Staff Selection Commission Combined Graduate Level Exam
Question : Find the value of $\cos 47^\circ \sec 133^\circ + \sin 44^\circ \text{cosec}\; 136^\circ $.
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $0$
Option 4: $–1$
Correct Answer: $0$
Solution : We know that $\sec (90°+ \theta) = – \ \text{cosec}\; \theta$ and $\text{cosec} \;(90°+\theta) = \sec \theta$ $\cos 47^\circ \sec 133^\circ + \sin 44^\circ \ \text{cosec}\;136^\circ $ $=\cos 47^\circ \sec (90^\circ + 43^\circ) + \sin 44^\circ \ \text{cosec} \;(90^\circ + 46^\circ) $ $=-\cos 47^\circ \text{cosec}\;43^\circ
Question : Which one of the following pairs in not correctly matched ?
Option 1: Hevea Tree - Brazil
Option 2: Sumatra - Indonesia
Option 3: Kajan River - Borneo
Option 4: Dekke Toba fish - Brazil
Correct Answer: Dekke Toba fish - Brazil
Solution : The correct answer is Dekke Toba fish - Brazil.
Dekke Toba fish is found in Lake Toba in Sumatra in Indonesian archipelago.
Other options-
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following sets. (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.) (11, 33, 17) (18, 44, 21)
Option 1: (12, 40, 18)
Option 2: (7, 32, 9)
Option 3: (16, 43, 22)
Option 4: (15, 34, 19)
Correct Answer: (16, 43, 22)
Solution : Given: (11, 33, 17); (18, 44, 21)
Add 5 to the sum of the first and the third numbers to get the second number. ⇒ (11, 33, 17)→(11 + 17) + 5 = 33 ⇒ (18, 44, 21)→(18 + 21) + 5 =
Question : Directions: In the following question, select the related number from the given alternatives. 42 : 20 :: 64 : ?
Option 1: 31
Option 2: 32
Option 3: 33
Option 4: 34
Correct Answer: 31
Solution : Given: 42 : 20 :: 64 : ?
Subtract 2 from the first number and then divide it by 2 to obtain the second number of each pair. Like, 42 : 20→(42 – 2) ÷ 2 = 40 ÷ 2 = 20 Similarly, follow the
Question : Given below are four sentences in jumbled order. Pick the option that gives their correct order.
A. He heard some robbers planning to commit a robbery at the moneylender's house. B. A man was roaming in the village at night. C. However, the robbers outnumbered him and overpowered him easily. D. He followed them and confronted them boldly.
Option 1: DBCA
Option 2: BCAD
Option 3: CDAB
Option 4: BADC
Correct Answer: BADC
Solution : The fourth option is the correct choice.
The sequence begins with sentence B, introducing a man wandering in the village at night. Sentence A follows, stating that he heard robbers planning a robbery at the moneylender's house. Sentence D comes next, describing how he
Question : Two pipes of lengths of 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of the same size that can be cut from these two lengths will be:
Option 1: 0.13 metre
Option 2: 0.4 metre
Option 3: 0.3 metre
Option 4: 0.41 metre
Correct Answer: 0.3 metre
Solution : Given: The lengths of the two pipes are 1.5 m and 1.2 m. HCF of (1.5, 1.2) = HCF of ($\frac{15}{10}, \frac{12}{10}$) = $\frac{3}{10}$ = 0.3 So, the greatest length of the pipe of the same size that can be cut from these two
Question : What is the chemical formula of vinegar?
Option 1: HCOOH
Option 2: CH3COOH
Option 3: (COOH)2
Option 4: C6H5COOH
Correct Answer: CH3COOH
Solution : The correct answer is CH3COOH.
Among the carboxylic acids, Acetic acid (CH3COOH), also referred to as Ethanoic acid, is crucial. Acetic acid is produced by fermentation and oxidation of natural carbohydrates, resulting in a diluted solution known as Vinegar
Question : Which of the following folk dances does not belong to the state of Mizoram?
Option 1: Munari
Option 2: Chailam
Option 3: Zangtalam
Option 4: Cheraw
Correct Answer: Munari
Solution : The correct option is Munari.
Munari is not typically associated with folk dances in Mizoram. Munari is a traditional folk dance form from the state of Assam, not Mizoram. In Mizoram, various traditional folk dances are performed, reflecting the rich cultural heritage of the
Question : What do you call the type of drugs that mimic the natural messenger by switching on the receptor?
Option 1: Antidepressants
Option 2: Depressants
Option 3: Agonists
Option 4: Antagonists
Correct Answer: Agonists
Solution : The correct option is Agonists.
The drugs that mimic the natural messenger by switching on the receptor are called agonists. These are useful when there is a lack of natural chemical messengers. Agonist drugs are widely used in medicine to either enhance or mimic the
Question : If $a+\frac{1}{a}=2$, then the value of $(a^{5}+\frac{1}{a^{5}})$ will be:
Option 1: 0
Option 2: 1
Option 3: 3
Option 4: 2
Correct Answer: 2
Solution : Given: $a+\frac{1}{a} = 2$ If we take $a=1$, then LHS = $1+\frac{1}{1}=2$ = RHS So, $a=1$ satisfies the equation. Now, $a^5+\frac{1}{a^5}=1^5+\frac{1}{1^5}=2$ Hence, the correct answer is 2.
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