A fraction is such that when 5 is added to the numerator then its value is 1, again when 6 is added to the denomtnator then the value is ^{1}⁄_{2} The fraction is

Solution
Let the fraction be ^{x}⁄_{y}
\(∴\frac{x+5}{y}=1\)
⇒ x+ 5 = y ...... (i)
Again,
\(\frac{x}{y+6}=\frac{1}{2}\)
⇒2x=y+6
⇒ 2x = x + 5 + 6 [From equation (i)]
⇒ 2xx= 11
From equation (i)
y = 11 + 5 = 16\(∴\frac{x}{y}=\frac{11}{16}\)
If \(x^{2}6x^{2}+1=0\), then\(x^{2}+\frac{1}{x^{2}}\)

Solution
x^{2}6x+1=0
⇒x^{2}+l=6x
⇒x+^{1}⁄_{x}=6
On squaring
x^{2}+^{1}⁄_{x2}+6=36
⇒x^{2}+^{1}⁄_{x2}= 36  2 = 34
If\(\left ( a+\frac{1}{a} \right )^{2}=3\) then the value of \(a^{3}+\frac{1}{a^{3}}\) is

Solution
\(\left ( a+\frac{1}{a} \right )^{2}=3\)
\(∴a+\frac{1}{a}=\sqrt{3}\)
On cubing,
\(a^{3}+\frac{1}{a^{3}}+3\left ( a+\frac{1}{a} \right )=3\sqrt{3}\)
\(\Rightarrow a^{2}+\frac{1}{a^{2}}+3\sqrt{3}=3\sqrt{3}\)
\(\Rightarrow a^{2}+\frac{1}{a^{3}}=0\)
The reverse order arrangements of the following words impromptu, impudent, improvise, imprudent in a dictionary will be

Solution
Reverse order as per dictionary.
A, B and C are statements such that if both A and B are true then C is false. Further A is always true. Then

Solution
A is always true. Then, if B is true, C is false.
Find the missing number in the following table :

Solution
(1)^{3}+ (2)^{3}= 1 + 8 = 9
(3)^{3}+ (4)^{3}= 27 + 64 = 91
(5)^{3}+ (6)^{3}= 125 + 216 = 341
If ‘+’ stands for ‘÷’, ‘‘ stands for ‘+’, ‘x’ for ‘+’ and ‘÷’ for ‘x’ then 4 + 4 × 2 ÷ 2 – 8 =

Solution
4+4×2÷28=?
⇒?=4÷4+2×2+8
⇒ ? = 1 + 4 + 8 = 13
32 boys are standing in front of X in a queue. Y is standing in the 19th position from the back in the same queue. If total number of boys is 45 then the number of boys standing in between X and Y is

Solution
There are five boys between X andY.
Starting from his house Arun moves 5km to the north east and then 4km towards south. He now moves 3km towards east and then moves 8 km towards north to reach his friend’s house. Then his friend’s house is

Solution
\(BF =\sqrt{(BE)^{2}+(EF)^{2}}\)
\(=\sqrt{(3)^{2}+(4)^{2}}\)
\(=\sqrt{9+16}=\sqrt{25}=5\)
Arun's friend's house is 10 km northeast of Arun's house.
Bimal is older than Chand but younger to Antl, Dipak is younger to Emon but older than Chand. If Anil is younger to Emon then which of the following can definitely be concluded?

Solution
Anil > Bimal > Chand
Emon > Deepak > Chand
Ernon > Anil
Chand is the youngest and Emon is the eldest.