Staff Selection Commission Combined Graduate Level Exam
Question : If $x+\frac{1}{x}=-14$, and $x<-1$, what will be the value of $x^2-\frac{1}{x^2}$?
Option 1: $-112 \sqrt{3}$
Option 2: $112 \sqrt{3}$
Option 3: $-140 \sqrt{2}$
Option 4: $140 \sqrt{2}$
Correct Answer: $112 \sqrt{3}$
Solution : Given, $x+\frac{1}{x}=-14$ Squaring both sides, we get, ⇒ $x^2+\frac{1}{x^2}+2=196$ ⇒ $x^2+\frac{1}{x^2}=196-2=194$ Subtracting 2 from both sides, we get, $x^2+\frac{1}{x^2}-2=194-2$ ⇒ $(x-\frac{1}{x})^2=192$ ⇒ $x-\frac{1}{x}=-\sqrt{192}$ [as $x<-1$] Now $x^2-\frac{1}{x^2}$ $=(x-\frac{1}{x})(x+\frac{1}{x})$ $=(-\sqrt{192})\times (-14)$ $=8\sqrt3\times 14 = 112\sqrt3$ Hence, the correct answer is $112\sqrt3$.
Question : The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:
Option 1: 4 metres
Option 2: 7 metres
Option 3: 9 metres
Option 4: 6 metres
Correct Answer: 6 metres
Solution : Given: The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower. $ \angle C$ and $ \angle D$ are complementary. We know that $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}$ and $\tan
Question :
Which is the anti-coagulant substance in blood ?
Option 1:
Fibrinogen
Option 2:
Heparin
Option 3:
Thrombin
Option 4: Globin
Correct Answer:
Solution : The correct option is Heparin.
Heparin is an anticoagulant that occurs naturally in the body. It inhibits the action of thrombin, an enzyme that transforms fibrinogen into fibrin, a protein that produces blood clots, by binding to antithrombin III. Antithrombin is a protein that prevents
Question : An item is sold at two successive gains of 30% and 20%. If the final selling price is Rs. 31,200, of the item what is the cost price (in Rs.) of the item?
Option 1: 15000
Option 2: 20000
Option 3: 22250
Option 4: 24000
Correct Answer: 20000
Solution : Let $x$ be the cost price. When profit = 30%, Selling price = $x$ + 30% of $x$ = 130% of $x$ When profit = 20%, Final selling price = 130% of $x$ + 20% of 130% of $x$ = 130% of $x$ + 26%
Question : Directions: Select the correct combination of mathematical signs to replace the * signs and balance the given equation. 5 * 15 * 320 * 2 * 45 = 190
Option 1: +, ÷, ×, −
Option 2: ×, +, ÷, −
Option 3: +, ×, ÷, −
Option 4: ×, ÷, −, +
Correct Answer: ×, +, ÷, −
Solution : Given: 5 * 15 * 320 * 2 * 45 = 190
Let's check the options – First option: +, ÷, ×, − ⇒ 5 + 15 ÷ 320 × 2 − 45 = 190 Solving the L.H.S. of the given equation
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error. My mother said / that Ben will done / the assignment / today.
Option 1: today
Option 2: My mother said
Option 3: that Ben will done
Option 4: the assignment
Correct Answer: that Ben will done
Solution : The correct choice is the third option.
The part of the sentence "that Ben will done" contains a grammatical error because it uses the past participle "done" instead of the base form "do" to form the future tense.
So, the correct sentence
Question : Which of the following is not included in domestic income?
Option 1: Income earned by the residents of the country
Option 2: Income earned by non-residents outside the country
Option 3: Income earned by all the employees of the country
Option 4: Profit of all the industries of the country
Correct Answer: Income earned by non-residents outside the country
Solution : The correct option is Income earned by non-residents outside the country.
The income generated by non-residents in foreign countries is not accounted for nation's domestic income calculation. The Gross Domestic Product (GDP) represents the total value of goods and
Question : Which of the statements given below are correct?
(i) The author of the novel 'Atonement' is Lan McEwan.
(ii) The author of the novel 'The Sound and the Fury' is L. Ron Hubbard.
(iii) The author of the Novel 'White Teeth' is Zadie Smith.
Option 1: (i) and (ii)
Option 2: (ii) and (iii)
Option 3: (i) and (iii)
Option 4: (i), (ii) and (iii)
Correct Answer: (i) and (iii)
Solution : The correct answer is (i) and (iii).
Question : A radio -active substance has a half life of six months. Three-fourth of the substance will decay in ______.
Option 1: Six months
Option 2: Ten months
Option 3: twelve months
Option 4: Twenty four months
Correct Answer: twelve months
Solution : The correct option is - twelve months
If the radioactive substance's half-life is six months, it means that in six months, 50% of the material will have decayed. Only 50% of the material is left when it decays. After another six months, the residual
Question : A dishonest dealer professes to sell his goods at a cost price but he uses 950 gm weight for a kilogram. His gain percentage is: (rounded off to two decimal places)
Option 1: 5.35%
Option 2: 5.26%
Option 3: 5.86%
Option 4: 5.96%
Correct Answer: 5.26%
Solution : There is a profit of 50 grams on 950 grams. By using the formula: Profit % = $\frac{\text{Profit}}{\text{CP}}$ × 100 = $\frac{50}{950}$ × 100 = 5.26 Hence, the correct answer is 5.26%.
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