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Question : If $m x^m-n x^n=0$, then what is the value of $\frac{1}{x^m+x^n}+\frac{1}{x^m-x^n}$ terms of $x^n$ is: Where $x,m,n$ are $>0$
Option 1: $\frac{2 m n}{x^n(n^2+m^2)}$
Option 2: $\frac{2 m n }{x^n(m^2-n^2)}$
Option 3: $\frac{2 m n}{x^n\left(m^2+n^2\right)}$
Option 4: $\frac{2 m n }{x^n(n^2-m^2)}$
Correct Answer: $\frac{2 m n }{x^n(n^2-m^2)}$
Solution : Given, $mx^m − nx^n = 0$ ⇒ $mx^m = nx^n$ ⇒ $\frac{x^m}{x^n} = \frac{n}{m}$ Now, $\frac{1}{x^m+x^n}+\frac{1}{x^m-x^n}$ = $\frac{x^m-x^n + x^m+x^n}{(x^m+x^n)(x^m-x^n)}$ = $\frac{2x^m}{(x^m+x^n)(x^{2m}-x^n)}$ = $\frac{n-m+n+m}{(n+m)(n-m)}$ = $\frac{2n}{(n^2−m^2)}$ Now, the value of $\frac{1}{x^m+x^n}+\frac{1}{x^m−x^n}$ in terms of $x^n$ = $\frac{2n}{n^2-m^2}\times\frac{x^n}{x^n}$ = $\frac{2nm}{x^n(n^2-m^2)}$ [As $x^n=m$] Hence,
Question : In which year was the Jammu and Kashmir Legislative Council abolished?
Option 1: 2019
Option 2: 2020
Option 3: 2022
Option 4: 2021
Correct Answer: 2019
Solution : The correct option is 2019.
The Jammu and Kashmir Legislative Council was formally abolished on October 31, 2019. This followed the passage of the Jammu and Kashmir Reorganisation Act, 2019, which reorganised the state into the Union Territories of Jammu Kashmir and Ladakh. As
Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four.
Two ___ were sent to garrison the town.
Option 1: Armies
Option 2: Regimes
Option 3: Troops
Option 4: Regiments
Correct Answer: Regiments
Solution : The fourth option is the correct choice since "regiments" means military units consisting of soldiers organised for specific tasks and fits perfectly in the sentence.
The meanings of the other options are as follows:
Question : What numerical scale was introduced in 1932 that determined the electronegativity of fluorine to be 4.0?
Option 1: Allred-Rochow scale
Option 2: Mulliken scale
Option 3: Pauling scale
Option 4: Jae scale
Correct Answer: Pauling scale
Solution : The correct option is the Pauling scale.
This scale was developed by Linus Pauling. The Pauling electronegativity scale quantifies the ability of an atom to attract electrons in a chemical bond. It's a dimensionless scale. Fluorine is set to 4.0 as it is
Question : Directions: From the given answer figures, select the one in which the question figure is hidden/embedded.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Because there is no restriction on the rotation of the figure, we will check all the possible angles where the question figure can fit itself in the given option figures. By comparison of all the option figures, the given question figure is embedded only in the
Question : Identify the segment in the sentence which contains a grammatical error. There was enough evidence to convict him on selling of fake medicines.
Option 1: to convict him
Option 2: fake medicines
Option 3: on selling of
Option 4: There was enough evidence
Correct Answer: on selling of
Solution : The correct choice is the third option.
In the given sentence, the phrase "on selling of" is incorrect. The correct usage should involve the noun form "sale" rather than the gerund "selling". Also, "of" is used to indicate possession or connection, typically
Question : Directions: In this question, 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 follows/follow from the statements. Statements: Some spoons are black. All black are crows. No crow is a plate. Conclusions: I. Some black are spoons. II. All crows are black. III. No plate is a crow.
Option 1: Only conclusion I follows
Option 2: Only conclusions I and III follow
Option 3: None of the conclusions follows
Option 4: Only conclusion II follows
Correct Answer: Only conclusions I and III follow
Solution : Based on the given statements, the Venn diagram will be –
Let's analyse the conclusions – Conclusion I: Some black are spoons – From the Venn diagram, it is clear that the circles that represent black and spoons overlap and
Question : Directions: Which term from among the given options can replace the question mark (?) in the following series to make it logically complete? XD 45, YE 53, ?, AG 58, BH 55
Option 1: ZG 52
Option 2: ZF 54
Option 3: AF 51
Option 4: ZF 50
Correct Answer: ZF 50
Solution : Given: XD 45, YE 53, ?, AG 58, BH 55
Add 8 and subtract 3 alternatively to the numbers given in the series and add 1 to the place value of each letter, to obtain the required missing term – XD 45→X + 1
Question : The difference between a discount of 30% and two successive discounts of 20% and 10% on the Marked Price of an article is Rs.144. The marked price of the article is:
Option 1: Rs. 7,200
Option 2: Rs. 7,400
Option 3: Rs. 7,500
Option 4: Rs. 7,000
Correct Answer: Rs. 7,200
Solution : Given: The difference between a discount of 30% and two successive discounts of 20% and 10% on the marked price of an article is Rs.144. Two successive discounts of 20% and 10% are equivalent to, $(20+10-\frac{20×10}{100})$% = (30 – 2)% = 28%. Now, the
Question : Directions: Select the word pair in which the two words are related in the same way as the two words in the given pair. Lion : Forest
Option 1: Bee : Honey
Option 2: Shark : Ocean
Option 3: Flower : Honey
Option 4: Sorrow : Love
Correct Answer: Shark : Ocean
Solution : Given: Lion : Forest (Lion lives in the forest.)
Let's check the given options – First option: Bee : Honey; Bee lives in the beehive. Second option: Shark : Ocean; Shark lives in the ocean. Third option: Flower : Honey; Flower is not
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