Selecting Consecutive Terms in A.P

Q. Which of the following is/are example(s) of a function?

1. Only $\left(1\right)$ and $\left(2\right)$
2. Only $\left(1\right),\left(2\right)$ and $\left(3\right)$
3. Only $\left(1\right)$ and $\left(3\right)$
4. $\left(1\right),\left(2\right),\left(3\right),\left(4\right)$

Q. Values of ${}^{\prime }{m}^{\prime }$ such that the roots of the equation $2x^2-x-1=0$ lie inside the roots of the equation $x^2+(2m-m^2)x-2m^3=0,$ is

1. $\frac{3}{4}$
2. $\frac{2}{3}$
3. $\frac{1}{8}$
4. $2$

Q. If the roots of the equation $x^3-9x^2+23x-15=0$ are the first three terms of an A.P, then the sum of first $20$ terms of the A.P. can be

1. $400$
2. $280$
3. $-400$
4. $-280$

Q.

If $a_1,a_2,\cdot \cdot \cdot ,a_{15}$ are in A.P. and $a_1+a_8+a_{15}=15$, then $a_2+a_3+a_8+a_{13}+a_{14}$ equals

1. 15

2. 10

3. 25

4. 33

Q. If $|3x-4|<11$, then $x\in$

1. $(\frac{7}{3},5)$
2. $(-\frac{7}{3},5)$
3. $[-\frac{7}{3},5]$
4. $R-(-\frac{7}{3},5)$

Q. If the product of $3$ consecutive numbers in G.P. is $216$ and the sum of their products in pairs is $156$, then the smallest term in the three is

1. $2$
2. $6$
3. $\frac{1}{2}$
4. $\frac{1}{4}$

Q. Consider the following statement $P\left(n\right):1+3+5+...+\left(2n-1\right)=3+n^2,n\in N$
then which of the folowing is true?

1. P(1) is correct.
2. P(1) is not correct.
3. P(n) $\Rightarrow$P(n+1)
4. P(n) $\nRightarrow$P(n+1)

Q. The sum of three numbers in A.P. is -3, and their product is 8. The numbers are:

1. -4, -1, 2
2. -4, 0, 2
3. -2, 1, 4
4. -4, -2, 1

Q. The sides of a right angled triangle are in arithmetic progression. If the triangle has an area of 24 sq. units, then what is the length of its smallest side?___

Q.

If three positive real numbers a, b, c are in A.P. such that abc $=4$, then the minimum value of b is

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

2. $2^{\frac{2}{3}}$

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

4. $2^{\frac{3}{2}}$

Q. If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$, respectively, then the value of its ${11}^{\text{th}}$ term is :

1. $-36$
2. $-25$
3. $25$
4. $-35$

Q. The degree measures of the angles in a convex $18$-sided polygon form an increasing arithmetic sequence with integer values. If $x$ is the degree measure of the smallest angle, then the number of divisors of $x$ is
(correct answer + 3, wrong answer 0)