Progression

Q. An H.M. is inserted between the number 1/3 and an unknown number. If we diminish the reciprocalof the inserted number by 6, it is the G.M. of the reciprocal of 1/3 and that of the unknown numberIf all the terms of the respective H.P. are distinct then (B) the unknown number is 1/27 (A) the unknown number is 27 (D) the G.M. is 21 (C) the H. M. is is 115

Q.

If all permutations of the letters of the word APPLE are arranged as in the dictionary, what is the 35^th word?

1. LPPAE

2. PPLEA

3. LAPPE

4. PPAEL

Q. The value of ${\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)}^6+{\left(\frac{1-i\sqrt{3}}{1+i\sqrt{3}}\right)}^6$

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

Q. If the $r^{th}$ term in the expansion of ${(\frac{x}{3}-\frac{2}{x^2})}^{10}$ contains $x^4$, there r is equal to

1. 4
2. 3
3. 2
4. None of these

Q. $Ifx+iy=\sqrt{\frac{a+ib}{c+id}},then(x^2+y^2{)}^2$, then is equal to

1. 
2. 
3. 
4. 

Q. Supposse $a,b,c$ are in A.P. and $a^2,b^2,c^2$ are in G.P. If $a<b<c$ and $a+b+c=\frac{3}{2}$, then the value of $a$ is

1. $\frac{1}{2\sqrt{2}}$
2. $\frac{1}{2}-\frac{1}{\sqrt{3}}$
3. $\frac{1}{2\sqrt{3}}$
4. $\frac{1}{2}-\frac{1}{\sqrt{2}}$

Q. 17.: I1.2 +1.2+.3+1.2+2.3+3.4+1.2 +2.3+3.4+4.5 be the sequence then find the sum of up to ten terms

Q. The coefficient of $x^n$ in the expansion of $(1-x)e^x$ is

1. $\frac{1}{n!}$
2. $\frac{1}{(n+1)!}$
3. $\frac{1-n}{n!}$
4. $\frac{n-1}{n!}$

Q.

How many words can be formed by taking 4 letters at a time from the letters of the word MORADABAD?

Q. Match the following by appropriately matching the lists based on the information given in Column I and Column II​​​​​​
$\begin{array}{cccc}& ColumnI& & ColumnII\\ a.& \text{If}a,b,c\text{are in}G.P.,\text{then}& \text{p.}& A.P.\\ & {\log }_{a}10,{\log }_{b}10,{\log }_{c}10\text{are in}& & \\ b.& \text{If}\frac{a+b{e}^x}{a-b{e}^x}=\frac{b+c{e}^x}{b-c{e}^x}=\frac{c+d{e}^x}{c-d{e}^x},& \text{q.}& H.P.\\ & \text{then}a,b,c,d& & \\ c.& \text{If}a,b,c\text{are in}A.P.;& \text{r.}& G.P.\\ & a,x,b\text{are in}G.P.\text{and}& & \\ & b,y,c\text{are in}G.P.,& & \\ & \text{then}{x}^2,b^2,y^2\text{are in}& & \end{array}$

1. $a\to p,b\to r,c\to q$
2. $a\to q,b\to p,c\to r$
3. $a\to q,b\to r,c\to p$
4. $a\to r,b\to q,c\to p$