Staff Selection Commission Combined Graduate Level Exam
Question : What is the value of (a + b)3 – a3 + b3?
Option 1: –3ab(a – b) + 2b3
Option 2: 3ab(a + b) + 2b3
Option 3: 3ab(a – b) + b3
Option 4: –3ab(a + b) + b3
Correct Answer: 3ab(a + b) + 2b3
Solution : Given expression is (a + b)3 _ a3 + b3 We know that (a + b)3 = a3 + b3 +3ab(a + b) So, (a + b)3 – a3 + b3
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figures – The figure inside each box is rotated at 45° in the anticlockwise direction. So, following the above pattern, the required figure will be as follows –
Therefore, the figure in the second option is the required figure. Hence, the second
Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All males are boys. Some teachers are boys. All students are teachers. Conclusions: I. Some boys are males. II. Some teachers are students. III. All males are students.
Option 1: All conclusions follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: Some boys are males – From the above Venn diagram, it is clear that some part of the circle of
Question : Evaluate the following:$\sqrt{2+\sqrt{2+\sqrt{2+2\cos8\theta}}}$
Option 1: $2 \cos \theta$
Option 2: $2 \cos 2 \theta$
Option 3: $\sin 2 \theta$
Option 4: $\cos 2 \theta$
Correct Answer: $2 \cos \theta$
Solution : We know, $\cos2\theta= 2\cos^2\theta-1$ ⇒ $\cos2\theta+1= 2\cos^2\theta$ Putting $\theta=4\theta$ on both sides, we get $\therefore \cos8\theta+1=2\cos^24\theta$ Given, $\sqrt{2+\sqrt{2+\sqrt{2+2\cos8\theta}}}$ = $\sqrt{2+\sqrt{2+\sqrt{2(1+\cos8\theta)}}}$ = $\sqrt{2+\sqrt{2+\sqrt{2(2\cos^24\theta)}}}$ = $\sqrt{2+\sqrt{2+2\cos4\theta}}$ = $\sqrt{2+\sqrt{2(1+\cos4\theta)}}$ = $\sqrt{2+\sqrt{2(2\cos^22\theta))}}$ = $\sqrt{2+2\cos2\theta}$ = $\sqrt{2(1+\cos2\theta)}$ = $\sqrt{2(2\cos^2\theta)}$ = $2 \cos \theta$ Hence, the correct answer is
Question : A sum of Rs. 730 was divided among A, B and C in such a way that if A gets Rs. 3, then B gets Rs. 4. And if B gets Rs. 3.50, then C gets Rs. 3. The share of B exceeds that of C by:
Option 1: Rs. 30
Option 2: Rs. 40
Option 3: Rs. 70
Option 4: Rs. 210
Correct Answer: Rs. 40
Solution : Given: A sum of Rs. 730 was divided among A, B and C in such a way that if A gets Rs. 3, then B gets Rs. 4. And if B gets Rs. 3.50, then C gets Rs. 3. So, A : B =
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 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.) (7, 15, 11) (9, 19, 14)
Option 1: (8, 16, 13)
Option 2: (6, 13, 9)
Option 3: (13, 25, 21)
Option 4: (11, 23, 17)
Correct Answer: (11, 23, 17)
Solution : Given: (7, 15, 11); (9, 19, 14)
The pattern is as follows – (7, 15, 11)→(7 + 15) ÷ 2 = 22 ÷ 2 = 11 (9, 19, 14)→(9 + 19) ÷ 2 = 28 ÷ 2 = 14 Let's check the options
Question : The value of $(\cos 53° – \sin 37°)$ is:
Option 1: $0$
Option 2: $1$
Option 3: $2 \sin 37°$
Option 4: $2 \cos 53°$
Correct Answer: $0$
Solution : Given: $(\cos 53° – \sin 37°)$ $= \cos (90°– 37°) – \sin 37°$ $= \sin 37°– \sin 37°$ $= 0$ Hence, the correct answer is 0.
Question : In which of the following states Vidhan Sabha elections was not held in 2022?
Option 1: Haryana
Option 2: Goa
Option 3: Punjab
Option 4: Uttar Pradesh
Correct Answer: Haryana
Solution : The correct answer is Haryana
The states that held elections for state assemblies in 2022 are Goa, Punjab, Uttarakhand, Uttar Pradesh, Manipur, Himachal Pradesh, and Gujarat. The elections in Haryana will take place in 2024.
Question : Wearing away of the landscape by different agents like water, wind and ice is called___________.
Option 1: weathering
Option 2: erosion
Option 3: metamorphosis
Option 4: sedimentation
Correct Answer: erosion
Solution : The correct answer is erosion.
The whole process of landform formation is referred to as erosion. Erosion is the process by which the earth's surface is worn away by wind, water, and glacial ice. Disintegrated and loose elements are in motion. Erosion and weathering
Question : Directions: Which of the following diagrams represents the relationship among the given classes Green, Mango, and Fruits?
Solution : Based on the general information, all mangoes are fruits and some fruits and mangoes can be green. So, the circle of mango lies inside that of fruits. Also, some mangoes and fruits are green in colour. So, they will have some areas in common. The Venn
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