Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\cos \theta+\sin \theta=\sqrt{2}$, then what is the value of $\sec \theta \operatorname{cosec} \theta$ ?
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $2$
Option 4: $0$
Correct Answer: $2$
Solution : Given: $\cos \theta+\sin \theta=\sqrt{2}$ Squaring both sides, we get: ⇒ $(\cos \theta+\sin \theta)^2=(\sqrt{2})^2$ ⇒ $\cos^2 \theta+\sin^2 \theta+2\sin\theta \cos\theta=2$ We know that $\cos^2 \theta+\sin^2 \theta = 1$ Thus, $1+2\sin\theta \cos\theta=2$ ⇒ $2\sin\theta \cos\theta=2-1$ ⇒ $\sin\theta \cos\theta=\frac{1}{2}$ ⇒ $\frac{1}{\operatorname{cosec}\theta}\frac{1}{\sec\theta}=\frac{1}{2}$ ⇒ $\operatorname{cosec}\theta \sec\theta = 2$ Hence, the correct
Question : The first World Deaf T20 Cricket Championship will be organised by_______.
Option 1: West Indies
Option 2: Australia
Option 3: England
Option 4: India
Correct Answer: India
Solution : The correct option is India.
The International Committee of Sports for the Deaf (ICSD) has given the All India Sports Council of the Deaf permission to hold Kerala as the site of the inaugural World Deaf T20 Cricket Championship. The dates of the event
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
He agreed ___ my business proposal.
Option 1: at
Option 2: for
Option 3: on
Option 4: to
Correct Answer: to
Solution : The fourth option is the correct answer, as ''to'' fits perfectly in the sentence.
The phrase "agree with" is used to refer to agreeing with a person, and the phrase "agree to" is used to refer to agreeing with a non-person,
Question : If the price of a product is first increased by 15% and then decreased by 20%, then what is the percentage change in the price?
Option 1: 5% decrease
Option 2: 8% increase
Option 3: 5% increase
Option 4: 8% decrease
Correct Answer: 8% decrease
Solution : Let the initial price be Rs. 100. After an increase of 15%, the price becomes: $100 +\frac{15}{100}\times100 = 100 + 15 =$ Rs. 115 Now, After a decrease of 20%, the price becomes: $115 -\frac{20}{100}\times115 = 115 - 23 =$ Rs. 92 ⇒ Total
Question : In India, National Statistics Day is celebrated on ______.
Option 1: 22nd June
Option 2: 15th June
Option 3: 28th June
Option 4: 29th June
Correct Answer: 29th June
Solution : The correct option is 29th June.
In India, National Statistics Day is celebrated on June 29th every year. This day is observed to commemorate the birth anniversary of Prof. P.C. Mahalanobis, an eminent statistician, and to recognise his invaluable contribution to the field of
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".
The people gathered at the funeral to pay respect.
(1) No Error
(2) The people gathered
(3) at the funeral
(4) to pay respect.
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The second option is the correct answer.
People is a plural noun that means multiple people in general. There is no need to use the definite article "the" before the noun.
Therefore, the correct sentence is: People gathered at the funeral to pay respect.
Question : If $\tan^{2}\alpha=1+2\tan^{2}\beta$ ($\alpha,\beta$ are positive acute angles), then $\sqrt2\: \cos\alpha -\cos\beta$ is equal to:
Option 1: $0$
Option 2: $\sqrt2$
Option 3: $1$
Option 4: $–1$
Correct Answer: $0$
Solution : $\tan^{2}\alpha=1+2\tan^{2}\beta$ $⇒\sec^{2}\alpha-1=1+2(\sec^{2}\beta-1)$ $⇒\sec^{2}\alpha-1=2\sec^{2}\beta-1$ $⇒\frac{1}{\cos^{2}\alpha}=\frac{2}{\cos^{2}\beta}$ Taking square root on both sides, we get, $⇒\sqrt2\cos\alpha=\cos\beta$ $⇒\sqrt2\cos\alpha-\cos\beta=0$ Hence, the correct answer is $0$.
Question : Liberty, Equality and Fraternity slogan of______finds an echo in the Preamble of the Indian Constitution.
Option 1: Mexican Revolution
Option 2: Greek War of Independence
Option 3: American Declaration of Independence
Option 4: French Revolution
Correct Answer: French Revolution
Solution : The correct answer is the French Revolution.
The French Revolution served as an inspiration for the principles of liberty, equality, and fraternity that are enshrined in the preamble of the Indian Constitution. The period of the French Revolution was 1789–1799. Justice, liberty, equality,
Question : Which of the following provisions of the Indian constitution is borrowed from the constitution of Canada?
Option 1: Independence of judiciary
Option 2: Concept of Republic
Option 3: Advisory jurisdiction of the Supreme court
Option 4: Concept of concurrent list
Correct Answer: Advisory jurisdiction of the Supreme court
Solution : The correct option is the Advisory jurisdiction of the Supreme Court.
The advisory jurisdiction of the Supreme Court is a provision in some legal systems that is borrowed from the Constitution of Canada. In the Indian legal system, the
Question : Directions: If 617 @ 342 = 572 and 483 @ 342 = 141, then 280 @ 82 = ?
Option 1: 632
Option 2: 891
Option 3: 188
Option 4: 721
Correct Answer: 891
Solution : Given: 617 @ 342 = 572; 483 @ 342 = 141
Equation I: 617 @ 342 = 572 617 – 342 = 275; On reversing the order of digits of 275, we get 572. Equation II: 483 @ 342 = 141 483 – 342 =
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