Question Detail
Which among following is not a prime number ?
- 97
- 33
- 45
- 72
Answer: Option A
1. Sum of a rational number and its reciprocal is 13/6. Find the number
- 2
- 3/2
- 4/2
- 5/2
Answer: Option B
Explanation:
\begin{aligned} => x + \frac{1}{x} = \frac{13}{6} \end{aligned}
\begin{aligned} => \frac{x^2+1}{x} = \frac{13}{6} \end{aligned}
\begin{aligned} => 6x^2-13x+6 = 0 \end{aligned}
\begin{aligned} => 6x^2-9x-4x+6 = 0 \end{aligned}
\begin{aligned} => (3x-2)(2x-3) \end{aligned}
\begin{aligned} => x = 2/3 or 3/2 \end{aligned}
2. Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number
- 5
- 15
- 7.5
- 4
Answer: Option A
Explanation:
Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5
3. find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.
- 214
- 216
- 114
- 116
Answer: Option B
Explanation:
Let the number is x,
\begin{aligned}
=> \frac{2}{3}x-50 = \frac{1}{4}x + 40
\end{aligned}
\begin{aligned}
<=> \frac{2}{3}x-\frac{1}{4}x = 90
\end{aligned}
\begin{aligned}
<=> \frac{5x}{12} = 90
\end{aligned}
\begin{aligned}
<=> x = 216
\end{aligned}
4. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
- 12
- 13
- 15
- 17
Answer: Option C
Explanation:
Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15
5. Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is
- \begin{aligned} \frac{290}{289} \end{aligned}
- \begin{aligned} \frac{1}{289} \end{aligned}
- \begin{aligned} \frac{290}{90} \end{aligned}
- \begin{aligned} \frac{290}{19} \end{aligned}
Answer: Option A
Explanation:
If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.
\begin{aligned} \frac{1}{a^2} + \frac{1}{b^2} =
\frac{1}{1^2} + \frac{1}{17^2}
\end{aligned}
\begin{aligned} = \frac{290}{289}
\end{aligned}