Mathematics · Quantitative Aptitude

Surds and Indices

408 Questions

Surds and indices questions focus on evaluating square roots, cube roots, and fractional exponents. These topics are a core part of the quantitative aptitude section in many competitive exams. Practicing these problems builds speed and accuracy for solving numerical equations.

Square roots evaluationCube roots calculationExponents and powersFractional exponentsSurds multiplication

Surds and Indices Questions

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

$\left(\large{\frac{-5}{3}}\right)^5$ $\div$ $\left(\large{\frac{-5}{3}}\right)^{7}$

  1. $\large{\frac{25}{9}}$
  2. $\large{\frac{9}{25}}$
  3. $\large{\frac{16}{25}}$
  4. $\large{\frac{25}{16}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\left(\large{\frac{-5}{3}}\right)^5$ $\div$ $\left(\large{\frac{-5}{3}}\right)^{7}$


$=-\left(\large{\frac{5}{3}}\right)^5$ $\times$ $-\left(\large{\frac{3}{5}}\right)^{7}$


$=\left(\dfrac{3}{5}\right)^2$

$=\dfrac{9}{25}$.

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

Evaluate: $\dfrac {\left(\dfrac {-3}{5}\right)^{3} \times \left(\dfrac {9}{25}\right)^{2} \times \left(\dfrac {-18}{125}\right)^{o}}{\left(\dfrac {-27}{125}\right) \times \left(\dfrac {-3}{5}\right)}$

  1. $\dfrac{27}{125}$
  2. $-\dfrac{27}{125}$
  3. $\dfrac{64}{125}$
  4. $-\dfrac{64}{125}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac {\left(\dfrac {-3}{5}\right)^{3} \times \left(\dfrac {9}{25}\right)^{2} \times \left(\dfrac {-18}{125}\right)^{0}}{\left(\dfrac {-27}{125}\right) \times \left(\dfrac {-3}{5}\right)}=\dfrac{\dfrac{-3^3\times 3^4\times 1}{5^3\times 5^4\times 1}}{\dfrac{3^3\times 3}{5^3\times 5}}=-\dfrac{3^{7-4}}{5^{7-4}}=-\dfrac{27}{125}$

Multiple choice maths complex numbers and linear inequations identities of complex numbers powers of imaginary unit i algebra of complex numbers

If $i^{2} = -1$, calculate the value of $3i^{2} + i^{3} - i^{4}$.

  1. $-4 - i$
  2. $-2 - i$
  3. $2 + i$
  4. $4 + i$
  5. $6 + 2i$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$i$ is an imaginary number whose value is $\sqrt { -1 } $

So, $i^2=-1$
$i^3=i^2*i=-1*i=-i$
$i^4=(i^2)^2={(-1)}^2=1$
So the value of $3i^2+i^3-i^4$ is
$\Rightarrow 3\times (-1)+(-i)-(1)$
$\Rightarrow -3-i-1=-4-i$

Multiple choice maths complex numbers and linear inequations identities of complex numbers powers of imaginary unit i algebra of complex numbers

The value of $( 1 + i ) ^ { 4 } + ( 1 - i ) ^ { 4 }$ is

  1. $8$
  2. $8 i$
  3. $-8$
  4. $32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$(1+i)^4+(1-i)^4$


$\Rightarrow$  $[(1+i)^2]^2+[(1-i)^2]^2$

We know, $(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=^2-2ab+b^2$

$\Rightarrow$  $[1+2i+i^2]^2+[1-2i+i^2]^2$      

$\Rightarrow$  $[1+2i-1]^2+[1-2i-1]^2$                       [ $i^2=-1$ ]

$\Rightarrow$  $(2i)^2+(-2i)^2$

$\Rightarrow$  $4i^2+4i^2$

$\Rightarrow$  $-4-4$

$\Rightarrow$  $-8$

$\therefore$   $(1+i)^4+(1-i)^4=-8$