Range

Q. The range of $f\left(x\right)=\frac{x^2}{x^4+1}$ is

1. $[0,\frac{1}{2}]$
2. $[0,\infty )$
3. $(0,\frac{1}{2})$
4. $[0,2]$

Q. The range of f(x) = sqrt(log_(1//4)((5x-x^(2))/4)) + (10)C_(x) is

Q.

The value of $\sin \left(\frac{\mathrm{\pi }}{14}\right)\sin \left(\frac{3\mathrm{\pi }}{14}\right)\sin \left(\frac{5\mathrm{\pi }}{14}\right)\sin \left(\frac{7\mathrm{\pi }}{14}\right)\sin \left(\frac{9\mathrm{\pi }}{14}\right)\sin \left(\frac{11\mathrm{\pi }}{14}\right)\sin \left(\frac{13\mathrm{\pi }}{14}\right)$ is equal to

1. $\frac{1}{8}$

2. $\frac{1}{16}$

3. $\frac{1}{32}$

4. $\frac{1}{64}$

Q. Let $f:R\to R$ be defined by $f\left(x\right)=\frac{x}{1+x^2},x\in R.$ Then the range of $f$ is

1. $R-[-\frac{1}{2},\frac{1}{2}]$
2. $R-[-1,1]$
3. $(-1,1)-\left\{0\right\}$
4. $[-\frac{1}{2},\frac{1}{2}]$

Q.

The range of the function $f\left(x\right){=}^{7-x}{P}_{x-3}$ is

1. $\{1,2,3\}$

2. $\{1,2,3,4,5\}$

3. $\{1,2,3,4\}$

4. $\{1,2,3,4.5,6\}$

Q. Find the general solution of the equation $\cos 4x=\cos 2x$

Q. The sum of solutions of the equation $\frac{\cos x}{1+\sin x}=|\tan 2x|,x\in (-\frac{\pi }{2},\frac{\pi }{2})-\{\frac{\pi }{4},-\frac{\pi }{4}\}$ is

1. $\frac{\pi }{10}$
2. $-\frac{7\pi }{30}$
3. $-\frac{11\pi }{30}$
4. $-\frac{\pi }{15}$

Q. Let $A$ be the set of first $10$ natural numbers and $R$ be a relation on $A$ defined by $(x,y)\in R\iff x+2y=10.$ Then the range of $R$ is

1. $\{1,2,3,\dots ,10\}$
2. $\{2,4,6,8\}$
3. $\{2,4,6,8,10\}$
4. $\{1,2,3,4\}$

Q. The number of solutions of ${\sin }^{7}x+{\cos }^{7}x=1,x\in [0,4\pi ]$ is equal to:

1. $5$
2. $7$
3. $11$
4. $9$

Q.

Let A = {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by

$R=\left\{\right(a,b):a,bϵA,b$ is exactly divisible by a}

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

Q. The system of equations
$2x^2-3y^2+z^2+6=0,$
$x^2-7y^2-2z^2-5=0$
and $5x^2-y^2+4z^2+23=0$ has

1. Unique real solution
2. Finitely many real solutions
3. Infinitely many solutions
4. No real solution

Q. $f\left(x\right)=\frac{x^2-3x+4}{x^2+3x+4}thenrangeoff\left(x\right)is$

1. 
2. 
3. 

Q. Let R = {(a, a³) : a is a prime number less than 5} be a relation. Find the range of R. [CBSE 2014]

Q. If $A=\{x:|x|\le 5;x\in Z-\{0\left\}\right\}$, $B=\{x:x\le 100;x\in W\}$ and $f:A\to B$ is a function defined by $f\left(x\right)=x^2+1$, then the number of elements in the range of $f$ that lie in $[5,26)$ is

1. $5$
2. $3$
3. $4$
4. $2$

Q. The range of the function $f\left(x\right)=\sqrt{x^2-3x+5}$ is

1. $(-\infty ,-\frac{\sqrt{11}}{2}]\cup [\frac{\sqrt{11}}{2},\infty )$
2. $[-\frac{\sqrt{11}}{2},\frac{\sqrt{11}}{2})$
3. $[\frac{\sqrt{11}}{2},\infty )$
4. $[\sqrt{5},\infty )$

Q. If $e^x+e^{f\left(x\right)}=e,$ then which among the following options are correct

1. Domain of $f\left(x\right)$ is $(-\infty ,1)$
2. Range of $f\left(x\right)$ is $(-\infty ,1)$
3. Domain of $f\left(x\right)$ is $(-\infty ,0]$
4. Range of $f\left(x\right)$ is $(-\infty ,0]$

Q.

f(x) = 2+3cosx

Find the range

Q.

If $A=\{1,2,3,\}\&B=\{1,4,6,9\}$ and $\mathrm{R}$ is a relation from $\mathrm{A}\mathrm{to}\mathrm{B}$ defined by $x>y,$where $x\in A\&y\in B$ The range of $\mathrm{R}$ is

1. $\{1,4,6,9\}$

2. $\{4,6,9\}$

3. $\left\{1\right\}$

4. None of these

Q. $\underset{x\to 3}{lim}\left(\right[x]+[-x\left]\right)$ is $($where $[.]$ denotes the greatest integer function$)$

1. $0$
2. $1$
3. $-1$
4. not defined

Q. find the domain and range of f(x)= cos[ln(5x^2-8x+7)] where [.] is the g.i.f.

Q. The correct option(s) for the function $f\left(x\right)=\sqrt{\left(\right[x]-1)}+\sqrt{(4-[x\left]\right)}$ is/are
(where [.] represents the greatest integer function).

1. Range of the function is $\{\sqrt{2},1+\sqrt{3}\}$
2. Domain of the function is $[1,5)$
3. Domain of the function is $(0,4]$
4. Range of the function is $\{\sqrt{3},1+\sqrt{2}\}$

Q. If $A=\{1,2,3,4\},B=\{1,2,3,4,\mathrm{5....25}\}$ and $f:A\to B$ is a function such that $f\left(x\right)=x^2,$ then the number of elements in the range of $f\left(x\right)$ is

Q. Let $A=\{x:x\text{is a prime factor of}30\}$ and $B=\{y:y\in N,-3\le y+3<8\}$. If $R$ is a relation from $A$ to $B$, then $R^{-1}$ can be

1. $\left\{\right(2,2),(3,3\left)\right\}$
2. $\left\{\right(3,2),(4,2),(4,3\left)\right\}$
3. $\left\{\right(2,1),(3,1),(5,2\left)\right\}$
4. $\left\{\right(1,5),(3,3),(4,2\left)\right\}$

Q. find the domain and range of (x^2 +3x+5)/ (x^2-5x+4)

Q. The range of the expression $f\left(x\right)=\frac{x^3+x^2+x-3}{x-1}$ is

1. $[2,\infty )$
2. $(2,\infty )$
3. $[2,6)\cup (6,\infty )$
4. $(-1,\infty )$

Q.

Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.

Q.

Let A={a1, a2, a3, a4, a5} and B={b1, b2, b3, b4, } where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1, b1), (a2, b1), (a3, b3), (a4, b2}, (a5, b2)} . Prove that R is neither one one nor onto

Q. Let $S$ be the sum of all solutions (in radians) of the equation ${\sin }^4\theta +{\cos }^4\theta -\sin \theta \cos \theta =0$ in $[0,4\pi ]$. Then $\frac{8S}{\pi }$ is equal to

Q. The number of integral value(s) of $x$ that are not in domain of $f\left(x\right)=\log \left(\frac{1}{|2x-3|}\right)+\frac{1}{\log (|2x-3|)}$ is

Q. The approximate value of $\sqrt[3]{3-0.99}$ is

1. $-0.9967$
2. $-0.9976$
3. $-1.0033$
4. $-1$