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Question : If $a+b+c=13$ and $a b+b c+c a=45$, find $a^2+b^2+c^2$.
Option 1: 79
Option 2: 65
Option 3: 57
Option 4: 85
Correct Answer: 79
Solution : Given: $a+b+c=13$ and $ab+bc+ca=45$ $a^2 + b^2 + c^2 = (a + b + c)^2 - 2 (ab + bc + ca)$ $= 13^2-2\times 45$ $= 169-90 = 79$ Hence, the correct answer is 79.
Question : Under the new IPL rule in 2023, who among the following Chennai Super King players became the first Impact player in the history of the tournament?
Option 1: MS Dhoni
Option 2: Deepak Chahar
Option 3: Akash Singh
Option 4: Tushar Deshpande
Correct Answer: Tushar Deshpande
Solution : The correct answer is Tushar Deshpande.
Making history, Tushar Deshpande became the inaugural 'Impact Player' in IPL history while representing Chennai Super Kings in the 2023 season. Chennai Super Kings clinched the IPL 2023 trophy, defeating Gujarat Titans in the final by 7
Question : The word "Satyameva Jayate" has been derived from which Upanishad?
Option 1: Akshi Upanishad
Option 2: Mundaka Upanishad
Option 3: Garuda Upanishad
Option 4: Mahavakya Upanishad
Correct Answer: Mundaka Upanishad
Solution : The correct answer is Mundaka Upanishad.
The phrase "Satyameva Jayate" in the Devanagari script is taken from the Mundaka Upanishad. It means truth alone triumphs. "Satyameva Jayate" is written below the Lion Capital of Ashoka, adopted as India's national emblem.
Question : Directions: Which letter cluster will replace the question mark (?) to complete the given series? PORK, NQPM, LSNO, JULQ, ?
Option 1: HXJS
Option 2: HXKS
Option 3: HWJS
Option 4: HWKR
Correct Answer: HWJS
Solution : Given: PORK, NQPM, LSNO, JULQ, ?
In the above-given series, subtract 2 from the place values of the first and third letters, and add 2 to the place values of the second and fourth letters to obtain the next letter cluster. PORK→P – 2 =
Question : The first American President to visit India is:
Option 1: D. D. Eisenhower
Option 2: Jimmy Carter
Option 3: George Washington
Option 4: Ronald Reagan
Correct Answer: D. D. Eisenhower
Solution : The correct answer is D. D. Eisenhower.
The first US president to visit India was D. D. Eisenhower in 1959. He travelled to New Delhi and Agra, where he spoke in front of the legislature and met with Prime Minister Jawaharlal Nehru
Question : In the following figure, AB is the diameter of a circle whose centre is O. If $\angle AOE=150^{\circ},\angle DAO=51^{\circ}$ then the measure of $\angle CBE$ is:
Option 1: 115°
Option 2: 110°
Option 3: 105°
Option 4: 120°
Correct Answer: 105°
Solution : According to the given figure in question, Given $\angle$AOE = 150° and $\angle$DAO = 51° Now, $\angle$EOB + $\angle$AOE = 180° ⇒ $\angle$EOB = 180° – 150° = 30° Also, OE = OB ⇒ $\angle$OEB = $\angle$OBE = $\frac{150}{2}$ = 75° ⇒ $\angle$CBE = 180°
Question : Which of the following is not mentioned in the Indian Constitution as a Fundamental Duty?
Option 1: To respect elders
Option 2: To promote harmony
Option 3: To safeguard public property
Option 4: To defend the country
Correct Answer: To respect elders
Solution : The Correct Option is To respect elders.
The Indian Constitution lays out a set of moral and civic duties known as fundamental duties. The 42nd Amendment Act of 1976 adds these duties to the Indian Constitution. India's residents are supposed to feel more
Question : The total surface area of a solid hemisphere is $942 \mathrm{~cm}^2$. Its volume (in $\mathrm{cm}^3$ ) is closest to: (Take $\pi=3.14$ )
Option 1: 2089
Option 2: 2093
Option 3: 2037
Option 4: 2097
Correct Answer: 2093
Solution : Given: The total surface area of a solid hemisphere = $942\ cm^2$ $3 \pi r^2=942$ ⇒ $3\times 3.14\times r^2=942$ ⇒ $3.14\times r^2=314$ ⇒ $ r^2=100$ ⇒ $ r=10$ Volume of hemisphere = $\frac{2}{3}\pi r^3$ = $\frac{2}{3}\times 3.14\times10\times10\times10$ = $\frac{6280}{3}$ = $2093.33 \approx 2093$ cm3
Question : A person marks an article 36% above the cost price and offers a 30% discount on the marked price. What is the loss or gain percentage?
Option 1: Loss 6.5%
Option 2: Loss 4.8%
Option 3: Gain 8.5%
Option 4: Gain 7.2%
Correct Answer: Loss 4.8%
Solution : Let the cost price be 100. Marked price above 36% = 100 + 36 = 136 Discount = 30% Selling price = $\frac{100-\text{discount %}}{100}\times$ marked price = $\frac{100-30}{100}\times136$ = $\frac{70}{100}\times136$ = $95.2$ Loss = Cost price – selling price = 100 – 95.2 =
Question : Directions: Select the option that is related to the third word in the same way as the second word is related to the first word. (The words must be considered meaningful words and must not be related to each other based on the number of letters/number of consonants/vowels in the word.) Wrestling : Arena :: Ice–Skating : ?
Option 1: Track
Option 2: Rink
Option 3: Stadium
Option 4: Ground
Correct Answer: Rink
Solution : Given: Wrestling : Arena :: Ice–Skating : ?
The second term is an area where the sport given in the first term has been played – Like in, Wrestling : Arena → The area where wrestling is played is known as Arena. Similarly, follow the
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