Staff Selection Commission Combined Graduate Level Exam
Question : The country can improve its balance of payments by devaluation when the sum of elasticity of demand for exports and imports is _____________.
Option 1: less than unity
Option 2: equal to unity
Option 3: greater than unity
Option 4: zero
Correct Answer: greater than unity
Solution : The correct option is greater than unity.
If the sum of the elasticity of demand for exports and imports is greater than unity (greater than 1 in absolute value), it implies that the overall responsiveness of both export and import quantities to changes
Question : If $\cot B=9 $, then what will be the value of $\sec ^2 B$?
Option 1: $\frac{98}{81}$
Option 2: $\frac{92}{81}$
Option 3: $\frac{42}{81}$
Option 4: $\frac{82}{81}$
Correct Answer: $\frac{82}{81}$
Solution : Given, $\cot B=9 $ ⇒ $\frac{1}{\tan B}=9$ ⇒ $\tan B = \frac{1}{9}$ ⇒ $\tan^2 B = \frac{1}{81}$ ⇒ $\sec^2 B-1 = \frac{1}{81}$ ⇒ $\sec^2 B = \frac{82}{81}$ Hence, the correct answer is $ \frac{82}{81}$.
Question : Directions: Select the word pair that best represents a similar relationship to the one expressed in the pair of words given below. Thermometer : Temperature
Option 1: Taseometer : Acceleration
Option 2: Micrometer : Speed
Option 3: Voltmeter : Voltage
Option 4: Galvanometer : Sound
Correct Answer: Voltmeter : Voltage
Solution : Given: Thermometer : Temperature (This depicts the relation between the instrument and the purpose for which it is used – A thermometer is an instrument that measures temperature.)
Let's check the options – First option: Taseometer : Acceleration→Taseometer is an instrument that measures
Question : If $\frac{\sqrt{26-7 \sqrt{3}}}{\sqrt{14+5 \sqrt{3}}}=\frac{b+a \sqrt{3}}{11}, b>0$, then what is the value of $\sqrt{(\mathrm{b}-\mathrm{a})}$?
Option 1: 5
Option 2: 25
Option 3: 12
Option 4: 9
Correct Answer: 5
Solution : Given: $\frac{\sqrt{26-7 \sqrt{3}}}{\sqrt{14+5 \sqrt{3}}}$ $= \frac{\sqrt{26-7 \sqrt{3}}}{\sqrt{14+5 \sqrt{3}}} \times \frac{\sqrt{14-5 \sqrt{3}}}{\sqrt{14-5 \sqrt{3}}} $ $= \frac{\sqrt{364-130\sqrt{3}+105-98\sqrt3}}{\sqrt{196-75}} $ $= \frac{\sqrt{361-228\sqrt{3}+108}}{\sqrt{196-75}} $ $= \frac{\sqrt{19^2+(6\sqrt3)^2-2\times19\times6\sqrt{3}}}{\sqrt{121}} $ $= \frac{\sqrt{(19-6\sqrt3)^2}}{11} $ $= \frac{(19-6\sqrt3)}{11} $ $\therefore \frac{(19-6\sqrt3)}{11}=\frac{b+a \sqrt{3}}{11} $ $b=19, a=-6$ Thus, $\sqrt{(b-a)}=\sqrt{(19-(-6))}=\sqrt{25}=5$ Hence, the correct answer is 5.
Question : Directions: In the following question, you have to identify the correct response from the given premises stated according to the following signs. If + means minus, – means multiplication, ÷ means plus and × means division, then 15 – 3 + 10 × 5 ÷ 5 = ?
Option 1: 52
Option 2: 48
Option 3: 22
Option 4: 5
Correct Answer: 48
Solution : Given: + means minus, – means multiplication, ÷ means plus and × means division. 15 – 3 + 10 × 5 ÷ 5 = ?
Replace the signs in the given equation as per the instructions and solve the equation – = 15 × 3
Question : If the ratio of corresponding sides of two similar triangles is $\sqrt{5}: \sqrt{7},$ then what is the ratio of the area of the two triangles?
Option 1: $\sqrt[3]{5}: \sqrt{7}$
Option 2: $25: 49$
Option 3: $\sqrt{5}: \sqrt{7}$
Option 4: $5: 7$
Correct Answer: $5: 7$
Solution : Given, the ratio of sides of similar triangles = $\sqrt{5}: \sqrt{7}$ We know the ratio of areas of similar triangles is equal to the square of the ratio of sides of those similar triangles $\therefore$ Ratio of areas of similar triangles = $(\sqrt{5})^2: (\sqrt{7})^2=5
Question : Which of the following statements is/are true?
(A) COP28 is proposed to be held in New Delhi, India.
(B) The first UN Climate Change Conference was held in 1995.
(C) The first UN Climate Change Conference was held in Paris, France.
Option 1: Only A
Option 2: A and B
Option 3: B and C
Option 4: Only B
Correct Answer: Only B
Solution : The correct answer is Only B.
The Conference of the Parties (COP) was first held in Berlin, Germany, in 1995. The 28th COP was held in Dubai, United Arab Emirates, which marked a significant milestone with the first Global Stocktake. During this process, participating
Question : The value of tan 25° tan 35° tan 45° tan 55° tan 65° is:
Option 1: $2$
Option 2: $1$
Option 3: $\sqrt{3}$
Option 4: $0$
Correct Answer: $1$
Solution : The trigonometric identity $\tan A.\cot A = 1$ and $\tan (90° -\theta) = \cot \theta$ $\tan 25° \tan 35° \tan 45° \tan 55° \tan 65°$ $ = \tan 25°×\tan 35° \times 1\times \tan(90° - 35°)×\tan(90° - 25°)$ $ = \tan 25° ×\tan 35° \times 1\times
Question : Maithili is primarily spoken in which state?
Option 1: Bihar
Option 2: Assam
Option 3: West Bengal
Option 4: Meghalaya
Correct Answer: Bihar
Solution : The correct option is Bihar.
Maithili is an Indo-Aryan language spoken primarily in the Indian states of Bihar and Jharkhand, as well as in the Terai region of Nepal. It holds the distinction of being one of the 22 scheduled languages of India. Maithili has
Question : Soham’s initial expenditure and savings were in the ratio of 5 : 3. His income increased by 25%. If his initial savings were Rs. 4,500, find his income (in Rs.) after the increment.
Option 1: 16,000
Option 2: 15,000
Option 3: 9,375
Option 4: 12,000
Correct Answer: 15,000
Solution : Let denote the initial expenditure as $E$, initial savings as $S$, and the initial income as $I$. Given that the ratio of expenditure to savings is 5 : 3. $E : S = 5 : 3$ ⇒ $E = \frac{5}{3}S$ $I = E + S$
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