Staff Selection Commission Combined Graduate Level Exam
Question : Which of the following statements is INCORRECT?
Option 1: If a chord is extended outside the circle on both ends then it is called a secant.
Option 2: Tangent is perpendicular to the radius of the circle at the point of contact.
Option 3: A line intersecting at two distinct points of a circle is called a tangent.
Option 4: A tangent is a line touching only one point of the circle.
Correct Answer: A line intersecting at two distinct points of a circle is called a tangent.
Solution : Third statement: A line that intersects two distinct points of a circle is called a tangent. It is incorrect. ⇒ A line that intersects two distinct points of a circle is called
Question : By what fraction must the selling price (SP) be multiplied to get the cost price (CP) if the loss is 20%?
Option 1: $\frac{4}{5}$
Option 2: $\frac{8}{5}$
Option 3: $\frac{5}{4}$
Option 4: $\frac{6}{5}$
Correct Answer: $\frac{5}{4}$
Solution : Cost price = Selling price × $\frac{100}{(100 - \text{Loss %)}}$ So, Cost price = Selling price × $\frac{100}{(100 - 20)}$ ⇒ Cost price = Selling price × $\frac{100}{80}$ $\therefore$ Cost price = Selling price × $\frac{5}{4}$ Hence, the correct answer is $\frac{5}{4}$.
Question : O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
Option 1: 26 cm
Option 2: 52 cm
Option 3: 13 cm
Option 4: 15 cm
Correct Answer: 26 cm
Solution : Given, PQ is a tangent, PQ = 24 cm and OQ = 10 cm Since tangent is perpendicular to the radius at its point of contact, $\angle$OQP = 90$^\circ$ Using Pythagoras theorem, OP2 = PQ2 + OQ2 ⇒ OP2 =
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
As if aware of my condition, (1)/ the infuriated bird suddenly doubled back on its course (2)/ and charged straight after me. (3)/ No Error (4)
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The third part of the sentence contains an error.
"Charged straight after me" is wrong as it would mean the bird is chasing the person. However, the scenario does not suggest that. The correct preposition to be used is "charged straight at me." "At" is
Question : Directions: Select the option that is related to the third term in the same way as the second term is related to the first term and the sixth term is related to the fifth term. 11 : 94 :: 23 : ? :: 18 : 150
Option 1: 190
Option 2: 199
Option 3: 129
Option 4: 109
Correct Answer: 190
Solution : Given: 11 : 94 :: 23 : ? :: 18 : 150
Like, 11 : 94→11 × 8 = 88; 88 + 6 = 94 18 : 150→18 × 8 = 144; 144 + 6 = 150 Similarly, for 23 : ?→23 × 8 =
Question : Heart attack occurs due to :
Option 1: Bacterial attack on the heart
Option 2: Stopping of heart beat
Option 3: Lack of blood supply to the heart itself
Option 4: Impairment of heart's working due to unkhown reasons
Correct Answer: Lack of blood supply to the heart itself
Solution : The correct option is Lack of blood supply to the heart itself.
A heart attack, also known as a myocardial infarction (MI), happens when blood supply to a portion of the heart muscle is suddenly cut off. The
Question : Directions: In the following question, select the related number from the given alternatives. 26 : 48 :: 82 : ?
Option 1: 125
Option 2: 122
Option 3: 115
Option 4: 120
Correct Answer: 120
Solution : Given: 26 : 48 :: 82 : ?
Like, (5)2 + 1 = 25 + 1 = 26 (7)2 – 1 = 49 – 1 = 48 5 and 7 are the consecutive odd numbers. Similarly, (9)2 + 1 = 81 +
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Ambition is a vital ingredient for success. Without ambition to push us, we will not be (1)_____of great achievements. We all need that special something (2)_____ourselves to give us the willpower to reach a higher goal (3)_____we imagine ourselves capable (4)_____Yet, ambition, (5)_____money and fire, is a good servant, but a bad master.
Select the most appropriate option to fill in the blank number 3.
Option 1: then
Option 2: than
Option 3: that
Option 4: what
Correct Answer: than
Solution : The correct choice is the second option.
In this context, than is used to make a comparison. It shows that with the help of ambition, individuals can reach a higher goal than what they might initially imagine themselves capable of achieving. Ambition acts as a
Question : As per the report released by NITI Aayog in September 2021 entitled 'Best Practices in the Performance of District Hospitals', on average, how many beds per lakh population do district hospitals have?
Option 1: 12 beds
Option 2: 40 beds
Option 3: 24 beds
Option 4: 36 beds
Correct Answer: 24 beds
Solution : The correct option is 24 beds.
According to a NITI Aayog report, district hospitals in India have an average of 24 beds per 1 lakh people, varying significantly between states. Bihar has only six beds, while Puducherry boasts 222 beds. This underscores the unequal
Question : If $\frac{\cos \alpha}{\sin \beta} = 10$ and $\frac{\cos \alpha}{\cos \beta} = 11$, the value of $\cos ^2 \beta$ is:
Option 1: $\frac{121}{132}$
Option 2: $\frac{100}{221}$
Option 3: $\frac{88}{108}$
Option 4: $\frac{221}{121}$
Correct Answer: $\frac{100}{221}$
Solution : Given: $\frac{\cos \alpha}{\sin \beta} = 10$ and $\frac{\cos \alpha}{\cos \beta} = 11$ ⇒ ${\cos \alpha} = 10\ {\sin \beta}$ and ${\cos \alpha} = 11\ {\cos \beta}$ ⇒ $10\ {\sin \beta} = 11\ {\cos \beta}$ ⇒ $\frac{\sin \beta}{\cos \beta} = \frac{11}{10}$ ⇒ ${\tan \beta} = \frac{11}{10}$
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