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Question : If $\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}$, find the value of $(pa+qb+rc)$.
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Correct Answer: 0
Solution : Given: $\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}$ Let $\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}=k$ $\frac{a}{q-r}=k$ Multiplying by $p$, we get: $pa=k(pq-pr)$ -------------------(1) Similarly, $qb=k(qr-qp)$ ------------------(2) and $rc=k(rp-rq)$ --------------------------(3) Adding equations (1), (2), and (3), we get, $⇒pa+qb+rc=k(pq-pr+qr-qp+rp-rq)$ $\therefore pa+qb+rc=0$ Hence, the correct answer is 0.
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence.
Football fans are feeling proud of their teams when they win.
Option 1: felt proud to their teams
Option 2: feel proud of their teams
Option 3: are feel to proud of their teams
Option 4: feeling proud of their teams
Correct Answer: feel proud of their teams
Solution : The correct choice is the second option.
The simple present tense is used to express a general truth or habitual action. Thus, feel proud is the correct usage.
Therefore, the correct sentence is: Football fans feel proud of their teams
Question : Directions: In the following question, select the related number from the given alternatives. 12 : 20 :: 30 : ?
Option 1: 15
Option 2: 35
Option 3: 42
Option 4: 48
Correct Answer: 42
Solution : Given: 12 : 20 :: 30 : ?
The number in each pair is the sum of a natural number and its square. Like, (12 : 20)→(3)2 + 3 = 9 + 3 = 12 (4)2 + 4 = 16 + 4 =
Question : Directions: If RATION is written as OXQFLK, then LUMBER may be written as?
Option 1: KTLADQ
Option 2: ITJABQ
Option 3: OXPEHU
Option 4: IRJYBO
Correct Answer: IRJYBO
Solution : Given: RATION is written as OXQFLK.
Subtract 3 from the place value of each letter of RATION, to get the required code – R – 3 = O; A – 3 = X; T – 3 = Q; I – 3 = F; O –
Question : The HCF of three numbers 72, 108, and 2010 is:
Option 1: 18
Option 2: 6
Option 3: 12
Option 4: 5
Correct Answer: 6
Solution : Prime factors of $72 = 2\times 2\times 2\times 3\times 3$ $108 = 2\times 2\times 3\times 3\times 3$ $2010 = 2\times 3\times 5\times 67$ $\therefore$ HCF of 72, 108, and 2010 is 2$\times$3 which is equal to 6. Hence, the correct answer is 6.
Question : Who is known for establishing the "Anand Van" ?
Option 1: Jubilant Buddha
Option 2: H. N. Bahuguna
Option 3: Baba Amte
Option 4: Motilal Nehru
Correct Answer: Baba Amte
Solution : The Correct Answer is Baba Amte
A center for the treatment, recovery, and empowerment of leprosy sufferers. The center expanded to include initiatives for people with disabilities and to support programs in health care, agriculture, small-scale industry, and conservation. Baba Amte, a well-known social
Question : The question below consists of a set of labelled sentences. Out of the four options given, select the most logical order of the sentences to form a coherent paragraph.
P. Basically, “smart farming” is applying information and data technologies for optimising complex farming systems. Q. With these tools, farmers can monitor field conditions without going to the field. R. The focus is on access to data and how farmers can use the collected information intelligently. S. The technologies used in smart farming range from IoT and robotics to drones and AI.
Option 1: RSQP
Option 2: PQSR
Option 3: PRSQ
Option 4: SPQR
Correct Answer: PRSQ
Solution : The correct choice is the first option.
Explanation:
Question : If the 9-digit number 97x4562y8 is divisible by 88, what is the value of $\left(x^2+y^2\right)$ for the smallest value of y, given that x and y are natural numbers?
Option 1: 64
Option 2: 68
Option 3: 76
Option 4: 80
Correct Answer: 80
Solution :
Factors of 88 = 8 × 11 If a number is divisible by 88 then it will be divisible by 8 and 11 also. The given number is 97x4562y8. For the smallest possible value of y considering that y is a natural number, 2y8 will
Question : Select the most appropriate meaning of the given idiom. To blaze the trail
Option 1: To oppose all criticism
Option 2: To cause the failure of
Option 3: To start a movement
Option 4: To mark the end of the movement
Correct Answer: To start a movement
Solution : The most appropriate meaning of the idiom is the third option.
Explanation: To blaze the trail is an idiomatic expression that originates from the act of marking a trail through a forest by making blazes, or distinctive marks, on trees. In
Question : A scooter runs at a speed of 49 km/hr after repair and runs at 42 km/hr before repair. It covers a certain distance in 7 hours after repair. How much time will it take to cover twice the distance before repairing?
Option 1: 8 hours 10 minutes
Option 2: 12 hours 20 minutes
Option 3: 16 hours 20 minutes
Option 4: 18 hours 30 minutes
Correct Answer: 16 hours 20 minutes
Solution : Use: Time = $\frac{\text{Distance}}{\text{Speed}}$ Speed of the scooter before repair = 42 km/hr Distance covered in 7 hours after repairing = 7 × 49 = 343 km When the distance is doubled = 2 × 343 = 686 km Time taken to
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