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Question : If $(a+b+c)=14$ and $\left(a^3+b^3+c^3-3 a b c\right)=98$, find the value of $(ab+bc+ca)$.
Option 1: 60
Option 2: 64
Option 3: 65
Option 4: 63
Correct Answer: 63
Solution : Given that: $a + b + c = 14$ and $a^3 + b^3 + c^3 - 3abc = 98$ We have to find the value of $ab +bc +ca$ We know that, $a^3 + b^3+ c^3 - 3abc = 98$ ⇒ $(a^2+ b^2+ c^2 -
Question : Directions: Each of the letters in the word WORKING is arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter which is third from the left and the one which is fourth from the right in the new letter cluster thus formed?
Option 1: One
Option 2: Six
Option 3: Two
Option 4: Four
Correct Answer: Two
Solution : Given: WORKING
Arrange the letters of WORKING in the alphabetical order – W O R K I N G→G I K N O R W
Now, according to the new letter cluster formed, the third letter from the left is K and the fourth letter
Question : Chlorine gas is a major component of which of the following?
Option 1: Water
Option 2: Tear gas
Option 3: Liquefied petroleum gas
Option 4: Gobar gas
Correct Answer: Tear gas
Solution : The correct option is Tear gas.
Chlorine is a prominent component of tear gas, which is normally composed of a variety of chemicals, one of which is chloroacetophenone (CN) or chlorobenzalmalononitrile (CS), both of which decompose and create chlorine gas. Tear gas can
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figure series – 1. The triangle inside the pentagon moves from top left to top right, then again from top right to top left, and so on. 2. The rectangle inside the pentagon moves from bottom right to bottom left, then again
Question : Directions: Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some cats are dogs. Some dogs are rats. All rats are tigers. Conclusions: I. Some tigers are cats. II. Some tigers are dogs. III. Some rats are dogs.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I follows
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions II and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some tigers are cats – From the Venn diagram, there is no definite relation between tigers and cats. Therefore, this
Question : Directions: If A means +, B means ×, C means ÷, and D means –, then the value of the given equation will be 9 A 2 B 6 D 4 C 2 = ?
Option 1: 16
Option 2: 19
Option 3: 27
Option 4: 30
Correct Answer: 19
Solution : Given: 9 A 2 B 6 D 4 C 2 = ?
After replacing the letters with mathematical signs, the equation becomes – = 9 + 2 × 6 – 4 ÷ 2 = 9 + 2 × 6 – 2 = 9 + 12
Question : A man covers half part of a certain distance at 60 km/hr. He covers 40% of the remaining distance at the speed of 12 km/hr and covers the rest of the distance at the speed of 18 km/hr. What is his average speed for the entire journey?
Option 1: 24 km/hr
Option 2: $\frac{58}{3}$ km/hr
Option 3: 36 km/hr
Option 4: 40 km/hr
Correct Answer: 24 km/hr
Solution : Let the total distance be 100 km. Half distance = $\frac{100}{2}$ = 50 km Speed = 60 km/hr Time taken to cover half the distance = $\frac{50}{60}$ = $\frac{5}{6}$ Remaining distance = 50 km Distance = 40% of the remaining distance = $\frac{40}{100}×50$ =
Question : Select the most appropriate ANTONYM of the given word.
IGNOBLE
Option 1: corrupt
Option 2: craven
Option 3: abject
Option 4: dignified
Correct Answer: dignified
Solution : The correct choice is the fourth option.
Ignoble is an adjective that is used to describe someone who lacks honour. It refers to actions or behaviour, considered shameful or not respectable.
Dignified is an adjective that is used to describe someone who possesses a
Question : Identify the INCORRECTLY spelt word in the given sentence.
Sharks often use their serated or smooth teeth for seizing prey, cutting or crushing.
Option 1: serated
Option 2: prey
Option 3: seizing
Option 4: crushing
Correct Answer: serated
Solution : The correct choice is the first option.
The word "serated" in the sentence provided is misspelt. The correct spelling is serrated, which refers to a notched or toothed edge, often seen in objects like knives or, in the context of your sentence, shark
Question : The seventh schedule of the Constitution of India deals with
Option 1: allocation of seats in the Council of States
Option 2: distribution of power between the Union and the States
Option 3: power and authority of the municipalities
Option 4: powers of the governor of the state
Correct Answer: distribution of power between the Union and the States
Solution : The correct option is the distribution of power between the Union and the States
The Seventh Schedule of the Indian Constitution addresses the division of responsibilities and powers between the Union government and the state governments. The
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