Staff Selection Commission Combined Graduate Level Exam
Question : Which of the following is constituted under Article 280 of the Constitution of India?
Option 1: Advocate General
Option 2: Central Vigilance Commission
Option 3: Finance Commission
Option 4: National Commission for Women
Correct Answer: Finance Commission
Solution : The correct option is the Finance Commission.
The Finance Commission is a constitutional body set up under Article 280 of the Constitution. After every five years, this commission is to be set up with a chairman along with four members. It is a constitutional
Question : Identify the INCORRECTLY spelt word from the given options.
Option 1: Weave
Option 2: Heave
Option 3: Obssess
Option 4: Sieve
Correct Answer: Obssess
Solution : The word spelt incorrectly is the third option.
The correct spelling is obsess. It means to preoccupy someone's thoughts or mind continually or intrusively.
The meanings of the other options are as follows:
Question : Using the identity, $\tan 2 \alpha = \frac{2 \tan \alpha}{1 – \tan ^2 \alpha},$ find the value of $\tan15°,$ correct to three decimal places. [Use $\sqrt{3} = 1.732$]
Option 1: 0.268
Option 2: 0.27
Option 3: 0.267
Option 4: 0.269
Correct Answer: 0.268
Solution : $\tan 2 \alpha = \frac{2 \tan \alpha}{1 – \tan^2 \alpha}$ Putting $\alpha = 15°$ $\tan 2 \times 15°= \frac{2 \tan 15°}{1 – \tan^2 15°}$ $⇒\tan 30°=\frac{2 \tan 15°}{1–\tan^2 15°}$ $⇒\frac{1}{\sqrt{3}} = \frac{2 \tan 15°}{1 – \tan ^2 15°}$ $⇒1 – \tan^2 15° = \sqrt{3}\times 2
Question : Which one of the following is not a HYV of wheat ?
Option 1: Sonalika
Option 2: Ratna
Option 3: Kalyan Sona
Option 4: Girja
Correct Answer: Ratna
Solution : The correct option is Ratna.
Ratna is a semi- dwarf varieties of rice developed in India. Sonalika is an excellent late-sowing variety. It is rust-resistant. Kalyan Sona is a double dwarf wheat with broad adaption that is recommended for planting across India. Girija is a
Question : Direction: Select the missing number from the given alternatives.
Option 1: 9
Option 2: 8
Option 3: 7
Option 4: 6
Correct Answer: 8
Solution : Given:
In the first column, (7 x 8 + 4) = 60
In the second column, (9 x 9 + 9) = 90
In the third column, (8 x ? + 6) =
Question : Directions: In a certain code language, PUBLIC is written as TIEIUY, and SERVER is written as WEUSEN. How will DIRECT be written in that language?
Option 1: HCUBIP
Option 2: PICBUH
Option 3: HICBUP
Option 4: PCUBIH
Correct Answer: HCUBIP
Solution : Given: PUBLIC is written as TIEIUY and SERVER is written as WEUSEN.
For PUBLIC –
Thus, PUBLIC is coded as TIEIUY. Likewise, for SERVER –
So, SERVER is coded as WEUSEN. Similarly, follow the same pattern for DIRECT –
So, DIRECT is coded as HCUBIP
Question : If $x=\sqrt2+1$, then the value of $x^{4}-\frac{1}{x^{4}}$ is:
Option 1: $8\sqrt2$
Option 2: $18\sqrt2$
Option 3: $6\sqrt2$
Option 4: $24\sqrt2$
Correct Answer: $24\sqrt2$
Solution : Given: $x=\sqrt{2}+1$ Thus, $\frac{1}{x}=\sqrt{2}-1$ $x+\frac{1}{x}=(\sqrt{2}+1)+(\sqrt{2}-1)=(\sqrt{2}+1+\sqrt{2}-1)=2\sqrt{2}$ $x-\frac{1}{x}=(\sqrt{2}+1)-(\sqrt{2}-1)=(\sqrt{2}+1-\sqrt{2}+1)=2$ So, $(x^2+\frac{1}{x^2})=6$ We know that, $x^4-\frac{1}{x^4}=(x^2+\frac{1}{x^2})(x^2-\frac{1}{x^2})=(x^2+\frac{1}{x^2})(x+\frac{1}{x})(x-\frac{1}{x})$ Putting the values we get, ⇒ $x^4-\frac{1}{x^4}=6×2×2\sqrt{2}$ $\therefore x^4-\frac{1}{x^4}=24\sqrt{2}$ Hence, the correct answer is $24\sqrt{2}$.
Question : Numan does half the work of Gagan in $\frac{4}{5}$ time. If they together take 16 days to complete a work, how much time will Gagan take to complete the work?
Option 1: 23 days
Option 2: 24 days
Option 3: 25 days
Option 4: 26 days
Correct Answer: 26 days
Solution : According to the question, Numan $× \frac{4}{5}$ = Gagan $× \frac{1}{2}$ ⇒ Numan = Gagan $× \frac{5}{8}$ ⇒ $\frac{\text{Numan}}{\text{Gagan}} = \frac{5}{8}$ Let Numan’s efficiency = 5 units/day And, Gagan’s efficiency = 8 units/day So, the total work $= 16 × (5 + 8)=16 ×
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation. 21 * 3 * 36 * 2 * 23 = 68
Option 1: ÷, −, ×, +
Option 2: ÷, ×, +, −
Option 3: +, ×, −, ÷
Option 4: ×, −, ÷, +
Correct Answer: ×, −, ÷, +
Solution : Given: 21 * 3 * 36 * 2 * 23 = 68
Let's check the given options – First option: ÷, −, ×, + ⇒ 21 ÷ 3 − 36 × 2 + 23 = 68 Solving the L.H.S. of the equation
Question : Simplify the following equation. What is the difference between the two values of $x$? $7 x+4\left\{x^2 \div(5 x \div 10)\right\}-3\left\{5 \frac{1}{3}-x^3 \div\left(3 x^2 \div x\right)\right\}=0$
Option 1: 8
Option 2: 16
Option 3: 5
Option 4: 17
Correct Answer: 17
Solution : Given expression, $7 x+4\left\{x^2 \div(5 x \div 10)\right\}-3\left\{5 \frac{1}{3}-x^3 \div\left(3 x^2 \div x\right)\right\}=0$ ⇒ $7x + 4\{\frac{x^2}{\frac{5x}{10}}\}-3\{\frac{16}{3}-\frac{x^3}{\frac{3x^2}{x}}\}=0$ ⇒ $7x+4(\frac{x^2}{\frac{x}{2}})-3(\frac{16}{3}-\frac{x^3}{3x})=0$ ⇒ $7x+4(2x)-3(\frac{16}{3}-\frac{x^2}{3})=0$ ⇒ $7x+8x-(16-x^2)=0$ ⇒ $x^2+15x-16=0$ ⇒ $x^2 +x-16x-16=0$ ⇒ $x(x+1)-16(x+1)=0$ ⇒ $(x-16)(x+1)=0$ ⇒ $x=16$ and $x=-1$ $\therefore$ Difference $=16-(-1) = 17$ Hence, the correct answer
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