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Question : If $\frac{1}{x^{2}}+x^{2}$ represents the radius of circle $P$ and $\frac{1}{x}+x=17$, which of the following best approximates the circumference of circle $P$?
Option 1: $287\pi$
Option 2: $547\pi$
Option 3: $574\pi$
Option 4: $278\pi$
Correct Answer: $574\pi$
Solution : Given: $\frac{1}{x}+x=17$ Squaring both sides, we have, ⇒ $(\frac{1}{x}+x)^{2}=17^{2}$ ⇒ $\frac{1}{x^{2}}+x^{2}+2=289$ ⇒ $\frac{1}{x^{2}}+x^{2}=287$ Circumference of circle $P$ = $2\pi r$ = $2×\pi ×287$ = $574\pi $ Hence, the correct answer is $574\pi $.
Question : How many minutes for each degree of longitude does the local time of any place vary from the Greenwich time?
Option 1: two minutes
Option 2: four minutes
Option 3: six minutes
Option 4: eight minutes
Correct Answer: four minutes
Solution : The correct answer is four minutes.
Change of one degree longitude corresponds to 4 minutes from Greenwich meridian line. Earth takes 24x60 minutes to complete one revolution and it is divided into 360 longitudes. So from dividing this we get the figure of 4
Question : The average of all the numbers between 14 and 61 which are divisible by 5 is:
Option 1: 37.5
Option 2: 38
Option 3: 40
Option 4: 44
Correct Answer: 37.5
Solution : The average of all the numbers between 14 and 61 which are divisible by 5 = $\frac{15+20+25+30+35+40+45+50+55+60}{10}$ = $\frac{75×5}{10}$ = $37.5$ Hence, the correct answer is 37.5.
Question : A ______________account is maintained by an Indian Bank in a foreign country usually in the currency of that country to carry out transactions there.
Option 1: NOSTRO
Option 2: VOSTRO
Option 3: LIBOR
Option 4: MIBOR
Correct Answer: NOSTRO
Solution : The correct option is NOSTRO.
A NOSTRO account is an account maintained by an Indian bank in a foreign country, typically denominated in the currency of that country. The primary purpose of establishing a NOSTRO account is to facilitate and conduct transactions in that foreign
Question : If $a =\cot A+\cos A$ and $b =\cot A-\cos A$, then find the value of $a^2-b^2-4 \sqrt{ab}$.
Option 1: 0
Option 2: –1
Option 3: 1
Option 4: –4
Correct Answer: 0
Solution : $a =\cot A+\cos A$ $b =\cot A-\cos A$ We have to find the value of $a^2-b^2-4 \sqrt{ab}$. $= (\cot A+\cos A)^{2}-(\cot A-\cos A)^{2}-4\sqrt{(\cot A+\cos A)(\cot A-\cos A)}$ $= \cot^{2} A+\cos^{2} A+2\cot A\times \cos A-(\cot^{2} A+\cos^{2} A-2\cot A\times \cos A)-4\sqrt{\cot^{2}A-\cos^{2}A}$ $= (\cot^{2} A+\cos^{2} A+2\cot A\times \cos
Question : If $\frac{3x-1}{x}+\frac{5y-1}{y}+\frac{7z-1}{z}=0$, what is the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}?$
Option 1: –3
Option 2: 0
Option 3: 15
Option 4: 21
Correct Answer: 15
Solution : Given: $\frac{3x-1}{x}+\frac{5y-1}{y}+\frac{7z-1}{z}=0$ ⇒$3-\frac{1}{x}+5-\frac{1}{y}+7-\frac{1}{z}=0$ ⇒$\frac{1}{x} + \frac{1}{y}+\frac{1}{z}= 3+5+7=15$ Hence, the correct answer is 15.
Question : A circle is circumscribing a triangle whose sides are 30 cm, 40 cm, and 50 cm. Find the circumference of the circle.
Option 1: $75 \pi$ cm
Option 2: $25 \pi$ cm
Option 3: $100 \pi$ cm
Option 4: $50 \pi$ cm
Correct Answer: $50 \pi$ cm
Solution : Given, the sides of the triangle are 30 cm, 40 cm, and 50 cm. 30 cm, 40 cm, and 50 cm form a pythagorean triplet. In a right triangle, the circumradius (radius of the circle circumscribing the triangle) is half the length of
Question : Shinzo Abe, who recently died, served as the Prime Minister of:
Option 1: North Korea
Option 2: Japan
Option 3: South Korea
Option 4: Thailand
Correct Answer: Japan
Solution : The correct option is Japan.
Shinzo Abe served as Prime Minister of Japan. He held the office in two separate terms: firstly, from 2006 to 2007 and then again from 2012 to 2020. He was the longest-serving Prime Minister of Japan, making him a
Question : Directions: Select the correct option that indicates the arrangement of the following terms in a logical and meaningful order. 1. Answer writing 2. Answer book 3. Admit card 4. Question paper 5. Examination form
Option 1: 3–5–2–4–1
Option 2: 5–3–2–4–1
Option 3: 3–2–4–1–5
Option 4: 5–2–3–1–4
Correct Answer: 5–3–2–4–1
Solution : Given: 1. Answer writing 2. Answer book 3. Admit card 4. Question paper 5. Examination form
The stages for writing an exam are as follows – First, a student has to fill out the examination form, then after successfully submitting of exam form a student
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
They have not and cannot be in the good books of the coach because they lack discipline.
(1) have not and can never been
(2) have not been and can never be
(3) have not and can never be
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The correct choice will be the second option.
The second option, "they have not been and can never be in the good books of the coach because they lack discipline" provides this parallel structure by placing both verbs in the same form, using have not
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