Insertion of AP's between 2 Numbers

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. If the ${10}^{th}$ term of an A.P. is $\frac{1}{20}$ and its ${20}^{th}$ term is $\frac{1}{10}$, then the sum of its first $200$ terms is

1. $99$
2. $100$
3. $101$
4. $100\frac{1}{2}$

Q. The sum up to $23$ terms of the A.P. $5,9,13,17,...$ is

1. $800$
2. $912$
3. $1127$
4. $1542$

Q. Each entry of $\text{List I}$ is to be matched with one entry of $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& 100(\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{99\cdot 100})\text{equals}& \text{(P)}& 7\\ \text{(B)}& \text{If}x\text{is the arithmetic mean between two real numbers}a\text{and}b\text{,}& \text{(Q)}& 9\\ & y=a^{2/3}\cdot b^{1/3}\text{and}z=a^{1/3}\cdot b^{2/3},\text{then}\frac{y^3+z^3}{xyz}\text{equals}& & \\ \text{(C)}& \text{If}198\text{arithmetic means are inserted between}\frac{1}{4}\text{and}\frac{3}{4}\text{, then}& \text{(R)}& 99\\ & \text{the sum of these arithmetic means is}& & \\ \text{(D)}& \text{If}n\text{is a positive integer such that}n\text{,}\frac{n(n-1)}{2}\text{and}& \text{(S)}& 100\\ & \frac{n(n-1)(n-2)}{6}\text{are in A.P., then the value of}n\text{is}& & \\ & & \text{(T)}& 2\end{array}$

Which of the following is the only CORRECT combination?

1. $\text{(A)}\to \text{(R)},\text{(B)}\to \text{(T)}$
2. $\text{(A)}\to \text{(Q)},\text{(B)}\to \text{(P)}$
3. $\text{(A)}\to \text{(S)},\text{(B)}\to \text{(P)}$
4. $\text{(A)}\to \text{(T)},\text{(B)}\to \text{(R)}$

Q.

16 A.Ms are inserted between 5 and 50. Find the sum of all the A.Ms.

1. 880

2. 820

3. 410

4. 440

Q. Each entry of $\text{List I}$ is to be matched with one entry of $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& 100(\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{99\cdot 100})\text{equals}& \text{(P)}& 7\\ \text{(B)}& \text{If}x\text{is the arithmetic mean between two real numbers}a\text{and}b\text{,}& \text{(Q)}& 9\\ & y=a^{2/3}\cdot b^{1/3}\text{and}z=a^{1/3}\cdot b^{2/3},\text{then}\frac{y^3+z^3}{xyz}\text{equals}& & \\ \text{(C)}& \text{If}198\text{arithmetic means are inserted between}\frac{1}{4}\text{and}\frac{3}{4}\text{, then}& \text{(R)}& 99\\ & \text{the sum of these arithmetic means is}& & \\ \text{(D)}& \text{If}n\text{is a positive integer such that}n\text{,}\frac{n(n-1)}{2}\text{and}& \text{(S)}& 100\\ & \frac{n(n-1)(n-2)}{6}\text{are in A.P., then the value of}n\text{is}& & \\ & & \text{(T)}& 2\end{array}$

Which of the following is the only CORRECT combination?

1. $\text{(C)}\to \text{(R)},\text{(D)}\to \text{(Q)}$
2. $\text{(C)}\to \text{(Q)},\text{(D)}\to \text{(P)}$
3. $\text{(C)}\to \text{(R)},\text{(D)}\to \text{(P)}$
4. $\text{(C)}\to \text{(S)},\text{(D)}\to \text{(R)}$