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Question : If $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, then the value of $\frac{ab+bc+ca}{abc}$ is:
Option 1: $2$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{1}{2}$
Correct Answer: $\frac{1}{2}$
Solution : Given that $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, we can rewrite this equation as: $⇒\frac{2}{a}+1+\frac{2}{b}+1+\frac{2}{c}+1=4$ Simplifying, we get: $⇒\frac{2}{a}+\frac{2}{b}+\frac{2}{c}=1$ Multiplying through by $abc$, we get: $⇒2bc+2ac+2ab=abc$ Rearranging terms, we get: $⇒abc=2(ab+bc+ca)$ $\therefore\frac{ab+bc+ca}{abc}=\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
Question : Ustad Zakir Hussain is one of the greatest exponents of ____________.
Option 1: Sitar
Option 2: Tabla
Option 3: Violin
Option 4: Shehnai
Correct Answer: Tabla
Solution : The correct option is Tabla.
Ustad Zakir Hussain is one of the greatest exponents of the tabla, which is a traditional Indian percussion instrument. He has collaborated with numerous musicians globally and has played a significant role in popularizing Indian classical music on the
Question : The ratio of monthly income and expenditure of a man is 7 : 3. If his expenditure is INR 5,400, find his monthly income.
Option 1: INR 12,600
Option 2: INR 13,300
Option 3: INR 11,500
Option 4: INR 10,400
Correct Answer: INR 12,600
Solution : Given: The ratio of monthly income and expenditure of a man = 7 : 3 Expenditure = INR 5,400 Let monthly income be $7x$ and monthly expenditure be $3x$ According to the question: $3x=5400$ ⇒ $x=1800$ Thus, monthly income $=7x=7\times1800 = 12600$ Hence, the
Question : Working together, A and B can do a job in 40 days, B and C in 36 days, and all three together in 24 days. In how many days can B alone do the job?
Option 1: 60
Option 2: 90
Option 3: 72
Option 4: 120
Correct Answer: 90
Solution : Let the total work = LCM of (40, 36, and 24) = 360 Efficiency of (A + B) = $\frac{360}{40}$ = 9 ----------------------------(1) Efficiency of (B + C) = $\frac{360}{36}$ = 10 --------------------------(2) Efficiency of (A + B + C) = $\frac{360}{24}$ = 15 ---------------------(3)
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).
She decided to go there, though her husband cautioned her on it.
(1) Against
(2) For
(3) About
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct answer is the first option.
The preposition on is not the most suitable choice for the sentence. When cautioning or warning someone, it's more common to use the preposition against.
Therefore, the correct sentence would be: She decided to go there, though
Question : The number of eggs normally released during one menstrual cycle is :
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 4
Correct Answer: 1
Solution : The correct answer is 1.
Only one egg is released during one menstrual cycle of 28 days. Egg is released during the ovulation phase of menstrual cycle. Menstrual cycle has 4 phases- Menstruation, the follicular phase, ovulation and the luteal phase. It is controlled by
Question : Directions: Arrange the given words in the sequence in which they occur in the dictionary. i. Treasure ii. Treadmill iii. Training iv. Translate
Option 1: iii, iv, i, ii
Option 2: iv, i, iii, ii
Option 3: i, iii, ii, iv
Option 4: iii, iv, ii, i
Correct Answer: iii, iv, ii, i
Solution : Given: (i) Treasure (ii) Treadmill (iii) Training (iv) Translate
Step 1: Compare the first letter of each word. Since all the words start with the same letter T, we move on to the next letter. Step 2: Let's move to the
Question : A trader buys an article at 80% of its marked price and sells it at a 10% discount on its marked price. His percentage profit is:
Option 1: $10 \frac{1}{2}$
Option 2: $10$
Option 3: $12 \frac{1}{2}$
Option 4: $15$
Correct Answer: $12 \frac{1}{2}$
Solution : Given: A trader buys an article at 80% of its marked price and sells it at a 10% discount on its marked price. Profit percentage = $\frac{\text{SP – CP}}{\text{CP}}\times 100$, where $SP$, $CP$ are the selling price and the cost price. Let the marked
Question : Directions: A, B, C, D, E, F, G, and H are sitting around a square table facing the centre of the table. Four of them are sitting at each of the corners, while the other four are sitting at the exact centre of each of the sides. E who sits at the centre of a side, sits to the fourth left of the G. Only one person sits between G and F. B is an immediate neighbour of E. Only three people sit between B and A. A is not a neighbour of D. H sits to the immediate left of C.C sits to the third right of E. Who sits third to the right of D?
Option 1: H
Option 2: C
Option 3: G
Option 4: B
Correct Answer: H
Solution : Given: (I) A, B, C, D, E, F, G, and H are sitting around a square table facing the centre of the table. Four of them are sitting at each of the corners, while the other four are sitting at the exact centre of each
Question : If $2 \frac{\cos ^2 x-\sec ^2 x}{\tan ^2 x}=a+b \cos 2 x$, then $a, b=$?
Option 1: $-\frac{3}{2}, -\frac{1}{2}$
Option 2: $\frac{3}{2}, \frac{1}{2}$
Option 3: $-3, -1$
Option 4: $3,1$
Correct Answer: $-3, -1$
Solution : $2 \frac{\cos ^2 x-\sec ^2 x}{\tan ^2 x}$ = $2 \frac{\cos ^2 x-\frac{1}{\cos ^2 x}}{\tan ^2 x}$ = $2 \frac{\cos ^4 x - 1}{\tan ^2 x\cos ^2 x}$ = $2 \frac{(\cos ^2 x - 1)(\cos ^2 x + 1)}{\frac{\sin^2 x}{\cos^2 x}\cos ^2 x}$ We
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