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Staff Selection Commission Combined Graduate Level Exam

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Question : If A's wealth is $\frac{4}{9}$ times of B's and C's is $\frac{7}{6}$ times of B's. What is the ratio of C's wealth to A's?

Option 1: 8:21

Option 2: 21:8

Option 3: 27:14

Option 4: 14:27

Team Careers360 24th Jan, 2024

Correct Answer: 21:8


Solution : Given: A's wealth is $\frac{4}{9}$ times of B.
C's wealth is $\frac{7}{6}$ times of B.
⇒ A's wealth = B's wealth × $\frac{4}{9}$
⇒ C's wealth = B's wealth × $\frac{7}{6}$
Ratio of C's wealth to A's wealth = $\frac{\frac{7}{6}}{\frac{4}{9}}$
$⇒\frac{21}{8}$
⇒ 21:8
Therefore, option

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Question : PQRS is a cyclic quadrilateral. If $\angle$P is three times of $\angle$R and $\angle$S is four times of $\angle$Q, then the sum of $\angle$S + $\angle$R will be:

Option 1: $169^{\circ}$

Option 2: $171^{\circ}$

Option 3: $187^{\circ}$

Option 4: $189^{\circ}$

Team Careers360 25th Jan, 2024

Correct Answer: $189^{\circ}$


Solution : $\angle$P = 3$\angle$R
$\angle$S = 4$\angle$Q
As PQRS is a cyclic quadrilateral,
$\angle$P + $\angle$R = $180^{\circ}$
⇒ 3$\angle$R + $\angle$R = $180^{\circ}$
⇒ 4$\angle$R = $180^{\circ}$
$\therefore$ $\angle$R = $45^{\circ}$
⇒ $\angle$P = 3 × $45^{\circ}$ = $135^{\circ}$
$\angle$S + $\angle$Q = $180^{\circ}$

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Question : If $a \cot \theta+b \operatorname{cosec} \theta=p$ and $b \cot \theta+a \operatorname{cosec} \theta=q$ then $p^2-q^2$ is equal to.

Option 1: $a^2+b^2$

Option 2: $a^2-b^2$

Option 3: $b^2-a^2$

Option 4: $b-a$

Team Careers360 25th Jan, 2024

Correct Answer: $b^2-a^2$


Solution : Given: $a \cot \theta+b \operatorname{cosec} \theta=p$
Squaring both sides,
We get $(a \cot \theta+b \operatorname{cosec} \theta)^{2} =p^{2}$
⇒ $a^{2} \cot^{2}\theta+b^{2} \operatorname{cosec}^{2}\theta +2ab \cot \theta\operatorname{cosec} \theta  =p^{2}$……(i) 
And $b \cot \theta+a \operatorname{cosec} \theta=q$
Squaring both sides,
We get $(b \cot \theta+a \operatorname{cosec} \theta)^{2}=q^2$
⇒ $b^2 \cot^{2}\theta+a^2

43 Views

Question : Direction: In each of the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?

ccbab _ caa _ bccc _ a _

Option 1: babc

Option 2: babb

Option 3: bbba

Option 4: baab

Team Careers360 25th Jan, 2024

Correct Answer: babb


Solution : Given -

ccbab _ caa _ bccc _ a _

Let's check the options.

option first: babc

The series becomes ccbabbcaaabcccbac

There is no pattern in the above series.

option second: babb

The series becomes ccbabbcaa

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Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No error".

He'd no sooner (1) / seen one continent (2) /when he saw another. (3) / No error (4)

Option 1: 1
 

Option 2: 2

Option 3: 3

 

Option 4: 4

Team Careers360 25th Jan, 2024

Correct Answer: 3

 


Solution : The error lies in the third part of the sentence.

Explanation: The correlative conjunction "no sooner...than" is used to indicate that one action or event happens immediately after another. In this case, "than" should be used after he'd no sooner seen one continent, which correctly

22 Views

Question : Directions: Select the option in which the following figure is embedded (Rotation is NOT allowed).

Option 1:

Option 2:

Option 3:

Option 4:

Team Careers360 24th Jan, 2024

Correct Answer:


Solution : Since there is a restriction on the rotation of the figure, 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.


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