Mathematics · Quantitative Aptitude

Algebra and Arithmetic

406 Questions

Algebra and arithmetic questions cover fundamental mathematical operations, inequalities, and binomial products. They assess core quantitative reasoning skills required for various aptitude tests. Solving these problems strengthens the understanding of number systems and algebraic identities.

Binomial productsLinear inequalitiesLeast common multipleQuadratic equationsInteger properties

Algebra and Arithmetic Questions

Multiple choice statistics time series moving average and variation simple moving average

If one regression coefficient is greater than one, then other will be:

  1. Less than one

  2. More than one

  3. Equal to one

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Both the regression coefficients $(b_{xy},b_{yx})$ must have the same sign. i.e., if one of them is positive other should positive or if one of them is negative other should be negative.

If one regression coefficient is greater than one, then other coefficient should be less than one.

Multiple choice statistics time series moving average and variation simple moving average

The sum of the difference between the actual values of $Y$ and its values obtained from the fitted regression line is always:

  1. Zero

  2. Positive

  3. Negative

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

Let the actual values be $y_1,y_2,...,y_n$

Let the values obtained from the fitted regression analysis be $\hat y_1,\hat y_2,...,\hat y_n$

Since, the values are obtained from the fitted regression line.
Therefore, the actual and obtained values are almost equal.
Therefore, $y_1=\hat y_1$, $y_2=\hat y_2$ , ... , $y_n=\hat y_n$

sum of the difference between the actual and obtained values is $(y_1-\hat y_1)+(y_2-\hat y_2)+...+(y_n-\hat y_n)=0$

Multiple choice mathematics and statistics set language de morgan's law for set theory complement of sets different sets de morgan's law

If $U = \left {x|x\epsilon N, x < 5\right }, A = \left {x|x\epsilon N, x\leq 2\right }$ then $A' =$ __________.

  1. $\left \{1, 2\right \}$
  2. $\left \{1, 2, 3, 4, 5\right \}$
  3. $\left \{3, 4\right \}$
  4. $\left \{3, 4, 5\right \}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$ \cup  = { x|x \in N,x < 5} $

${\rm A} = \left| {x|x \in N,x \leqslant 2} \right|$
then $A' = { 3,4} $
part $C$ is correct answer.

Multiple choice maths four operations whole number operations on the number line whole numbers on number line introduction to multiples and factors

Let $x$ be a real variable, and let $3 < x < 4.$ Which of the following values, $x$ might have?

  1. $-3.1$
  2. $\sqrt{11}$
  3. $\sqrt{\dfrac{10}{11}}$
  4. $4.1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$x$ can have any values between $3$ and $4$ so it can be rational or irrational. 
option $c$=$0.9$  and options $A$ and $D$ are outside the given range.
Hence, correct answer is option $B=\sqrt11=3.3$.

Multiple choice maths cube and cube root estimation of cube root estimation of cube roots cubes and cube roots

If $x = \sqrt [3]{a + \sqrt {a^{2} - b^{3}}} + \sqrt [3]{a - \sqrt {a^{2} - b^{3}}}$ then $x^{3} + 3bx = $ ____________.

  1. $2a$
  2. $2b$
  3. $3a$
  4. $4a$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,
$x = \sqrt [3]{a + \sqrt {a^{2} - b^{3}}} + \sqrt [3]{a - \sqrt {a^{2} - b^{3}}}$.......(1).
Now cubing both sides we get,
$x^3=a+\sqrt{a^2-b^3}+a-\sqrt{a^2-b^3}-3$$\sqrt [3]{a + \sqrt {a^{2} - b^{3}}}  \sqrt [3]{a - \sqrt {a^{2} - b^{3}}}$$( \sqrt [3]{a + \sqrt {a^{2} - b^{3}}} + \sqrt [3]{a - \sqrt {a^{2} - b^{3}}})$
or, $x^3=2a-3bx$ [ Using (1)and $ (\sqrt [3]{a + \sqrt {a^{2} - b^{3}}})(\sqrt [3]{a - \sqrt {a^{2} - b^{3}}})=\sqrt[3]{a^2-(a^2-b^3)}=b$]
or, $x^3+3bx=2a$.
Multiple choice business maths limits and continuity of a function graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

If $|z-1|+ |z+3| \le 8$, then the range of values of $|z-4|$ is

  1. $(0, 7)$
  2. $(1,8)$
  3. $[1,9]$
  4. $[2,5]$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation |z-1| + |z+3| = 8 represents an ellipse with foci at 1 and -3. The distance between foci is 4. The major axis 2a = 8, so a = 4. The center is at -1. The vertices are at -1 +/- 4, i.e., 3 and -5. The range of |z-4| is the distance from 4 to the ellipse. The minimum distance is |3-4| = 1 and the maximum is |-5-4| = 9.

Multiple choice lines in planes applications of determinants inverse of a matrix and linear equations matrix algebra maths

If $\mathrm{a}\neq b\neq \mathrm{c}$ and if $ax+by+\mathrm{c}=0\  bx+cy+\mathrm{a}=0$ and $cx+ay+b=0$ are concurrent, 

then find the value of 
$ 2^{\mathrm{a}^{2}b^{-1}\mathrm{c}^{-1}}2^{b^{2}\mathrm{c}^{-1}\mathrm{a}^{-1}}2^{\mathrm{c}^{2}\mathrm{a}^{-1}b^{-1}}$

  1. 1

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the lines to be concurrent, the determinant of the coefficients must be zero: |a, b, c; b, c, a; c, a, b| = 0. This expands to -(a^3 + b^3 + c^3 - 3abc) = 0, implying a+b+c=0 or a=b=c. Given a!=b!=c, we must have a+b+c=0. The exponent is (a^2/bc + b^2/ca + c^2/ab) = (a^3+b^3+c^3)/abc. Since a^3+b^3+c^3 = 3abc when a+b+c=0, the exponent is 3. Thus, 2^3 = 8.

Multiple choice maths multiply and divide division trick division division of numbers

Let $Q = \dfrac{x}{y}$ where $x$ and $y$ are real numbers. If both $x$ and $y$ are increased equally then

  1. $Q$ will increase
  2. $Q$ will decrease
  3. $Q$ will remain the same

  4. none of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If x/y = 1, adding 1 to both gives 2/2 = 1 (no change). If x/y < 1, adding a constant increases the ratio. If x/y > 1, adding a constant decreases the ratio. No single outcome is universal.

Multiple choice national income identity for open economy open economy macroeconomics determination of income and employment economics

Coefficient of correlation will be always ______________.

  1. More than 0

  2. More than-1

  3. Less than-1

  4. Between-1 and + 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Pearson correlation coefficient, denoted by r, measures the strength and direction of a linear relationship between two variables. Its mathematical range is strictly defined as being between -1 and +1 inclusive.

Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

$|z-4| < |z-2|$ represents the region given by?

  1. $Re(z) > 3$
  2. $Re(z) < 0$
  3. $Re(z) > 2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

|z-4| < |z-2| represents the set of points closer to 4 than to 2 on the complex plane. This is the half-plane to the right of the perpendicular bisector of the segment connecting 2 and 4, which is the line Re(z) = 3.

Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

If $a, b \notin R$, then $|e^{a + ib}| $ is equal to


  1. $e^a$
  2. $e^b$
  3. $1$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$|e^{a + ib}| = |e^a . e^{ib}|$


            $= |e^a . (\cos b + i \sin b)|$


            $= e^a |(\cos b + i \sin b)|$

            $= e^a . \sqrt{(\cos b)^2 + (\sin b)^2}$

            $= e^a . \sqrt{1}$

            $= e^a$

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

For rational numbers, $x$ and $y,$ if $x > y,$ then which of the following is always a positive rational number?

  1. $ y - xy$
  2. $ xy-x$
  3. $ y-x$
  4. $ x- y $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
If $x>y$

$y-xy\rightarrow $ can be both positive and negative.

Example coside $x>1$ & $y>0$

$\left(y-xy\right)<0$

$xy-x\rightarrow $ can be both positive and negative 

$y-x\rightarrow $ always negative

$\boxed {x-y\rightarrow always\ positive\ since\ x>y}$