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Question : In the shown figure, BC is a chord and CD is a tangent through the point C. If $\angle AOC=112^{\circ}$, then find $\angle ACD$.
Option 1: 63°
Option 2: 59°
Option 3: 65°
Option 4: 56°
Correct Answer: 56°
Solution : The angle subtended by an arc of a circle at its centre is twice the angle it subtends on any point of the circle's circumference. So, $\angle$AOC = 2 $\angle$ABC ⇒ 112°= 2 $\angle$ABC ⇒ $\angle$ABC = 56° Also, $\angle$ABC = $\angle$ACD ⇒ $\angle$ACD =
Question : Directions: Find the missing number from the given responses in the following question.
Option 1: 5052
Option 2: 5100
Option 3: 5094
Option 4: 4860
Correct Answer: 5100
Solution : Multiply the given numbers by 3 and then add 6 to the resultant number to obtain the next number (pattern starting from 18).
(18 × 3) + 6 = 54 + 6 = 60 (60 × 3) + 6 = 180 + 6 = 186
Question : Directions: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. 1, 4, 2, 3, 2, ?
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 5
Correct Answer: 4
Solution : Given: 1, 4, 2, 3, 2, ?
Add the numbers first in decreasing order and then in increasing order to the numbers of the given series –
So, the missing number is 4. Hence, the third option is correct.
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
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