Aptitude · all questions

Algebra
practice.

Practice every MCQ with options. Use Show answers when you want the correct option and solution.

548

Questions

14/28

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Q261

Open question

(a + \frac{1}{a})^{2} = 3,

then find the value of

a^{30}

a^{24}

a^{18}

a^{12}

a^{6}

1

= ?

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Q262

Open question

If x : y = 3 : 5 and x - y = -2, then the value of x + y is?

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Q263

Open question

If x = 1 +

2

3

and y = 1 +

2

3,

then the value of

\frac{x ^{2} + 4 x y + y ^{2}}{x + y}

is?

Select an option to see the answer and solution.

Q264

Open question

x + \frac{1}{x} = 3,

where

x \neq = 0,

then the value of

\frac{x ^{4} + 3 x ^{3} + 5 x ^{2} + 3 x + 1}{x ^{4} + 1}

= ?

Select an option to see the answer and solution.

Q265

Open question

If p(x + y)² = 5 and q(x - y)² = 3, then the simplified value of p²(x + y)² + 4pqxy - q²(x - y)² is?

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Q266

Open question

If α and β are the roots of equation x² + αx + β = 0 then find α³ + β³ = ?

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Q267

Open question

x^{2} + \frac{1}{x ^{2}} = 1,

then the value of

x^{102}

+

x^{96}

+

x^{90}

+

x^{84}

+

x^{78}

+

x^{72}

+

5

is?

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Q268

Open question

Find the value of a and b if (x - 1) and (x + 1) are factors of x⁴ + ax³ - 3x² + 2x + b = ?

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Q269

Open question

Find the minimum value of x which the expression x³ - 7x² + 11x - 5 ≥ 0.

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Q270

Open question

If a + b + c = 26 and ab + bc + ca = 109, find the value of a² + b² + c² = ?

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Q271

Open question

a + b + c = 0, then the value of

\frac{a ^{2} + b ^{2} + c ^{2}}{ab + b c + c a}

is?

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Q272

Open question

If a + b + c = m and

\frac{1}{a}

\frac{1}{b}

\frac{1}{c},

then average of a², b², c² is?

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Q273

Open question

(a + b)

= 15 and

(a - b)

= 3, then the value of

\frac{ab}{4}

is?

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Q274

Open question

a + \frac{1}{a} = 3,

then the value of

a^{3} + \frac{1}{a ^{3}}

is?

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Q275

Open question

x = a \root 3 \of ab a \root 3 \of ab .... \propto

then the value of x is?

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Q276

Open question

\frac{m - 3 a ^{3}}{b ^{3} + c ^{3}}

+

\frac{m - 3 b ^{3}}{c ^{3} + a ^{3}}

+

\frac{m - 3 c ^{3}}{a ^{3} + b ^{3}}

= 9, then the value of m is?

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Q277

Open question

If a² = b + c, b² = a + c, c² = b + a, then what will be the value of

\frac{1}{a + 1}

\frac{1}{b + 1}

\frac{1}{c + 1}

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Q278

Open question

a + b = 2 c,

find

\frac{a}{a - c}

\frac{c}{b - c}

= ?

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Q279

Open question

\frac{a}{b} = \frac{1}{2},

find the value of the expression

\frac{( 2 a - 5 b )}{( 5 a + 3 b )}

= ?

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Q280

Open question

If for a non - zero x, 3x² + 5x + 3 = 0, then the value of

x^{3} + \frac{1}{x ^{3}}

is?

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Algebrapractice.

Algebra
practice.