Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $x\cos \theta -y\sin \theta =\sqrt{x^{2}+y^{2}}$ and $\frac{\cos ^2{\theta }}{a^{2}}+\frac{\sin ^{2}\theta}{b^{2}}=\frac{1}{x^{2}+y^{2}},$ then the correct relation is:
Option 1: $\frac{x^{2}}{b^{2}}-\frac{y^{2}}{a^{2}}=1$
Option 2: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
Option 3: $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1$
Option 4: $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
Correct Answer: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
Solution : $x\cos \theta -y\sin \theta =\sqrt{x^{2}+y^{2}}$ ..................................(1) $\frac{\cos ^2{\theta }}{a^{2}}+\frac{\sin ^{2}\theta }{b^{2}}=\frac{1}{x^{2}+y^{2}}$ .......................................(2) From equation (1), $\frac{x\cos \theta}{\sqrt{x^{2}+y^{2}}} -\frac{y\sin \theta}{\sqrt{x^{2}+y^{2}}} =1$ Comparing with $\cos^2 \theta + \sin^2 \theta = 1$, we get, $\sin \theta = -\frac{y}{\sqrt{x^{2}+y^{2}}}$ and $\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}$ Putting in (2), $\frac{x^2}{(x^2 +
Question : The area and the length of one of the diagonals of a rhombus are 84 cm2 and 7 cm respectively. Find the length of its other diagonal (in cm).
Option 1: 12
Option 2: 24
Option 3: 48
Option 4: 36
Correct Answer: 24
Solution : Given: Area = $84\ cm^2$ 1st diagonal = 7 cm 2nd diagonal = $D_2$ We know that Area of rhombus = $\frac{1}{2}\times$(Product of the diagonals) ⇒ $84 = \frac{1}{2}\times7\times D_2$ ⇒ $D_2 = 24\ cm$ Hence, the correct answer is 24.
Question : Identify the segment in the sentence which contains a grammatical error. If there is no error, then select the option "No error".
The London-based Brodsky / Quartet, meanwhile, is one of / the world's leading string quartet.
Option 1: The London-based Brodsky
Option 2: the world's leading string quartet.
Option 3: Quartet, meanwhile, is one of
Option 4: No error
Correct Answer: the world's leading string quartet.
Solution : The error lies in the second option.
The phrase "one of" should be followed by a plural noun to maintain the agreement in the sentence. Thus, string quartet should be replaced with string quartets to make the sentence grammatically accurate, as
Question : If the density of oxygen is 16 times that of hydrogen, what will be their corresponding ratio to the velocity of sound?
Option 1: 4:1
Option 2: 2:1
Option 3: 1:16
Option 4: 1:4
Correct Answer: 1:4
Solution : The correct option is 1:4.
If the density of oxygen is 16 times that of hydrogen, the ratio of their velocities of sound will be the same as the ratio of their densities
The velocity of sound from oxygen to hydrogen is 1:4.
v=√γP/ρ.
Question : A can complete a piece of work in 9 days. B and C can complete the same work in 12 days and 18 days respectively. If A, B, and C work together, then in how many days will they complete the work?
Option 1: 10 days
Option 2: 8 days
Option 3: 4 days
Option 4: 15 days
Correct Answer: 4 days
Solution : 1 day's work of A = $\frac{1}{9}$ 1 day's work of B = $\frac{1}{12}$ 1 day's work of A = $\frac{1}{18}$ 1 day's work of (A + B + C) $=\frac{1}{9}+\frac{1}{12}+\frac{1}{18}=\frac{4+3+2}{36}=\frac{9}{36}$ $\therefore$ So they can complete the whole work in $\frac{36}{9}$ = 4 days
Question : Who among the following received the OSCAR for the best actor in a leading role in 2022?
Option 1: Benedict Cumberbatch
Option 2: Andrew Garfield
Option 3: Denzel Washington
Option 4: Will Smith
Correct Answer: Will Smith
Solution : The correct answer is Will Smith.
On March 28, 2022, the 94th Academy Awards, also known as the Oscars, were announced. The best actor went to Will Smith for "King Richard.
Jessica Chastain, however, took home the Oscar for best actress for "The Eyes
Question : Choose the word that means the same as the given word. Genial
Option 1: Tense
Option 2: Lacuna
Option 3: Laconic
Option 4: Convivial
Correct Answer: Convivial
Solution : The correct option is the fourth option.
The word that means the same as the given word "genial" is "convivial."
Genial is an adjective that describes someone or something as friendly, warm, and pleasant. It often refers to a person's demeanour or atmosphere.
Convivial is
Question : Directions: Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusions logically follow/s from the given statements. Statements: I. All magnets are poles. II. All poles are telescopes. III. Some telescopes are computers. Conclusions: I. All telescopes are magnets. II. Some poles are computers.
Option 1: Both conclusions (I) and (II) are true
Option 2: Only conclusion (I) is true
Option 3: Only conclusion (II) is true
Option 4: Neither conclusion (I) nor (II) is true
Correct Answer: Neither conclusion (I) nor (II) is true
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All telescopes are magnets – From the Venn diagram, it is evident that some parts of the circle representing
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error. When I was in 5th grade, / I use to / ride on my / red bicycle.
Option 1: red bicycle
Option 2: I use to
Option 3: When I was in 5th grade,
Option 4: ride on my
Correct Answer: I use to
The correct phrase for describing a past habitual action is "used to" instead of "use to". "Used to" is used to describe the past habitual actions or states that are no longer true in the present.
Question : Choose the correct option in the context of given sentences.
Assertion: Self-help groups (SHGs) have emerged as an effective model for microfinance in India.
Reason: SHGs can pool resources and negotiate better loan terms with microfinance institutions.
Option 1: Both assertion and reason are true, and the reason is the correct explanation of the assertion.
Option 2: Both assertion and reason are false.
Option 3: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.
Option 4: The assertion is true, but the reason is false.
Correct Answer: Both assertion and reason are true, and the reason is the correct explanation of the assertion.
Solution : The correct answer is Both assertion and reason are true, and the reason is the correct explanation of the assertion.
Self-help groups (SHGs) are unofficial gathering places for individuals
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
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The Question is not relevant to User
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