MCQ 1511 Mark
$3x - 4y + 5z$ is an example of ......... in an algebraic expression:
Answer$3x - 4y + 5z$ is an example of unlike terms. Because different variables $(x, y, z)$ are used.
View full question & answer→MCQ 1521 Mark
If $x = a + b$ then $= 2^x + 2^a.2^b =$
- ✓
$2(2^a + b)$
- B
$2^{a + b} + 2^{ab}$
- C
$2^{2a + 2ab}$
- D
$2^{a + b + 1}$
AnswerCorrect option: A. $2(2^a + b)$
Given: $x = a + b 2^x + 2^a⋅2^b = ?$
So. $2^{a + b}+ 2^a+ 2^b⇒ 2^{a + b} + 2^{a + b}$ (according to exponent product rule)
$⇒ 2(2^{a + b})$
View full question & answer→MCQ 1531 Mark
If $x$ is a natural number, then the minimum value of $(x^2 - 6x + 12)$ is:
AnswerGiven: $f(x) = x^2 - 6x + 12$ Minimum value of f (x) is at $x = x_1,$ where $x_1$ is that value of x where $f′(x) = 0$ Here,
$f′(x) = 2x - 6$ So, $f(x) = 0 = 2x - 6 x = x_1 = 3$
$\therefore$ maximum value of $f(x)$ is $= f(3) = 3^2 - 6 (3) + 12 = 21 - 18 = 3$
View full question & answer→MCQ 1541 Mark
The coefficient of $x^2$ in the product $(x - 1) (1 - 2x)$ is:
Answer$(x - 1) (1 - 2x) = -2x^2 + 3x - 1$ A Coefficient s a constant number multiplied with a variable. Here as $-2$ is multiplied with $x^2.$ so it becomes the coefficient.
View full question & answer→MCQ 1551 Mark
Write the coefficient of ${\text{x}}^2 \text{ in } \sqrt 2-12−1$
AnswerClearly, the given expression $\sqrt2-1$ is constant polynomial and there is not any term containing $x^2.$
View full question & answer→MCQ 1561 Mark
If $\text{a}\times\text{ b}=\frac {\text{ a }}{\text{ b} } -\frac { \text{b} }{\text{ a} }$ find $ \frac { 5 \times 6 }{ 6\times 5 }$
AnswerGiven $ \text{a}\times \text{b}=\frac {\text{ a} }{\text{b}} -\frac{\text{b}}{\text{a}}$
$\Rightarrow \frac{\text{a}\times\text{b}}{\text{b}\times \text{a}}=\frac{\frac{\text{a}}{\text{b}}-\frac{\text{b}}{\text{a}}}{\frac{\text{b}}{\text{a}}-\frac{\text{a}}{\text{b}}}=-1$
View full question & answer→MCQ 1571 Mark
How many terms are there in the algebraic expression $7x^3 + 2xy + z - 7y?$
AnswerThe terms are $7x^3, 2xy, z, 7y$
View full question & answer→MCQ 1581 Mark
Identify the unlike terms which have different variables with the same exponents?
- A
$x^2 - y^3 + x$
- B
$z^2 + z^3 + f$
- ✓
$a^3 + b^3 - c^3$
- D
$x^4 - y^4 - 4^4$
AnswerCorrect option: C. $a^3 + b^3 - c^3$
$a^3 + b^3 - c^3$ is the unlike term which has different variables with the same exponents.
View full question & answer→MCQ 1591 Mark
Which of the following pairs of terms is a pair of like terms?
- A
$3x, 2xy$
- ✓
$-xy^2, – 2xy^2$
- C
$-6x^2, 20x^2y$
- D
$8x^2, 7y$
AnswerCorrect option: B. $-xy^2, – 2xy^2$
B. $-xy^2, – 2xy^2$
View full question & answer→MCQ 1601 Mark
What should be added to $xy + yz + zx$ to get $-xy - yz - zx?$
- ✓
$-2xy - 2yz - 2zx$
- B
$-3xy - yz - zx$
- C
$-3xy - 3yz - 3zx$
- D
$2xy + 2yz + 2zx$
AnswerCorrect option: A. $-2xy - 2yz - 2zx$
Since, $(-xy - yz - zx) - (xy + yz + zx)$
$= -xy - yz - zx - xy - yz - zx$
$= -2xy - 2yz - 2zx$
$So, -2xy - 2yz - 2zx$ should be added to $xy + yz + zx$ to get $-xy - yz - zx.$
Hence, the correct alternative is option $(a).$
View full question & answer→MCQ 1611 Mark
If we substract $-3p^2q^2$ from $p^2q^2,$ then we get:
- A
$-4p^2q^2$
- B
$-2p^2q^2$
- C
$2p^2q^2$
- ✓
$4p^2q^2$
AnswerCorrect option: D. $4p^2q^2$
$p^2q^2 - (-3p^2q^2) = 4p^2q^2$
View full question & answer→MCQ 1621 Mark
Which of the following is a trinomial in $x?$
AnswerCorrect option: B. $x^3 + x^2 + x$
$x^3 + x^2 + x$
View full question & answer→MCQ 1631 Mark
What is the coefficient of $y^2$ in the expression $3y^2 + 4x?$
View full question & answer→MCQ 1641 Mark
What should be subtracted from $2a + 6b - 5$ to get $-3a + 2b + 3?$
- A
$5 + 4b - 8$
- ✓
$5a + 4b - 8$
- C
$5a + 4ab - 8$
- D
$5a + 4b - 10$
AnswerCorrect option: B. $5a + 4b - 8$
Let $X = -3a + 2b + 3$ and $Y = 2a + 6b - 5$
Let $Z$ be the required expression
Now, $X = Y - Z = > Z = Y - X$
$2a + 6b - 5 - (-3a + 2b + 3)$
$= 2a + 6b - 5 + 3a - 2b - 3$
$= 5a + 4b - 8$
View full question & answer→MCQ 1651 Mark
Express the following decimal in the form $\frac{\text{p}}{\text{q}}: 0.39$
- ✓
$\frac{39}{100}$
- B
$\frac{390}{100}$
- C
$\frac{3.9}{100}$
- D
$\frac{380}{100}$
AnswerCorrect option: A. $\frac{39}{100}$
Given, $0.39$ multiple and divide by $100$
$ = {0.39}\times\frac{100}{100}$
$ = \frac{39}{100}$
View full question & answer→MCQ 1661 Mark
If $a + b + c = 0,$ the the value of $a^3 + b^3+ c^3$ is:
- ✓
$3abc$
- B
$2abc$
- C
$4abc$
- D
$0$
AnswerCorrect option: A. $3abc$
A. $3abc$
View full question & answer→MCQ 1671 Mark
Which of the following is a polynomial?
- ✓
$2x$
- B
$x^2 + y^{-2} - 2z^2$
- C
$5x^3y^2z^3$
- D
$x + x^2 + x^3 + x^4$
AnswerA polynomial is an algebraic expression in which the variables have powers as whole numbers. Option $C$ contains power as $-2$ which is not the whole number, options $A, C$ and $D$ are polynomials.
View full question & answer→MCQ 1681 Mark
The Peoduct of the coeffiecients of terms in $-\frac{4}{3}\text{ab}^2+\frac14\text{bc}^2+3\text{ca}^2$ is
AnswerAs, the coefficient of the term $-\frac43\text{ab}^2$ is $-\frac43,$ the coefficient of the term $\frac14\text{bc}^2$ is $\frac14$ and the coefficient of the term $3ca^2$ is $3.$
So, the product of the coefficients of the terms $=-\frac43\times14\times3=-1$
Hence, the correct alternative is option $(c).$
View full question & answer→MCQ 1691 Mark
If $x = 997, y = 998, z = 999,$ then thevalue of $x^2 + y^2 + z^2 - xy - yz - zx$ will be:
View full question & answer→MCQ 1701 Mark
Simplify: $(x + y)^3 + (x - y)^3 +6x (x^2 - y^2)$
- ✓
$8x^3$
- B
$6x^3$
- C
$6x^2$
- D
$8x^2$
AnswerCorrect option: A. $8x^3$
Given, $(x + y)^3+ (x - y)^3 +6x (x2 - y2)$
$\because$ $(x + y)^3 = x^3 + y^3 + 3xy (x + y)$
$\because$ $(x - y)^3 = x^3 - y^3- 3xy (x - y)$
$⇒ x^3+ y^3 + 3xy (x + y) + x^3 - y^3 - 3xy (x - y) + 6x (x^2 − y^2)$
$⇒ x^3 + y^3 + 3x^2y + 3xy^2 + x^3 - y^3 - 3x^2y + 3xy^2 + 6x^3 - 6xy^2$
$⇒ 8x^3$
View full question & answer→MCQ 1711 Mark
....... of a term is called its numerical coefficient:
AnswerThe numerical factor of a term is called coeffiicient. As for example $3x + 6$ Coefficient of $x$ is $3.$
View full question & answer→MCQ 1721 Mark
$4x - (-2y + 5x)$ is equal to:
- A
$9x - 2y$
- B
$9x + 2y$
- C
$x + 2y$
- ✓
$-x + 2y$
AnswerCorrect option: D. $-x + 2y$
Given, $4x - (-2y + 5x)$
$= 4x + 2y - 5x = -x + 2y$
simplified form is $-x + 2y$
View full question & answer→MCQ 1731 Mark
Three cubes of metal whose edges are $6\ cm, 8\ cm$ and $10\ cm$ respectively are melted and a single cube is formed What is the length (in cm) of the diagonal of the newly formed cube?
- A
$10$
- B
$3\sqrt{10}$
- ✓
$12\sqrt{2}$
- D
$10\sqrt{2}$
AnswerCorrect option: C. $12\sqrt{2}$
Three cubes of metal whose edges are $6\ cm, 8\ cm$ and $10\ cm$ respectively are melted Then volume of first cube $= (6)^3= 216\ cm^3$And volume of second cube $= (8)^3 = 512\ cm^3$ And volume of first cube $= (10)^3= 1000\ cm^3$Then volume of cube $= (10)^3 = 1000\ cm^3$ Then volume of cube made by melted three cube $= 216 + 512 + 1000 = 1728$ Then side of cube = $\sqrt{1728}=12\text{ cm}$ Then diagonal of cube $=\sqrt{3\times (12)^{2}}=12\sqrt{3}\text{ cm}$
View full question & answer→MCQ 1741 Mark
An algebraic expression containing three terms is called a:
AnswerAn algebraic expression containing one term is called monomial, two terms is called binomial and three terms is called trinomial.
View full question & answer→MCQ 1751 Mark
If a and b are respectively the sum and product of coefficients of terms in the expression $x^2 + y^2 + z^2 - xy - yz - zx,$ then $a + 2b =$
AnswerWe have,
The expression $x^2 + y^2 + z^2 - xy - yz - zx,$
|
Terms
|
Coefficients
|
|
$x^2$
|
$1$
|
|
$y^2$
|
$1$
|
|
$z^2$
|
$1$
|
|
$-xy$
|
$-1$
|
|
$-yz$
|
$-1$
|
|
$-zx$
|
$-1$
|
|
Sum, a
|
$0$
|
|
Product, b
|
$-1$
|
So,$ a + 2b$
$= 0 + 2(-1)$
$= -2$
Hence, the correct alternative is option $(c).$ View full question & answer→MCQ 1761 Mark
The coefficient of $x$ in the product $(x - 1)(1 - 2x)$ is:
Answer$(x - 1)(1 - 2x) = -2x^2 + 3x - 1$ as $3$ is multiplied with $x,$ hence, coefficient of $x$ is $3.$
View full question & answer→MCQ 1771 Mark
What is an algebraic expression?
- ✓
An expression having one or more variables.
- B
An expression having one or more forms.
- C
An expression having constant value.
- D
AnswerCorrect option: A. An expression having one or more variables.
An algebraic expression is an expression which contains one or more than one variable.
View full question & answer→MCQ 1781 Mark
Find the coefficient of $x^2$ in $x^2 + 3x + 5:$
Answer$x^2 + 3x + 5 = 1x^2 + 3x + 5$ Coefficient of $x^2 = 1$
View full question & answer→MCQ 1791 Mark
$x^4 + x^3- 1$ is an example of:
Answer$x^4 + x^3 - 1$ is an example of algebraic expression. An algebraic expression is a collection of real numbers, variables, grouping and arithmetic operational symbols.
View full question & answer→MCQ 1801 Mark
If the value of the expression $x^{2}-5 x+k$ for $x=0$ is $5,$ then the value of $k$ is
Answer$(0)^{2}-5(0)+k=5$ $\Rightarrow k=5$
View full question & answer→MCQ 1811 Mark
Find the value of the expression $a^{3}+b^{3}+c^{3}-3 a b c$ for $a=2, b=3, c=4$
Answer$(2)^{3}+(3)^{3}+(4)^{3}-3(2)(3)(4)$
$=8+27+64-72=27$
View full question & answer→MCQ 1821 Mark
Find the value of the expression $3p + 7$ for $p = -2$
View full question & answer→MCQ 1831 Mark
Find the value of the expression $– x + 2$ for $x = -2$
View full question & answer→MCQ 1841 Mark
Find the value of the expression $z^{3}-2(z-10)$ for $z=10$
- A
$10$
- B
$100$
- ✓
$1000$
- D
$10000$
AnswerCorrect option: C. $1000$
$(10)^{3}-2(10-10)=1000$
View full question & answer→MCQ 1851 Mark
Find the value of the expression 3x + 5 (x – 2) for $x = 2$
Answer$3(2)+ 5(2 – 2) = 6$
View full question & answer→MCQ 1861 Mark
Find the value of the expression $a^{2}+a b+1$ for $a=0, b=1$
Answer$(0)^{2}+(0)(1)+1=1$
View full question & answer→MCQ 1871 Mark
Find the value of the expression $\mathrm{a}^{2}+\mathrm{b}^{2}$ for $\mathrm{a}=1, \mathrm{b}=0$
Answer$(1)^{2}+(0)^{2}=1$
View full question & answer→MCQ 1881 Mark
Find the value of the expression $\mathrm{a}^{2}-\mathrm{b}^{2}$ for $\mathrm{a}=2, \mathrm{b}=1$
Answer$(2)^{2}-(1)^{2}=3$
View full question & answer→MCQ 1891 Mark
Find the value of the expression $a^{2}-2 a b+b^{2}$ for $a=1, b=1$
Answer$(1)^{2}-2(1)(1)+(1)^{2}=0$
View full question & answer→MCQ 1901 Mark
Find the value of the expression $a + b$ for $a = 1, b = 2$
View full question & answer→MCQ 1911 Mark
Find the value of the expression $x^{2}+2 x+1$ for $x=-1$
Answer$(-1)2 + 2(-1) + 1 = 0$
View full question & answer→MCQ 1921 Mark
Find the value of the expression $5n – 3$ for $n = -1$
View full question & answer→MCQ 1931 Mark
Find the value of the expression $100 – 10 x 3$ for $x = 0$
Answer$100 – 10(0)3 = 100$
View full question & answer→MCQ 1941 Mark
Find the value of the expression $4x – 3$ for $x = 1$
View full question & answer→MCQ 1951 Mark
Find the value of the expression $x + 2$ for $x = -2$
View full question & answer→MCQ 1961 Mark
What should be subtracted from $x^{2}+y^{2}-2 x y$ to get $x^{2}+y^{2} ?$
- A
$2 x y$
- ✓
$-2 x y$
- C
$x y$
- D
$-x y$
AnswerCorrect option: B. $-2 x y$
$x^{2}+y^{2}-2 x y-\left(x^{2}+y^{2}\right)=-2 x y$
View full question & answer→MCQ 1971 Mark
What should be added to $x^{2}+y^{2}$ to get $x^{2}+y^{2}+2 x y ?$
- A
$xy$
- ✓
$2 x y$
- C
$4 x y$
- D
$-2 x y$
AnswerCorrect option: B. $2 x y$
$x^{2}+y^{2}+2 x y-\left(x^{2}+y^{2}\right)=2 x y$
View full question & answer→MCQ 1981 Mark
Subtract $y^{2}$ from $-5 y^{2}$
- ✓
$-6 y 2$
- B
$6y2$
- C
$y2$
- D
$-5 y 2$
AnswerCorrect option: A. $-6 y 2$
$-5 y^{2}-y^{2}=-6 y^{2}$
View full question & answer→MCQ 1991 Mark
Subtract $– xy$ from $xy$
Answer$xy – (-xy) = xy + xy = 2xy$
View full question & answer→MCQ 2001 Mark
Simplify: $z^{2}+11 z^{2}-5 z-11 z^{2}+5 z$
- A
$z^{2}$
- ✓
$-z^{2}$
- C
$5 z$
- D
$-5 z$
AnswerCorrect option: B. $-z^{2}$
$(-1+11-11) z^{2}+(5-5) z=-z^{2}$
View full question & answer→