If $$ an \alpha = \frac{a}{b} $$ then the value of $$ \sin \alpha + \cos \alpha $$ is:

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

If $$ an \alpha = \frac{a}{b} $$ then the value of $$ \sin \alpha + \cos \alpha $$ is:

A$$ \frac{a+b}{\sqrt{a^2+b^2}} $$

B$$ \frac{\sqrt{a^2+b^2}}{a+b} $$

C$$ \frac{a+b}{\sqrt{a^2-b^2}} $$

D$$ \frac{\sqrt{a^2-b^2}}{a+b} $$

Akhilesh ? Apr 3 '25 at 21:00

undefined

View Answer

Discuss

In which body part can one find the Synovial fluid?

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

In which body part can one find the Synovial fluid?

AMuscles

BLiver

CKidney

DJoints

Akhilesh ? Apr 1 '25 at 20:40

correct answer is: option d (d)[Joints]
Explanation: Synovial fluid is a viscous, non-Newtonian fluid found in the cavities of synovial joints. Its primary function is to reduce friction between the articular cartilage of synovial joints during movement. It also provides nutrients to the cartilage.

• Option a: Muscles are composed of muscle fibers and are responsible for movement. They do not contain synovial fluid.
• Option b: The Liver is a major organ involved in detoxification, protein synthesis, and the production of biochemicals necessary for digestion. It does not contain synovial fluid.
• Option c: The Kidney is responsible for filtering waste products from the blood and regulating fluid balance. It does not contain synovial fluid.
• Option d: Joints, specifically synovial joints, are where synovial fluid is located. The fluid lubricates the joint and reduces friction during movement.

View Answer

Discuss

Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No actor is an engineer. All engineers are magicians. Conclusions: I. No magician is an engineer. II. Some magicians are engineers.

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No actor is an engineer. All engineers are magicians. Conclusions: I. No magician is an engineer. II. Some magicians are engineers.

AOnly conclusion I follows

BBoth conclusions follow

CEither conclusion I or II follows

DOnly conclusion II follows

Akhilesh ? Apr 1 '25 at 20:40

correct answer is: option d : Only conclusion II follows
Explanation: The statements establish a relationship between actors, engineers, and magicians. Let's analyze each conclusion:

• Conclusion I: No magician is an engineer. This conclusion is incorrect. The statement "All engineers are magicians" implies that engineers are a subset of magicians. Therefore, some magicians *must* be engineers.
• Conclusion II: Some magicians are engineers. This conclusion is correct. Since all engineers are magicians, it directly follows that at least some magicians are engineers. This can be visualized with a Venn diagram where the 'Engineers' circle is entirely within the 'Magicians' circle.

View Answer

Discuss

If $$ \sin A = \frac{1}{x} $$ then $$ \cos A = ? $$

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

If $$ \sin A = \frac{1}{x} $$ then $$ \cos A = ? $$

A$$ \frac{\sqrt{x^2+1}}{x} $$

B$$ \frac{x}{\sqrt{x^2-1}} $$

C$$ \frac{\sqrt{x^2-1}}{x} $$

D$$ \frac{x}{\sqrt{x^2+1}} $$

Akhilesh ? Apr 1 '25 at 20:40

correct answer is: option c [\( \frac{\sqrt{x^2-1}}{x} \)]
Explanation: We know that \( \sin^2 A + \cos^2 A = 1 \). Therefore, \( \cos^2 A = 1 - \sin^2 A \). Given that \( \sin A = \frac{1}{x} \), we can substitute this into the equation to get \( \cos^2 A = 1 - (\frac{1}{x})^2 = 1 - \frac{1}{x^2} = \frac{x^2 - 1}{x^2} \). Taking the square root of both sides, we get \( \cos A = \sqrt{\frac{x^2 - 1}{x^2}} = \frac{\sqrt{x^2 - 1}}{x} \).

• Option a: \( \frac{\sqrt{x^2+1}}{x} \) is incorrect because it uses addition instead of subtraction under the square root. It incorrectly calculates \( \cos A \) using a flawed manipulation of the Pythagorean identity.
• Option b: \( \frac{x}{\sqrt{x^2-1}} \) is incorrect because it is the reciprocal of the correct answer, and incorrectly places x in the numerator and the root in the denominator.
• Option c: \( \frac{\sqrt{x^2-1}}{x} \) is the correct answer, as shown in the explanation.
• Option d: \( \frac{x}{\sqrt{x^2+1}} \) is incorrect for two reasons: it contains a '+' instead of a '-', and the numerator and denominator are swapped from the correct response following algebraic manipulation.

View Answer

Discuss

Which disease is caused due to deficiency of Iodine?

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

Which disease is caused due to deficiency of Iodine?

ARickets

BScurvy

CGoitre

DGrowth retardation

Akhilesh ? Apr 1 '25 at 20:40

correct answer is: option c [Goitre]
Explanation: Goitre is a disease caused by iodine deficiency, leading to the enlargement of the thyroid gland. Iodine is essential for the production of thyroid hormones, which regulate metabolism. When iodine is deficient, the thyroid gland enlarges in an attempt to capture more iodine from the bloodstream, resulting in goitre.

• Option a: Rickets is caused by a deficiency in vitamin D, calcium, or phosphate, not iodine.
• Option b: Scurvy is caused by a deficiency in vitamin C, not iodine.
• Option d: Growth retardation can be caused by various factors including malnutrition and hormonal imbalances, but it's not specifically and directly linked to iodine deficiency in the same way as goitre is. While severe iodine deficiency during development can contribute to impaired growth, goitre is the most direct consequence.

View Answer

Discuss

Read the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements. Statements: 1) All students in my class are active. 2) Rohini is not active. Conclusions: I. Rohini is not a student of my class. II. Rohini must be active.

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

Read the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements. Statements: 1) All students in my class are active. 2) Rohini is not active. Conclusions: I. Rohini is not a student of my class. II. Rohini must be active.

ABoth conclusions I and II follow.

BOnly conclusion I follows.

COnly conclusion II follows.

DNeither conclusion I nor II follows.

Akhilesh ? Apr 1 '25 at 20:40

correct answer is: option b : Only conclusion I follows.
Explanation: The first statement indicates that all students in the class possess the characteristic of being "active." The second statement says Rohini is not active. Conclusion I logically follows because if all students in the class are active, and Rohini is not active, then Rohini cannot be a student in the class. Conclusion II is incorrect because the premise states that Rohini is *not* active.

• Option a: Both conclusions I and II do not follow simultaneously. Conclusion II contradicts the given statement that Rohini is not active.
• Option b: This option correctly states that only conclusion I follows logically from the statements.
• Option c: Conclusion II is incorrect as it contradicts the provided statement that Rohini is not active.
• Option d: Conclusion I logically follows from the statements; therefore, this option is incorrect.

View Answer

Discuss

If x + y = 25 and xy = 35, then 1/x + 1/y =?

Report

Report an issue

Name

Email

Message

Submit

Cancel

RRB NTPC Exam 27 Jan 2021 click here to view all questions

If x + y = 25 and xy = 35, then 1/x + 1/y =?

A$$ \frac{\sqrt{57}}{57} $$

B$$ \frac{7}{5} $$

C$$ \frac{5}{7} $$

D$$ \frac{\sqrt{75}}{75} $$

Akhilesh ? Apr 3 '25 at 21:12

correct answer is: \(\frac{5}{7}\)
Explanation: To find \( \frac{1}{x} + \frac{1}{y} \), we use the identity \( \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} \) Given \( x + y = 25 \) and \( xy = 35 \), we substitute these values into the equation: \[ \frac{1}{x} + \frac{1}{y} = \frac{25}{35} = \frac{5}{7} \] Thus, the correct answer is \( \frac{5}{7} \)

• OPTION A: Incorrect. \( \frac{\sqrt{57}}{57} \) does not simplify to the correct value.
• OPTION B: Incorrect. \( \frac{7}{5} \) is the reciprocal of the correct answer.
• OPTION C: Correct. \( \frac{5}{7} \) matches the derived result.
• OPTION D: Incorrect. \( \frac{\sqrt{75}}{75} \) simplifies to \( \frac{\sqrt{3}}{15} \), which is not the correct value.

View Answer

Discuss