what will be there on the bottom when C is at the top?
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