MCQ 1011 Mark
Solve : $m - 2 = 3$
Answer$m - 2 = 3$
$\Rightarrow m = 3 + 2 = 5$
View full question & answer→MCQ 1021 Mark
Perimeter of the square, whose each side is $‘n’$ $cm$ is.
View full question & answer→MCQ 1031 Mark
The expression for ‘ $1$ added to $-p’$ is.
- ✓
$-p + 1$
- B
$-p - 1$
- C
$p + 1$
- D
$p - 1$
AnswerCorrect option: A. $-p + 1$
$-p + 1$
View full question & answer→MCQ 1041 Mark
The rule, which gives the number of matchsticks required to make the matchstick pattern S, is.
MCQ 1051 Mark
Who is the father of algebra?
Answeral-Khwarizmi is the father of Algebra.
View full question & answer→MCQ 1061 Mark
If $\text{A}=\pi(\text{R}^2-\text{r}^2)$ than R is equal to.
- A
$\sqrt{\frac{\text{A}-\pi\text{r}^2}{\pi}}$
- ✓
$\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$
- C
$\sqrt{\frac{\text{r}^2\pi-\text{A}}{\pi}}$
- D
$\sqrt{\frac{\text{r}^2\pi-\text{A}}{\text{r}}}$
AnswerCorrect option: B. $\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$
Given, $\text{A}=\pi(\text{R}^2-\text{r}^2)$
Therefore $\text{A}=\pi\text{R}^2-\pi\text{r}^2\Rightarrow\text{A}+\pi\text{r}^2=\pi\text{R}^2$
$\Rightarrow\text{R}^2={\frac{\text{A}+\pi\text{r}^2}{\pi}}$
$\Rightarrow\text{R}=\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$
View full question & answer→MCQ 1071 Mark
If the point $(2, -3)$ lies on $kx^2 - 3y^2 + 2x + y - 2 = 0$ then $k$ is equal to
- A
$\frac{1}{7}$
- B
$16$
- ✓
$7$
- D
$12$
AnswerAs the point lies on the given line, it should satisfy the equation of the line, if we substitute $x = 2$ and $y = -3$ in it.
So, $k(2)^2 3(-3)^2 + 2(2) - 32 = 0$
$\Rightarrow 4k - 27 + 4 - 3 - 2 = 0$
$4k = 28$
$k = 7$
View full question & answer→MCQ 1081 Mark
If $2x^2y$ and $3xy^2$ denote the length and breadth of a rectangle, the its area is:
- A
$6xy$
- B
$6x^2y^2$
- ✓
$6x^3y^3$
- D
$x^3y^3$
AnswerCorrect option: C. $6x^3y^3$
Area of the rectangle = Length $\times $ Breadth,
$= 2x^2y \times 3xy^2$
$= 6x^3y^3$
View full question & answer→MCQ 1091 Mark
If Apala’s present age is $x$ years, what will be her age in years after $20$ years from now?
AnswerCorrect option: A. $\text{x}+20$
$\text{x}+20$
View full question & answer→MCQ 1101 Mark
$a^2b^3 × 2ab^2$ is equal to:
- A
$2a^3b^4$
- ✓
$2a^3b^5$
- C
$2ab$
- D
$a^3b^5$
AnswerCorrect option: B. $2a^3b^5$
$a^2b^3 \times 2ab^2$
$= 2a^2 \times a \times b^3 \times b^2$
$= 2a^3b^5$
View full question & answer→MCQ 1111 Mark
- A
A symbol that takes a fixed numerical value.
- ✓
A symbol that takes various numerical value.
- C
A symbol some time fixed and some time variable.
- D
AnswerCorrect option: B. A symbol that takes various numerical value.
A variable is a symbol or letter, such as $x$ or $y$, that represents a value.
In algebraic equations, the value of one variable is often dependent on the value of
another. Hence its a symbol that takes various numerical values.
e.g. in the polynomial $x+5, x$ is a variable.
View full question & answer→MCQ 1121 Mark
The expression for $‘p$ divided by $2’$ is.
AnswerCorrect option: A. $\big(\frac{\text{p}}{2}\big)$
$\big(\frac{\text{p}}{2}\big)$
View full question & answer→MCQ 1131 Mark
Which of the following terms contain maximum number of variables?
- A
$3xy$
- B
$5x^3$
- C
$8yz$
- ✓
$xyz$
AnswerOption $(d)$ contains the variables $x, y$ and $z$.
View full question & answer→MCQ 1141 Mark
Mark the correct alternative in the following question:
Thrice x added to y squared is written as:
- A
$3xy^2$
- B
$x^2 + y$
- C
$x + y^2$
- ✓
$3x + y^2$
AnswerCorrect option: D. $3x + y^2$
As, thrice of $x = 3x$
And, the square of $y = y^2$
So, the sum of the thrice of $x$ and square of $y = 3x + y^2$
View full question & answer→MCQ 1151 Mark
Solve: $\big(\frac{1}{2}\big)+5=7$
Answer$\big(\frac{1}{2}\big)+5=7$
$\Rightarrow\big(\frac{1}{2}\big)+5=7-5-2$
$\Rightarrow\text{l}=2\times2=4$
View full question & answer→MCQ 1161 Mark
Classify the following polynomial as polynomial in one variable, two variables etc. $x^2 - 2xy + y62 + 1$
AnswerThere are two variables in the given equation, i.e. $x$ and $yy$ while $1$ is a constant.
View full question & answer→MCQ 1171 Mark
Solve: $7u = 21$
View full question & answer→MCQ 1181 Mark
Mark the correct alternative in the following question:
$x^2 × 2y^3 × 5x^3y^2$ is equal to:
- A
$10x^2y^5$
- B
$10x^5y^2$
- ✓
$10x^5y^5$
- D
$x^5y^5$
AnswerCorrect option: C. $10x^5y^5$
$x^2 \times 2y^3 \times 5x^3y^2$
$= (2 \times 5) \times (x^2 \times x^3) \times (y^3 \times y^2)$
$= 10 \times x^{2 + 3} \times y^{3 + 2}$
$= 10x^5y^5$
View full question & answer→MCQ 1191 Mark
Mark $(\checkmark)$ against the correct answer in the following:
By how much does I exceed $2x - 3y - 4$?
- A
$2x - 3y - 5$
- B
$2x - 3y - 3$
- ✓
$5 - 2x + 3y$
- D
AnswerCorrect option: C. $5 - 2x + 3y$
$1$ exceeds $2x - 3y - 4.$
$\therefore$ $1 - (2x - 3y - 4) = 1 - 2x + 3y + 4$
$= 5 - 2x + 3y$
$\therefore$ $1$ exceeds $2x - 3y - 4$ by $5 - 2x + 3y$
View full question & answer→MCQ 1201 Mark
The side of a regular pentagon is $l$. Its perimeter is.
View full question & answer→MCQ 1211 Mark
The variable in the polynomial $z^3 + 2z^2 + 5z + 1$ is
AnswerThe value of the polynomial changes as the variable changes. Hence, $z$ is the variable in the polynomial.
View full question & answer→MCQ 1221 Mark
Find the number of variables in the expression:
$3x^2 + 25xy + 7x^2 + 5y^2 + z^2$
AnswerThe variables are $x, y$ and $z$
View full question & answer→MCQ 1231 Mark
Solve: $k - 3 = 3$
View full question & answer→MCQ 1241 Mark
$10 - x$ means:
- A
$10$ is subtracted $x$ times.
- B
$x$ is subtracted $10$ times.
- ✓
$x$ is subtracted from $10.$
- D
$10$ is subtracted from $x.$
AnswerCorrect option: C. $x$ is subtracted from $10.$
$10 - x$ means $x$ is subtracted from $10$.
Hence, $(c)$ is correct option.
View full question & answer→MCQ 1251 Mark
If $x^2 - 11x + 1 = 0$ then value of $\text{x}+\frac{1}{\text{x}}$ is.
Answer$\therefore\text{x}^2+1=3\text{x}\frac{\text{x}^2+1}{\text{x}}=\frac{11\text{x}}{\text{x}}$
$\Rightarrow\text{x}^2+1=3$
View full question & answer→MCQ 1261 Mark
$4a^2b^3 × 3ab^2 × 5a^3$b is equal to:
- A
$60a^3b^5$
- B
$60a^6b^5$
- ✓
$60a^6b^6$
- D
$a^6b^6$
AnswerCorrect option: C. $60a^6b^6$
$4a^2b^3 \times 3ab^2 \times 5a^3b$
$= 4 \times 3 \times 5 \times a^2 \times a \times a^3 \times b^3 \times b^2 \times b$
$= 60a^6b^6$
View full question & answer→MCQ 1271 Mark
An important development in algebra in the $16th$ century was the
- ✓
Introduction of unknown symbols
- B
- C
Introduction to exponents
- D
AnswerCorrect option: A. Introduction of unknown symbols
An important development in algebra in the $16th$ century was the introduction to unknown symbols.
View full question & answer→MCQ 1281 Mark
Which one is the constant term of $4x^3 - 3x^2 + 2x - 5$
AnswerGeneral equation is $ax^3+ bx^2 + cx + d$ where $d$ is constant term
so in given equation,
$4x^3 - 3x^2 + 2x - 5$
Constant term is$ -5$
View full question & answer→MCQ 1291 Mark
$9$ taken away from the sum of $x$ and $y$ is:
AnswerCorrect option: A. $\text{x}+\text{y}-9$
$\text{x}+\text{y}-9$
View full question & answer→MCQ 1301 Mark
If $x$ takes the value $2$, then the value of $x + 10$ is:
AnswerGiven, expression $= x + 10$
On substituting $x = 2$, we get $x + 10 = 2 + 10 = 12$
Hence, $(b)$ is correct option.
View full question & answer→MCQ 1311 Mark
The expression for $‘1$ added top’ is.
- ✓
$P + 1$
- B
$p - 1$
- C
$1 - p$
- D
$-1 - P$
AnswerCorrect option: A. $P + 1$
$P + 1$
View full question & answer→MCQ 1321 Mark
Mark the correct alternative in the following question:
$2x^2 \times 3xy^2 \times 4x^3y^5$ is equal to:
- A
$24x^6y^6$
- ✓
$24x^6y^7$
- C
$24x^7y^6$
- D
$24x^7y^7$
AnswerCorrect option: B. $24x^6y^7$
$2x^2 \times 3xy^2 \times 4x^3y^5$
$= (2 \times 3 \times 4) \times (x^2 \times x \times x^3) \times (y^2 \times y^5)$
$= 24x^6y^7$
View full question & answer→MCQ 1331 Mark
For any two integers $x$ and $y$, which of the following suggests that operation of addition is commutative?
AnswerCorrect option: A. $x + y = y + x$
Let $a$ and $b$ be two integers, then in commutative property
$a + b = b + a$
Here, $x$ and $y$ are integers.
Then, $x + y = y + x$
Hence, $(a)$ is correct option.
View full question & answer→MCQ 1341 Mark
Find the constant in the polynomial $y^3 + y^2 + y$
AnswerThe terms $y^3, y^2$ and y are not constants.
Therefore, there are no constants in the given polynomial.
View full question & answer→MCQ 1351 Mark
Solve: $p + 1 = 2$
View full question & answer→MCQ 1361 Mark
Give expression for: “ $5$ times of $‘y’$ to which $3$ is added”.
- ✓
$5y + 3$
- B
$5y - 5$
- C
$5y - 3$
- D
AnswerCorrect option: A. $5y + 3$
$5y + 3$
View full question & answer→MCQ 1371 Mark
Mark $(\checkmark)$ against the correct answer in the following:
What must be added to $5x^3 - 2x^2 + 6x + 7$ to make the sum $x^3 + 3x^2 - x + 1?$
- A
$4x^3 - 5x^2 + 7x + 6$
- ✓
$-4x^3 + 5x^2 - 7x - 6$
- C
$4x^3 + 5x^2 - 7x + 6$
- D
AnswerCorrect option: B. $-4x^3 + 5x^2 - 7x - 6$
In order to find what must be added, we subtract $(5x^3 - 2x^2 + 6x + 7)$ from $(x^3 + 3x^2 - x + 1)$
$\Rightarrow (x^3 + 3x^2 - x + 1) - ( 5x^3 - 2x^2 + 6x + 7)$
$\Rightarrow x^3 + 3x^2 - x + 1 - 5x^3 + 2x^2 - 6x - 7$
$\Rightarrow x^3 - 5x^3+ 3x^2+ 2x^2- x - 6x+ 1 - 7$
$\Rightarrow -4x^3+ 5x^2 - 7x - 6$
View full question & answer→MCQ 1381 Mark
The side of a square is l. Its perimeter is.
MCQ 1391 Mark
How many constants are there in the expression $3x^2 + y?$
AnswerBoth the terms of the given expression have either $x$ or$ y$ as the variable. Constants are terms without variables.
Hence, there are no constants.
View full question & answer→MCQ 1401 Mark
The quotient of $x$ by $3$ is multiplied by $y$ is written as:
- A
$\frac{\text{x}}{3\text{y}}$
- B
$\frac{3\text{x}}{\text{y}}$
- C
$\frac{3\text{y}}{\text{x}}$
- ✓
$\frac{\text{xy}}{3}$
AnswerCorrect option: D. $\frac{\text{xy}}{3}$
$\frac{\text{x}}{3}\times\text{y}=\frac{\text{xy}}{3}$
View full question & answer→MCQ 1411 Mark
The expression obtained when $x$ is multipled by $2$ and then subtracted from $3$ is:
- A
$2x - 3$
- B
$2x + 3$
- ✓
$3 - 2x$
- D
$3x - 2$
AnswerCorrect option: C. $3 - 2x$
First $x$ is multiplied by $2$.
$2 \times x - 2x$
Now, $2x$ is subtracted from $3 = 3 - 2x$
Hence, $(c)$ is correct option.
View full question & answer→MCQ 1421 Mark
Mark $(\checkmark)$ against the correct answer in the following:
$2x - [3y - {2x - (y - x)}] = ?$
- ✓
$5x - 4y$
- B
$4y - 5x$
- C
$5y - 4x$
- D
$4x - 5y$
AnswerCorrect option: A. $5x - 4y$
$2x - [3y - {2x - (y - x)}]$
$= 2x - [3y - {2x - y + x}]$
$= 2x - [3y - {3x - y}]$
$= 2x - [3y - 3x + y]$
$= 2x - [4y - 3x]$
$= 2x - 4y + 3x$
$= 5x - 4y$
View full question & answer→MCQ 1431 Mark
The rule, which gives the number of matchsticks required to make the matchstick pattern $C$, is.
View full question & answer→MCQ 1441 Mark
What is the literal meaning of algebra?
AnswerThe word Algebra literally means the re-union of broken parts.
View full question & answer→MCQ 1451 Mark
If $\text{x}+\frac{\text{a}}{\text{x}}$ then the value $\frac{\text{x}^2+\text{bx}+\text{a}}{\text{bx}^2-\text{x}^3}$
- A
$\frac{6\text{b}}{\text{a}}$
- B
$\frac{5\text{b}}{\text{a}}$
- ✓
$\frac{2\text{b}}{\text{a}}$
- D
$\frac{4\text{b}}{\text{a}}$
AnswerCorrect option: C. $\frac{2\text{b}}{\text{a}}$
Given $\text{x}+\frac{\text{a}}{\text{x}}=\text{b}$ Multiply by $x$ both sides
$x^2+ a = bx$
$\Rightarrow x^2 - bx + a = 0$
So,
$\frac{\text{x}^2+\text{bx}+\text{a}}{\text{bx}^2-\text{x}^3}$
$=\frac{\text{x}^2-\text{bx}+\text{a}+\text{2bx}}{\text{-x}(\text{x}^2-\text{bx})}$
$=\frac{0+\text{2bx}}{\text{-x}(\text{- a})}=\frac{\text{2bx}}{\text{ax}}$
$=\frac{\text{2b}}{\text{a}}$
View full question & answer→MCQ 1461 Mark
The sum of the reciprocals of $\frac{\text{x}+3}{\text{x}^2+1}$ and $\frac{\text{x}^2-9}{\text{x}^2+3}$
AnswerCorrect option: B. $\frac{\text{x}^2-2\text{x}^2+\text{x}}{\text{x}^2-9}$
Reciprocals will be $\frac{\text{x}^2+1}{\text{x}+3},\frac{\text{x}^2+3}{\text{x}^2-9}$
Their sum will be
$\frac{\text{x}^2+1}{\text{x}+3},\frac{\text{x}^2+3}{\text{x}^2-9}$
$=\frac{(\text{x}+3)(\text{x}^2+1)+\text{x}^2+3}{\text{x}^2-9}$
$=\frac{\text{x}^2+\text{x}-\text{3x}^2-3+\text{x}^2+3}{\text{x}^2-9}$
$=\frac{\text{x}^2-\text{2x}^2+\text{x}}{\text{x}^2-9}$
View full question & answer→MCQ 1471 Mark
Kanta has $p$ pencils in her box. She puts $q$ more pencils in the box. The total number of pencils with her are:
AnswerCorrect option: A. $p + q$
Given, pencils in Kanta’s box $= p$
When q more pencils are put in the box, then total number of pencils $= p + q$
Hence, $(a)$ is correct option.
View full question & answer→MCQ 1481 Mark
Which of the following equations does not have a solution in integers?
- A
$x + 1 = 1$
- B
$x - 1 = 3$
- ✓
$2x + 1 = 6$
- D
$1 - x = 5$
AnswerCorrect option: C. $2x + 1 = 6$
We know that, integers are
$-4, -3, -2, -1, 0, 1, 2, 3, 4$
Now, we check the equations.
For option $(a).$
$x + 1 = 1$
$\Rightarrow x = 1 - 1$ [transposing $+1$ to $RHS$]
$\Rightarrow x = 0,$ which is an integer.
For option $(b)$.
$x - 1 = 3$
$\Rightarrow x = 3 + 1$ [transposing $-1$ to $RHS$]
$\Rightarrow x = 4,$ which is an integer.
For option $(c)$,
$2x + 1 = 6$
$\Rightarrow 2x = 6 - 1$ [transposing $+1$ to $RHS$]
$\Rightarrow 2x = 5$
$\Rightarrow\frac{2\text{x}}{2}=\frac{5}{2}$ [dividing both sides by $2$]
$\Rightarrow\text{x}=\frac{5}{2},$ which is not an integer.
For option $(d)$.
$1 - x = 5$
$\Rightarrow -x = 5 - 1$ [transposing $+1$ to $RHS]$
$\Rightarrow -x = 4$
$\Rightarrow x = -4$, which is an integer. [dividing both sides by $-1$]
Hence, $(c)$ is correct option.
View full question & answer→