Introduction to Algebraic Identities

Q.

What is the simplest rationalising factor of cube root of 500

Q.

In the expansion of ${(1+3x+2x^2)}^6$is , the coefficient of $x^{11}$ is

1. $144$

2. $288$

3. $216$

4. $576$

5. $3.2^{11}$

Q. The value of $\frac{(0.013{)}^3+(0.007{)}^3}{(0.013{)}^2-0.013\times 0.007+(0.007{)}^2}$ is

(a) 0.006

(b) 0.02

(c) 0.0091

(d) 0.00185

Q. Find $21\times 23$, using a suitable algebraic identity.

1. 483

Q. Question 89

What figure is formed if only the height of a cube is increased or decreased?

Q. How can we find the cube root of small numbers like 1, 2, 3.... ?

Q.

The sum of the any three distinct natural numbers arranged in ascending order is $200$ such that the second number is a perfect cube. How many possible values are there for this number.

1. $4$

2. $3$

3. $2$

4. $1$

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the constant term .

Q. 38. The sum of cubes of 2 positive numbers is same as the cube of their sum. The 2 numbers are not equal to 0. What is the sum of the two number

Q.

What is the value of 5³ - 1³(without solving cube)?

1. 142

2. 104

3. 124

4. 126

Q. If $a,b,c$ are natural numbers such that $a^2+b^2+c^2=29$ and $ab+bc+ca=26$, and $a+b+c=$_____.

Q.

What is the value 8³ - 3³ (without solving the cubes)?

1. 845

2. 854

3. 458

4. 485

Q. Evaluate 71 x 74 using algebraic identity.

1. 5241
2. 5244
3. 5251
4. 5254

Q. $(a^{\frac{1}{3}}+b^{\frac{1}{3}})(a^{\frac{2}{3}}-a^{\frac{1}{3}}.b^{\frac{1}{2}}+b^{\frac{2}{3}})=?$

1. $a^3+b^3$
2. $a^2+b^2$
3. None of these
4. $a+b$

Q.

(Cube root x^2)3/4

Q.

Which one is Greater in the following

1- √2

2- cube root 3

3- cube root 4

4- cube root 2

Q. Expand $\left(3a+\frac{2}{b}\right)\left(2a-\frac{3}{b}\right)$

1. $6a^2-\frac{5a}{b}-\frac{6}{b^2}$
2. $6a^2+\frac{5a}{b}-\frac{6}{b^2}$
3. $6a^2+\frac{5a}{b}+\frac{6}{b^2}$
4. $6a^2-\frac{5a}{b}+\frac{6}{b^2}$

Q. Question 37

Fill in the blanks to make the statement true.

The number of cubes in

are ___.

Q. Without actually calculating the cubes, find the value of : Without actually calculating the cubes, find the value of :(1/2)³+(1/3)³-(5/6)³

Q. $(a+b{)}^2$ expands as $a^2+b^2+2ab$.

1. True
2. False

Q. Expand $\left(3a+\frac{2}{b}\right)\left(2a-\frac{3}{b}\right)$

1. $6a^2+\frac{5a}{b}-\frac{6}{b^2}$
2. $6a^2-\frac{5a}{b}-\frac{6}{b^2}$
3. $6a^2+\frac{5a}{b}+\frac{6}{b^2}$
4. $6a^2-\frac{5a}{b}+\frac{6}{b^2}$

Q. Find the value of ${4.9}^2$ using a suitable algebraic identity.

1. 24.01

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the coefficient of $x$.

1. 5
2. -12
3. 8
4. 20

Q. In the expansion of $(5x-3)(x+2{)}^2$ ; find the constant term .

1. 8
2. -12
3. 5
4. 17

Q. Expand $\left(2x-\frac{1}{x}\right)\left(3x+\frac{2}{x}\right)$

Q. If the sum of two numbers is 11 and there cubes sum is 737 .Find the numbers

Q. find the value of (64/125)raised to the power of -2/3 + 1/(256/625)raised to the power of 1/4 + root 25 / cube root 64

Q. Expand $\left(2x-\frac{1}{x}\right)\left(3x+\frac{2}{x}\right)$

1. $6x^2-1-\frac{2}{x^2}$
2. $6x^2-1+\frac{2}{x^2}$
3. $6x^2+1+\frac{2}{x^2}$
4. $6x^2+1-\frac{2}{x^2}$

Q. Expand $(5x-3y+2)(5x+3y+2)$

1. $25x^2+20x+4-9y^2$
2. $25x^2-20x-4-9y^2$
3. $16x^2+20x+4-9y^2$
4. $16x^2+25x+4-9y^2$

Q. The sum of two numbers is 9 and their product is 20. Find the sum of their cubes.

1. 1269
2. 79
3. 190
4. 189