Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $a+b+c=9$ (where $a,b,c$ are real numbers), the minimum value of $a^2+b^2+c^2$ is:
Option 1: 100
Option 2: 9
Option 3: 27
Option 4: 81
Correct Answer: 27
Solution : Given: If $a+b+c=9$ (where $a,b,c$ are real numbers). For the minimum value, $a=b=c$ ⇒ $3a = 9$ ⇒ $a = \frac{9}{3}=3$ Similarly, $b=3$ and $c=3$ Replacing $a$, $b$, and $c$ with their values, the equation, $a+b+c=9$, is satisfied. So, the minimum value of ($a^{2}+b^{2}+c^{2}$) is
Question : Which tributary of the Indus River originates near the Rohtang Pass at an altitude of 4,000 metres above mean sea level?
Option 1: Chenab
Option 2: Musi
Option 3: Beas
Option 4: Indravati
Correct Answer: Beas
Solution : The correct option is Beas.
The tributary of the Indus River that originates near the Rohtang Pass at an altitude of 4,000 metres above mean sea level is the Beas River. The Beas River flows through the northern part of India and eventually joins
Question : Find the surface area of a sphere whose radius is 3.5 cm. Use $(\left.\pi=\frac{22}{7}\right)$.
Option 1: 154 cm2
Option 2: 152 cm2
Option 3: 146 cm2
Option 4: 160 cm2
Correct Answer: 154 cm2
Solution : Given, Radius = 3.5 cm The surface area of the sphere = $4\pi r^2$, where $r$ is the radius of the sphere. ⇒ Surface area = $4\times \frac{22}{7}\times 3.5\times 3.5=4\times 22\times 0.5\times 3.5=$ 154 cm2 Hence, the correct answer is 154 cm
Question : In an isosceles triangle, if the unequal angle is 4 times the sum of the equal angles, then each equal angle is:
Option 1: $25^{\circ}$
Option 2: $30^{\circ}$
Option 3: $21^{\circ}$
Option 4: $18^{\circ}$
Correct Answer: $18^{\circ}$
Solution :
In an isosceles triangle, two angles are equal. Let the equal angles be $\angle B$ and $\angle C$ ($\angle B=\angle C$). The third angle which is unequal is $\angle A$. Given that the unequal angle is $4$ times the sum of the equal angles. $=4(\angle
Question : Who made a history by winning 8 gold medals in the Beijing Olympics in one event ?
Option 1: Van Lee Chu of China
Option 2: Marcus Michael of France
Option 3: Michael Phelps of U.S.A.
Option 4: Ian Kraken of U.S.A.
Correct Answer: Michael Phelps of U.S.A.
Solution : The correct answer is Michael Phelps of U.S.A.
Michael Phelps is a swimmer from USA. He holds the record of having won the maximum number of medals in Olympics. In total he has 23 olympic medals. In the Beijing Olympic itself he
Question : In which year was Razia Sultan removed from the throne of the Delhi Sultanate?
Option 1: 1244
Option 2: 1240
Option 3: 1238
Option 4: 1236
Correct Answer: 1240
Solution : The correct option is 1240.
Razia Sultan was removed from the throne of the Delhi Sultanate in 1240. After a relatively brief and tumultuous reign, she faced opposition from various quarters, leading to her eventual dethronement. Razia Sultana succeeded her father, Iltutmish, upon his death
Question : In a circle of radius 8 units, a chord of length 10 units is drawn. What is the perpendicular distance of the chord from the centre of the circle in units?
Option 1: $\sqrt{39}$ Units
Option 2: $\sqrt{35}$ Units
Option 3: $\sqrt{30}$ Units
Option 4: $\sqrt{33}$ Units
Correct Answer: $\sqrt{39}$ Units
Solution : Let O be the centre of the circle of radius 8 units. Let AB be the chord of length 10 units. Let OD be perpendicular from the centre to the chord AB. We know the perpendicular from the centre to a chord bisects the
Question : The JALDOOT application launched in September 2022 is used by Gram Rojgar Sahayak to measure ________.
Option 1: rainfall
Option 2: water level in the well
Option 3: crop yield
Option 4: humidity
Correct Answer: water level in the well
Solution : The correct answer is the water level in the well.
The Rural Development Ministry developed the JALDOOT app to capture the water level of selected wells in villages nationwide. The launch took place in New Delhi. The JALDOOT app facilitated Gram
Question : The bar graph below gives the runs scored by Team A in the first six overs of a cricket match. The runs scored by Team A in the 7th over was 5 more than the runs scored by them in the 8th over, but 6 less than the runs scored by them in the 9th over. If the average runs scored per over by Team A in the first nine overs of the match was 9, how many runs did the team score in the 8th over?
Option 1: 5
Option 2: 7
Option 3: 6
Option 4: 8
Correct Answer: 6
Solution : Total runs in 6 overs = 4 + 15 + 8 + 7 + 10 + 3 = 47 Let the total runs scored in the 7th over be $x$. ⇒ Runs scored in the 8th over = $x$ – 5 And, Runs scored in
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