defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Trigonometry Trigonometric Functions
If 2tan2θ - 5secθ = 1 has exactly 7 solutions in the interval \(\left[0,\frac{\mathrm{n\pi}}{2}\right]\) , for the least value of n ϵ N then \(\sum_{k=1}^n\frac{k}{2^k}\) is equal to :
1
\( \frac{1}{2^{15}}\left(2^{14}-14\right)\)
2
\( \frac{1}{2^{14}}\left(2^{15}-15\right)\)
3
\( 1-\frac{15}{2^{13}}\)
4
\(\frac{1}{2^{13}}\left(2^{14}-15\right) \)