Domain

Q. Domain of definition of the function $f\left(x\right)=\sqrt{si{n}^{-1}\left(2x\right)+\frac{\pi }{6}}$ for real valued x, is

1. $[-\frac{1}{4},\frac{1}{2}]$
2. $(-\frac{1}{2},\frac{1}{9})$
3. $[-\frac{1}{2},\frac{1}{2}]$
4. $[-\frac{1}{4},\frac{1}{4}]$

Q.

How to find domain and range of a function?

Q.

Let $f\left(x\right)=\left\{\begin{array}{l}\sin \left(\frac{\mathrm{\pi x}}{2}\right),0\le x\le 1\\ 3-2x,x\ge 1\end{array}\right.$then

1. $f\left(x\right)$ has a local maxima at $x=1$

2. $f\left(x\right)$ has a local minima at $x=1$

3. $f\left(x\right)$ does not have any local extrema at $x=1$

4. None of these

Q. f(x)=(x/1-|x|) ^1/1996

Q. Domain of definition of the function$f\left(x\right)=\frac{3}{4-x^2}+lo{g}_{10}(x^3-x)$

1. (1, 2)∪(2 , ∞)
2. (1, 2)
3. (-1 , 0)∪(1 , 2)
4. (-1 , 0) ∪ (1 , 2)∪( 2, ∞)

Q. Find the factor which will rationalise:
$2+\sqrt[4]{47}$

Q.

$\text{Let}f\left(x\right)=\left[x\right]cos\left(\frac{\pi }{[x+2]}\right)\text{where denotes the greatest integer function. Then, the domain of f is}$

1. 

2. 

3. 

4. 

Q. Explain the polynomial geometrically: $(x-2z)(x+2z)=x^2-(2z{)}^2$.

Q. Evaluate ${\int }_1^4\{|x-1|+|x-2|+|x-4|\}dx$

Q.

Which of the following is not a polynomial?

1. x+ x2

2. x+ √3

3. 3√y + y2

4. x

Q. $27+84-26÷13$

Q. The number of negative values of $a$ for which the inequation $4^{x^2}+2(2a+1)2^{x^2}+{4a}^2-3>0$ is satisfied for any $x$ is

1. $\infty$
2. $1$
3. $0$
4. None of these

Q. Domain of f(x)=(x÷1-|x|)^1÷1996

Q.

If f(x) = sin log $\left(\frac{\sqrt{4-x^2}}{1-x}\right)$, then the domain of f(x) is ___

1. $(1,2)$

2. $(0,2)$

3. $(-2,1)$

4. $(-1,2)$

Q. Pointer is

1. data type
2. integer
3. a variable for storing address
4. the address of variable

Q. 49. If k is an integer root of equation ax2+bx+c=abc(where abc is a 3 digit number whose digits are a b and c ) then

Q.

$f\left(x\right)=\frac{1}{x+|x-1|},g\left(x\right)=\frac{1}{x+|x+1|}$

1. Domain of $f$ is $R$ but domain of $g$ is not $R$

2. Domain of $g$ is $R$ but domain of $f$ is not $R$

3. Domain of both $f$ and $g$ are $R$.

4. Domain of neither $f$ nor $g$ is $R$