New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Trigonometric Functions and Equations question

2024 · 27 Jan · Shift 2 · Q43

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Trigonometric Functions and Equations
2024 · 27 Jan · Shift 2 · Q43

Trigonometric Functions and Equations question

2024 · 27 Jan · Shift 2 · Q43

JEE MainMathematicsTrigonometric Functions and EquationsMCQ+4 / −1

If

2 \tan ^2 \theta-5 \sec \theta=1

has exactly 7 solutions in the interval

\left[0, \frac{n \pi}{2}\right]

, for the least value of

n \in \mathbf{N}

, then

\sum_{k=1}^n \frac{k}{2^k}

is equal to:

A
$\frac{1}{2^{14}}\left(2^{15}-15\right)$
B
$1-\frac{15}{2^{13}}$
C
$\frac{1}{2^{15}}\left(2^{14}-14\right)$
D
$\frac{1}{2^{13}}\left(2^{14}-15\right)$

More from Trigonometric Functions and Equations

If $α, - \frac{π}{2} < α < \frac{π}{2}$ is the solution of $4 cos θ + 5 sin θ = 1$ , then the value of $tan α$ is2024 · MCQ
The sum of the solutions $x \in R$ of the equation $\frac{3 c o s 2 x + c o s ^{3} 2 x}{c o s ^{6} x - s i n ^{6} x} = x^{3} - x^{2} + 6$ is2024 · MCQ
If $2 sin^{3} x + sin 2 x cos x + 4 sin x - 4 = 0$ has exactly 3 solutions in the interval $[0, \frac{n π}{2}], n \in N$ , then the roots of the equation $x^{2} + n x + (n - 3) = 0$ belong to :2024 · MCQ
If $θ \in [- 2 π, 2 π]$ , then the number of solutions of $22 cos^{2} θ + (2 - 6) cos θ - 3 = 0$ , is equal to:2025 · MCQ
If $θ ϵ [- \frac{7 π}{6}, \frac{4 π}{3}]$ , then the number of solutions of $3 cosec^{2} θ - 2 (3 - 1) cosec θ - 4 = 0$ , is equal to :2025 · MCQ
$The number of solutions of the equation 2 x + 3 tan x = π, x \in [- 2 π, 2 π] - {\pm \frac{π}{2}, \pm \frac{3 π}{2}} is:$ 2025 · MCQ
The number of solutions of the equation $(4 - 3) sin x - 23 cos^{2} x = - \frac{4}{1 + 3}, x \in [- 2 π, \frac{5 π}{2}]$ is2025 · MCQ
The number of solutions of the equation $cos 2 θ cos \frac{θ}{2} + cos \frac{5 θ}{2} = 2 cos^{3} \frac{5 θ}{2}$ in $[- \frac{π}{2}, \frac{π}{2}]$ is :2025 · MCQ