8th Class Mathematics Algebraic Expressions Question Bank

Algebraic Expressions and Identities Total Questions - 25

1)

Multiply \[6{{x}^{3}}-y+3{{x}^{2}}y\,\,by\,\,{{x}^{2}}+{{y}^{2}}\]

A)
\[6{{x}^{5}}-3{{x}^{4}}y-6{{x}^{3}}{{y}^{2}}-6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{4}}\]

B)
\[6{{x}^{5}}+3{{x}^{4}}y+6{{x}^{3}}{{y}^{2}}-{{x}^{2}}y+3{{x}^{2}}{{y}^{3}}-{{y}^{3}}\]

C)
\[6{{x}^{5}}-3{{x}^{4}}y+6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{5}}\]

D)
\[6{{x}^{5}}+3{{x}^{4}}y-6{{x}^{3}}{{y}^{2}}+2{{x}^{2}}{{y}^{3}}-{{y}^{5}}\]
View Solution
2)

If \[3x+4y=18\] and \[xy=6\], find the value of \[9{{x}^{2}}+16{{y}^{2}}\].

A)
180

B)
144

C)
324

D)
       170
View Solution
3)

Simplify: \[{{\left[ 2{{x}^{2}}-\frac{1}{400}{{y}^{2}} \right]}^{2}}-{{\left[ 2{{x}^{2}}+\frac{1}{400}{{y}^{2}} \right]}^{2}}\]

A)
\[-\frac{{{x}^{2}}{{y}^{2}}}{40}\]

B)
\[-\frac{{{x}^{2}}{{y}^{2}}}{50}\]

C)
\[\frac{xy}{50}\]

D)
       \[-\frac{{{x}^{2}}{{y}^{2}}}{5}\]
View Solution
4)

Square of \[9x-7xy\] is

A)
\[81{{x}^{2}}+49{{x}^{2}}{{y}^{2}}\]

B)
\[81{{x}^{2}}-49{{x}^{2}}{{y}^{2}}\]

C)
\[81{{x}^{2}}+49{{x}^{2}}{{y}^{2}}-126{{x}^{2}}y\]

D)
\[81{{x}^{2}}+49{{x}^{2}}{{y}^{2}}-63{{x}^{2}}y\]
View Solution
5)

If \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=53\], find the value of \[x-\frac{1}{x}\].

A)
\[\sqrt{51}\]

B)
\[\sqrt{53}\]

C)
       \[\sqrt{61}\]

D)
       \[\sqrt{63}\]
View Solution
6)

If \[3x-7y=10\] and \[xy=-1\], then the value of \[9{{x}^{2}}+49{{y}^{2}}\] is __.

A)
58

B)
142

C)
104

D)
       -104
View Solution
7)

The product of \[({{x}^{2}}+3x+5)\] and \[({{X}^{2}}-1)\] is______.

A)
\[{{x}^{4}}+3{{x}^{3}}-4{{x}^{2}}-3x-5\]

B)
\[{{x}^{4}}+3{{x}^{3}}+4{{x}^{2}}-3x-5\]

C)
\[{{x}^{4}}+3{{x}^{3}}+4{{x}^{2}}+3x-5\]

D)
\[{{x}^{4}}+{{x}^{3}}+x+5\]
View Solution
8)

Find the missing term in the following problem. \[{{\left( \frac{3x}{4}-\frac{4y}{3} \right)}^{2}}=\frac{9{{x}^{2}}}{16}+\frac{16{{y}^{2}}}{9}+\underline{\,\,\,\,\,\text{?}\,\,\,\,\,}\]

A)
2xy

B)
-2xy

C)
12xy

D)
       -12xy
View Solution
9)

What should be added to \[4{{p}^{2}}+5p+7\] to get\[7{{p}^{2}}+2p+9?\]

A)
\[3{{p}^{2}}-3p+2\]

B)
\[3{{p}^{2}}+3p+2\]

C)
       \[-3{{p}^{2}}+3p-2\]

D)
       \[3{{p}^{2}}-3p-2\]
View Solution
10)

Simplify: \[\frac{3}{2}{{x}^{2}}({{x}^{2}}-1)+\frac{1}{4}{{x}^{2}}({{x}^{2}}+x)-\frac{3}{4}x({{x}^{3}}-1)\]

A)
\[{{x}^{4}}+\frac{1}{2}{{x}^{3}}+\frac{1}{4}{{x}^{2}}+x\]

B)
\[2{{x}^{4}}+\frac{1}{4}{{x}^{3}}-\frac{3}{4}{{x}^{2}}+\frac{1}{4}x\]

C)
\[{{x}^{4}}+\frac{1}{4}{{x}^{3}}-\frac{3}{2}{{x}^{2}}+\frac{3}{4}x\]

D)
\[2{{x}^{4}}+\frac{3}{4}{{x}^{3}}-\frac{1}{4}{{x}^{2}}+\frac{3}{4}x\]
View Solution
11)

What must be subtracted from \[{{x}^{4}}+2{{x}^{2}}-3x+7\] to get \[{{x}^{3}}+{{x}^{2}}+x-1?\]

A)
\[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}-4x+8\]

B)
\[{{x}^{3}}+{{x}^{2}}-4x+8\]

C)
\[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}+4x-8\]

D)
\[{{x}^{4}}-{{x}^{3}}-{{x}^{2}}+4x-8\]
View Solution
12)

If \[x+\frac{1}{x}=5\], find the value of \[{{x}^{4}}+\frac{1}{{{x}^{4}}}\].

A)
144

B)
400

C)
236

D)
       527
View Solution
13)

Multiply: \[\left( 4x+\frac{3y}{5} \right)\] and \[\left( 3x-\frac{4y}{5} \right)\]

A)
\[12{{x}^{2}}+\frac{7xy}{5}-\frac{12{{y}^{2}}}{25}\]

B)
\[12{{x}^{2}}+\frac{7xy}{5}+\frac{12{{y}^{2}}}{5}\]

C)
\[12{{x}^{2}}-\frac{7xy}{5}-\frac{12{{y}^{2}}}{25}\]

D)
None of these
View Solution
14)

Add : \[5{{x}^{2}}-\frac{1}{3}x+\frac{5}{2},-\frac{1}{2}{{x}^{2}}+\frac{1}{2}x-\frac{1}{3}\] and \[-2{{x}^{2}}+\frac{1}{5}x-\frac{1}{6}\].

A)
\[\frac{5}{2}{{x}^{2}}+\frac{11}{30}x+2\]

B)
\[\frac{3}{2}{{x}^{2}}+\frac{30}{11}x+3\]

C)
\[\frac{5}{2}{{x}^{2}}+\frac{13}{30}x+1\]

D)
\[\frac{3}{4}{{x}^{2}}+\frac{12}{11}x+5\]
View Solution
15)

Find the value of a if\[pqa={{(~3p+q)}^{2}}-{{(3p-q)}^{2}}\].

A)
11

B)
21

C)
10

D)
       12
View Solution
16)

The perimeter of a triangular field is \[6{{p}^{2}}-4p+9\] and two of its sides are \[{{p}^{2}}-2p+1\] and \[3{{p}^{2}}-5p+3\], Find the third side of the field.

A)
\[8{{p}^{2}}+11p-7\]

B)
\[2{{p}^{2}}+3p+5\]

C)
       \[3{{p}^{2}}+5p-4\]

D)
       \[5{{p}^{2}}-5p+9\]
View Solution
17)

If (x - 5) notebooks cost Rs. \[({{x}^{2}}-13x+40)\], what is the cost of one notebook?

A)
\[(x-1)\]

B)
\[(x-2)\]

C)
\[(x-6)\]

D)
       \[(x-8)\]
View Solution
18)

Ameesha and Prachi love gardening. They water their garden regularly. The length and breadth of Ameesha's kitchen garden are x m and y m respectively. The length of Prachi's kitchen garden is 5 m more than that of Ameesha's garden and the breadth of Prachi's garden is 3 m more than that of Ameesha's garden. Find the difference between the area of Ameesha's kitchen garden and Prachi's kitchen garden.

A)
\[(5x+8y+10){{m}^{2}}\]

B)
\[(3x+5y-15){{m}^{2}}\]

C)
\[(3x+5y+15){{m}^{2}}\]

D)
\[(xy+3y+5y+15){{m}^{2}}\]
View Solution
19)

Amit want to buy a rectangular field whose area is \[(3{{a}^{2}}+5ab+2{{b}^{2}})sq\]. units. One of its sides is \[(a+b)\] units. Find the length of the fence around the field.

A)
\[\text{(10a+20b) units}\]

B)
\[\text{(4a+30) units}\]

C)
\[\text{(2a + 2b) units}\]

D)
\[\text{(8a + 60) units}\]
View Solution
20)

A T-shirt costs \[Rs.({{x}^{2}}-xy-{{y}^{2}})\] and a sweater costs \[Rs.({{x}^{2}}+8xy-2{{y}^{2}})\] and a jeans cost \[Rs.({{x}^{2}}-3xy+{{4}^{2}})\]. After buying these items Mohit paid \[Rs.{{(2x+y)}^{2}}\] to the cashier. How much amount Mohit receive from the cashier?

A)
Rs. 0

B)
Rs. 2x

C)
Rs. (x+y)

D)
       Rs. 2y
View Solution

21)

Study the following statements.

Statement 1: The value of the product \[(4{{a}^{2}}+3b)(4{{a}^{2}}+3b)\] at \[a=1\] and \[b=2\] is 100.

Statement II: Value of \[\frac{{{(997+496)}^{2}}-{{(997-496)}^{2}}}{997\times 496}\] is 2.

Both Statement - I and Statement - II are true.

Statement - I is true but Statement - II is false

Statement - I is false but Statement- II is true

Both Statement - I and Statement - II are false.

View Solution

22)

Match the following.

Column - I	Column - II
P. \[(3{{x}^{2}}-4xy)\] \[(3{{x}^{2}}-3xy)\]	(i) \[12{{x}^{2}}+53xy+55{{y}^{2}}\]
Q. \[({{x}^{2}}+4)\] \[(9{{x}^{2}}+9y)\]	(ii) \[9{{x}^{2}}+2{{y}^{4}}+11x{{y}^{2}}\]
R. \[(3x+5y)\] \[(4x+11y)\]	(iii) \[9{{x}^{4}}-21{{x}^{3}}y+12{{x}^{2}}{{y}^{2}}\]
S. \[({{y}^{2}}+x)\] \[(2{{y}^{2}}+9x)\]	(iv) \[9{{x}^{4}}+45{{x}^{2}}y+36{{y}^{2}}\]

P \[\to \](iii); Q \[\to \](iv); R\[\to \](i); S \[\to \](ii)

P\[\to \](ii); Q\[\to \](i); R\[\to \](iv); S\[\to \](iii)

P\[\to \](iv); Q\[\to \](iii); R\[\to \](i): S\[\to \](ii)

P\[\to \](iii); Q\[\to \](ii); R\[\to \](iv); S\[\to \](i)

View Solution

23)

If \[{{x}^{2}}+{{y}^{2}}=29\] and \[xy=2\], find the value of (i) \[x+y\]        (ii) \[xy\]           (iii) \[{{x}^{4}}+{{y}^{4}}\]

A)

(i) (ii) (iii)

\[\pm \sqrt{35}\] \[\pm 6\] 849

B)

(i) (ii) (iii)

\[\pm \sqrt{23}\] \[\pm 5\] 833



C)

(i) (ii) (iii)

\[\pm \sqrt{33}\] \[\pm 5\] 833



D)

(i) (ii) (iii)

\[\pm \sqrt{29}\] \[\pm 3\] 849

View Solution

24)

Fill in the blanks.

(i) The product of two monomials is always P

(ii) An equation is true for Q. values of the variable.

(iii) An identify is true for R values of the variable.

(iv) The numerical factor of a term is called S

P	Q	R	S
Binomial	all	certain	variable

P	Q	R	S
Monomial	certain	all	coefficient

P	Q	R	S
Binomial	certain	all	variable

P	Q	R	S
Monomial	all	certain	coefficient

View Solution

25)

Simplify:- \[\frac{{{a}^{2}}-13a+30}{(a-10)}=\frac{{{a}^{2}}+4a+4}{a+2}\]

A)
\[{{a}^{2}}-8a-20=0\]

B)
\[{{a}^{2}}+30a-40=0\]

C)
\[{{a}^{2}}-80a-30=0\]

D)
\[{{a}^{2}}+7a-30=0\]
View Solution

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(i)	(ii)	(iii)
\[\pm \sqrt{35}\]	\[\pm 6\]	849

(i)	(ii)	(iii)
\[\pm \sqrt{23}\]	\[\pm 5\]	833

(i)	(ii)	(iii)
\[\pm \sqrt{33}\]	\[\pm 5\]	833

(i)	(ii)	(iii)
\[\pm \sqrt{29}\]	\[\pm 3\]	849

8th Class Mathematics Algebraic Expressions Question Bank

done Algebraic Expressions and Identities Total Questions - 25

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Algebraic Expressions and Identities Total Questions - 25