Mathematics Part1

Online MCQs about First Year Mathematics Part1 and Part2, Intermediate Mathematics Part1 multiple choice questions with answers

MCQs Quadratic Equation 1

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First-year pre-engineering mathematics multiple choice questions online examination. The quiz is about the MCQS Quadratic Equation online examination. The quiz will help First-year (Intermediate) Pre-Engineering mathematics students prepare for the examination. There are 20 questions with answers. Let us start with the Online MCQs Quadratic Equation Quiz.

First-year (Intermediate) Pre-Engineering mathematics examination preparation.
Pakistan All boards Pre-Engineering Mathematics MCQs Online Test

1. To convert $ 4^{1+x} + 4^{1-x} =10$ into quadratic, the substitution is

 
 
 
 

2. $16\omega^4 + 16 \omega^8$

 
 
 
 

3. $(-1 + \sqrt{-3})^5 + (-1 – \sqrt{-3})^5$ is equal to

 
 
 
 

4. Solution set of the equation $x^2 – 4x + 4 = 0$ is

 
 
 
 

5. The sum of all four fourth roots of unity is

 
 
 
 

6. The quadratic formula for solving the equation $ax^2 + bx + c =0$ is $(a\ne 0)$

 
 
 
 

7. The sum of all four fourth roots is 16 is

 
 
 
 

8. The sum of all cube roots of 64 is

 
 
 
 

9. The equation in which variable quantity occurs in the exponent is called

 
 
 
 

10. The roots that satisfy the radical free equation but not the radical equation are called

 
 
 
 

11. The complex cube roots of the unit are __________ each other.

 
 
 
 

12. The convert $ax^{2n} + bx^n + c =0 (a\ne 0) $ into quadratic form, the correction substitution

 
 
 
 

13. The equations involving radical expressions of the variable are called

 
 
 
 

14. The product of all four fourth roots of unity is

 
 
 
 

15. The product of all cube roots of $-1$ is

 
 
 
 

16. The product of all four fourth roots of 81 is

 
 
 
 

17. The cube roots of $-1$ are

 
 
 
 

18. The equation $ax^2 + bx + 9 =0$ will be quadratic if

 
 
 
 

19. The equation which remains unchanged if $x$ is replaced by $\frac{1}{x}$, then it is called

 
 
 
 

20. The cube roots of unity are

 
 
 
 

An equation of the form $ax^2 + bx + c = 0$ is called a Quadratic Equation, where $a, b,$ and $c$ are all real numbers and $a\ne0$. This generic form of Quadratic Equations is a second-degree equation in variable $x$.

MCQs Quadratic Equations

MCQs Quadratic Equations with Answers

  • The equation $ax^2 + bx + 9 =0$ will be quadratic if
  • Solution set of the equation $x^2 – 4x + 4 = 0$ is
  • The quadratic formula for solving the equation $ax^2 + bx + c =0$ is $(a\ne 0)$
  • The convert $ax^{2n} + bx^n + c =0 (a\ne 0) $ into quadratic form, the correction substitution
  • The equation in which variable quantity occurs in the exponent is called
  • To convert $ 4^{1+x} + 4^{1-x} =10$ into quadratic, the substitution is
  • The equation which remains unchanged if $x$ is replaced by $\frac{1}{x}$, then it is called
  • The equations involving radical expressions of the variable are called
  • The roots that satisfy the radical free equation but not the radical equation are called
  • The cube roots of unity are
  • The cube roots of $-1$ are
  • The sum of all cube roots of 64 is
  • The product of all cube roots of $-1$ is
  • $16\omega^4 + 16 \omega^8$
  • $(-1 + \sqrt{-3})^5 + (-1 – \sqrt{-3})^5$ is equal to
  • The sum of all four fourth roots of unity is
  • The product of all four fourth roots of unity is
  • The sum of all four fourth roots is 16 is
  • The product of all four fourth roots of 81 is
  • The complex cube roots of the unit are _______ each other

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Matrices and Determinants 1

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The post is about Online MCQS about Matrices and Determinants quiz with answers. The quiz contains 20 multiple-choice questions about matrices and determinants from Chapter 3 of First-Year Mathematics. Let us start with the Matrices and Determinants Quiz.

Please go to Matrices and Determinants 1 to view the test

A matrix is a rectangular array of numbers arranged in a sequence and enclosed in brackets. A matrix is a rectangular array of mathematical elements arranged into rows and columns according to algebraic rules.

Matrices and Determinants

A pair of parentheses $\begin{pmatrix}a&b\\c&d\end{pmatrix}$or a square bracket $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is used to write matrices (plural of matrix). A matrix is usually denoted by capital letters such as $A, B, C,$ and $X, Y,$ and $Z$. The matrices are used to solve the simultaneous equations.

The horizontal lines of elements of a matrix are called rows of the matrix. The vertical lines of elements of a matrix are called the columns of a matrix. The number of rows and columns of a matrix is called the order of the matrix.

Online MCQs Matrices and Determinants

  • A rectangular array of numbers enclosed by a pair of brackets is called a
  • The horizontal lines of numbers in a matrix are called
  • The verticle lines of numbers in a matrix are called
  • If a matrix $A$ has $m$ rows and $n$ column, then order of $A$ is
  • The element $a_{ij}$ of any matrix $A$ is present in
  • Any matrix $A$ is called real if all $a_{ij}$ are
  • If any matrix $A$ has only one row, then it is called
  • If any matrix $A$ has only one column, then it is called
  • If a matrix $A$ has the same number of rows and columns, then Matrix $A$ is called
  • If any Matrix $A$ has different numbers of rows and columns, then matrix $A$ is
  • Any matrix of order $m\times 1$ is called
  • Any matrix of order $1\times n$ is called
  • For the square matrix $A=[a_{ij}]{n\times n}$, the elements $a{11}, a_{22}, \cdots, _{nn}$ are
  • For the matrix $A=[a_{ij}]{n\times n}$, the elements $a{1n}, a_{2n-1}, a_{3n-2}, a_{4n-3}, \cdots, a_{n1}$ form
  • For the square matrix $A=[a_{ij}]$, if all $a_{ij}=0, i\ne j$ and at least one $a_{ii}\ne 0, i=j$, then $A$ matrix is called
  • For the square matrix $A=[a_{ij}]$, if all $a_{ij}=0, i\ne j$ and all $a_{ij}=k$ (non-zero) for $i=j$, then matrix $A$ is called
  • If all off-diagonal elements are zeros and at least one of the leading diagonals is non-zero, then the matrix is called
  • The matrix $[6]$ is
  • If matrix $A$ is of order $m\times n$, then the matrix of order $n\times m$ is called
  • Two matrices $A$ and $B$ are said to be conformable for addition if

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Basic Statistics and Data Analysis

Important MCQs Sequence and Series 2

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This post is about an Online Quiz on sequence and series from First Year Mathematics. A sequence is an ordered set of numbers formed according to some definite rule. Let us start with the Sequence and Series Quiz.

Please go to Important MCQs Sequence and Series 2 to view the test

A sequence can be defined as a function whose domain is a subset of natural numbers. Mathematically, the sequence is denoted by $\{a_n\}$ where $n\in N$.

Some examples of sequence are:

  • $1,2,3,\cdots$
  • $2, 4, 6, 8, \cdots$
  • $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$

The term $a_n$ is called the general term or $n$th term of a sequence. If all numbers of a sequence are real numbers then it is called a real sequence. If the domain of a sequence is a finite set, then the sequence is finite otherwise the sequence is infinite. An infinite sequence has no last term.

If the terms of a sequence follow a certain pattern, then it is called a progression:

  • Arithmetic Progression (AP)
    A sequence $\{a_n\}$ is an Arithmetic Sequence or Arithmetic Progression if the difference $a_n – a_{n-1}$ is the same for all $n \in N$ and $n>1$.
  • Geometric Progression (GP)
    A sequence $\{a_n\}$ in which $\frac{a_n}{a_{n-1}}$ is same non-zero number for al l$n\in N$ and $n>1$ is called Geometric Sequence or Geometric Progression.
  • Harmonic Progression (HP)
    A Harmonic Progression is a sequence of numbers whose reciprocals form an Arithmetic Progression. A general form of Harmonic Progression is $\frac{1}{a_1}, \frac{1}{a_1+d}, \frac{1}{a_1+2d}, \cdots$, where $a_n=\frac{1}{a_1+(n-1)d}$
Sequence and Series

MCQs Sequence and Series with Answers

  • Sequence is also called
  • A sequence is a function whose domain is
  • If all the members of a sequence are real numbers then the sequence is called
  • The symbol used to represent the sequence $a$ is
  • If the domain of a sequence is finite then the sequence is called
  • A sequence in which every term after the first can be obtained by adding a fixed number in the preceding term is called
  • The generl term $a_n$ of an A.P. is
  • If in an A.P. $a_5=13$ and $a_17=49$, then $a_15=?$
  • If $a_{n-2}=3n-11$ then $n$th term will be
  • The sequence $1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \cdots $, then $a_7=?$
  • Which of the following cannot be the term of sequence 17, 13, 9, …
  • If $\frac{1}{a}, \frac{1}{b}$ and D\frac{1}{c}$ are in A.P. then which one is true:
  • Find the number of terms in an A.P. in which $a=3, d=7$, and $a_n=59$
  • The $n$th A.M. between $a$ and $b$ is
  • The A.M. between $1-x+x^2$ and $1+x-x^2$ is
  • If 5, 8 are two A.M. between $a$ and $b$ then $a$ and $b$ are
  • The arithmetic mean between 2+\sqrt{2}$ and $2-\sqrt{2}$ is
  • The sum of the series $-3+(-1)+(1) +3+5 +\cdots+ a_{16}$ is
  • The number of terms of the series $-7+(-5)+(-3)+\cdots$ amount to 65
  • If $S_2, S_3, S_5$ are the sums of $2n, 3n, 5n$ terms of an A.P. then which one is true

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Important MCQS Sequence and Series 1 Class 11

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This post concerns the Online MCQs sequence and series from Mathematics Part I. A sequence is an ordered set of numbers formed according to some definite rule. Let us with MCQs Sequence and Series, mathematics Class 11 Quiz with answers.

Please go to Important MCQS Sequence and Series 1 Class 11 to view the test

A sequence can be defined as a function whose domain is a subset of natural numbers. Mathematically, a sequence is denoted by $\{a_n\}$ where $n\in N$.

Some examples of sequence are:

  • $1,2,3,\cdots$
  • $2, 4, 6, 8, \cdots$
  • $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$
MCQs Sequence and Series Mathematics Class 11

The term $a_n$ is called the general term or $n$th term of a sequence. If all numbers of a sequence are real, then it is called a real sequence. If the domain of a sequence is a finite set, then the sequence is finite otherwise the sequence is infinite. An infinite sequence has no last term.

If the terms of a sequence follow a certain pattern, then it is called a progression:

  • Arithmetic Progression (AP)
    A sequence $\{a_n\}$ is an Arithmetic Sequence or Arithmetic Progression if the difference $a_n – a_{n-1}$ is the same for all $n \in N$ and $n>1$.
  • Geometric Progression (GP)
    A sequence $\{a_n\}$ in which $\frac{a_n}{a_{n-1}}$ is same non-zero number for al l$n\in N$ and $n>1$ is called Geometric Sequence or Geometric Progression.
  • Harmonic Progression (HP)
    A Harmonic Progression is a sequence of numbers whose reciprocals form an Arithmetic Progression. A general form of Harmonic Progression is $\frac{1}{a_1}, \frac{1}{a_1+d}, \frac{1}{a_1+2d}, \cdots$, where $a_n=\frac{1}{a_1+(n-1)d}$
Sequence and Series

MCQs Sequence and Series Mathematics Class 11

  • An arrangement of numbers according to some definite rule is called
  • A sequence is also known as
  • A sequence is a function whose domain is a set of
  • A sequence whose range is R i.e. set of real numbers is called
  • If $a_n={n+(-1)^n}$, then $a_{10}$
  • The last term of an infinite sequence
  • The next term of the sequence $1, 2, 12, 40, \cdots$ is
  • If $a_n-a_n-1=n+1$ and $a_4=14$ then $a_5=$?
  • If $a_n=n\,a_{n-1}$, $a_1=1$ then $a_4=$?
  • A sequence ${a_n}$ in which $a_n-a_n$ is the same number for all $n \in N$, $n>1$, is called
  • The general term of an A.P. is
  • If $a_n=5-3n+2n^2$, then $a_{2n}=$?
  • If $a_{n-2}=3n-11$, then $a_4=$?
  • If $n$th term of an A.P. is $3n-1$ then 10th term is
  • $n$th term of the series $\left(\frac{1}{3}\right)+ \left(\frac{5}{3}\right)^2+\left(\frac{7}{3}\right)^2+\cdots$
  • Arithmetic mean between $c$ and $d$ is
  • If $a_{n-1}, a_n, a_{n+1}$ are in A.P. then $a_n=$?
  • The Arithmetic mean between $\sqrt{2}$ and $3\sqrt{2}$ is
  • The sum of terms of a sequence is called
  • Forth partial sum of the sequence ${n^2}$ is

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