Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\frac14\text{ of }\frac45+\frac95\text{ of }\frac{17}{3}-\frac{3}{10}=p$, then what is the value of $p$?
Option 1: $\frac{127}{5}$
Option 2: $\frac{177}{5}$
Option 3: $\frac{255}{2}$
Option 4: $\frac{51}{2}$
Correct Answer: $\frac{127}{5}$
Solution : Given expression, $\frac14\text{ of }\frac45+\frac92\text{ of }\frac{17}{3}-\frac{3}{10}=p$ ⇒ $p=\frac{1}{5}+\frac{51}{2}-\frac{3}{10}$ ⇒ $p=\frac{2+255-3}{10}$ ⇒ $p=\frac{254}{10}=\frac{127}{5}$ Hence, the correct answer is $\frac{127}{5}$.
Question : The equation $\cos ^{2}\theta=\frac{(x+y)^{2}}{4xy}$ is only possible when,
Option 1: $x=-y$
Option 2: $x>y$
Option 3: $x=y$
Option 4: $x<y$
Correct Answer: $x=y$
Solution : $\cos ^{2}\theta=\frac{(x+y)^{2}}{4xy}$ We know that $(x+y)\geq 2\sqrt{xy}$ (Since the arithmetic mean is always greater than or equal to the geometric mean) $⇒(x+y)^2\geq 4xy$ $⇒\frac{(x+y)^2}{4xy}\geq 1$ Since $0\leq \cos ^{2}\theta\leq 1$, solution exists when $\frac{(x+y)^2}{4xy}=1$ $\therefore \frac{(x+y)^2}{4xy}=1$ $⇒4xy =x^2+y^2 + 2xy$ $⇒x^2+y^2 - 2xy=0$ $⇒(x-y)^2 =
Question : Directions: In the following question below, some statements are followed by some conclusions. Taking the given statements to be true, even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows from the given statements. Statements: (I) No women can vote. (II) Some women are politicians. Conclusions: (I) Male politicians can vote. (II) Some politicians can vote.
Option 1: Conclusion I follows
Option 2: Conclusion II follows
Option 3: Neither I nor II follows
Option 4: Both I and II follow
Correct Answer: Neither I nor II follows
Solution : According to the above given statement,
Conclusion (I): Male politicians can vote. This conclusion isn't directly supported by the given statements. We know that no woman can vote, but the statements don't give us any information about whether male politicians can
Question : Directions: Select the word pair that best represents a similar relationship to the one expressed in the pair of words given below. (The words must be considered meaningful English words and must not be related to each other based on the number of letters/number of consonants/vowels in the word.) Big – Small
Option 1: Old – Young
Option 2: Present – Gift
Option 3: Crow – Black
Option 4: Rich – Wealthy
Correct Answer: Old – Young
Solution : Given: Big – Small (Here, big means large whereas small means not large in size, number, amount etc. Thus, big and small are antonyms.)
First option: Old – Young→Old means that has existed for a long time or lived a long time whereas
Question : Select the correct passive form of the given sentence.
The police have apprehended the criminal.
Option 1: The criminal had been apprehended by the police.
Option 2: The criminal had been apprehend by the police.
Option 3: The criminal was apprehended by the police.
Option 4: The criminal has been apprehended by the police.
Correct Answer: The criminal has been apprehended by the police.
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
Question : In which year was the Dowry Prohibition Act passed in India?
Option 1: 1973
Option 2: 1982
Option 3: 1961
Option 4: 1954
Correct Answer: 1961
Solution : The correct answer is 1961.
On July 1, 1961, the Dowry Prohibition Act was passed to outlaw the giving and receiving of dowries. As defined by the Dowry Prohibition Act, a "dowry" is any valuable security or property provided or agreed to be delivered, whether
Question : Which of the following blood groups is a universal recipient?
Option 1: A
Option 2: B
Option 3: AB
Option 4: O
Correct Answer: AB
Solution : The correct option is AB.
The four main blood types or groups are A, B, AB, and O.The classification of blood-based on the presence or absence of antibodies and hereditary antigenic substances on the surface of red blood cells (RBCs) is known as a
Question : Find 2 numbers such that their mean proportional is 25 and their third proportional is 25.
Option 1: 5 and 5
Option 2: 5 and 25
Option 3: 25 and 125
Option 4: 25 and 25
Correct Answer: 25 and 25
Solution : Let, the two numbers be $x$ and $y$, respectively. The mean proportional between $x$ and $y$ is 25. $x:25=25:y$ ⇒ $xy=625$ The third proportional to $x$ and $y$ is 25. $x:y=y:25$ ⇒ $y^2=25x$ ⇒ $y^2=25×\frac{625}{y}$ ⇒ $y^3=25×625=15625=25$ $∴y=25$ Now, $x=\frac{625}{y}=25$ So, the two
Question : O is the centre of the circle and AB is the tangent to it touching at B. If OB = 3 cm and OA = 5 cm, then the measure of AB (in cm) is:
Option 1: $\sqrt{34}$
Option 2: $2$
Option 3: $8$
Option 4: $4$
Correct Answer: $4$
Solution : Given: O is the centre of the circle and AB is tangent to it touching at B. OB = 3 cm and OA = 5 cm Using the Pythagoras theorem, from $\triangle$AOB, we get, AB2 = OA2 – OB2 $\therefore$ AB $=\sqrt{5^2-3^2}=\sqrt{16}=4$
Question : Select the option that expresses the given sentence in passive voice.
Do the Basus visit the Shuklas?
Option 1: Are the Shuklas been visited by the Basus?
Option 2: Are the Shuklas visit by the Basus?
Option 3: Are the Shuklas being visited by the Basus?
Option 4: Are the Shuklas visited by the Basus?
Correct Answer: Are the Shuklas visited by the Basus?
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
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