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Staff Selection Commission Combined Graduate Level Exam

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Question : $\sqrt{\frac{1+\sin A}{1-\sin A}}=$_______.

Option 1: $\operatorname{coesc} A-\cot A$

Option 2: $\sec A-\tan A$

Option 3: $\sec A+\tan A$

Option 4: $\sec A$

Team Careers360 19th Jan, 2024

Correct Answer: $\sec A+\tan A$


Solution : $\sqrt{\frac{1+\sin A}{1-\sin A}}$
$=\sqrt{\frac{1+\sin A}{1-\sin A}\times\frac{1+\sin A}{1+\sin A}}$
$=\sqrt{\frac{(1+\sin A)^2}{(1+\sin A)(1-\sin A)}}$
$=\sqrt{\frac{(1+\sin A)^2}{(1-\sin^2 A)}}$
$=\sqrt{\frac{(1+\sin A)^2}{(\cos^2 A)}}$
$=\frac{1+\sin A}{\cos A}$
$=\frac{1}{\cos A}+\frac{\sin A}{\cos A}$
$=\sec A+\tan A$
Hence, the correct answer is $\sec A+\tan A$.

17 Views

Question : Direction: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.

36, 34, 30, 28, 24, ?

Option 1: 20

Option 2: 26

Option 3: 22

Option 4: 23

Team Careers360 24th Jan, 2024

Correct Answer: 22


Solution : Given –

36, 34, 30, 28, 24, ?

The pattern follow for the series is –

36 – 2 = 34; 34 – 4 = 30; 30 – 2 = 28; 28 - 4 = 24; 24 – 2 = 22

The series is 36,

15 Views

Question : Directions: In the following question, from the given alternative words, select the word that cannot be formed using the letters of the given word.
CONSOLIDATE

Option 1: CONSOLE

Option 2: ONSET

Option 3: SALTY

Option 4: SOLID

Team Careers360 19th Jan, 2024

Correct Answer: SALTY


Solution : Given:
CONSOLIDATE

Let's check the options –
First option: CONSOLE; All the letters of CONSOLE are present in the word CONSOLIDATE.
Second option: ONSET; All the letters of ONSET are present in the word CONSOLIDATE.
Third option: SALTY; The letter Y in the word SALTY

14 Views

Question : Select the most appropriate ANTONYM of the underlined word.

Trivial issues have always interested our boss.

Option 1: Fierce

Option 2: Hopeful

Option 3: Significant

Option 4: Common

Team Careers360 21st Jan, 2024

Correct Answer: Significant


Solution : The correct choice is the third option.

Trivial means of little value or importance; insignificant, while significant means having importance or meaning; noteworthy.

The meanings of the other options are as follows:

  • Fierce: Intense or aggressive.

  • Hopeful: Full of hope or optimism.

  • Common: Usual or

22 Views

Question : Comprehension:

Read the given passage and answer the questions that follow.

We sit in the last row, bumped about but free of stares. The bus rolls out of the dull crossroads of the city, and we are soon in the open countryside, with fields of sunflowers as far as the eye can see, their heads all facing us. Where there is no water, the land reverts to the desert. While still on level ground, we see in the distance the tall range of Mount Bogda, abrupt like a shining prism laid horizontally on the desert surface. It is over 5,000 metres high, and the peaks are under permanent snow, in powerful contrast to the flat desert all around. Heaven Lake lies part of the way up this range, about 2,000 metres above sea level, at the foot of one of the highest snow peaks.

As the bus climbs, the sky, brilliant before, grows overcast. I have brought nothing warm to wear. It is all down at the hotel in Urumqi. Rain begins to fall. The man behind me is eating overpoweringly smelly goat's cheese. The bus window leaks inhospitably but reveals a beautiful view. We have passed quickly from the desert through arable land to pasture and the ground is now green with grass, the slopes dark with pine. A few cattle drink at a clear stream flowing past moss-covered stones; it is a Constable landscape. The stream changes into a white torrent, and as we climb higher I wish more and more that I had brought with me something warmer than the pair of shorts that have served me so well in the desert. The stream (which, we are told, rises in Heaven Lake) disappears, and we continue our slow ascent. At about noon, we arrive at Heaven Lake and look for a place to stay at the foot, which is the resort area. We get a room in a small cottage, and I am happy to note that there are thick quilts on the bed.

Standing outside the cottage, we survey our surroundings. Heaven Lake is long, sardine shaped and fed by snowmelt from a stream at its head. The lake is an intense blue, surrounded on all sides by green mountain walls, dotted with distant sheep. At the head of the lake, beyond the delta of the inflowing stream, is a massive snow-capped peak which dominates the vista; it is part of a series of peaks that culminate, a little out of view, in Mount Bogda itself.

For those who live in the resort, there is a small mess hall by the shore. We eat here sometimes and sometimes buy food from the vendors outside, who sell kabab and naan until the last buses leave. The kababs, cooked on skewers over charcoal braziers, are particularly good; highly spiced and well done. Horse's milk is available too from the local Kazakh herdsmen, but I decline this. I am so affected by the cold that Mr. Cao, the relaxed young man who runs the mess, lends me a spare pair of trousers, several sizes too large but more than comfortable. Once I am warm again, I feel a pre-dinner spurt of energy will be long in coming — and I ask him whether the lake is good for swimming in.

Question:

Select the most appropriate ANTONYM of the word 'accept' from the passage.

Option 1: Reject

Option 2: Refuse

Option 3: Decline

Option 4: Turn down

Team Careers360 23rd Jan, 2024

Correct Answer: Decline


Solution : The correct choice is the third option.

Explanation:

In the passage, the word accept is not explicitly used, but there is a mention of the protagonist declining or refusing something. The relevant sentence is: "Horse's milk is available too from the local Kazakh herdsmen, but

27 Views

Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?
6– 20 + (28 ÷ 7) – [(√4) × 8 ] + 22 = 40

Option 1: 6 and 8

Option 2: 7 and 2

Option 3: 2 and 8

Option 4: 20 and 8

Team Careers360 19th Jan, 2024

Correct Answer: 6 and 8


Solution : Given:
6– 20 + (28 ÷ 7) – [(√4) × 8 ] + 22 = 40

Interchange the numbers according to the given options.
Let's check each option – 
First option: 6 and 8
8– 20 + (28

15 Views

Question : Directions: In the following question, find the odd number pair from the given alternatives.

Option 1: 1629

Option 2: 3418

Option 3: 2349

Option 4: 1834

Team Careers360 24th Jan, 2024

Correct Answer: 1834


Solution : Let's check the options –
First option: 1629→1 + 6 + 2 = 9 
Second option: 3418→3 + 4 + 1 = 8
Third option: 2349→2 + 3 + 4 = 9
Fourth option: 1834→1 + 8 + 3 = 12 ≠ 4

Hence,

15 Views

Question : In a right-angled triangle $\triangle$DEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is:

Option 1: 3 cm

Option 2: 4 cm

Option 3: 6 cm

Option 4: 12 cm

Team Careers360 21st Jan, 2024

Correct Answer: 6 cm


Solution : As per the given question, we draw a figure of a right-angled triangle DEF.

The median DX splits the right triangle into two isosceles triangles, and the median is half the length of the hypotenuse.
$\therefore$ EF = 12 cm
⇒ DX = XE

42 Views

Question : A dealer marks his goods at 15% above the cost price and allows a discount of 5% for cash payment. His profit percentage is:

Option 1: 9.25%

Option 2: 7.25%

Option 3: 11.25%

Option 4: 10.25%

Team Careers360 22nd Jan, 2024

Correct Answer: 9.25%


Solution : Let Rs. 100 be the cost price.
Marked price = 115% of cost price = Rs. 115
Discount = 5% of marked price
= $\frac{5}{100}×115$
= Rs. 5.75
Selling price = 115 – 5.75 = 109.25
So, the profit = 109.25 – 100 = 9.25

36 Views

Question : The average of six numbers is 20. If one number is removed, the average becomes 15, what is the number removed?

Option 1: 5

Option 2: 35

Option 3: 112

Option 4: 45

Team Careers360 19th Jan, 2024

Correct Answer: 45


Solution : Given:
The average of 6 numbers is 20.
If one number is removed, the new average is 15.
By using the formula,
The sum of observations = average of observations × total number of observations
⇒ Sum of 6 numbers = 20 × 6 =

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