Range

Q. Standard deviation is a measure of central tendency.

1. True
2. False

Q.

The equations x2− 4x + k = 0 and x2+ kx − 4 = 0, where k is a real number, have exactly one common root. What is the value Ofp k?

Q. Find the value of discriminant.
(1) x² + 7x – 1 = 0
(2) 2y² – 5y + 10 = 0
(3) $\sqrt{2}{x}^2+4x+2\sqrt{2}=0$

Q. If $x+\frac{1}{x}=11$, find the value of $x^2+\frac{1}{x^2}$.

1. $121$
2. $119$
3. $1$
4. $11$

Q. If $y=\sqrt{\frac{1+e^x}{1-e^x}}$ then $\frac{dy}{dx}$ is :

1. $\frac{e^x}{(1-e^x)\sqrt{1-e^{2x}}}$
2. $\frac{e^x}{(1-e^x)\sqrt{1-e^x}}$
3. $\frac{e^x}{(1-e^x)\sqrt{1+e^{2x}}}$
4. $\frac{e^x}{(1-e^x)\sqrt{1+e^x}}$

Q. The arrow diagram shows a relationship between the sets P and Q.Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.

Q.

Define $x\%a$ as the remainder obtained when $x$ is divided by $a$.
Let $f:Z\to R$ be defined as $f\left(x\right)=x\%k$, where $kϵN$. If Y is the range of $f\left(x\right)$, then

1. $Y=N\cup \left\{0\right\}$

2. $n\left(Y\right)=k$

3. $Y=[0,k]$

4. $Y=R$

Q. Which of the following are sets? Justify your answer.
(i) The collection of good books
(ii) The collection of prime numbers less than 30
(iii) The collection of ten most talented mathematics teachers.
(iv) The collection of all students in your school
(v) The collection of all even numbers

Q. The range of the function f(x) given by $f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}is$

1. R-Z
2. $[1,\infty )$
3. $\left(1,\infty \right)$
4. $\left(0,\infty \right]$

Q. There are 2n observations whose range is 3. Further one half of its observations are equal to 5 and
other half of observations all are equal. The values of each of these observations can be

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

Q. The equation (x^2)-4x+K=0 & (x^2)+Kx-4=0 where k is a real number, have exactly one common root. What is the value of K.

Q. The arrow diagram shows a relationship between the sets $P$ and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of $R$.

Q. Find value of X,
1/a+b+X=1/a+1/b+1/x

Q. The complete set of values of k for which $\frac{x^2-x}{1-kx}$ attains all real values is

1. $\left(0,\infty \right)$
2. $[0,\infty )$
3. $\left(1,\infty \right)$
4. $[1,\infty )$

Q. If the numbers a, b , c , d, e are in an A.P .

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. No real value of b &c

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

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

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

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

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

Q. Solve the inequality :
$x^2+3x-4>0$

1. $(-4,1)$
2. $(-\infty ,-4)\cup (1,+\infty )$
3. $(1,+\infty )$
4. no solutions
5. $(-\infty ,-4]\cup [1,+\infty )$

Q. Answer the Following :
What is a complex table?

Q.

If the range of n observations $x_1,x_n$ is zero , then the mean of these observations is

1. 1

2. 0

3. 2

4. $x_1$

Q.

$f:R\to R$ is defined as $f\left(x\right)=x^4-6x^2+12$. The range of f(x) is

1. $(-\infty ,\infty )$

2. $[-3,\infty )$

3. $[3,\infty )$

4. $[12,\infty )$

Q. The range of the function $f\left(x\right)=\frac{1}{3-\sin 3x},x\in R$ is

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

Q. If | |x| - 1 | < | 1 - x |, x belongs to R, then find range of x

Q. Find the value of k belons to R such that (k-1)x^2-2kx+(k+3)<0

Q. Find the roots of the equation $\frac{1}{a+b+x}-\frac{1}{x}=\frac{1}{a}+\frac{a}{b}$.

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

Q. for what value of k will 7/3 be a root of 3x2-13k-k=0
(A)14 (B) 3/7 (C) -7/2 (D) -14

Q. 5 kids have an average weight of 50 pounds. Jim is the heaviest kid, while Tim is the lightest. If Jim is excluded, the average becomes 40 pounds, and if Tim is excluded, the average becomes 60 pounds. What is the average weight of Jim and Tim?