Staff Selection Commission Combined Higher Secondary Level Exam
Question : In $\Delta ABC$, the external bisector of the angles, $\angle B$ and $\angle C$ meet at the point $O$. If $\angle A = 70^\circ$, then the measure of $\angle BOC$:
Option 1: $55^\circ$
Option 2: $75^\circ$
Option 3: $60^\circ$
Option 4: $50^\circ$
Correct Answer: $55^\circ$
Solution : Given: $\angle A = 70^\circ$ To find: $\angle BOC$ We know that, Angle formed by external angle bisectors = $90^\circ-\frac{1}{2}\angle A$ ⇒ $\angle BOC$ = $90^\circ-\frac{1}{2}\angle A$ = $90^\circ-\frac{1}{2}×70^\circ$ = $90^\circ-35^\circ$ = $55^\circ$ Hence, the correct answer is $55^\circ$.
Question : Who built the famous Shiva temple at Ellora?
Option 1: Rashtrakuta Ruler Krishna I
Option 2: Mauryan Emperor Ashoka
Option 3: Gupta King Samudragupta
Option 4: Chalukya King Pulakeshin II
Correct Answer: Rashtrakuta Ruler Krishna I
Solution : The correct answer is Rashtrakuta Ruler Krishna I.
The temple of Kailasa at Ellora in Maharashtra was constructed during the 8th century AD by King Krishna I of Rashtrakuta in Kannada. The Ellora monuments were constructed between 600 and 1000 AD during
Question : Find two numbers such that their mean proportion is 16 and the third proportion is 1024.
Option 1: 4 and 32
Option 2: 4 and 64
Option 3: 8 and 64
Option 4: 8 and 32
Correct Answer: 4 and 64
Solution : Let the two numbers as $a$ and $b$. The mean proportion of two numbers is the square root of their product. $\sqrt{ab} = 16$ Squaring both sides, $ab = 256$.....................................(1) The third proportional of two numbers $a$ and $b$ is the number which
Question : If $\sec \theta=2 \frac{4}{23}$,find the value of $\tan^2 \theta$.
Option 1: $2 \frac{16}{529}$
Option 2: $1 \frac{200}{529}$
Option 3: $3 \frac{384}{529}$
Option 4: $3 \frac{177}{529}$
Correct Answer: $3 \frac{384}{529}$
Solution : Given: $\sec \theta=2 \frac{4}{23}=\frac{50}{23}$ We know, $\tan^2\theta=\sec^2\theta-1$ ⇒ $\tan^2\theta=(\frac{50}{23})^2-1$ ⇒ $\tan^2\theta=\frac{2500}{529}-1$ ⇒ $\tan^2\theta=\frac{1971}{529}$ $\therefore \tan^2\theta=3 \frac{384}{529}$ Hence, the correct answer is $3 \frac{384}{529}$.
Question : Directions: How many maximum triangles are there in the given figure?
Option 1: 20
Option 2: 11
Option 3: 14
Option 4: 17
Correct Answer: 17
Solution : The given figure can be labelled as shown below –
Now, in the above figure, there are a total of 17 triangles. They are ABL, BLJ, ABJ, JKL, KBJ, BJF, BCD, BDF, BCF, DEF, BEF, FGH, FGJ, FHJ, FJI, JHI, AEI.
Hence, the fourth option
Question : The basic objective of all production is to:
Option 1: satisfy human wants
Option 2: provide employment
Option 3: make profit
Option 4: increase physical output
Correct Answer: satisfy human wants
Solution : The correct answer is to satisfy human wants.
The fundamental goal of all manufacturing is to generate commodities and services that fulfil human desires and needs. To put it another way, the primary goal of production is to create items that may
Question : Which of the following is consistent with the import substitution policy?
Option 1: Capital account convertibility
Option 2: Flexible exchange rate policy
Option 3: Tariffs and quotas
Option 4: Current account convertibility
Correct Answer: Tariffs and quotas
Solution : The correct option is Tariffs and quotas.
Both tariffs and quotas are consistent with import substitution policies. Import substitution is an economic policy that aims to promote domestic industries by reducing reliance on imported goods. Tariffs involve imposing taxes on imported goods,
Question : If the sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Find the number.
Option 1: 8
Option 2: 9
Option 3: 7
Option 4: 6
Correct Answer: 7
Solution : Given: The sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Let the number be $x$. According to the question, $x+\frac{3}{x}=\frac{52}{7}$ $\Rightarrow 7x^2-52x+21=0$ $\Rightarrow (7x-3)(x-7)=0$ $\Rightarrow (7x-3)$ or $(x-7)=0$ $\Rightarrow x=7$ or $ \frac{3}{7}$ After checking the options, we get, $x=7$ Hence, the
Question : Simplify the given expression. $40 \times 7-2 \times\left(11^3 \div 11\right) \div 22+30$
Option 1: 297
Option 2: 298
Option 3: 300
Option 4: 299
Correct Answer: 299
Solution : $40 \times 7-2 \times\left(11^3 \div 11\right) \div 22+30$ $=40 \times 7-2 \times(11^2) \div 22+30$ $=40 \times 7-2 \times(\frac{11}{2}) +30$ $=40 \times 7-11 +30$ $=280-11 +30$ $=310-11$ $=299$ Hence, the correct answer is 299.
Question : Capacity utilisation is:
Option 1: is usually near 100 per cent
Option 2: represents the per cent of the labour force that is employed
Option 3: is a measure of the proportion of the existing capital stock used for current production
Option 4: it rises as the economy moves into a recession since firms must replace unemployed workers with some other resources to maintain production
Correct Answer: is a measure of the proportion of the existing capital stock used for current production
Solution : The correct answer is a measure of the proportion of the existing capital stock used for current production.
Capacity utilisation can also be interpreted as a measure of the proportion
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