Staff Selection Commission Combined Graduate Level Exam
Question : The value of $\frac{p^{2}- (q - r)^{2}}{(p + r)^{2} - (q)^{2}}$ + $\frac{q^{2} - (p - r)^{2}}{(p + q)^{2} - (r)^{2}}$ + $\frac{r^{2}- (p - q)^{2}}{(q + r)^{2} - (p)^{2}}$ is:
Option 1: 1
Option 2: 2
Option 3: 0
Option 4: 3
Correct Answer: 1
Solution : $\frac{p^{2} - (q - r)^{2}}{(p + r)^{2} - (q)^{2}}$ + $\frac{q^{2} - (p - r)^{2}}{(p + q)^{2} - (r)^{2}}$ + $\frac{r^{2} - (p – q)^{2}}{(q + r)^{2} - (p)^{2}}$ = $\frac{(p + q - r)(p - q + r)}{(p + q + r)(p - q
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, in every alternate box, the geometrical figures/ numbers/ letters shift their position following the below pattern – 1. From Box 1 to Box 2 – Top centre ⇔ Bottom centre; Bottom left ⇔ Bottom right; Top left→Centre of the box→Top
Question : Vinegar is
Option 1: Diluted acetic acid
Option 2: Glacial acetic acid
Option 3: Glacial formic acid
Option 4: Diluted formic acid
Correct Answer: Diluted acetic acid
Solution : The correct answer is Diluted acetic acid.
Vinegar is a diluted acetic acid solution often comprising 4-8% acetic acid in water. Glacial acetic acid, on the other hand, is pure acetic acid in its concentrated state and often appears as a clear, colourless
Question : Simplify the following expression: $[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}÷\frac{27}{135})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$
Option 1: $3 \frac{1}{5}$
Option 2: $3 \frac{3}{4}$
Option 3: $3 \frac{1}{2}$
Option 4: $3 \frac{1}{4}$
Correct Answer: $3 \frac{1}{4}$
Solution : Given: $[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}÷\frac{27}{135})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$ $=[\frac{85}{34}×\frac{1}{18}–${${{(\frac{46}{69}×\frac{135}{27})}}–(\frac{86}{129}×\frac{91}{14})$} of $\frac{112}{36}]$ $=[\frac{5}{2}×\frac{1}{18}–${${{(\frac{2}{3}×\frac{5}{1})}}–(\frac{1}{3}×\frac{13}{1})$} of $\frac{28}{9}]$ $=[\frac{5}{36}–${${{\frac{10}{3}}}–\frac{13}{3}$} ×$\frac{28}{9}]$ $=[\frac{5}{36}+{\frac{3}{3}}×\frac{28}{9}]$ $=[\frac{5}{36}+\frac{28}{9}]$ $=[\frac{5+112}{36}]$ $=\frac{117}{36} = 3 \frac{1}{4}$ Hence, the correct answer is $3 \frac{1}{4}$.
Question : Identify the idiom/phrase that can best substitute the underlined segment.
I'm going to be in trouble if I don't submit my homework to the teacher.
Option 1: a devil's advocate
Option 2: off base
Option 3: the lion's share
Option 4: up the creek
Correct Answer: up the creek
Solution : The fourth option is the correct choice.
The idiom, up the creek means to be in serious trouble or a predicament.
The meanings of the other options are as follows:
You showed me your true personality when you asked me to get out of the house at midnight.
Option 1: true colours
Option 2: bed of roses
Option 3: hot potato
Option 4: white elephant
Correct Answer: true colours
Solution : The first option is the correct answer.
Explanation:
Question : Select the correct direct form of the given sentence.
She told me that she knew I wanted to help her but she could manage on her own.
Option 1: She said to me, “I know I want to help you but you can manage on your own.”
Option 2: She said to me, “I knew you want to help her but I could manage on my own.”
Option 3: She said to me, “I know you want to help me but I can manage on my own.”
Option 4: She said to me, “I know you wanted to help me but she can manage on her own.”
Correct Answer: She said to me, “I know you want to help me but I can manage on my own.”
Solution : The correct choice is the third option.
Narration Conversion:
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 81 : 243
Option 2: 16 : 64
Option 3: 64 : 192
Option 4: 25 : 75
Correct Answer: 16 : 64
Solution : Let's check the options – First option: 81 – 243→81 × 3 = 243 Second option: 16 – 64→16 × 3 = 48 ≠ 64 Third option: 64 – 192→64 × 3 = 192 Fourth option: 25 – 75→25 × 3 = 75
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.
Nature has been suffering mutely for hundreds of years but the problem did not (1)______ serious proportions so long as the damage was (2)______ and not beyond self-repair. These limits were crossed with (3)______ technological breakthroughs accomplished during the recent years. The developed nations (4)______ benefitted most from these were the first to (5)______ the environmental diseases bred by advanced technology.
Question:
Select the most appropriate option to fill in the blank 4.
Option 1: whose
Option 2: whom
Option 3: who
Option 4: which
Correct Answer: which
Solution : The correct choice is the fourth option.
Using which here connects the sentence logically, indicating that the developed nations were affected by these specific technological breakthroughs, making it the suitable choice to maintain coherence in the sentence.
Question : Rearrange the parts of the sentence in correct order. The decision not P. to include any kind of wealth or Q. crisis, has proven controversial R. income tax, which would be the fairer option S. for solving the social care funding
Option 1: SQPR
Option 2: PRSQ
Option 3: RSPQ
Option 4: QPRS
Correct Answer: PRSQ
Solution : The second option is the correct answer.
It starts by presenting the decision not to include any kind of wealth or income tax (P). Following this, it introduces the alternative solution of implementing an income tax, which is suggested to be a fairer option for
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