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Question : If a 10-digit number $620x976y52$ is divisible by 88, then the least value of $(x^2+y^2)$ will be:
Option 1: 8
Option 2: 7
Option 3: 11
Option 4: 10
Correct Answer: 10
Solution : Given number = $620x976y52$ Co-prime factors of $88 = 8 × 11$ For the smallest possible value of $y$, $y52$ will be divisible by 8 So, $y$ will be 1 for 152, which is divisible by 8. As $y = 1$, the possible value of
Question : A man wills 40% of his wealth to his wife and the rest to his children. What percentage of the wealth willed to the wife do the children get?
Option 1: 150
Option 2: 66.6
Option 3: 50
Option 4: 20
Correct Answer: 150
Solution : Let the total wealth be $x$. The man wills 40% of his wealth to the wife = 40% of $x$ = 0.4$x$ Wealth for the children = $x$ – 0.4$x$ = 0.6$x$ So, the required percentage $=\frac{\text{wealth for children}}{\text{wealth to the wife}} × 100 =
Question : International Tiger Day is observed on ______.
Option 1: July 5th
Option 2: July 30th
Option 3: July 29th
Option 4: July 4th
Correct Answer: July 29th
Solution : The correct option is July 29th.
International Tiger Day is observed on July 29th every year. This day is dedicated to raising awareness about tiger conservation and the need to protect the habitats of these magnificent creatures. Various organisations and initiatives use this day
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
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