Staff Selection Commission Combined Graduate Level Exam
Question : Rekha alone can complete a task in 16 days and Bina alone can complete the same task in 12 days. Starting with Rekha, they work on alternate days. The task will be completed in:
Option 1: $12 \frac{3}{4}\ \text{days}$
Option 2: $12\ \text{days}$
Option 3: $13\ \text{days}$
Option 4: $13 \frac{3}{4}\ \text{days}$
Correct Answer: $13 \frac{3}{4}\ \text{days}$
Solution : Given: Rekha alone can complete the task in 16 days. Bina alone can complete the same task in 12 days. Let the total work be the LCM of (16, 12) = 48 units. So, Rekha's efficiency is $\frac{48}{16} = 3$ units per day,
Question : Directions: In the following question, find the odd number from the given alternatives.
Option 1: 234
Option 2: 345
Option 3: 243
Option 4: 432
Correct Answer: 345
Solution : Let's check the options – First option: 234; 2 + 3 + 4 = 9 Second option: 345; 3 + 4 + 5 = 12 ≠ 9 Third option: 243; 2 + 4 + 3 = 9 Fourth option: 432; 4 + 3 + 2
Question : The factors of $ x^4+x^2+25$ are:
Option 1: $\left(x^2+3 x-5\right)\left(x^2-3 x+5\right)$
Option 2: $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$
Option 3: $\left(x^2-3 x+5\right)\left(x^2-3 x+5\right)$
Option 4: $\left(x^2+3 x+5\right)\left(x^2+3 x+5\right)$
Correct Answer: $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$
Solution : $ x^4+x^2+25$ $= x^4+10x^2-9x^2+25$ $= x^4+10x^2+25-9x^2$ $=(x^2+5)^2-9x^2$ $=(x^2+5)^2-(3x)^2$ $=\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$ Hence, the answer is $\left(x^2+3 x+5\right)\left(x^2-3 x+5\right)$.
Question : The following table shows the number of different items in different shops and their respective selling prices per unit.
Find the percentage of total revenue which comes from Cooler from shop E, considering all given items are being sold from shop E and from all the given shops only given three items are being sold. (Rounded off to three decimal places)
Option 1: 4.226%
Option 2: 3.516%
Option 3: 10.45%
Option 4: 8.910%
Correct Answer: 4.226%
Solution : Total cooler sold by shop E $=\frac{1}{10}\times4000=400$ Selling price of 400 coolers = 400 × 8000 = 3200000 Total AC sold by shop E $=\frac{5}{10}\times4000=2000$ Selling price of 2000 AC = 2000 × 26500 = 53000000 Total fan sold by shop E $=\frac{4}{10}\times4000=1600$ Selling price
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 English words and must NOT be related to each other based on the number of letters/number of consonants/vowels in the word.) Plant : Pot :: Fish : ?
Option 1: Mud
Option 2: Sand
Option 3: Stone
Option 4: Aquarium
Correct Answer: Aquarium
Solution : Given: Plant : Pot :: Fish : ?
Like, plants are kept in pots. Similarly, fishes are kept in aquariums.
Hence, the fourth option is correct.
Question : Directions: Select the option related to the third letter cluster in the same way as the second letter cluster is related to the first letter cluster. SEASONAL : OEAALNSS :: FRUITS : ?
Option 1: BRUVDR
Option 2: BRUART
Option 3: UIFRST
Option 4: IUSTRF
Correct Answer: UIFRST
Solution : Given: SEASONAL : OEAALNSS :: FRUITS : ?
Firstly arrange vowels in reverse alphabetical order and then arrange all consonants in alphabetical order – SEASONAL → Vowels = OEAA, Consonants = LNSS Thus, SEASONAL is coded as OEAALNSS. Similarly, by following the same pattern for
Question : If $(\frac{5}{9}\times x)-(\frac{2}{5}\times \frac{9}{4})=-\frac{4}{5}$, then find $x$.
Option 1: 0.18
Option 2: 0.12
Option 3: 2
Option 4: 0.54
Correct Answer: 0.18
Solution : Given: $(\frac{5}{9}\times x)-(\frac{2}{5}\times \frac{9}{4})=-\frac{4}{5}$ ⇒ $\left ( \frac{5}{9} \times x \right ) - \frac{9}{10} = -\frac{4}{5}$ ⇒ $\frac{5}{9}x = -\frac{4}{5} + \frac{9}{10}$ ⇒ $\frac{5}{9}x = \frac{1}{10}$ ⇒ $x=\frac{9}{50}$ ⇒ $x$ = 0.18 Hence, the correct answer is 0.18.
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? $\left [ \frac{1}{176} \right ],\left [ \frac{1}{88} \right ],?,\left [ \frac{1}{22} \right ],\left [ \frac{1}{11} \right ]$
Option 1: $\left[\frac{1}{32}\right]$
Option 2: $\left\lceil\frac{1}{44}\right]$
Option 3: $\left\lceil\frac{1}{48}\right]$
Option 4: $\left\lceil\frac{1}{42}\right]$
Correct Answer: $\left\lceil\frac{1}{44}\right]$
Solution : Given: $\left[\frac{1}{176}\right],\left[\frac{1}{88}\right], ?,\left[\frac{1}{22}\right],\left[\frac{1}{11}\right]$
In the above-given series, the numerator will remain the same and the denominator will be divided by 2. $\left[\frac{1}{176}\right]$; 176 ÷ 2 = 88; $\left[\frac{1}{88}\right]$ $\left[\frac{1}{88}\right]$; 88 ÷ 2 = 44; $\left[\frac{1}{44}\right]$ $\left[\frac{1}{44}\right]$; 44 ÷ 2 = 22; $\left[\frac{1}{22}\right]$ $\left[\frac{1}{22}\right]$; 22 ÷
Question : What is the rate of interest per annum for simple interest at which Rs. 880 amounts to Rs. 913 in $1 \frac{1}{2}$ years?
Option 1: $2 \frac{2}{3}$%
Option 2: $2 \frac{1}{4}$%
Option 3: $2 \frac{1}{2}$%
Option 4: $2 \frac{1}{3}$%
Correct Answer: $2 \frac{1}{2}$%
Solution : Given: Principal amount, $P$ = Rs. 880 Time, $t$ = 1.5 years Simple interest = Rs. (913 – 880) = Rs. 33 Let the rate of interest be $r$% per annum. Now, SI = $\frac{Prt}{100}$ ⇒ 33 = $\frac{880\times r\times 1.5}{100}$ ⇒ $r=\frac{33\times 100}{880\times
Question : Directions: In the given figure, how many are musical toys?
Option 1: 53
Option 2: 61
Option 3: 42
Option 4: 45
Correct Answer: 42
Solution : In the diagram, the shaded part represents the region common between musicals and toys. The numbers of the asked fields that fall in the region of electronic will also be counted as there is no direction given that the region belonging to electronic can not
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