SATHEE: Functions 2 Question 13

Functions 2 Question 13

14. If $f (x) = \cos [π^{2}] x + \cos [- π^{2}] x$ , where $[x]$ stands for the greatest integer function, then

(1991, 2M)

(a) $f (π / 2) = - 1$

(b) $f (π) = 1$

(d) $f (π / 4) = 1$

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Answer:

Correct Answer: 14. (d)

Solution:

Since, $f (x) = \cos [π^{2}] x + \cos [- π^{2}] x$

$\Rightarrow f (x) = \cos (9) x + \cos (- 10) x$

$[using [π^{2}] = 9 and [- π^{2}] = - 10]$

$∴ f \frac{π}{2} = \cos \frac{9 π}{2} + \cos 5 π = - 1$

$f (π) = \cos 9 π + \cos 10 π = - 1 + 1 = 0$

$f (- π) = \cos 9 π + \cos 10 π = - 1 + 1 = 0$

$f \frac{π}{4} = \cos \frac{9 π}{4} + \cos \frac{10 π}{4} = \frac{1}{\sqrt{2}} + 0 = \frac{1}{\sqrt{2}}$

Hence, (a) and (c) are correct options.

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Functions 2 Question 13

14. If f(x)=cos⁡[π2]x+cos⁡[−π2]x, where [x] stands for the greatest integer function, then

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14. If $f (x) = \cos [π^{2}] x + \cos [- π^{2}] x$ , where $[x]$ stands for the greatest integer function, then