MCQ 11 Mark
If $x < -1,$ then $x^2$
Answer$x < -1$
$x^2 < (- 1)^2$ squaring both side
$x^2 > 1$
View full question & answer→MCQ 21 Mark
Solve: $(3x - 5)^2 + (3x + 5)^2 = (18x + 10) (x - 2)$
- ✓
$\frac{-35}{13}$
- B
$\frac{-25}{13}$
- C
$\frac{-15}{13}$
- D
$\frac{-45}{13}$
AnswerCorrect option: A. $\frac{-35}{13}$
We will solve the given expression
$(3x - 5)^2 + (3x + 5)^2 =(18x + 10) (x - 2)$ as shown below:
$(3x - 5)^2 + (3x + 5)^2 = (18x + 10)(x - 2)$
$\Rightarrow [(3x)^2 + (5)^2 - (2 \times 3x \times 5)] + [(3x)^2 + (5)^2 + (2 \times 3x \times 5)] = 18x (x - 2) + 10(x - 2)$
$\therefore (a + b)^2 = a^2 + b^2 + 2ab, (a - b)^2 = a^2 + b^2 - 2ab)$
$\Rightarrow 9x^2 + 25 - 30x + 9x^2 + 25 + 30x = 18x^2 - 36x + 10x - 20$
$\Rightarrow 18x^2 + 50 =18x^2 - 26x - 20$
$\Rightarrow 18x^2 + 50 - 18x^2 + 26x + 20 = 0$
$\Rightarrow 26x + 70 = 0$
$\Rightarrow 26x = -70$
$\Rightarrow \text{x}=-\frac{70}{26}$
$\Rightarrow\text{x}=-\frac{35}{13}$
Hence, $\text{x}=-\frac{35}{13}$
View full question & answer→MCQ 31 Mark
The side of an equilateral triangle is l. Its perimeter is.
MCQ 41 Mark
If $\text{x}-\frac{1}{\text{x}}=3$ then the value of $\frac{3\text{x}^2-3}{\text{x}^2+2\text{x}-1}$ is.
- ✓
$\frac{9}{5}$
- B
$\frac{8}{5}$
- C
$\frac{7}{5}$
- D
$\frac{6}{5}$
AnswerCorrect option: A. $\frac{9}{5}$
Given $\text{x}+\frac{1}{\text{x}}=3$ multiply by x both sides
Then $x^2 - 1 = 3x$
$\Rightarrow x^2 - 3x - 1 = 0$
So, $\frac{3\text{x}^2-3}{\text{x}^2+2\text{x}-1}=\frac{3(\text{x}^2-1)}{\text{x}^2-3\text{x}-1+5\text{x}}=\frac{3\times3\text{x}}{0+5\text{x}}=\frac{9\text{x}}{5\text{x}}=\frac{9}{5}$
View full question & answer→MCQ 51 Mark
“Variable” means that it:
AnswerCorrect option: A. Can take different values.
Since, the value of a variable is not fixed.
So, variable means that it can take different values.
Hence, $(a)$ is correct option.
View full question & answer→MCQ 61 Mark
Mark the correct alternative in the following question:
The product of $x$ and $y$ is decreased by $4$ is written as:
- A
$4 - xy$
- B
$x(y - 4)$
- ✓
$xy - 4$
- D
$xy + 4$
AnswerCorrect option: C. $xy - 4$
Since, the product of $x$ and $y = xy$
So, the expression when the product is decreased by $4$ is written as $xy - 4$
View full question & answer→MCQ 71 Mark
The expression for $‘ 1$ subtracted from $2p$’ is.
- ✓
$2p - 1$
- B
$2p + 1$
- C
$1 - 2p$
- D
$-2p -1$
AnswerCorrect option: A. $2p - 1$
$2p - 1$
View full question & answer→MCQ 81 Mark
$x - 4 = -2$ has a solution:
AnswerGiven equation is $x - 4 = -2$
$\Rightarrow x = -2 + 4$
$\Rightarrow x = 2$
Hence, $(b)$ is correct option.
View full question & answer→MCQ 91 Mark
Identify the number of constants in the expression $5x^3 - 8xy.$
AnswerBoth the terms in the given expression contain atleast one variable, $x$ and $xy.$
Hence, there is no constant term in the given expression.
View full question & answer→MCQ 101 Mark
The expression for $‘x$ is divided by $2$ and the result is added to $1’$ is.
AnswerCorrect option: C. $1+\big(\frac{\text{x}}{2}\big)$
$1+\big(\frac{\text{x}}{2}\big)$
View full question & answer→MCQ 111 Mark
The expression for ‘ $1$ added to $2p’$ is.
- ✓
$2p + 1$
- B
$2p - 1$
- C
$1 - 2p$
- D
$-1 -2p$
AnswerCorrect option: A. $2p + 1$
$2p + 1$
View full question & answer→MCQ 121 Mark
The expression for $‘ 1$ subtracted from $-p’$ is.
- ✓
$-p -1$
- B
$p - 1$
- C
$1 - p$
- D
$1 + p$
AnswerCorrect option: A. $-p -1$
$-p -1$
View full question & answer→MCQ 131 Mark
Mark the correct alternative in the following question:
If the lengths of edges of a cuboid are $2x,$ $3y$ and $4xy,$ then its volume is:
- A
$24xy$
- B
$9x^2y^2$
- ✓
$24x^2y^2$
- D
$6x^2y^2$
AnswerCorrect option: C. $24x^2y^2$
Volume of the cuboid $= 2x \times 3y \times 4xy$
$= (2 \times 3 \times 4) \times (x \times x) \times (y \times y)$
$= 24x^2y^2$
View full question & answer→MCQ 141 Mark
If $\text{a}-\frac{1}{3}=\frac{1}{\text{a}}$ then the value of $\text{a}^3-\frac{1}{\text{a}^3}$ is.
- ✓
$1\frac{1}{27}$
- B
$1\frac{2}{27}$
- C
$1\frac{3}{27}$
- D
$1\frac{4}{27}$
AnswerCorrect option: A. $1\frac{1}{27}$
Given $\text{a}-\frac{1}{3}=\frac{1}{\text{a}}= \text{a}-\frac{1}{\text{a}}=\frac{1}{3}$
We know that $x^3 - y^3 = (x - y)3 + 3xy (x + y)$
Then $\text{a}^3-(\frac{1}{3})^3=(\text{a}-(\frac{1}{\text{a}}))^3+3\text{a}(\frac{1}{\text{a}})(\text{a}+(\frac{1}{\text{a}})$
$=(\frac{1}{3})^3+3\times(\frac{1}{3})=\frac{1}{27}+1=\frac{28}{27}=1\frac{1}{27}$
View full question & answer→MCQ 151 Mark
The rule, which gives the number of matchsticks required to make the matchstick pattern $V$, is.
View full question & answer→MCQ 161 Mark
Find the constant in thepolynomial $x + 5$
AnswerThe constant in the polynomial $x + 5$ is $5.$
View full question & answer→MCQ 171 Mark
In algebra, $a \times b$ means ab, but in arithmetic $3 \times 5$ is:
AnswerGiven, in algebra, $a \times b = ab$, which means a is multiplied by $b.$
Also, in arithmetic, $3 \times 5$ means $3$ is multiplied by $5.$
$3 \times 5 = 15$
Hence, $(c)$ is correct option.
View full question & answer→MCQ 181 Mark
Classify the following polynomial as a polynomial in one variable, two variables, etc. $xy + yz + zx$
AnswerThe given polynomial has three variables i.e. $x, y$ and $z.$
View full question & answer→MCQ 191 Mark
The equation $4x = 16$ is satisfied by the following value of $x:$
AnswerGiven equations $4x = 16$
$\Rightarrow\frac{4\text{x}}{4}=\frac{16}{4}$
$\Rightarrow\text{x}=4$
Verification
Put $x = 4$ in Eq. $(i)$ then we get
$4 \times 4 = 16 \Rightarrow 16 = 16$
Therefore, value of $x$ is $4.$
Hence, $(a)$ is correct option.
View full question & answer→MCQ 201 Mark
How many degree of polynomials are there in constant term?
AnswerConstant term has zero degree of polynomial. Because the constant term in an expression or equation has a fixed value and does not contain variables.
Example: $p(x) = k$ Where $k$ is a constant.
View full question & answer→MCQ 211 Mark
The quotient of $x$ by $2$ is added to $5$ is writen as:
- ✓
$\frac{\text{x}}{2}+5$
- B
$\frac{2}{\text{x}}+5$
- C
$\frac{\text{x}+2}{5}$
- D
$\frac{\text{x}}{2+5}$
AnswerCorrect option: A. $\frac{\text{x}}{2}+5$
$\frac{\text{x}}{2}+5$
View full question & answer→MCQ 221 Mark
Mark $(\checkmark)$ against the correct answer in the following:
If $\frac{1}{3}\text{x}+5=8,$ then $\text{x}={}?$
Answer$\Rightarrow\frac{1}{3}\text{x}+5=8$
$\Rightarrow\frac{1}{3}\text{x}+5-5=8-5$ [Substracting 5 from both sides]
$\Rightarrow\frac{1}{3}\text{x}\times3=3\times3$ [Multiplying both sides by $3]$
$\text{x}=9$
View full question & answer→MCQ 231 Mark
If $x^2 - 3x + 1 = 0$ then the value of $\text{x}-\frac{1}{\text{x}}$ is.
- ✓
$\sqrt{5}$
- B
$\sqrt{3}$
- C
$\sqrt{2}$
- D
$\sqrt{6}$
AnswerCorrect option: A. $\sqrt{5}$
$\text{x}^2-3\text{x}+1$
$\therefore\text{x}^2+1=3\text{x}$
$\Rightarrow\frac{\text{x}^2+1}{\text{x}}=\frac{3\text{x}}{\text{x}}$
$\Rightarrow\text{x}+\frac{1}{\text{x}}^2=(\text{x}^2+1)^2-2=(3)^2-=9-2=7$
We know $(\text{x}+\frac{1}{\text{x}})^2=\text{x}^2+\frac{1^2}{\text{x}}-2=7-2=5$
$\therefore\text{x}-\frac{1}{\text{x}}=\sqrt{5}$
View full question & answer→MCQ 241 Mark
A basket has $x$ mangoes, how many mangoes are there in $5$ baskets?
View full question & answer→MCQ 251 Mark
Which of the following is an expression with numbers only?
- A
$x + 1$
- B
$2x$
- C
$1 - x$
- ✓
$3$
View full question & answer→MCQ 261 Mark
The output of $z^3 + 2z^2 + 5z + 1,$ where $z = -1$
Answer$z^3 + 2z^2 + 5z + 1$
$= (-1)^3 + 2 × (-1)^2 + 5 × (-1) + 1$
$= −1 + 2 - 5 + 1$
$= -3$
View full question & answer→MCQ 271 Mark
Number of matchsticks required to make a pattern of $“A”$
View full question & answer→MCQ 281 Mark
If Meenu’s present age is $x$ years, what was her age in years, $10$ years back?
- A
$10 - x$
- B
$-x - 10$
- C
$10x$
- ✓
$x - 10$
AnswerCorrect option: D. $x - 10$
$x - 10$
View full question & answer→MCQ 291 Mark
What is the output of $x^2 + 3x + 5,$ where x(variable) $= -1?$
Answer$x^2 + 3x + 5$
$= (-1)^2 + 3 × (-1) + 5$
$= 1 - 3 + 5$
$= 6 - 3$
$= 3$
View full question & answer→MCQ 301 Mark
What is the value of $x$ if $\frac{3\text{x}}{4+8}=17$?
View full question & answer→MCQ 311 Mark
Mark $(\checkmark)$ against the correct answer in the following:
if $\frac{\text{x}}{5}=1,$ then,
- A
$\text{x}=\frac{1}{5}$
- ✓
$x = 5$
- C
$x = (5 + 1)$
- D
AnswerCorrect option: B. $x = 5$
$\frac{\text{x}}{5}=1$
$\Rightarrow\frac{\text{x}}{5}\times5=1\times5$ [Multiplying both the side by $5]$
$x = 5$
View full question & answer→MCQ 321 Mark
Mark the correct alternative in the following question:
The product of $a$ and $b$ is added to their sum is written as:
- ✓
$ab + a + b$
- B
$a + b - ab$
- C
$a + ab$
- D
$b + ab$
AnswerCorrect option: A. $ab + a + b$
=As, the sum of $a$ and $b = a + b$
And, the product of $a$ and $b = ab$
So, the expression when the product is added to the sum $= a + b + ab$
View full question & answer→MCQ 331 Mark
The area of a square having each side $x$ is:
- ✓
$x \times x$
- B
$4x$
- C
$x + x$
- D
$4 + x$
AnswerCorrect option: A. $x \times x$
Here, side $= x$
We know that, area of square = Side $\times$ Side
Area of square $= x \times x$
Hence, $(a)$ correct option.
View full question & answer→MCQ 341 Mark
Which of the following is an equation in a variable?
- A
$2 < 10$
- B
$3 > 12$
- ✓
$x - 1 =0$
- D
$2 + 3 = 3 + 2$
AnswerCorrect option: C. $x - 1 =0$
$x - 1 =0$
View full question & answer→MCQ 351 Mark
$\frac{4}{2}=2$ denotes a:
- ✓
- B
- C
Equation with a variable.
- D
AnswerWe know that, an equation which contains only numbers is called a numerical equation.
Since, equation $\frac{4}{2}=2$ contains only numbers, so it is a numerical equation.
Hence,$ (a)$ is correct option.
View full question & answer→MCQ 361 Mark
Which of the following contains minimum number of variables?
- ✓
$15$
- B
$5x^3y^2$
- C
$yz$
- D
$y^3$
AnswerThe number of variables in $(A)$ is zero.
View full question & answer→MCQ 371 Mark
Who used the symbol heap for the unknown in algebra?
AnswerEgyptians used the symbol heap for the unknown in algebra.
View full question & answer→MCQ 381 Mark
Which of the following is an equation?
- A
$x + 1$
- B
$x - 1$
- ✓
$x - 1 = 0$
- D
$x + 1 > 0$
AnswerCorrect option: C. $x - 1 = 0$
We know that, an expression with a variable, constants and the sign of equality $(=)$ is called an equation.
So, $x - 1 = 0$ is an equation.
Hence, $(c)$ is correct option.
View full question & answer→MCQ 391 Mark
Mark the correct alternative in the following question:
The initial count of bacteria is x and it becomes y times every day. The total count of bacteria after one week is:
- A
$7xy$
- B
$x + 7y$
- C
$xy^7$
- ✓
$xy^6$
AnswerCorrect option: D. $xy^6$
Since, the total count of the bacteria after one week,
$= x \times y \times y \times y \times y \times y \times y = x \times y^6 = xy^6$
View full question & answer→MCQ 401 Mark
Mark the correct alternative in the following question:
$9$ less than a literal $x$ is written as:
- A
$9 - x$
- ✓
$x - 9$
- C
$x + 9$
- D
AnswerCorrect option: B. $x - 9$
Since, $9$ less than $x$ is written as $x - 9$
View full question & answer→MCQ 411 Mark
Solve: $ (\frac {\text{y }}{ 3 }) = 5$
Answer$\big(\frac{\text{y}}{3}\big)=5$
$\Rightarrow \text{y} = 5 \times 3 = 15$
View full question & answer→MCQ 421 Mark
The expression for $‘ 1$ subtracted from $p’$ is.
- ✓
$p - 1$
- B
$p + 1$
- C
$1 - p$
- D
$-1 - p.$
AnswerCorrect option: A. $p - 1$
$p - 1$
View full question & answer→MCQ 431 Mark
The rule, which gives the number of matchsticks required to make the matchstick pattern $F$, is.
View full question & answer→MCQ 441 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The coefficient of $x$ in $-5xyz$ is:
AnswerCorrect option: C. $-5yz$
All the terms in the expression $-5xyz$ barring $x$ will be the coefficient of $x$, i.e. $-5yz.$
View full question & answer→MCQ 451 Mark
If $a + b + c = 0$ then $a^3+ b^3 + c^3$ is equal to
AnswerCorrect option: A. $3\text{abc}$
Using $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 - 3abc = 0 \times (a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 = 3abc$
Here if $a + b + c$ is $0$ then answer will be $3abc$
View full question & answer→MCQ 461 Mark
The constant term of $0.4x^7 - 75y^2 - 0.75$ is ___
- A
$0.4$
- B
$0.75$
- ✓
$-0.75$
- D
$-75$
AnswerCorrect option: C. $-0.75$
Given equation is $0.4x^7 - 75y^2 - 075$ A constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.
Then constant term of equation $0.4x^7 - 75y^2 - 075$ is $- 0.75$
View full question & answer→MCQ 471 Mark
The rule, which gives the number of matchsticks required to make the matchstick pattern $U$, is.
View full question & answer→MCQ 481 Mark
If $x^3 + mx^2 + nx + 6$ has $(x - 2)$ as factor and leaves a remainder $3$ when divided by $(x - 3)$ find the values of m, n
- A
$m = 2, n = 2$
- B
$m = 2, ,n = -2$
- C
$m = -2, n = 1$
- ✓
$m = -3, n = -1$
AnswerCorrect option: D. $m = -3, n = -1$
$x - 2$ is factor
$\Rightarrow x = 2$
$f(2) = 14 + 4m + 2n$
Remainder is zero
$\Rightarrow 7 + 2m + n = 0 ⟶ (i)$
Now, $x - 3 = 0$ gives remainder $3$
$\Rightarrow f (3) = 3$
$\Rightarrow 33 + 9m + 3n = 3$
$\Rightarrow 10 + 3m + n = 0 ⟶ (ii)$
From $(i)\&(ii)$
$m = -3n = −1$
View full question & answer→MCQ 491 Mark
Which expression has more variables?
$(1)$ $x^3 + 3x^2 + 5x^2 y^2 + 7y$
$(2)$ $5x + 3y + z$
AnswerVariables in $(1)$ are $x$ and $y$ where as variables in $(2)$ are $x, y, z.$
View full question & answer→MCQ 501 Mark
The variable in the polynomial $x^2 + 3x + 5$ is:
AnswerThe value of the polynomial changes as the variable changes. Hence, $x$ is the variable in the polynomial.
View full question & answer→