Staff Selection Commission Combined Graduate Level Exam
Question : $\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\left.\theta \neq \frac{\pi}{2}\right)?$
Option 1: $\frac{1+\cos \theta}{\sin \theta}$
Option 2: $\frac{\tan \theta+1}{\tan \theta-1}$
Option 3: $\frac{\tan \theta-1}{\tan \theta+1}$
Option 4: $\frac{\cos \theta}{1-\sin \theta}$
Correct Answer: $\frac{\cos \theta}{1-\sin \theta}$
Solution : Given, $\frac{1+\sin \theta}{\cos \theta}$ Multiplying numerator and denominator by $(1-\sin \theta)$ = $\frac{(1+\sin \theta)\times (1-\sin \theta)}{\cos \theta\times (1-\sin \theta)}$ = $\frac{(1-\sin^2 \theta)}{\cos \theta\times (1-\sin \theta)}$ = $\frac{\cos^2 \theta}{\cos \theta\times (1-\sin \theta)}$ = $\frac{\cos \theta}{1-\sin \theta}$ Hence, the correct answer is $\frac{\cos \theta}{1-\sin \theta}$.
Question : Directions: Three of the following letter clusters are alike in some manner and hence form a group. Which letter cluster does not belong to that group?
Option 1: KPW
Option 2: QGM
Option 3: DIP
Option 4: SXE
Correct Answer: QGM
Solution : Let's check each option – First option: KPW; K + 5 = P, P + 7 = W Second option: QGM; Q – 10 = G, G + 6 = M Third option: DIP; D + 5 = I, I + 7 = P Fourth
Question : Match the following
A.Brahmo Samaj 1.Bombay
B.Veda Samaj 2.Bengal
C.Arya Samaj 3.Madras
D.Prarthana Samaj 4.North India
Code:
(A) (B) (C) (D)
Option 1:
1 3 2 4
Option 2:
3 2 4 1
Option 3:
2 4 1 3
Option 4: 2 3 4 1
Correct Answer: 2 3 4 1
Solution : Correct Answer is 2 3 4 1
A movement founded in 1875 by Swami Dayananda Saraswati was a Hindu Monotheistic Social-Religion .Brahmo Samaj (Brahmo's Samaj) was founded by Raja Ram Mohan in the year 1867. He is also known as the father
Question : If $xy+yz+zx=1$ , then the value of $\frac{1\:+\:y^2}{(x\:+\:y)(y\:+\:z)}$ is:
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 1
Correct Answer: 1
Solution : Given: $xy+yz+zx=1$ Now, $\frac{1\:+\:y^2}{(x\:+\:y)(y\:+\:z)}$ = $\frac{1\:+\:y^2}{xy\:+\:yz\:+\:zx\:+\:y^2}$ = $\frac{1\:+\:y^2}{1\:+\:y^2}$ = $1$ Hence, the correct answer is 1.
Question : In which field is B.C.Roy Award given ?
Option 1: Music
Option 2: Journalism
Option 3: Medicine
Option 4: Environment
Correct Answer: Medicine
Solution : The correct answer is Medicine.
The Medical Council of India established the Bidhan Chandra Roy Award in 1962 in honor of Dr. B. C. Roy. It is presented by the President of India every year on July 1, which is National Doctor's Day
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".
Bobby learnt the alphabets at the age of two.
(1) No error
(2) age of two.
(3) Bobby learnt the
(4) alphabets at the
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : The word "alphabets" should be corrected to "alphabet" in this context. When referring to the set of letters used in a language, we use "alphabet" in the singular form. Additionally, the past tense of "learn" should be "learned" (in American English) or "learnt" (in
Question : The average of $n$ numbers is $a$. The first number is increased by 2, the second one is increased by 4, the third one is increased by 8, and so on. The average of the new numbers is:
Option 1: $a+\frac{2^{n–1}–1}{n}$
Option 2: $a+\frac{2(2n–1)}{n}$
Option 3: $a+\frac{2^{n–1}}{n}$
Option 4: $a+\frac{2^{n}–1}{n}$
Correct Answer: $a+\frac{2(2n–1)}{n}$
Solution : Given: The average of $n$ numbers is $a$. The sum of $n$ numbers is $n×a$. According to the question, Let S be the sum of increased value and $r$ = common ratio = $\frac{4}{2}= 2$ S = 2 + 4 + 8 + 16 ....
Question : President Ram Nath Kovind conferred which award on Matha B. Manjamma for Jogati Nritya?
Option 1: Padma Bhushan
Option 2: Padma Shri
Option 3: Padma Vibhushan
Option 4: Sangeet Natak Akademi
Correct Answer: Padma Shri
Solution : The correct option is Padma Shri.
\In 2021, Manjamma Jogati, a transgender folk dancer, received the prestigious Padma Shri for her remarkable artistic achievements. This distinguished honour was presented to her by President Ram Nath Kovind during the Padma Awards ceremony held at
Question : The table given below shows the sales turnover of 5 different companies.
The sales turnover of company A is what percentage of the sales turnover of company C?
Option 1: 60%
Option 2: 50%
Option 3: 40%
Option 4: 75%
Correct Answer: 60%
Solution : Sales turnover of company A = 120 Sales turnover of company C = 200 Required percentage = $\frac{120}{200}\times 100$% = 60% Hence, the correct answer is 60%.
Question : Select the most appropriate option to fill in the blank. APJ Abdul Kalam’s house, located on Mosque Street, was within the reach of the famous temple of Rameswaram. It was just________from it.
Option 1: a stone’s throw away
Option 2: at one’s fingertip
Option 3: at arm’s length
Option 4: from pillar to post
Correct Answer: a stone’s throw away
Solution : The correct option is the first option.
Explanation: A stone’s throw away means a very short distance, usually close enough to be reached by throwing a stone. In this context, it implies that APJ Abdul Kalam's house was very close to the
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