Staff Selection Commission Combined Graduate Level Exam
Question : A man bought a watch at a 10% discount. If he had bought it at a 20% discount, he would have gotten the watch for Rs. 125 less. The marked price of the watch is:
Option 1: Rs. 2,500
Option 2: Rs. 1,250
Option 3: Rs. 3,750
Option 4: Rs. 1,000
Correct Answer: Rs. 1,250
Solution : Given: A man bought a watch at a 10% discount. If he had bought it at a 20% discount, he would have gotten the watch for Rs. 125 less. Here (20 – 10) = 10% is equivalent to Rs. 125 So 100% is equivalent
Question : If $\left (x+\frac{1}{x} \right)=5$, what is the value of $\left (x^{5}+\frac{1}{x^{5}} \right)$?
Option 1: 1875
Option 2: 2525
Option 3: 2530
Option 4: 3120
Correct Answer: 2525
Solution : Given: $\left (x+\frac{1}{x} \right)=5$ Squaring both sides, we get, $⇒\left (x+\frac{1}{x} \right )^{2}=5^{2}$ $⇒x^{2}+\frac{1}{x^{2}}+2=25$ $⇒x^{2}+\frac{1}{x^{2}}=23$ Also, $\left ( x+\frac{1}{x} \right )^{3}=5^{3}$ $⇒x^{3}+\frac{1}{x^{3}}+3(x)(\frac{1}{x})(x+\frac{1}{x})=125$ $⇒x^{3}+\frac{1}{x^{3}}+3(1)(5)=125$ $⇒x^{3}+\frac{1}{x^{3}}=110$ Now, $(x^{3}+\frac{1}{x^{3}})( x^2+\frac{1}{x^2})=x^{5}+\frac{1}{x^{5}}+x+\frac{1}{x}$ $⇒110\times 23=x^{5}+\frac{1}{x^{5}}+5$ $\therefore x^{5}+\frac{1}{x^{5}} = 2525$ Hence, the correct answer is 2525.
Question : In how much time will a sum of Rs. 10200 amount to Rs. 19125 at the rate of 12.5% per annum at simple interest?
Option 1: 6 years
Option 2: 5 years
Option 3: 8 years
Option 4: 7 years
Correct Answer: 7 years
Solution : Given, Principal Amount, $P$ = Rs. 10200 The amount received after interest = Rs. 19125 Rate of interest, $R$ = 12.5% Let the time taken for the amount to become Rs. 19125 be $T$ years Simple interest here = Rs. (19125 – 10200) =
Question : Having started from the same point simultaneously, two runners P and Q are running around a circular track of length 500 m in opposite directions with speeds of 6 m/s and 10 m/s, respectively. If they exchange their speeds after meeting for the first time, who will reach the starting point first?
Option 1: Q
Option 2: P
Option 3: Both P and Q will reach at the same time
Option 4: No one of the P and Q
Correct Answer: Both P and Q will reach at the same time
Solution : Two runners P and Q run in a circular track of length with speeds 6 m/s and 10 m/s. The time they meet for the first time $=\frac{\text{Length of Circular Track}}{\text{Relative Speed}}$ $= \frac{500}{10 + 6}
Question : Peroxyacetyl nitrate is a
Option 1: Acidic dye
Option 2: Plant hormone
Option 3: Vitamin
Option 4: Secondary pollutant
Correct Answer: Secondary pollutant
Solution : The correct option is secondary pollutant.
Chemically, peroxyacetyl nitrate has the formula C2H3NO5 It is a major contributor to smog and a secondary pollutant. Through a sequence of chemical processes involving volatile organic chemicals, nitrogen oxides, and sunlight, peroxyacetyl
Question : If $a+b+c = 0$, then the value of $\small \frac{1}{(a+b)(b+c)}+\frac{1}{(b+c)(c+a)}+\frac{1}{(c+a)(a+b)}$ is:
Option 1: 0
Option 2: 1
Option 3: 3
Option 4: 2
Correct Answer: 0
Solution : Given: $a+b+c = 0$ Solution: $\frac{1}{(a+b)(b+c)}+\frac{1}{(b+c)(c+a)}+\frac{1}{(c+a)(a+b)}$ Taking the LCM, we get = $\frac{(c+a)+(a+b)+(b+c)}{(a+b)(b+c)(c+a)}$ = $\frac{2(a+b+c)}{(a+b)(b+c)(c+a)}$ Substituting the value of $(a+b+c)$ in the equation: = $\frac{2\times 0}{(a+b)(b+c)(c+a)}$ = 0 Hence, the correct answer is 0.
Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All machines are factories. Some factories are shops. Some shops are houses. Conclusions: I. Some houses are factories. II. Some machines are houses. III. Some factories are machines.
Option 1: Only conclusion II follows
Option 2: Only conclusion I follows
Option 3: All conclusions follow
Option 4: Only conclusion III follows
Correct Answer: Only conclusion III follows
Solution : According to the given statements, the following Venn diagram can be drawn – Let's check each conclusion – Conclusion I: Some houses are factories – As per the above Venn diagram, it is clear that there is no direct relation between houses
Question : Who among the following was the author of 'Indica', an account of India under the reign of the Maurya dynasty?
Option 1: Strabo
Option 2: Pliny
Option 3: Diodorus Siculus
Option 4: Megasthenes
Correct Answer: Megasthenes
Solution : The correct option is Megasthenes.
The author of Indica, an account of India under the reign of the Maurya dynasty, was Megasthenes. The original text of 'Indica' has been lost, but fragments of it survive in the works of later Greek and Latin authors. These
Question : Find the sum of the measures of all the interior angles of a polygon having twelve sides.
Option 1: 1800°
Option 2: 2520°
Option 3: 2880°
Option 4: 3240°
Correct Answer: 1800°
Solution : Given: Sides of the polygon, $n$ = 12 A polygon with $n$ sides has an interior angle sum = $(n -2)×180°$ = $(12 - 2)×180°$ = $10×180°$ = $1800°$ Hence, the correct answer is 1800°.
Question : Waksman got the Nobel Prize for the Discovery of:
Option 1: Streptomycin
Option 2: Choloromycetin
Option 3: Neomycin
Option 4: Penicillin
Correct Answer: Streptomycin
Solution : The correct option is - Streptomycin
For his successful studies of the soil microbes," which helped discover streptomycin, Waksman won the Nobel Prize in 1952. Waksman's discovery of streptomycin led to him being referred to as "one of the greatest benefactors to mankind" during the
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