Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:
Option 1: $\frac{16}{25}$
Option 2: $\frac{40}{41}$
Option 3: $\frac{41}{40}$
Option 4: $\frac{31}{30}$
Correct Answer: $\frac{41}{40}$
Solution : Given: $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$ ⇒ $5\sin \theta - 5\cos \theta = 4\sin \theta + 4\cos \theta$ $\sin \theta = 9\cos \theta$ Dividing both sides by $\cos \theta$, we get: $\tan \theta = 9$ Now, we know that: $\tan\theta=\frac{p}{b}=\frac{9}{1}$ So, $h=\sqrt{p^2+b^2}=\sqrt{9^2+1^2}=\sqrt{82}$ Now, $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2
Question : Select the correct spelling of the underlined word.
It would be proodent to wait for some more time before selling off the property.
Option 1: prudent
Option 2: proudent
Option 3: prodent
Option 4: proodant
Correct Answer: prudent
Solution : The correct choice is the first option.
The correct spelling of the underlined word is prudent, which means showing care and thought for the future.
Therefore, the correct sentence is: It would be prudent to wait for some more time before selling off
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
The modern pizza was originally (1)._________ in Naples, Italy but the word pizza is Greek in (2)._________ derived from the Greek word pktos meaning solid or clotted. The ancient (3).___________ covered their bread with oils, herbs and cheese. The first major (4).__________ that led to flatbread pizza was the use of tomato as a topping. It was common for the poor of the area around Naples to add (5)._________ to their yeast-based flat bread, and so the pizza began.
Question: Select the most appropriate option to fill in the blank No. 5.
Option 1: tomato
Option 2: potato
Option 3: onion
Option 4: herb
Correct Answer: tomato
Tomato is the correct choice, as it is the most common ingredient used to make pizza, according to the passage.
Question : If $a^3+b^3=9$ and $a+b=3$, then the value of $\frac{1}a+\frac{1}b$ is:
Option 1: $\frac{1}2$
Option 2: $\frac{3}2$
Option 3: $\frac{5}2$
Option 4: $–1$
Correct Answer: $\frac{3}2$
Solution : Given: That $a+b=3$ and $a^{3} + b^{3} = 9$ We know that $(a+ b)^{3}=a^3 + b^3 + 3ab(a + b)$ So, $a^3 + b^3 + 3ab(a + b) = 27$ ⇒ $9 + 3ab(a + b) = 27$ ⇒ $3ab(3) = 27 - 9$ ⇒
Question : Directions: In the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it? gfe_ig_eii_fei_gf_ii
Option 1: eifgi
Option 2: figie
Option 3: ifgie
Option 4: ifige
Correct Answer: ifgie
Solution : Given: gfe_ig_eii_fei_gf_ii
To fill the series we have to divide the series→gfe_i / g_eii / _fei_ / gf_ii Let's check each option – First option: eifgi; gfeei / gieii / ffeig / gfiii (No repeated pattern
Question : Directions: In the following question, select the missing number from the given series. 47, 49, 53, 61, 77, ?, 173
Option 1: 103
Option 2: 109
Option 3: 99
Option 4: 111
Correct Answer: 109
Solution : Given: 47, 49, 53, 61, 77, ?, 173
Add consecutive powers of 2 to the previous term to get the next term of the series. 47 + 21 = 47 + 2 = 49 49 + 22 = 49 + 4 = 53
Question : If $x+\left [\frac{1}{(4x)} \right]=\frac{5}{2}$; then, what is the value of $\frac{64x^{6}+1}{8x^{3}} \;?$
Option 1: 110
Option 2: 115
Option 3: 125
Option 4: 140
Correct Answer: 110
Solution : The given expression $x+\left [ \frac{1}{(4x)} \right ]=\frac{5}{2}$ can be written as $4x^2+1 = 10x$. We have, $\frac{64x^{6}+1}{8x^{3}}$ .......(1) Here, we can write $64x^{6}+1$ as $(4x^2+1)(16x^4+1-4x^2)$. ⇒ $(4x^2+1)(16x^4+1-4x^2)$ ⇒ $(4x^2+1)((4x^2+1)^2 - 8x^2-4x^2)$ ⇒ $(4x^2+1)((4x^2+1)^2-12x^2)$ ⇒ $(4x^2+1)((10x)^2-12x^2)$ ⇒ $(10x)(88x^2) = 880x^3$ Putting this value in equation
Question : Select the correct passive form of the given sentence. Khushi wiped down the tables.
Option 1: The tables were being wiped down by Khushi.
Option 2: The tables was wiped down by Khushi.
Option 3: The tables are wiped down by Khushi.
Option 4: The tables were wiped down by Khushi.
Correct Answer: The tables were wiped down by Khushi.
Solution : The correct choice is the fourth option.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in the
Question : AB is a chord of the circle and AOC is its diameter such that $\angle$ACB = 65°. If AT is the tangent to the circle at the point A, then $\angle$BAT is equal to:
Option 1: 65°
Option 2: 75°
Option 3: 55°
Option 4: 40°
Correct Answer: 65°
Solution : In a circle, the angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment. Here, AB is the chord and AT is the tangent at point A. So, the angle
Question : The most important element of weather affecting agriculture in India is :
Option 1: Temperature
Option 2: Humidity
Option 3: Wind
Option 4: Rainfall
Correct Answer: Rainfall
Solution : The correct answeris Rainfall.
The most important factor which influences the agricultural pattern in India is rainfall. India is heavily dependent on rainfall for its agricultural needs as 12% of the geographical area in India comes under Arid zone. In India about 51% of total
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
And never miss an important update
