Staff Selection Commission Combined Graduate Level Exam
Question : If $p+q=6$ and $pq=4$, then what is the value of $3(p^3+q^3)$?
Option 1: 512
Option 2: 144
Option 3: 288
Option 4: 432
Correct Answer: 432
Solution : Given, $p+q=6$ and $pq=4$ Cubing both sides, we get ⇒ $p^3+q^3+3pq(p+q)=216$ Substituting the values, we get ⇒ $p^3+q^3+3\times4(6)=216$ ⇒ $p^3+q^3=144$ ⇒ $3(p^3+q^3)=432$ Hence, the correct answer is 432.
Question : Which Grand Slam tournament was played between 17 to 30 January 2022?
Option 1: French Open
Option 2: Wimbledon open
Option 3: Australian Open
Option 4: US Open
Correct Answer: Australian Open
Solution : The correct option is the Australian Open.
The Australian Open takes place between 17 to 30 January 2022. It is the 110th edition of the event. Kia, a South Korean multinational automobile manufacturer, sponsored the tournament. The men's singles title was won by Rafael
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2, and 3 which may improve the sentence. Choose the correct alternative. In case no improvement is needed your answer is 4.
It is much too important to be made a joke of.
(1) too much important
(2) too many important
(3) very much important
(4) No improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct choice is the fourth option since the sentence is grammatically accurate and doesn't need any change. The sentence conveys the idea that the particular matter is of great significance and should not be treated lightly. Much too is an adverb that specifically explains
Question : If $\frac{4\left[(17)^3-(7)^3\right]}{\left(17^2+7^2+p\right)}=40$, then what is the value of $p$?
Option 1: –119
Option 2: –129
Option 3: 119
Option 4: 129
Correct Answer: 119
Solution : $\frac{4\left[(17)^3-(7)^3\right]}{\left(17^2+7^2+p\right)}=40$ We know that, $(a^3-b^3)=(a-b)(a^2+ab+b^2)$ ⇒ $\frac{\left(17-7)\right(17^2+17\times 7+7^2)}{\left(17^2+7^2+p\right)}=10$ ⇒ $\frac{10(17^2+17\times 7+7^2)}{\left(17^2+7^2+p\right)}=10$ ⇒ $\frac{(17^2+17\times 7+7^2)}{\left(17^2+7^2+p\right)}=1$ ⇒ $17^2+17\times 7+7^2=17^2+7^2+p$ $\therefore p=17\times7=119$ Hence, the correct answer is 119.
Question : Masai is a tribe of which of the following country ?
Option 1: Kenya
Option 2: Germany
Option 3: Australia
Option 4: India
Correct Answer: Kenya
Solution : The correct answer is Kenya.
Masai tribe is an ethnic group found in Kenya and northern Tanzania. They inhabit the regions of Lake Turkana and nearby areas of Lower Nile river. The Maasai are worldwide recognized for their particular culture, celebrations, 'high jumping dance,'
Question : Directions: If A denotes +, B denotes –, C denotes × and D denotes ÷, then which of the following equations is true?
Option 1: 8 B 6 D 2 A 4 C 3 = 15
Option 2: 8 A 8 B 8 C 8 = – 48
Option 3: 9 C 9 B 9 D 9 A 9 = 17
Option 4: 3 A 3 B 3 C 3 A 3 D 3 = 4
Correct Answer: 8 A 8 B 8 C 8 = – 48
Solution : Let's check the options – First option: 8 B 6 D 2 A 4 C 3 = 15 On replacing the letters with mathematical signs, we get – 8 – 6 ÷ 2 + 4 ×
Question : Select the option that expresses the given sentence in active voice.
The painting was not made by you.
Option 1: You should not make the painting.
Option 2: You does not make the painting.
Option 3: You did not make the painting.
Option 4: You do not make the painting.
Correct Answer: You did not make the painting.
Solution : The correct choice is the third option.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.
The structure
Question : Simplify the following expression. 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}]
Option 1: $\frac{120}{61}$
Option 2: $\frac{61}{120}$
Option 3: $3$
Option 4: $-3$
Correct Answer: $3$
Solution : 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}] = 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 + 3}] = 120 ÷ 15 of 4 + [11
Question : The sum of the three numbers is 540. The ratio of second to third is 9 : 13 and that of first to third is 2 : 7. The third number is:
Option 1: 273
Option 2: 280
Option 3: 250
Option 4: 286
Correct Answer: 273
Solution : The ratio of 2nd : 3rd = 9 : 13 And the ratio of 1st : 3rd = 2:7 3rd number is common in both ratios, so to make the value equal, we need to multiply by 7 in 9 : 13 and by 13
Question : The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be $\alpha$ and $\beta(\alpha>\beta)$. The height of the tower is $h$ units. A possible distance (in the same unit) between the points is:
Option 1: $\frac{h(\cot\beta–\cot\alpha)}{\cos(\alpha+\beta)}$
Option 2: $h(\cot\alpha–\cot\beta)$
Option 3: $\frac{h(\tan\beta–\tan\alpha)}{\tan\alpha\tan\beta}$
Option 4: $h(\cot\alpha+\cot\beta)$
Correct Answer: $h(\cot\alpha+\cot\beta)$
Solution : $AD=h$ unit In $\Delta ADB$, $\tan\alpha=\frac{AD}{BD}$ $⇒\tan\alpha=\frac{h}{BD}$ $⇒BD=h\cot\alpha$ --------------------------------------(1) In $\Delta ADC$, $\tan\beta=\frac{AD}{DC}$ $⇒\tan\beta=\frac{h}{DC}$ $⇒DC=h\cot\beta$ -------------------------------------(2) Now $BC=BD+DC$ $⇒BC=h\cot\alpha+h\cot\beta$ $\therefore BC=h(\cot\alpha+\cot\beta)$ Hence, the correct answer is $h(\cot\alpha+\cot\beta)$.
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
