Staff Selection Commission Combined Higher Secondary Level Exam
Question : PX is a tangent drawn from point X, that touches the circle at P. O is the centre of the circle. The radius of this circle is 10 cm and OX = 26 cm. What is the length of PX?
Option 1: 24.5 cm
Option 2: 24 cm
Option 3: 23.5 cm
Option 4: 25 cm
Correct Answer: 24 cm
Solution : In a circle, the radius is perpendicular to the tangent at the point of tangency. Therefore, in this case, OP is perpendicular to PX. This forms a right-angled triangle OPX. $OX^2 = OP^2 + PX^2$ Substituting the given values, $⇒26^2 = 10^2 + PX^2$
Question : Directions: Select the related letter cluster from the given alternatives in the given question. HJLN : PRTV :: BDFH : ?
Option 1: JMOR
Option 2: JLNP
Option 3: KLOR
Option 4: JKOR
Correct Answer: JLNP
Solution : Given: HJLN : PRTV :: BDFH : ?
Add 8 to the place value of each letter of HJLN to get the related letter cluster. H + 8 = P; J + 8 = R; L + 8 = T; N + 8 = V
Question : Study the given pie chart and answer the question that follows. Percentage-wise distribution of teachers in six different subjects in a school is given in the pie chart. The total number of teachers is 600. The ratio of male and female teachers is 3 : 1. Find the total number of teachers in Mathematics, Biology, and Social Studies.
Option 1: 320
Option 2: 420
Option 3: 360
Option 4: 400
Correct Answer: 360
Solution : From the Pie chart, ⇒ Total number of Mathematics teachers = 20% of the total number of teachers $=\frac{20}{100} \times 600=120$ ⇒ Total number of Biology teachers = 20% of the total number of teachers $=\frac{20}{100} \times 600=120$ ⇒ Total number of Social Studies teachers
Question : If $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$, then the value of $\sin^{4}\theta$ is:
Option 1: $\frac{2}{5}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{16}{25}$
Option 4: $\frac{3}{5}$
Correct Answer: $\frac{16}{25}$
Solution : Given that $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$ $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=\frac{3}{1}$ Applying Componendo and Dividendo, $⇒\frac{2\sin\theta}{2\cos\theta} = \frac{4}{2}$ $⇒\frac{\sin\theta}{\cos\theta} = 2$ $⇒\tan\theta = \frac{2}{1}$ We know that, $\tan\theta =\frac{\text{Perpendicular}}{\text{Base}}$ Let be perpendicular = $2k$, and base = $k$. Using Pythagoras theorem, hypotenuse = $\sqrt{(2k)^2+k^2}=\sqrt5k$ $\sin\theta =\frac{2}{\sqrt5}$ ⇒ $\sin^{4}\theta=(\frac{2}{\sqrt5})^4=\frac{16}{25}$ Hence, the correct answer
Question : MX is the median of $\triangle M N O$. Y is the centroid of $\triangle M N O$. If YX = 12 cm, then what is the length of MX?
Option 1: 30 cm
Option 2: 36 cm
Option 3: 28 cm
Option 4: 24 cm
Correct Answer: 36 cm
Solution : Given, YX = 12 cm ⇒ Length of MY = 2 × YX = 2 × 12 = 24 cm ⇒ Length of MX = MY + YX = 24 + 12 = 36 cm Hence, the correct answer is 36 cm.
Question : Rearrange the parts of the sentence in the correct order. Corruption is P. misuse and abuse of public office, either directly Q. typified by dishonesty, exploitation, or the R. or indirectly, for personal gains or unjust enrichment S. in the negation of due process or established protocol
Option 1: QPRS
Option 2: PSRQ
Option 3: RSPQ
Option 4: PQSR
Correct Answer: QPRS
Solution : The correct answer is the first option.
Part Q: Sets the stage by presenting the characteristics that define corruption.
Part P: Following the introduction of corruption's characteristics, this part delves into specific actions that constitute corruption, such as the misuse and abuse of public office.
Question : A man purchased 7 bags of rice at the rate of Rs. 800 each, 8 bags of rice at Rs. 1,000 each, and 5 bags of rice at the rate of Rs. 1,200 each. What is the average cost of one bag of rice?
Option 1: Rs. 1,000
Option 2: Rs. 980
Option 3: Rs. 1,120
Option 4: Rs. 1,050
Correct Answer: Rs. 980
Solution : The average cost of one bag of rice = $\frac{7 \times 800+8 \times 1000+5 \times 1200}{7+8+5}$ The average cost of one bag of rice = $\frac{5600+8000+6000}{20}$ The average cost of one bag of rice = $\frac{19600}{20}$ The average cost of one bag of rice
Question : Directions: In the following question, some parts of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
Seldom we have been (1) / treated in such (2) / a rude manner. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
"Seldom we have been" should be replaced with "seldom have we been" to convey the intended meaning that they have been rarely treated in such an ill-mannered way.
The adverb "seldom" modifies the verb "have been" which means
Question : The rate of Simple interest per annum of the bank decreased from 5% to $3\frac{1}{2}$% and the annual income of a person from interest was less by Rs. 105. The sum deposited at the bank was:
Option 1: Rs. 6,000
Option 2: Rs. 7,200
Option 3: Rs. 6,800
Option 4: Rs. 7,000
Correct Answer: Rs. 7,000
Solution : Given: The rate of Simple interest per annum of the bank decreased from 5% to $3\frac{1}{2}$% and the annual income of a person from interest was reduced by Rs. 105. $3\frac{1}{2}$% = $\frac{7}{2}$% Now, interest decreased = $(5-\frac{7}{2})=\frac{3}{2}$% According to the question, $\frac{3}{2}$% of
Question : Comprehension: In the following passage, some of the words have been deleted. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
A recent study that (1)___________ people's brains at different points in their workday (2)_______ high-demand tasks which require intense, constant concentration can lead to the buildup of a (3)_________ toxic chemical called glutamate. Normally used to (4)___________ signals from nerve cells, in large quantities glutamate alters the (5)__________ of a brain region involved in planning and decision-making, the lateral prefrontal cortex (IPFC). Question: Select the most appropriate option to fill in the blank number (1).
Option 1: buzzed
Option 2: illuminated
Option 3: scanned
Option 4: answered
Correct Answer: scanned
Solution : The correct choice is the third option.
The sentence discusses a recent study that involved examining people's brains at different points in their workday. The term "scanned" is suitable in this context because it implies the use of imaging technology, such as MRI or CT
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