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Question : If $x^2-8x+1=0$, what is the value of $(x^2+\frac{1}{x^2})$?
Option 1: $18$
Option 2: $34$
Option 3: $40$
Option 4: $62$
Correct Answer: $62$
Solution : Given: $x^2-8x+1=0$ Dividing both sides by $x$, we get, $⇒x-8+\frac{1}{x}=0$ $⇒x+\frac{1}{x}=8$ Squaring both sides, we get, $⇒(x+\frac{1}{x})^2=8^2$ $⇒x^2+\frac{1}{x^2}+2=64$ $\therefore x^2+\frac{1}{x^2}=64-2=62$ Hence, the correct answer is $62$.
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 27, 32, 42, 57, 77, 102, 132, ?
Option 1: 172
Option 2: 167
Option 3: 149
Option 4: 158
Correct Answer: 167
Solution : Given: 27, 32, 42, 57, 77, 102, 132, ?
In the above-given series, add multiples of 5 to the previous number to get the next number. 27 + 5 = 32, 32 + 10 = 42, 42 + 15 = 57, 57 + 20 =
Question : Directions: Which one of the given responses would be a meaningful order of the following words? a. Book b. Words c. Letters d. Sentences e. Chapters f. Pages
Option 1: c, b, f, e, d, a
Option 2: c, b, e, d, f, a
Option 3: c, b, d, e, f, a
Option 4: c, b, d, f, e, a
Correct Answer: c, b, d, f, e, a
Solution : Given: a. Book b. Words c. Letters d. Sentences e. Chapters f. Pages
Books are fascinating objects that consist of various elements that work together to convey a message or tell a story. The most basic building blocks of a
Question : Directions: In the following question, four number pairs are given. In each pair, the number on the left side of (-) is related to the number on the right side of (-) with some Logic/Rule /Relation. Three pairs are similar based on the same Logic/Rule/Relation. Select the odd one out from the given alternatives. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Option 1: 64 – 4032
Option 2: 38 – 1444
Option 3: 42 – 1764
Option 4: 52 – 2704
Correct Answer: 64 – 4032
Solution : Let's check each option – First option: (64 – 4032); 642 = 4096 ≠ 4032 Second option: (38 – 1444); 382 = 1444 Third option: (42 – 1764); 422 = 1764 Fourth option: (52 – 2704); 522 = 2704
Question : River Indus originates from :
Option 1: Hindukush range
Option 2: Himalayan range
Option 3: Karakoram range
Option 4: Kailash range
Correct Answer: Kailash range
Solution : The correct answer is Kailash range
The Indus River originates from mountain springs northeast of Mount Kailash in Western Tibet, flows through the conflict region of Kashmir to the north, makes a sharp left turn after the Nanga Parbat massif, and then flows through
Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:
Option 1: 24
Option 2: 25
Option 3: 0
Option 4: 27
Correct Answer: 0
Solution : Given: $a+b=3$ Cubing both sides, we get $(a+b)^3=3^3$ ⇒ $a^3+b^3+3ab(a+b)=27$ Putting, $(a+b)=3$ ⇒ $a^3+b^3+3ab×3=27$ ⇒ $a^3+b^3+9ab=27$ Thus, $a^3+b^3+9ab–27=0$ Hence, the correct answer is 0.
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".
The servant (1) / hanged the lamp (2) / on the wall. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
The word hanged is incorrect in this context. Both hung and hanged are the past participle forms of the verb hang. The correct verb form to use when suspending or attaching something, like a lamp,
Question : Most of the Himalayan rivers are of which type?
Option 1: Exotic
Option 2: Perennial
Option 3: Seasonal
Option 4: Episodic
Correct Answer: Perennial
Solution : The correct option is Perennial.
The majority of the rivers in the Himalayan region are perennial, meaning they flow all year round. Because these rivers receive their water from both rainfall and the melting of snow from the Himalayan glaciers, they are considered perennial. A
Question : Direction: In the following question, select the one which is different from other three alternatives.
Option 1: LNOR
Option 2: TRPS
Option 3: CEFI
Option 4: GIJM
Correct Answer: TRPS
Solution : Given:
First option:LNOR ; Follows alphabetical order
Second option:TRPS ; Does not follows alphabetical order
Third option:CEFI ; Follows alphabetical order
Fourth option:GIJM ; Follows alphabetical order
Hence, second option is correct.
Question : Directions: Select the number from among the given options that can replace the question mark (?) in the following series. 183, 173, 153, 123, 83, ?
Option 1: 43
Option 2: 33
Option 3: 23
Option 4: 53
Correct Answer: 33
Solution : Given: 183, 173, 153, 123, 83, ?
Subtract multiples of 10 to the previous number to obtain the next number. 183 – 10 = 173, 173 – 20 = 153, 153 – 30 = 123, 123 – 40 = 83, 83 – 50 = 33
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