Staff Selection Commission Combined Graduate Level Exam
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.) (15, 9, 4); (7, 2, 3)
Option 1: (21, 12, 6)
Option 2: (19, 13, 4)
Option 3: (24, 9, 11)
Option 4: (18, 7, 7)
Correct Answer: (19, 13, 4)
Solution : Given: (15, 9, 4); (7, 2, 3)
Here, (15, 9, 4)→(9 + 4) + 2 = 13 + 2 = 15 (7, 2, 3)→(2 + 3) + 2 = 5 + 2 = 7
Let's check the options – First option: (21, 12,
Question : If $a+b+c=0$, the value of $\frac{a^2+b^2+c^2}{a^2-bc}$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
Correct Answer: 2
Solution : Given: $a+b+c=0$ $\therefore b+c=-a$ Now, $a+b+c=0$ By squaring both sides, we get, $(a+b+c)^2=0$ ⇒ $a^2+b^2+c^2+2(ab+bc+ca)=0$ ⇒ $a^2+b^2+c^2+2[a(b+c)+bc]=0$ ⇒ $a^2+b^2+c^2+2[a(-a)+bc]=0$ ⇒ $a^2+b^2+c^2-2[a^2-bc]=0$ ⇒ $a^2+b^2+c^2=2[a^2-bc]$ $\therefore\frac{a^2+b^2+c^2}{a^2-bc}=2$ Hence, the correct answer is $2$.
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
This palace (has been belonging) to our family since generations.
(1) has belonging
(2) has belonged
(3) belonged
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Solution : The correct improvement for the sentence is: has belonged.
Explanation: The original phrase "has been belonging" is not grammatically correct in this context. When expressing ownership or possession that has continued over a period of time, we typically use the present perfect tense. "Has belonged"
Question : If $\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta}=\frac{1}{7}, \theta$ lies in first quadrant, then the value of $\frac{\operatorname{cosec} \theta+\cot ^2 \theta}{\operatorname{cosec} \theta-\cot ^2 \theta}$ is:
Option 1: $\frac{19}{5}$
Option 2: $\frac{22}{3}$
Option 3: $\frac{37}{12}$
Option 4: $\frac{37}{19}$
Correct Answer: $\frac{19}{5}$
Solution : $\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta}=\frac{1}{7}$ Using the identity $\sec \theta = \frac{1}{\cos \theta}$ and $\tan \theta = \frac{\sin \theta}{\cos \theta}$, $\frac{\frac{1}{cos\theta}-\frac{\sin \theta}{\cos \theta}}{\frac{1}{cos\theta}+\frac{\sin\theta}{\cos\theta}}=\frac{1}{7}$ $⇒\frac{1-\sin \theta}{1+\sin \theta}=\frac{1}{7}$ On applying componendo and dividendo, $⇒\sin \theta = \frac{3}{4}$ Using the identity $\sin^2 \theta + \cos^2 \theta = 1$,
Question : Direction: X and Y both start from the same point; X walks 17 m west. then turns to his right and walks 13 meters. At the same time. Y walks 9 m North, then turns East and walks 9 m north, then turns to his left and walks 4 m. Where is Y now with respect to the position of X?
Option 1: 24 metre west
Option 2: 10 metre east
Option 3: 10 metre west
Option 4: 24 metre east
Correct Answer: 24 metre east
Solution : Given:
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. OILS : UNLS :: PAIN : PKDT :: QUIK : ?
Option 1: MLXU
Option 2: MKXV
Option 3: MLYV
Option 4: MKXU
Correct Answer: MKXU
Solution : Given: OILS : UNLS :: PAIN : PKDT :: QUIK : ?
Add the consecutive natural numbers, in decreasing order (starting from 4) to the place value of the first three letters and 2 to the place value of the fourth letter of OILS and
Question : Directions: Select the option figure in which the given figure is embedded. (Rotation is NOT allowed.)
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation of the figure is not allowed, we will check where the question figure can exactly fit itself in the given option figures. By comparison of all the option figures, the given question figure is embedded only in the fourth option figure.
Hence, the
Question : Japan is called the 'Land of the Rising Sun' because
Option 1: Sun rises there as soon as it sets
Option 2: Sun always remains in the eastern part of the sky throughout the day in Japan
Option 3: Japan being the easternmost country in the world has the earliest sunrise
Option 4: The rays of the sun get reflected from the waters of the sea and make the sunrise beautiful in Japan
Correct Answer: Japan being the easternmost country in the world has the earliest sunrise
Solution : The correct answer is Japan being the easternmost country in the world, it has the earliest sunrise
Because it faces the earliest sunrise, Japan is known as the "Land of the Rising Sun". Japanese
Question : Direction: In the following question, select the related number from the given alternatives.
1/8 : 1/64 :: 1/16 : 1/ ?
Option 1: 128
Option 2: 126
Option 3: 144
Option 4: 132
Correct Answer: 128
1/8 : 1/64 :: 1/16 : 1/?
In the first pair, the second fraction is 1/8 times of the first fraction, which can be expressed as 1/8 × 1/8 = 1/64
Similarly, in the second pair, the second fraction will be 1/16 × 1/8
Question : Select the most appropriate ANTONYM of the underlined word.
She was upset seeing the scattered documents.
Option 1: Perished
Option 2: Dissipated
Option 3: Sprinkled
Option 4: Gathered
Correct Answer: Gathered
Solution : The correct choice is the fourth option.
Gathered means to collect or bring together, whereas scattered means disorganised.
The meanings of the other options are as follows:
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
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