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Question : Raju and Ramu together can do a piece of work in 8 days, and Raju alone can do it in 12 days. In how many days can Ramu alone do it?
Option 1: 18 days
Option 2: 20 days
Option 3: 22 days
Option 4: 24 days
Correct Answer: 24 days
Solution : Raju and Ramu together can do a piece of work in 8 days. Their 1 day's work = $\frac{1}{8}$ Raju alone can do it in 12 days. Raju's 1 day's work = $\frac{1}{12}$ So, Ramu's 1 day's work = $\frac{1}{8}-\frac{1}{12}=\frac{1}{24}$ $\therefore$ Ramu can complete
Question : Directions: How many quadrilaterals are there in the following figure?
Option 1: 6
Option 2: 7
Option 3: 8
Option 4: 9
Correct Answer: 9
Solution : The given figure can be labeled as shown below –
Now, in the above figure, there are a total of 9 quadrilaterals. They are PQRS, QOWP, POUQ, QOVS, SOTQ, ROUS, SOWR, POVR, ROTS.
Hence, the fourth option is correct.
Question : What is the simplified value of: $\frac{1}{8}\left\{\left(x+\frac{1}{y}\right)^2-\left(x-\frac{1}{y}\right)^2\right\}$
Option 1: $\frac{x}{y}$
Option 2: $\frac{2x}{y}$
Option 3: $\frac{x}{2y}$
Option 4: $\frac{4x}{y}$
Correct Answer: $\frac{x}{2y}$
Solution : $\frac{1}{8}\left\{\left(x+\frac{1}{y}\right)^2-\left(x-\frac{1}{y}\right)^2\right\}$ $=\frac{1}{8}(x^2 +\frac{1}{y^2} + 2×x×\frac{1}{y} - x^2 - \frac{1}{y^2} + 2×x×\frac{1}{y})$ $=\frac{1}{8}(\frac{4x}{y})$ $=\frac{x}{2y}$ Hence, the correct answer is $\frac{x}{2y}$.
Question : A boat takes half the time to move a certain distance downstream than upstream. The ratio of the speed of the boat in still water to that of the current is:
Option 1: $2:1$
Option 2: $1:2$
Option 3: $4:3$
Option 4: $3:1$
Correct Answer: $3:1$
Solution : Given: A boat takes half the time to move a certain distance downstream than upstream. Use the given formula, Time × Speed = Distance Also, boat speed in still water is $p$ km/hr. Current speed = $q$ km/hr The downstream speed is $(p + q)$
Question : Direction: How many such pairs of letters are there in the word 'RECOVERED', which have as many letters between them in the word as in the English alphabet?
Option 1: THREE
Option 2: FOUR
Option 3: SIX
Option 4: FIVE
Correct Answer: FOUR
Solution : Given: RECOVERED
First, check the sequence of the letters from the left hand side –
Question : The table given below shows the number of spoons manufactured by five factories.
What is the ratio of the number of spoons manufactured by P to the number of spoons manufactured by R?
Option 1: 3 : 2
Option 2: 2 : 3
Option 3: 14 : 1
Option 4: 1 : 3
Correct Answer: 2 : 3
Solution : The ratio of the number of spoons manufactured by P to the number of spoons manufactured by R = 100 : 150 = 2 : 3 Hence, the correct answer is 2 : 3.
Question : Directions: Six houses P, Q, R, S, T, and U are located in two rows with three houses in each row. The houses in both rows face each other. P is facing T. Q is not facing U. S is between P and U. Which three houses are in the same row?
Option 1: Q, R, T
Option 2: S, T, U
Option 3: P, Q, R
Option 4: P, S, T
Correct Answer: Q, R, T
Solution : Given: (I) Six houses P, Q, R, S, T, and U are located in two rows with three houses in each row. The houses in both rows face each other.
(II) P is facing T. Q is not facing U. S is between
Question : Select the option that can be used as a one-word substitute for the underlined segment. The child was not guilty of any wrongdoing and lacked knowledge or awareness of wrongdoing.
Option 1: ignorant
Option 2: inexperienced
Option 3: innocent
Option 4: cruel
Correct Answer: innocent
Solution : The correct choice is the third option.
Explanation: The underlined segment describes a state of not being guilty and lacking knowledge or awareness of wrongdoing. The word "innocent" precisely captures this meaning. Innocent refers to someone who is not guilty of a crime or
Question : The foremost right among rights to freedom is_________.
Option 1: right to life and personal liberty
Option 2: preventive detention
Option 3: freedom to assemble
Option 4: right to freedom of speech and expression
Correct Answer: right to life and personal liberty
Solution : The correct answer is the right to life and personal liberty.
The foremost right among rights to freedom is the right to life and personal liberty. This is mentioned in Article 21 of the Indian Constitution. Part 3 of
Question : Directions: Study the following graph and answer the question given below. Production of salt by a company (in 1000 tonnes) over the years.
What was the percentage increase in the production of salt in 2008 compared to that of 2001?
Option 1: 55.5%
Option 2: 125%
Option 3: 150%
Option 4: 220%
Correct Answer: 125%
Solution : Given: The production of salt in 2008 was 90. The production of salt in 2001 was 40. The percentage increase in production $= \frac{\text{Production of salt in 2008 – Production of salt in 2001}}{\text{Production of salt in 2001}}×100$ $= \frac{90-40}{40}×100$ $= \frac{50}{40}×100$ $= 125$% Hence,
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