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Question : $\frac{1}{2}$ of A = $\frac{2}{5}$ of B = $\frac{1}{3}$ of C, then A : B : C is:
Option 1: 4 : 5 : 6
Option 2: 6 : 4 : 5
Option 3: 4 : 6 : 5
Option 4: 5 : 4 : 6
Correct Answer: 4 : 5 : 6
Solution : Given: $\frac{1}{2}× A=\frac{2}{5} × B=\frac{1}{3} × C$ ⇒ $\frac{1}{2} × A=\frac{2}{5} × B$ ⇒ $\frac{A}{B} = \frac{4}{5}$ And, $\frac{2}{5} × B = \frac{1}{3} × C$ ⇒ $\frac{B}{C} = \frac{5}{6}$ Taking B as common, the value of B is the same in
Question : If $\operatorname{cosec} A+\cot A=7$, then $\operatorname{cosec} A$ is equal to:
Option 1: $\frac{11}{7}$
Option 2: $\frac{16}{7}$
Option 3: $\frac{25}{7}$
Option 4: $\frac{19}{7}$
Correct Answer: $\frac{25}{7}$
Solution : We know if $\operatorname{cosec}x + \cot x = a$, then $\operatorname{cosec} x - \cot x = \frac{1}{a}$ Given, $\operatorname{cosec} A+\cot A=7$ ........(1) ⇒ $\operatorname{cosec} A-\cot A=\frac17$ .........(2) Solving these equations to get the value of $\operatorname{cosec} A$ (1) + (2), we get, ⇒ $\operatorname{cosec} A+\cot
Question : The fourth proportion of the numbers 8, 12, and 14 is:
Option 1: 15
Option 2: 18
Option 3: 24
Option 4: 21
Correct Answer: 21
Solution : Given: The numbers are 8, 12, and 14. Let the fourth proportion be $x$. So, $8:12::14:x$ ⇒ $\frac{8}{12} = \frac{14}{x}$ ⇒ $x = \frac{14 \times 12}{8}=21$ Hence, the correct answer is 21.
Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All hexagons are pentagons. All pentagons are octagons. All octagons are decagons. Conclusions: I. All decagons are hexagons. II. All hexagons are octagons.
Option 1: Both conclusions I and II follow
Option 2: Neither conclusion I nor II follows
Option 3: Only conclusion II follows
Option 4: Only conclusion I follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyze the conclusions – Conclusion (I): All decagons are hexagons – From the Venn diagram, it is evident that some parts of the circle representing decagons lie inside
Question : A shopkeeper allows a discount of 20% on the marked price and still gains 12% on the whole. Find at what percentage above the cost price he marks his goods.
Option 1: 30%
Option 2: 10%
Option 3: 40%
Option 4: 20%
Correct Answer: 40%
Solution : Let the cost price (CP) be 100. The gain percentage is 12%. So, the selling price (SP) = 100 + 100 × $\frac{12}{100}$ = 112 Now, discount = 20%, So, the marked price (MP) × $\frac{(100-\text{discount percentage})}{100}$ = SP ⇒ MP × $\frac{(100-20)}{100}$ = 112
Question : Select the option that can be used as a one-word substitute for the given group of words. Never changing, and therefore boring.
Option 1: Outdated
Option 2: Impractical
Option 3: Idealistic
Option 4: Monotonous
Correct Answer: Monotonous
Solution : The correct choice is the fourth option.
Monotonous means lacking in variety and interest, being repetitive and dull, which precisely describes the concept of never changing and being boring.
The meanings of other options are as follows:
Outdated: This term refers to something
Question : Directions: In the following question, select the odd word pair from the given alternatives.
Option 1: Scalpel - Surgeon
Option 2: Axe - Woodcutter
Option 3: Sword - Warrior
Option 4: Sculptor-Chisel
Correct Answer: Sculptor-Chisel
Solution : Let's check each option – First option: Scalpel - Surgeon; The scalpel is an essential tool used by surgeons. Second option: Axe - Woodcutter; An axe is a tool used by woodcutter. Third option: Sword - Warrior; A sword is used by a warrior. Fourth
Question : Directions: Select the letter cluster that can replace the question mark (?) in the given letter cluster series. THC, DIU, VJE, FKW, XLG, ?
Option 1: GMX
Option 2: HNZ
Option 3: HMY
Option 4: FKX
Correct Answer: HMY
Solution : Given: THC, DIU, VJE, FKW, XLG, ?
Follow the pattern as shown below to obtain the next letter cluster –
So, HMY is the missing term in the series. Hence, the third option is correct.
Question : Directions: If A stands for ÷, B stands for ×, C stands for +, and D stands for – what will come in place of the question mark (?) in the following equation? 13 B 145 A 29 C 69 D 17 = ?
Option 1: 119
Option 2: 121
Option 3: 115
Option 4: 117
Correct Answer: 117
Solution : Given: A stands for ÷, B stands for ×, C stands for +, D stands for – 13 B 145 A 29 C 69 D 17 = ?
Changing the sign as per the instruction and solving the equation, we will get – = 13
Question : What will be the length of the longest diagonal of the cuboid having a length of 13 cm, width of 11 cm, and height of 20 cm?
Option 1: 23.45 cm
Option 2: 26.27 cm
Option 3: 34.65 cm
Option 4: 22.65 cm
Correct Answer: 26.27 cm
Solution : Given: Length($l$) = 13 cm, width($b$) = 11 cm, and height($h$) = 20 cm Length of the longest diagonal of the cuboid $=\sqrt{13^2 + 11^2 + 20^2}$ $= \sqrt{169 + 121 + 400}$ $= \sqrt{690}$ $= 26.27$ cm Hence, the correct answer is 26.27
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