If the sum of two extreme numbers of an AP with four terms is 8 and product of remaining two middle terms is 15, these greatest number of the AP will be
Statement I: Let \[\left( 2,\sqrt{2} \right)\] be any point on hyperbola\[{{x}^{2}}-{{y}^{2}}=2\], then product of distances of foci from P is equal to 6.
Statement II: If S and S' be the foci, C the centre and P be any point on a hyperbola\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\] then\[SP.S'P=C{{P}^{2}}\]
A)
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
doneclear
B)
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together, is
If \[\frac{x}{\cos \theta =}\frac{y}{\cos \left( \theta -\frac{2\pi }{3} \right)}=\frac{z}{\cos \left( \theta +\frac{2\pi }{3} \right)}\]then x + y + z is equal to
A man on the top of a cliff 100 m high observes the angles of depression of two points on the opposite sides of the cliff as \[30{}^\circ \] and
\[60{}^\circ \]
respectively. Then, the distance between the two points is
Product of the perpendicular from the foci upon any tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\left( a<b \right)\]is equal to