Staff Selection Commission Combined Graduate Level Exam
Question : The table given below shows the production of refrigerators by 6 companies.
What is the ratio of the production of refrigerators by company G to the production of refrigerators by company I?
Option 1: 12 : 13
Option 2: 11 : 13
Option 3: 13 : 11
Option 4: 13 : 12
Correct Answer: 13 : 11
Solution : Production of refrigerators by company G = 260 Production of refrigerators by the company I = 220 ⇒ Required ratio = 260 : 220 = 13 : 11 Hence, the correct answer is 13 : 11.
Question : If $x^{3}-y^{3}=81$ and $x-y=3$, what is the value of $x^{2}+y^{2}$?
Option 1: 18
Option 2: 21
Option 3: 27
Option 4: 36
Correct Answer: 21
Solution : Given: $x^{3}-y^{3}=81$ and $x-y=3$ We know, $x^{3}-y^{3}=(x-y)^{3}+3xy(x-y)$ Substituting the values of $x^{3}-y^{3}$ and $x-y$, we get, $81=3^{3}+3×3xy$ $⇒xy=6$ Now, $x^{2}+y^{2}=(x-y)^{2}+2xy=3^{2}+2\times 6=21$ Hence, the correct answer is 21.
Question : If $1+2 \tan ^2 \theta+2 \sin \theta \sec ^2 \theta=\frac{a}{b}, 0^{\circ}<\theta<90^{\circ}$, then $\frac{a+b}{a-b}=?$
Option 1: $\sin \theta$
Option 2: $\cos \theta$
Option 3: $\operatorname{cosec} \theta$
Option 4: $\sec \theta$
Correct Answer: $\operatorname{cosec} \theta$
Solution : According to the question $1+2 \tan ^2 \theta+2 \sin \theta \sec ^2 \theta=\frac{a}{b}$ ⇒ 1 + $\frac{2\sin^{2}\theta}{\cos^{2}\theta}$ + $\frac{2\sin^{2}\theta}{\cos^{2}\theta}=\frac{a}{b}$ ⇒ $\frac{\cos^{2}\theta + 2\sin^{2}\theta + 2\sin\theta }{\cos^{2}\theta}= \frac{a}{b}$ ⇒ $\frac{[1- \sin^{2}\theta + 2\sin^{2}\theta + 2\sin\theta]}{[1 - \sin^{2}\theta]}= \frac{a}{b}$ ⇒ $\frac{[1+ \sin^{2}\theta + 2\sin\theta]}{[1 - \sin^{2}\theta]}=
Question : Directions: Select the option figure that is embedded in the given figure (rotation is NOT allowed).
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of all the option figures, only the second option figure is embedded in the given question figure.
Hence, the second option is correct.
Question : The base of a right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:
Option 1: $10 \sqrt{\frac{23}{3}}$
Option 2: $5 \sqrt{3}$
Option 3: $10 \sqrt{3}$
Option 4: $5 \sqrt{\frac{23}{3}}$
Correct Answer: $10 \sqrt{\frac{23}{3}}$
Solution : The base of the right pyramid is an equilateral triangle, each side, (a) = 20 cm Each slant edge, (E) = 30 cm According to the question Each side of an equilateral triangle = 20 cm We know that, circumradius of the equilateral triangle
Question : An article is sold for INR 54,120 after two successive discounts of 12 percent and 18 percent. What is the marked price of the article?
Option 1: INR 75,000
Option 2: INR 78,000
Option 3: INR 72,000
Option 4: INR 81,000
Correct Answer: INR 75,000
Solution : Given: An article is sold for INR 54,120 after two successive discounts of 12 percent and 18 percent. For two successive discounts Selling price = $\frac{100-\text{Discount}_1\%}{100}× \frac{100-\text{Discount}_2\%}{100}×$ marked price $54120=(1–\frac{12}{100})\times(1–\frac{18}{100})\times MP$ ⇒ $54120=\frac{88}{100}\times \frac{82}{100}\times MP$ ⇒ $MP=\frac{54120\times100\times100}{88\times 82}=$ INR 75,000 Hence, the correct answer
Question : Directions: A # B means A is the mother of B; A @ B means A is the son of B; A & B means A is the brother of B; A % B means A is the wife of B. If W # Q @ T & Y @ M % K, then how is K related to W?
Option 1: Father
Option 2: Father-in-law
Option 3: Brother-in-law
Option 4: Brother
Correct Answer: Father-in-law
Solution : Given: W # Q means W is the mother of Q. Q @ T means Q is the son of T. T & Y means T is the brother of Y. Y @ M means Y is the son of M. M % K means
Question : Select the option that expresses the given sentence in passive voice.
The teacher is explaining the lesson.
Option 1: The lesson explained the teacher.
Option 2: The teacher explained the lesson.
Option 3: The lesson is being explained by the teacher.
Option 4: The lesson was explained by the teacher.
Correct Answer: The lesson is being explained by the teacher.
Solution : The correct choice is the third option.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in
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).
A major water pollutant due to the growth of large cities is the sewages.
(1) a sewage
(2) a sewages
(3) the sewage
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The word "sewages" is incorrect because it should be in singular form, which is "sewage," as it refers to a collective term for wastewater. Additionally, in this context, it is appropriate to use the definite article "the" to specify a particular type of pollutant.
Therefore,
Question : A dealer sells a machine having a marked price of Rs. 3840 at a discount of 20%. What is the selling price (in Rs.) of the machine?
Option 1: 3072
Option 2: 3500
Option 3: 4608
Option 4: 3240
Correct Answer: 3072
Solution : Marked price = Rs. 3840 Discount = 20% $\therefore$ Selling price = 80% of marked price = 80% of 3840 = $\frac{80 × 3840}{100}$ = Rs. 3072 Hence, the correct answer is 3072.
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