Staff Selection Commission Combined Graduate Level Exam
Question : $\sec \theta \sqrt{1-\sin ^2 \theta}=$?
Option 1: –1
Option 2: 1
Option 3: $\infty$
Option 4: 0
Correct Answer: 1
Solution : $\sec \theta \sqrt{1–\sin^2\theta}$ $=\sec \theta \sqrt{\cos^2 \theta}$ $=\sec \theta \cos\theta$ $=\sec\theta×\frac{1}{\sec\theta}$ $=1$ Hence, the correct answer is 1.
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figure series – 1. The circle at the bottom of the figure becomes shaded and unshaded alternatively. 2. The position of the X type symbol is constant. The following figure will complete the given pattern –
Hence, the third option is correct.
Question : Directions: Select the Venn diagram that best illustrates the relationship between the following classes. Leafy Vegetables, Salad, Food Leafy Vegetables = L; Salad = S; Food = F
Solution : Leafy vegetables and salad both belong to the category of food. So, their circles will lie inside that of food. Also, some leafy vegetables are consumed as salads. So, their circles will overlap with each other. Therefore, the Venn diagram is as follows –
Hence, the
Question : Directions: In the following question, select the related number from the given alternatives. 72 : 90 :: 156 : ?
Option 1: 184
Option 2: 168
Option 3: 182
Option 4: 176
Correct Answer: 182
Solution : Given: 72 : 90 :: 156 : ?
Add the square of the consecutive natural numbers to itself to obtain the numbers of each pair. Like, 72 : 90→(8)2 + 8 = 64 + 8 = 72 (9)2 + 9 = 81 +
Question : Which of the following comes under the jurisdiction of both the High Court and the Supreme Court?
Option 1: Disputes between the states inter se
Option 2: Protection against the violation of the constitution
Option 3: Protection of fundamental Rights
Option 4: Disputes between centre and the states
Correct Answer: Protection of fundamental Rights
Solution : Correct answer is protection of fundamental rights
Fundamental rights are mentioned in part 3 of the constitution and article 12 to 35 belongs to the fundamental rights. Fundamental rights comes under the jurisdiction of both the high court and the supreme court.
Question : On increasing each side of a square by 50%, the ratio of the area of the new square formed and the given square will be:
Option 1: 9 : 5
Option 2: 9 : 3.5
Option 3: 9 : 7
Option 4: 9 : 4
Correct Answer: 9 : 4
Solution : Let the side of the square be 10 units. Area of the square = 10 × 10 = 100 sq. units New side of square after increment of 50% = $\frac{150}{100}\times10$ = 15 units Area of new square = 15 × 15 =
Question : Select the correct direct form of the given sentence. Rohan asked me if Rohit still cried.
Option 1: Rohan said to me, “Did Rohit still cry?”
Option 2: Rohan says to me, “Does Rohit still cry?”
Option 3: Rohan said to me, “Does Rohit still cry?”
Option 4: Rohan said to me, “Has Rohit still cried?”
Correct Answer: Rohan said to me, “Does Rohit still cry?”
Solution : The correct choice is the third option.
In reported or indirect speech, when converting a question to its direct form, the tense, pronouns, and sentence structure may change.
The steps of conversion are as follows:
Question : The famous Sun Temple at Konark was built by
Option 1: Prataparudra
Option 2: Anantavarman
Option 3: Narasimha -I
Option 4: Narasimha - Ii
Correct Answer: Narasimha -I
Solution : Correct Answer is Narasimha -I
The temple is believed to have been constructed around 1250 CE under the rule of King Narasimhadeva I of the East Ganga dynasty. The temple is dedicated to the Hindu god Surya, the Sun God. The Sun Temple is
Question : If $a + b = 6$ and $ab = 5$, then what is the value of $a^3 + b^3$?
Option 1: 106
Option 2: 136
Option 3: 126
Option 4: 116
Correct Answer: 126
Solution : Given: The values of $a + b = 6$ and $ab = 5$. We know the algebraic identities, $(a+b)^2=a^2 + b^2 +2ab$ and $a^3 + b^3=(a+b)(a^2 + b^2–ab)$. $a + b = 6$ (equation 1) Squaring on both sides of the equation (1), ⇒ $(a
Question : Directions: Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(NOTE: Operations should be performed on the whole numbers, without breaking down the number into its constituent digits. For example, 13 - Operations on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Option 1: 31
Option 2: 27
Option 3: 25
Option 4: 30
Correct Answer: 27
Solution : Add the number given in column one and column two and add 4, 3, and 2 to the resultant to get the third column –
In row one: 16 + 15 = 31; 31 + 4 = 35 In row two: 12 + 18 =
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