Staff Selection Commission Combined Graduate Level Exam
Question : Direction: In this question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. 'U' can be represented by 01,12, etc,. and 'L' can be represented by 56, 67, etc. Similarly, you have to identify the set for the word.
'SPARE'
Option 1: 22, 41, 85, 32, 14
Option 2: 12, 24, 21, 68, 14
Option 3: 44, 78, 67, 32, 42
Option 4: 33, 30, 43, 40, 43
Correct Answer: 22, 41, 85, 32, 14
Solution : Given: SPARE
Number representations of each letter: S → 00, 11, 22, 33, 44 P → 30, 41, 02, 13, 24 A → 85, 96, 57, 68, 79 R → 10, 21, 32, 43, 04 E → 20, 31, 42, 03,
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
It is (all but same) to me whether I am transferred to Mumbai or Kolkata.
(1) all or same
(2) all the same
(3) all one
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The sentence can be improved using the second option.
The phrase "all the same" means makes no difference and is the appropriate choice for this sentence. The rest of the options are incorrect as they are not phrases in the standard English language.
Therefore, the
Question : Directions: Which of the following interchange of signs would make the given equation correct? 5 + 3 × 8 – 12 ÷ 4 = 3
Option 1: – and ÷
Option 2: + and ×
Option 3: + and ÷
Option 4: + and –
Correct Answer: – and ÷
Solution : Given: 5 + 3 × 8 – 12 ÷ 4 = 3
Replace the given signs in the options one by one with those in the given equation. First option: – and ÷ = 5 + 3 × 8 ÷ 12 – 4
Question : The ratio of the length of each equal side and the third side of an isosceles triangle is 3 : 5. If the area of the triangle is $30 \sqrt{11}$ cm2, then the length of the third side (in cm) is:
Option 1: $10\sqrt{6}$
Option 2: $5\sqrt{6}$
Option 3: $13\sqrt{6}$
Option 4: $11\sqrt{6}$
Correct Answer: $10\sqrt{6}$
Solution : Let the equal sides be $3x$ cm and the third side be $5x$ cm. By heron's formula, Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$ Where, $s=\frac{a+b+c}{2}$ Here, $s=\frac{3x+3x+5x}{2}$ ⇒ $s=\frac{11x}2$ So, $\sqrt{\frac{11x}2(\frac{11x}2-3x)(\frac{11x}2-3x)(\frac{11x}2-5x)} = 30\sqrt{11}$ ⇒ $\sqrt{\frac{11x}2(\frac{5x}2)(\frac{5x}2)(\frac{1x}2)} = 30\sqrt{11}$ ⇒ $\frac{5}{4}\sqrt{11}x^2 = 30\sqrt{11}$ ⇒ $x^2 = 24$ ⇒
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".
While provisions on equality and non-discrimination (1) / would promote equal opportunity, (2) / in the process, reservations at jobs should not be denied. (3) / No Error (4)
Correct Answer: (3)
Solution : The correct choice is the third option.
In this context, when referring to job reservations, it is more appropriate to use "in" to indicate that reservations are related to jobs. "At" is less suitable in this context, as it defines specification.
So, the correct
Question : What is the value of $\left(27 x^3-58 x^2 y+31 x y^2-8 y^3\right)$, when $x=-5$ and $y=-7?$
Option 1: 1924
Option 2: – 1924
Option 3: – 1926
Option 4: 1926
Correct Answer: 1924
Solution : Given: $x=-5$ and $y=-7$ $\left(27 x^3-58 x^2 y+31 x y^2-8 y^3\right)$ $= (3x)^3-3×(3x)^2×2y+3×3x×(2y)^2-(2y)^3-4x^2y-5xy^2$ $= (3x-2y)^3-xy(4x+5y)$ $= (3×(-5)-2×(-7))^3-(-5×(-7))(4×(-5)+5×(-7))$ $=-1-35(-20-35)$ $= -1-35(-55)$ $= -1+1925$ $= 1924$ Hence, the correct answer is 1924.
Question : What is the smallest number that should be added to 756896 to obtain a multiple of 11?
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The given number is 756896. Sum of digits in odd places = 7 + 6 + 9 = 22 Sum of digits in even places = 5 + 8 + 6 = 19 Difference in sums = 22 – 19 = 3 If we add
Question : Select the most appropriate ANTONYM of the given word. Repulsive
Option 1: Steadfast
Option 2: Superfluous
Option 3: Pleasant
Option 4: Hopeless
Correct Answer: Pleasant
Explanation: Repulsive is an adjective used to describe something that causes a strong feeling of disgust or aversion. Its antonym, pleasant, denotes the opposite meaning by representing something that is agreeable, enjoyable, or pleasing.
The meanings of
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
The old man has acquired experience through age.
(1) No Improvement
(2) developed experience
(3) experienced
(4) got experience
Correct Answer: 1
Solution : The sentence is already correct and does not need any improvement because the original phrase "acquired experience through age" effectively conveys the idea that the old man has gained knowledge and wisdom over time, which is the intended meaning. Therefore, the correct answer is:
No
Question : A tower is broken at a point P above the ground. The top of the tower makes an angle of $60^\circ$ with the ground at Q. From another point R on the opposite side Q angle of elevation of point P is $30^\circ$. If QR = 180 m, what is the total height (in meters) of the tower?
Option 1: $90$
Option 2: $45\sqrt{3}$
Option 3: $45(\sqrt{3}+1)$
Option 4: $45(\sqrt{3}+2)$
Correct Answer: $45(\sqrt{3}+2)$
Solution : Let OP = $h$ m In $\triangle$OPQ, $\tan60°=\frac{h}{OQ}$ ⇒ $OQ=\frac{h}{\sqrt3}$ ------------------(equation 1) In $\triangle$OPR, $\tan30^\circ=\frac{h}{OR}$ ⇒ $OR=h\sqrt3$ ----------------------(equation 2) According to the question, $h\sqrt3+\frac{h}{\sqrt3}=180$ ⇒ $3h+h=180\sqrt3$ ⇒ $h=\frac{180\sqrt3}{4}$ ⇒ $h=45\sqrt3$ m Now, in $\triangle$OPQ, $\sin60^\circ=\frac{h}{PQ}$ ⇒ $PQ=45\sqrt3×\frac{2}{\sqrt3}$ ⇒ PQ = 90 m So, the total
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