Quantitative Aptitude

Number System and Simplification

548 Questions

Number system and simplification questions assess mathematical proficiency in handling fractions, decimals, and complex algebraic expressions. Test takers must simplify surds, calculate reciprocals, and solve intricate number pattern equations. This foundational quantitative aptitude topic is critical for achieving high scores in SSC and banking exams.

Fraction simplificationDecimal operationsSurds and indicesPercentage calculationsComplex number algebra

Number System and Simplification Questions

Multiple choice

What is the general formula for the Madhava series for pi?

  1. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
  2. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
  3. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
  4. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

The general formula for the Madhava series for pi is $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$.

Multiple choice

What is the value of the following expression: (\frac{1}{2} + \frac{1}{3} + \frac{1}{6})?

  1. \(\frac{11}{6}\)
  2. \(\frac{5}{6}\)
  3. \(\frac{7}{6}\)
  4. \(\frac{9}{6}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the value of the expression, we can add the fractions as follows: (\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{6}{6} = \frac{11}{6}).

Multiple choice

What is the general formula for the Madhava series for the arctangent function?

  1. $$arctan(x) = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$
  2. $$arctan(x) = x + \frac{x^3}{3} + \frac{x^5}{5} + \frac{x^7}{7} + \cdots$$
  3. $$arctan(x) = x - \frac{x^3}{3} - \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$
  4. $$arctan(x) = x + \frac{x^3}{3} - \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The general formula for the Madhava series for the arctangent function is $$arctan(x) = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots$$. This series converges for all values of x between -1 and 1.

Multiple choice

What is the general formula for the Madhava series for pi?

  1. $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
  2. $$\pi = 4 \left(1 + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \cdots\right)$$
  3. $$\pi = 4 \left(1 - \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
  4. $$\pi = 4 \left(1 + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \cdots\right)$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The general formula for the Madhava series for pi is $$\pi = 4 \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots\right)$$. This series converges very slowly, but it was the first series expansion for pi to be discovered.

Multiple choice

The equation (\frac{a}{b} = \frac{c}{d}) is known as:

  1. Pythagorean theorem

  2. Euler's formula

  3. Cross-multiplication rule

  4. Law of sines
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation (\frac{a}{b} = \frac{c}{d}) is known as the cross-multiplication rule, which is used to solve proportions.

Multiple choice

In modular arithmetic, what is the value of 7^3 mod 5?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Modular arithmetic involves calculations with integers modulo a fixed integer. In this case, we are working modulo 5. To find 7^3 mod 5, we can calculate 7^3 = 343, and then divide it by 5 to get the remainder. 343 รท 5 = 68 remainder 3. Therefore, 7^3 mod 5 = 3.

Multiple choice

What is the value of the Gamma function at (\frac{1}{2})?

  1. $\sqrt{\pi}$
  2. $\frac{1}{\sqrt{\pi}}$
  3. $\frac{\pi}{2}$
  4. $\frac{2}{\pi}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Gamma function at (\frac{1}{2}) is equal to (\sqrt{\pi}).

Multiple choice

What is the role of mathematics in the practice of yoga?

  1. It helps practitioners understand the body's energy systems.

  2. It is used to create sequences of poses that promote balance and harmony.

  3. It is used to calculate the duration of meditation sessions.

  4. It is used to design yoga mats and props.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Mathematics plays a multifaceted role in the practice of yoga, including helping practitioners understand the body's energy systems, creating sequences of poses that promote balance and harmony, calculating the duration of meditation sessions, and designing yoga mats and props.