Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: 75 is related to 25 in a certain way. Following the same logic, 69 is related to 23. To which of the following is 93 related, following the same logic?
Option 1: 31
Option 2: 39
Option 3: 30
Option 4: 38
Correct Answer: 31
Solution : Given: 75 is related to 25. 69 is related to 23.
Divide the first number by 3 to get the second number – 75 is related to 25 = 75 ÷ 3 = 25 69 is related to 23 = 69 ÷ 3 = 23
Question : In $\triangle ABC$ and $\triangle PQR, \angle B=\angle Q, \angle C=\angle R$ and $AB=2PQ$, then the two triangles are:
Option 1: congruent as well as similar
Option 2: neither similar nor congruent
Option 3: similar but not congruent
Option 4: congruent but not similar
Correct Answer: similar but not congruent
Solution : Given: In the triangles ABC and PQR, $\angle B = \angle Q$, $\angle C = \angle R$ Also, AB = 2PQ We have to find if the triangles are similar and congruent or not. Angle-Angle-Angle(AAA) criterion states that if two angles of
Question : Directions: Four number-pairs have been given, out of which three are alike in some manner and one is different. Select a different one. (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.)
Option 1: 52 : 93
Option 2: 40 : 69
Option 3: 38 : 65
Option 4: 61 : 133
Correct Answer: 61 : 133
Solution : Let's check each option – First option: 52 : 93 ⇒ (52 × 2) – 11 = 104 – 11 = 93 Second option: 40 : 69 ⇒ (40 × 2) – 11 = 80 – 11 = 69 Third option: 38 :
Question : Directions: In a certain code language, A + B means A is the mother of B; A – B means A is the brother of B; A × B means A is the wife of B; A ÷ B means A is the father of B. Based on the above, how is M related to P if M + N ÷ O × P – Q?
Option 1: Wife's Father's Mother
Option 2: Mother's husband
Option 3: Brother's wife
Option 4: Daughter
Correct Answer: Wife's Father's Mother
Solution : Given: A + B ⇒ A is the mother of B A – B ⇒ A is the brother of B A × B ⇒ A is the wife of B A ÷ B ⇒ A is the father of B
As per
Question : Directions: In the following number pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the option in which the numbers are related in the same way as the numbers of the following pairs. (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.) (16, 99); (13, 81)
Option 1: (9, 57)
Option 2: (8, 42)
Option 3: (11, 74)
Option 4: (17, 115)
Correct Answer: (9, 57)
Solution : Given: (16, 99); (13, 81)
Here, (16, 99)→(16 × 7) – (16 – 3) = 112 – 13 = 99 (13, 81)→(13 × 7) – (13 – 3) = 91 – 10 = 81
Let's check the options – First option: (9, 57)→(9 ×
Question : If in a $\triangle ABC$, $\angle ABC=5\angle ACB$ and $\angle BAC=3\angle ACB$, then what is the value of $\angle ABC$?
Option 1: $130°$
Option 2: $80°$
Option 3: $100°$
Option 4: $120°$
Correct Answer: $100°$
Solution : Given: $\angle ABC$ = $5\angle ACB$ $\angle BAC$ = $3\angle ACB$ Now, $\angle ABC+\angle ACB+\angle BAC$ = $180^{\circ}$ ⇒ $5\angle ACB+\angle ACB+3\angle ACB$ = $180^{\circ}$ ⇒ $9\angle ACB=180^{\circ}$ ⇒ $\angle ACB=20^{\circ}$ ⇒ $\angle ABC =5\times20^{\circ} =100^{\circ}$ Hence, the correct answer is $100^{\circ}$.
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
All of us are devoted _________ one another.
Option 1: For
Option 2: Of
Option 3: At
Option 4: To
Correct Answer: To
Solution : The fourth option is the correct answer because 'to' is used after the word 'devoted' to indicate a relationship between the subject (all of us) and the object of their devotion (one another).
In this case, "devoted" implies a strong commitment or attachment to "one
Question : Directions: How many triangles are there in the given figure?
Option 1: 8
Option 2: 11
Option 3: 9
Option 4: 10
Correct Answer: 11
Solution : The given figure can be labelled as shown below –
In the above-labelled figure, there are 11 triangles. Namely, ABQ, BQC, AQC, BHD, DOE, DHF, OHG, GOF, FOE, FOD, HOF.
So, a total of 11 triangles are there in the given figure. Hence, the second
Question : Directions: Find the missing number from the given responses.
Option 1: 9
Option 2: 14
Option 3: 12
Option 4: 8
Correct Answer: 12
Solution : Here, diagonally opposite numbers are squares of the given numbers – 82 = 64 112 = 121 (?)2 = 144 ⇒ (?) = 12
So, the missing number is 12. Hence, the third option is correct.
Question : Directions: Which of the following four options can replace the question mark (?) in the following series? 74, 93, ?, 145, 176, 213
Option 1: 121
Option 2: 116
Option 3: 135
Option 4: 105
Correct Answer: 116
Solution : Given: 74, 93, ?, 145, 176, 213
Add the consecutive prime numbers (starting from 19) to the previous number to get the next number in the series. 74 + 19 = 93; 93 + 116; 116 + 29 = 145; 145 + 31 = 176;
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