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

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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.

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In the following question, which mathematical operators can be used so that the expression will become correct? 8 * 5 * 27 * 3 * 16

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

In the following question, which mathematical operators can be used so that the expression will become correct? 8 * 5 * 27 * 3 * 16

A×,=,−,÷

B $$\text{=+,÷,=,−}$$

C×,=,−+

D $$\text{+,×,−,=}$$

Akhilesh ? Apr 3 '25 at 19:34

correct answer is: OPTION c: ×,=,−+
Explanation: The correct operators are ×, =, −, and +. Here's how they can be used to create a valid equation:
- 8 × 5 = 40
- 27 − 3 = 24
- 40 + 24 = 64 This shows how the operators can be applied to make the expression correct.

• OPTION A: ×, =, −, ÷
  - Incorrect, as it doesn't balance the equation properly.
• OPTION B: =, +, ÷, −
  - Incorrect, as it doesn't form a valid equation.
• OPTION C: ×, =, −, +
  - Correct, as shown in the explanation.
• OPTION D: +, ×, −, =
  - Incorrect, as it doesn't form a valid equation.

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The quotient in a division sum is 403. The divisor is 100 and the remainder is 58. The dividend is _

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RRB ASM Exam (Bhubaneshwar) 2009 click here to view all questions

The quotient in a division sum is 403. The divisor is 100 and the remainder is 58. The dividend is _

A40458

B34058

C43058

D40358

maheshguru ? Jan 12 '2019 at 20:20

Answer is : D [40358]

Explanation:

Dividend = (divisor * quotient) + remainder

dividend = 403*100+58

= 40358

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561204 x .58 =? x 55555

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RRB ASM Exam (Bhubaneshwar) 2009 click here to view all questions

561204 x .58 =? x 55555

A606

B646

C586

D716

usest ? Jan 3 '2019 at 21:16

Correct Answer : C [586]

Explanation:

$561204 \times 58 = ? \times 55555$

$? = \frac{561204 \times 58}{55555}$

$10.x \times 58 \equiv 580$

$= 586$

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(9321 + 5406 ÷ 1001) (498 + 929 + 660) =?

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RRB ASM Exam (Bhubaneshwar) 2009 click here to view all questions

$$\left(9321 + 5406 + 1001\right) \div \left(498 + 929 + 660\right) = ?$$

A13.5

B4.5

C16.5

D7.5

gaurish ? Jan 2 '2019 at 21:10

Answer is: D [7.5]

Explanation:

$? = \left(9321 + 5406 + 1001\right) \div \left(498 + 929 + 660\right)$

=$15728 \div 2087 = 7.5$

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