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Question : If $a=\frac{1}{a - 5}(a>0)$, then the value of $a+\frac{1}{a}$ is:
Option 1: $\sqrt{29}$
Option 2: $–\sqrt{27}$
Option 3: $-\sqrt{29}$
Option 4: $\sqrt{27}$
Correct Answer: $\sqrt{29}$
Solution : Given: $a=\frac{1}{a-5}(a>0)$ ⇒ $a^{2}-5a=1$ Dividing both sides by $a$ we have, ⇒ $a - 5=\frac{1}{a}$ ⇒ $a-\frac{1}{a}=5$ We know that: $(a+\frac{1}{a})^{2}-(a-\frac{1}{a})^{2}=4$ ⇒ $(a+\frac{1}{a})^{2}-(5)^{2}=4$ ⇒ $(a+\frac{1}{a})^{2}=25+4$ $\therefore(a+\frac{1}{a})=\sqrt{29}$ Hence, the correct answer is $\sqrt{29}$.
Question : Select the most appropriate meaning of the bracketed idiom in the given sentence. After repeated failures and disappointments he was tempted (to throw up the sponge), but continued perseverance finally brought success.
Option 1: To catch somebody of guard
Option 2: To surrender or give up the contest
Option 3: To reveal secret information
Option 4: To be afraid
Correct Answer: To surrender or give up the contest
Solution : The second option is the correct choice.
The idiom to throw up the sponge is an expression that means to give up, surrender, or quit a contest or endeavour.
In the context of the sentence, the individual was tempted
Question : If $A=30^{\circ}$, then find the value of $\frac{(2 \tan A)}{\left(1-\tan^2 A\right)}$.
Option 1: $4 \sqrt{3}$
Option 2: $\frac{3}{\sqrt{3}}$
Option 3: $3$
Option 4: $2 \sqrt{3}$
Correct Answer: $\frac{3}{\sqrt{3}}$
Solution : Given: $A=30^{\circ}$ And we know, $\tan 30° = \frac{1}{\sqrt3}$ So, $\frac{(2 \tan A)}{\left(1-\tan ^2 A\right)}$ $= \frac{2\tan 30°}{1-\tan^2 30°}$ $= \frac{2\times \frac{1}{\sqrt3}}{1-\frac{1}{3}} = \frac{2\times 3}{2\times \sqrt3} = \frac{3}{\sqrt 3}$ Hence, the correct answer is $\frac{3}{\sqrt3}$.
Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which conclusions logically follow the given statements. Statements: I. Some V are P. II. Some F are V. Conclusions: I. Some F are P. II. Some V are F.
Option 1: Both conclusions I and II follow
Option 2: Only conclusion I follows
Option 3: Only conclusion II follows
Option 4: Neither conclusion follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions – Conclusion I: Some F are P – From the Venn diagram, it is evident that there is no definite relation between F and P.
Question : Which was the tallest of all Medieval Indian Temple ?
Option 1: Kailasa Temple
Option 2: Sun Temple at Konark
Option 3: Nilkantheswara Temple at Udaipur
Option 4: Brihadeswara Temple at Tanjore
Correct Answer: Brihadeswara Temple at Tanjore
Solution : Correct Answer is Brihadeswara Temple at Tanjore
Brihadishvara Temple, also known as Rajarajesvaram by its architect, was built in the Chola architectural style. It contained the gopura, the main temple's enormous tower, and inscriptions primarily pertaining to Shaivism but also to Vaishnavism
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
Jyoti refused to be _________ by her long illness.
Option 1: dispersed
Option 2: dispensed
Option 3: dispatched
Option 4: dispirited
Correct Answer: dispirited
Solution : The correct answer is in option four.
The correct sentence is: "Jyoti refused to be dispirited by her long illness."
Dispirited means lacking courage or enthusiasm. In this context, it means that Jyoti refused to let her illness bring her down. She remained positive and
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
Reyansh (gave) most of his time to music.
(1) devoted
(2) spent
(3) lent
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct choice is the first option.
Devoted implies a strong commitment or dedication to something. In the context of the sentence, it suggests that Reyansh is committed to spending a significant amount of time on music.
The meanings of the other options are as
Question : The length of a side of a square inscribed in a circle is $a\sqrt2$ units. The circumference of the circle is:
Option 1: $2\pi a$ units
Option 2: $\pi a$ units
Option 3: $4\pi a$ units
Option 4: $\frac{2a}{\pi}$ units
Correct Answer: $2\pi a$ units
Solution : Given, Side of a square = AB = $\sqrt2 a$ units We know, the length of the diagonal of a square = $\sqrt2\times$ side ⇒ AC = Diagonal = $\sqrt2 × \sqrt2 a=2a$ units = Diameter of the circle, $d$ $\therefore$ Circumference of
Question : A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They started the work together and completed the work such that B was not working in the last 2 days and A did not work in the last 3 days. In how many days (total) was the work completed?
Option 1: $\frac{82}{7}$ days
Option 2: $\frac{79}{7}$ days
Option 3: $\frac{65}{7}$ days
Option 4: $\frac{72}{7}$ days
Correct Answer: $\frac{72}{7}$ days
Solution : Given: A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. Use the formula, Total work = efficiency × time.
Question : Directions: Ravi had five subjects in his final examination. The maximum marks in each subject are 100. If his percentage in four subjects is 80, and he scores 65 marks in the fifth subject, determine his overall percentage for the five subjects.
Option 1: 0.78
Option 2: 0.79
Option 3: 0.77
Option 4: 0.76
Correct Answer: 0.77
Solution : Given: Total number of Subjects→5 Maximum marks in each subject→100 % scored by Ravi in 4 subjects = 80% Marks scored by Ravi in the 5th subject = 65
From the given information – Maximum marks in all 5 subjects = 100 × 5 =
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