Algebraic Identities - Maharashtra Board STD 9 Maths Questions - Vidyadip

Question types

Algebraic Identities question types

154 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

154

Questions

5

Question groups

5

Question types

MCQ(1M)

2 Mark Question

3 Mark Question

4 Mark Question

5 Mark Question

Sample Questions

Algebraic Identities questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ(1M)1 Mark

If $\text{x}+\frac{1}{\text{x}}=3,$ then $\text{x}^6+\frac{1}{\text{x}^6}=$

A
$927$
B
$414$
C
$364$
✓
$322$

Answer: D.

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Q 2MCQ(1M)1 Mark

If $49\text{a}^2-{\text{b}}=\Big(7\text{a}+\frac{1}{2}\Big)\Big(7\text{a}-\frac{1}{2}\Big),$ then the value of $b$ is:

A
$0$
✓
$\frac{1}{4}$
C
$\frac{1}{\sqrt2}$
D
$\frac{1}{2}$

Answer: B.

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Q 3MCQ(1M)1 Mark

$(a-b)^3+(b-c)^3+(c-a)^3=$

A
$(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
B
$(a-b)(b-c)(c-a)$
✓
$3(a-b)(b-c)(c-a)$
D
None of these.

Answer: C.

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Q 4MCQ(1M)1 Mark

If $a + b + c = 0,$ then $\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}=$

A
$0$
B
$1$
C
$-1$
✓
$3$

Answer: D.

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Q 5MCQ(1M)1 Mark

If $a - b = -8$ and $ab = -12$, then $a^3 - b^3 =$

A
$-244$
B
$-240$
✓
$-224$
D
$-260$

Answer: C.

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Q 62 Mark Question2 Marks

Write the following in the expanded form:
$(x+2 y+4 z)^2$

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Q 72 Mark Question2 Marks

Write the following in the expanded form:
$(-3 x+y+z)^2$

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Q 82 Mark Question2 Marks

Find the following:
$\left(x^3+1\right)\left(x^6-x^3+1\right)$

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Q 92 Mark Question2 Marks

Find the following products:
$\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)$

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Q 102 Mark Question2 Marks

Evaluate the following using identities:
$(0.98)^2$

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Q 113 Mark Question3 Marks

Evaluate the following:
$(98)^3$

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Q 123 Mark Question3 Marks

Evaluate the following using identities:
$991 \times 1009$

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Q 133 Mark Question3 Marks

Find the following products:
$(4 x-3 y+2 z)\left(16 x^2+9 y^2+4 z^2+12 x y+6 y z-8 z x\right)$

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Q 143 Mark Question3 Marks

Evaluate:$\Big(\frac{1}{2}\Big)^3+\Big(\frac{1}{3}\Big)^3=\Big(\frac{5}{6}\Big)^3$

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Q 153 Mark Question3 Marks

If $9 x^2+25 y^2=181$ and $x y=-6$, find the value of $3 x+5 y$

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Q 164 Mark Question4 Marks

Find the cube of the following binomial expressions:$\frac{3}{\text{x}}-\frac{2}{\text{x}^2}$

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Q 174 Mark Question4 Marks

If $\text{x}^2+\frac{1}{\text{x}^2}=98,$ find the value of $\text{x}^3+\frac{1}{\text{x}^3}.$

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Q 184 Mark Question4 Marks

Simplify:
$(a + b + c)^2 + (a - b + c)^2$

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Q 194 Mark Question4 Marks

Simplify the following:$\Big(\frac{\text{x}}{2}+\frac{\text{y}}{3}\Big)^3-\Big(\frac{\text{x}}{2}-\frac{\text{y}}{3}\Big)^3$

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Q 204 Mark Question4 Marks

If $\text{x}-\frac{1}{\text{x}}=5,$ find the value of $\text{x}^3-\frac{1}{\text{x}^3}.$

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Q 215 Mark Question5 Marks

Simplify the following:$\Big(\text{x}+\frac{2}{\text{x}}\Big)^3+\Big(\text{x}-\frac{2}{\text{x}}\Big)^3$

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Q 225 Mark Question5 Marks

Simplify:
$(a + b + c)^2 + (a - b + c)^2 + (a + b - c)^2$

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Q 235 Mark Question5 Marks

Simplify the following expressions:$\big(\text{x}+\text{y}+\text{z}\big)^2+\Big(\text{x}+\frac{\text{y}}{2}+\frac{\text{z}}{3}\Big)^2-\Big(\frac{\text{x}}{2}+\frac{\text{y}}{3}+\frac{\text{z}}{4}\Big)^2$

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Q 245 Mark Question5 Marks

If $\text{x}^4+\frac{1}{\text{x}^4}=119,$ find the valu of $\text{x}^3-\frac{1}{\text{x}^3}.$

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Q 255 Mark Question5 Marks

If $\text{x}+\frac{1}{\text{x}}=3,$ calculate $\text{x}^2+\frac{1}{\text{x}^2},\ \text{x}^3+\frac{1}{\text{x}^3}$ and $\text{x}^4+\frac{1}{\text{x}^4}.$

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