Staff Selection Commission Combined Graduate Level Exam
Question : Direction: In the following question you have to identify the correct response from the given premises stated according to the following symbols.
If – stands for addition, ÷ stands for multiplication, × stands for subtraction, and + for division, then which one of the following equations is correct?
Option 1: 25 – 15 + 5 ÷ 4 × 16 = 21
Option 2: 25 + 11 – 4 ÷ 10 × 6 = 20
Option 3: 25 × 12 – 14 ÷ 4 + 6 = 16
Option 4: 25 – 12 + 14 ÷ 2 × 4 = 15
Correct Answer: 25 – 15 + 5 ÷ 4 × 16 = 21
Solution : Let's check the options —
First option: 25 – 15 + 5 ÷ 4 × 16 = 21;
After replacing the symbols as per the code language, the equation becomes 25 + 15 ÷ 5
Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.
Option 1: $3 \sqrt{5}$
Option 2: $4 \sqrt{5}$
Option 3: $-4\sqrt{3}$
Option 4: $-3\sqrt{5}$
Correct Answer: $-3\sqrt{5}$
Solution : $(x-\frac{1}{x})^{2}=(x^2+\frac{1}{x^2}-2)$ ⇒ $(x-\frac{1}{x})^{2}=7-2$ ⇒ $(x-\frac{1}{x})^{2}=5$ ⇒ $(x-\frac{1}{x})=-\sqrt{5}$ since $0<x<1$ Again, $(x+\frac{1}{x})^{2}=(x^2+\frac{1}{x^2}+2)$ ⇒ $(x+\frac{1}{x})^{2}=(7+2)$ ⇒ $(x+\frac{1}{x})^{2}=9$ ⇒ $(x+\frac{1}{x})=3$ since $0<x<1$ Now we know $(x-\frac{1}{x})(x+\frac{1}{x})= x^2-\frac{1}{x^2}$ ⇒ $x^2-\frac{1}{x^2}=-\sqrt{5}\times 3$ ⇒ $x^2-\frac{1}{x^2}=-3\sqrt{5}$. Hence the correct answer is $-3\sqrt{5}$.
Question : Directions: Arrange the following words as per the order in a dictionary. 1. Drum 2. Drubbing 3. Drunken 4. Drudgery 5. Duster
Option 1: 3, 1, 5, 4, 2
Option 2: 2, 4, 1, 3, 5
Option 3: 1, 3, 4, 5, 2
Option 4: 2, 1, 4, 3, 5
Correct Answer: 2, 4, 1, 3, 5
Solution : Given: 1. Drum 2. Drubbing 3. Drunken 4. Drudgery 5. Duster
Step 1: Compare the first letter of each word. Since all the words start with the same letter D, then move on to the next letter. Step 2: The
Question : Directions: A series is given with one term missing. Select the correct alternative from the given ones that will complete the series. RMTS, WGAK, BAHC, GUOU, ?
Option 1: LMNO
Option 2: LOVM
Option 3: LOVQ
Option 4: LMNQ
Correct Answer: LOVM
Solution : Given: RMTS, WGAK, BAHC, GUOU, ?
Add and subtract alternatively consecutive natural numbers (starting from 5) from each letter of the previous term to obtain the next term –
RMTS→R + 5 = W; M – 6 = G; T + 7 = A; S
Question : The synagogue is the place of worship of
Option 1: Zoroastrianism
Option 2: Taoism
Option 3: Judaism
Option 4: Shintoism
Correct Answer: Judaism
Solution : The correct answer is Judaism.
In Judaism, a synagogue, usually spelt synagog, is a community building of worship that serves not just for liturgical services but also for assembly and study. Three Hebrew synonyms for synagogue, bet ha-tefilla (house of prayer), bet ha-Knesset and bet
Question : Nallamal Hills are located in the state of
Option 1: Orissa
Option 2: Meghalaya
Option 3: Andhra Pradesh
Option 4: Gujarat
Correct Answer: Andhra Pradesh
Solution : The correct option is Andhra pradesh.
The Nallamal Hills, situated in the state of Andhra Pradesh, are not only known for their scenic beauty but also for their significant biodiversity and the role they play in the region's hydrology. The Nallamal Hills are a
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 27, 38, ?, 68, 87, 110
Option 1: 47
Option 2: 50
Option 3: 51
Option 4: 53
Correct Answer: 51
Solution : Given: 27, 38, ?, 68, 87, 110
Add consecutive prime numbers (starting from 11) to each number in the given series to get the next number of the series. 27 + 11 = 38; 38 + 13 = 51; 51 + 17 = 68; 68
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. LMA, NOB, PQC, ?, TUE
Option 1: TUV
Option 2: RSD
Option 3: DOA
Option 4: BRD
Correct Answer: RSD
Solution : Given: LMA, NOB, PQC, ?, TUE
In the given series, add 2 to the place value of the first and second letters and add 1 to the place value of the third letter of the previous term to obtain the next term – LMA→L +
Question : The area of two similar triangles is 324 cm2 and 289 cm2, respectively. What is the ratio of their corresponding altitudes?
Option 1: $\frac{17}{18}$
Option 2: $\frac{17}{19}$
Option 3: $\frac{19}{17}$
Option 4: $\frac{18}{17}$
Correct Answer: $\frac{18}{17}$
Solution : The ratio of their altitudes will be equal to the ratio of the square roots of their area. $\frac{A{_1}}{A{_2}} = \frac{h{_1}^2}{h{_2}^2}$ ⇒ $\frac{324}{289} = \frac{h{_1}^2}{h{_2}^2}$ ⇒ $\frac{h{_1}}{h{_2}}=\sqrt\frac{324}{289}$ ⇒ $\frac{h{_1}}{h{_2}} = \frac{18}{17}$ Hence, the correct answer is $\frac{18}{17}$.
Question : Find the value of the given expression. $\frac{4}{3} \tan^2 45^{\circ}+3 \cos^2 30^{\circ}-2 \sec^2 30^{\circ}-\frac{3}{4} \cot^2 60^{\circ}$
Option 1: $\frac{2}{3}$
Option 2: $\frac{3}{2}$
Option 3: $\frac{\sqrt{2}}{3}$
Option 4: $\frac{3}{\sqrt{2}}$
Correct Answer: $\frac{2}{3}$
Solution : Given: $\frac{4}{3} \tan^2 45^{\circ}+3 \cos^2 30^{\circ}-2 \sec^2 30^{\circ}-\frac{3}{4} \cot^2 60^{\circ}$ $=\frac{4}{3} \times 1 +3 ( \frac{\sqrt3}{2})^2-2 (\frac{2}{\sqrt3})^2-\frac{3}{4} (\frac{1}{\sqrt3})^2$ $= \frac{4}{3} \times 1^2 +\frac{9}4-\frac{8}3-\frac{3}{4}\times \frac{1}3$ $= \frac{4}3+\frac{9}4-\frac{8}3-\frac{1}4$ $= \frac{16+27-32-3}{12}$ $= \frac{2}3$ Hence, the correct answer is $\frac{2}3$.
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