Staff Selection Commission Combined Graduate Level Exam
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: $\sec A$
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 $\sec A+\tan A$.
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
Correct Answer: 22
Solution : Given –
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,
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
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
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
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
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
Correct Answer: Decline
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
Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct? 62 – 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
Correct Answer: 6 and 8
Solution : Given: 62 – 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 82 – 20 + (28
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
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,
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
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
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%
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
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
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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