Range

Q.

x = $\frac{-b+\sqrt{b^2-4ac}}{2a}$, then express the given formula in terms of b.

1. {(c/x) – ax}/x

2. ( - c - ax² )​/x​

3. {(c/x) + ax}/4

4. {-(c/x) – x/a}/2

Q. (x^2-5)(x^2-4)/(x-1) < or equal to 0 find the range of x

Q. A kennel can accommodate 12 dogs that weigh (in pounds) 6, 14, 23, 17, 19, 27, 39, 7, 33, 4, 11, and 13. Find the range of their weights.

1. 35 pounds
2. 37 pounds
3. 39 pounds
4. None of these

Q.

When analyzing a scatterplot with a cluster, why should outliers generally be excluded when interpreting the relationship of the variables?

Q. For a data set, the value of the range is 100. The lowest score is 1.25. Find the value of the highest score.

1. 99.75
2. 98.25
3. 99.25
4. 101.25

Q. The range of the data 7, 22, 6, 33, 21, 35, 7, 33, 86, 35 and 81 is _______ .

1. 79
2. 92
3. 80
4. 88

Q. If x is real , then value of the expression $\frac{x^2+14x+9}{x^2+2x+3}$ lies between

1. – 5 and 4
2. 5 and 4
3. None of these
4. 5 and –4

Q. For a data set, the value of the range is 70. The highest score is 77. Find the value of the lowest score.

1. 71
2. 7
3. 72
4. 70

Q. Direction: In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion (A): The difference between the maximum and the minimum values of a given observation is called range.​

Reason (R): The maximum value is 150 if the range is 38 and minimum value is 82.

1. Assertion (A) is true but, reason (R) is false.
2. Both assertion (A) and reason (R) are false.
3. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).​
4. Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).

Q.

If x = $\frac{-b+\sqrt{b^2-4ac}}{2a}$, then express the given formula in terms of a.

1. x(-c/x – 4b)

2. (c/x – 4b)/x

3. (-c/x – 4bx)/x

4. - ( c + xb )​/x²

Q. Let $f\left(x\right)=sin\left[\frac{\pi }{6}sin\left(\frac{\pi }{2}sinx\right)\right]\forall xϵR\text{and}g\left(x\right)=\frac{\pi }{2}sinx\forall xϵR$. Let (fog) (x) denotes f{g(x)} and (gof) (a) denotes g{f(x)}. Then, which of the following is / are true?

1. Range of f is $[-\frac{1}{2},\frac{1}{2}]$
2. Range of fog is $[-\frac{1}{2},\frac{1}{2}]$
3. $li{m}_{x\to 0}\frac{f\left(x\right)}{g\left(x\right)}=\frac{\pi }{6}$
4. There is an x $ϵ$R such that (gof) (x) = 1

Q. If $\sqrt{3-2x}+\sqrt{7+2x}=4$, then find the possible value of $x$?

1. $1,-3$
2. $2,3$
3. $-1,3$
4. $2,-3$

Q.

The marks obtained by 17 students a mathematics test (out of 100) are given below:
90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68. Find the range of the above data.

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.

The marks obtained by 17 students a mathematics test (out of 100) are given below:
90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68.
Find the range of the above data.

Q.

If $f\left(x\right)=x^2+2bx+2c^2$ and $g\left(x\right)=-x^2-2cx+b^2$ such that in $f\left(x\right)>maxg\left(x\right)$, then the relation between $b$ and $c$, is

1. $0<c<b\sqrt{2}$

2. $|c|>|b|\sqrt{2}$

3. No real value of b &c

4. $|c|<|b|\sqrt{2}$

Q. If the relation $R:A\to B$ where $A=\{1,2,3\}B=\{1,3,5\}$ is defined by $R=\left\{\right(x,y,):x<y,x\in A,y\in B\}$ then

1. $R=\left\{\right(1,3),(1,5),(2,3),(2,5),(3,5\left)\right\}$
2. $R=\left\{\right(1,1),(1,5),(2,3),(3,5\left)\right\}$
3. $R^{-1}=\left\{\right(3,1),(5,1),(3,2),(5,3\left)\right\}$
4. $R^{-1}=\left\{\right(1,1),(5,1),(3,2),(5,3\left)\right\}$

Q. If 2x + 4 < 0, what is the value of x?

1. x < 2
2. x > 2
3. x > - 2
4. x < -2

Q.

The range of the function $y=\frac{x-1}{(x^2-3x+3)}$ is [a, b] where a, b are respectively

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

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

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

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

Q. $\frac{(x^2-5x+7)(x^2-x)}{(x+1)}\ge 0$

Q. Which of the below option is correct by applying the mean, median and mode for the set of numbers $1,1,1,3,4,6,5?$

1. The mean is the greatest
2. The median is the greatest
3. The mode is the greatest
4. Mean and median are equal

Q. If A={1, 2, 3, 4} and $f:A\to R$ is a function defined by $f\left(x\right)=\frac{x^2-x+1}{x+1}$ then find the range of 'f'

Q.

If $A=\{8,16,24,32\}$ and $B=\{5,25,125\}$ and $R$ is relation defined from A to B such that $aRb$ means $a<b$ for all $a\in A,b\in B$ and $(a,b)\in R,$ then $R=$ ___.

1. $R=\left\{\right(8,25),(8,125),(16,25),(16,125),(24,25),(24,125),(32,125\left)\right\}.$

2. $R=\left\{\right(8,25),(8,125),(8,5),(16,25),(24,25),(32,5),(32,25\left)\right\}$

3. $R=\left\{\right(16,25),(16,125),(24,5),(24,25),(24,125),(32,25),(32,125\left)\right\}$

4. $R=\left\{\right(16,5),(16,125),(16,25),(24,25),(24,5),(24,125),(32,25\left)\right\}$

Q. If $(mx+7)(5x+n)=p{x}^2+15x+14,\forall xϵR$, then $m+n+p=$

1. $62$
2. $-62$
3. $-58$
4. $None$

Q. ________ of the data is the difference between the maximum and theminimum values of the observations.

1. Range
2. Median
3. Mean
4. Mode

Q.

The entire graphs of the equation $y=x^2+kx-x+9$ is strictly above the x-axis if and only if

1. k>-5
2. -7<k<5
3. k<7
4. -5<k<7