Download App

STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
MCQ
The function $f(x) = \sin \left( {\log (x + \sqrt {{x^2} + 1} )} \right)$ is
  • A
    Even function
  • ✓
    Odd function
  • C
    Neither even nor odd
  • D
    Periodic function
✓

Answer

Correct option: B.
Odd function
b
(b) $f(x) = \sin \,\left( {\log \,(x + \sqrt {1 + {x^2}} )} \right)$

==> $f( - x) = \sin \,[\log \,( - x + \sqrt {1 + {x^2}} )]$

==> $f( - x) = \sin \,\log \left( {(\sqrt {1 + {x^2}} - x)\frac{{(\sqrt {1 + {x^2}} + x)}}{{(\sqrt {1 + {x^2}} + x)}}} \right)$

==> $f( - x) = \sin \,\log \,\left[ {\frac{1}{{(x + \sqrt {1 + {x^2}} )}}} \right]$

==> $f( - x) = \sin \left[ {\log {{(x + \sqrt {1 + {x^2}} )}^{ - 1}}} \right]$

==> $f( - x) = \sin \left[ { - \log (x + \sqrt {1 + {x^2}} )} \right]$

==> $f( - x) = - \sin \left[ {\log (x + \sqrt {1 + {x^2}} )} \right]$==> $f( - x) = - f(x)$

$f(x)$ is odd function.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $A^2-A+I=0$, then the inverse of $A$ is:
→
The minimum value of $(\text{x}^{2}+\frac{250}{\text{x}})$ is:
→
If $a + b + c = 50$ and $a$, $b$, $c$ are non negative even integers, then greatest value of $ab^2c$ is 
→
The volume of a spherical balloon is increasing at the rate of  $40$  cubic centrimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is $8$  centimetre, is ........ $sq \,cm/\min$.
→
If $f(x)$ is a polynomial function satisfying the condition $f(x) . f(1/x) = f(x) + f(1/x)$ and $f(2) = 9$ then :
→
Consider two events $A$ and $B$ such that $P(A) = \frac{1}{4},\,\,P\left( {\frac{B}{A}} \right) = \frac{1}{2},\,\,P\left( {\frac{A}{B}} \right) = \frac{1}{4}.$ For each of the following statements, which is true

$I.$    $P\,({A^c}/{B^c}) = \frac{3}{4}$

$II.$   The events $A$ and $B$ are mutually exclusive

$III.$  $P(A/B) + P(A/{B^c}) = 1$

→
Let $f(x)=\sqrt{2-x-x^2}$ and $g(x)=\cos x$. Which of the following statements are true?

$I$. Domain of $f\left((g(x))^2\right)=$ Domain of $f(g(x))$

$II$. Domain of $f(g(x))+g(f(x))=$ Domain of $g(f(x))$

$III$. Domain of $f(g(x))=$ Domain of $g(f(x))$

$IV.$ Domain of $g\left((f(x))^3\right)=$ Domain of $f(g(x))$

→
$\int {{e^{\sin x}}\left( {\sin x + {{\sec }^2}x} \right)} \,dx$ is equal to
→
The differential equation for the family of curves ${x^2} + {y^2} - 2ay = 0,$ where $a$ is an arbitrary constant, is
→
Choose the correct answer from the given four options.If $\text{P}(\text{A})=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:
→