Question
If P . cos θ + Q . sin θ = 8 and P . sin θ - Q . cos
θ = 5, what is the value of (P² + Q²)?Solution
Given, P . cos θ + Q . sin θ = 8 ⇒ P² . cos² θ + Q² . sin² θ + 2PQ . sin θ . cos θ = 64  … (i) Also given, P . sin θ - Q . cos θ = 5 ⇒ P² . sin² θ + Q² . cos² θ - 2PQ . sin θ . cos θ = 25  … (ii) Adding equations (i) and (ii) P² + Q² = 89
What should come in place of (?) question mark in the given number series.
81, 73, 66, 60, 55, ?
14 6 4 4 ? 48
...What should come in place of (?) question mark in the following number series.
5, 11, 23, 47, 95, ?
In each of the following number series, one term is missing. Find the missing term.
1, 4, 9, 16, 25, ?
What will come in place of the question mark (?) in the following series?
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31    32      35      ?      47       56
...What should come in place of (?) question mark in the following number series.
1, 2, 6, 24, 120, ?
What value should come in the place of (?) in the following number series?
71, 72, 76, 103, ?, 244254, ?, 1022, 1150, 1214, 1246
