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Class 10 Math Partial Fractions Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}


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Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}

Q.27 Partial fractions of \frac{7 x^{2}+25}{(x+3)(x+4)} will be of the form(a) \frac{A}{x+3}+\frac{B}{x+4} (b) 1+\frac{A}{x+3}+\frac{B}{x+4} (c) 7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these
Q.27 Partial fractions of  \frac{7 x^{2}+25}{(x+3)(x+4)}  will be of the form(a)  \frac{A}{x+3}+\frac{B}{x+4} (b)  1+\frac{A}{x+3}+\frac{B}{x+4} (c)  7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these

Q.27 Partial fractions of \frac{7 x^{2}+25}{(x+3)(x+4)} will be of the form(a) \frac{A}{x+3}+\frac{B}{x+4} (b) 1+\frac{A}{x+3}+\frac{B}{x+4} (c) 7+\frac{A}{x+3}+\frac{B}{x+4} (d) none of these

Example 1: Resolve the fraction \frac{x^{3}-x^{2}+x+1}{x^{2}+5} into proper fraction.
Example 1: Resolve the fraction  \frac{x^{3}-x^{2}+x+1}{x^{2}+5}  into proper fraction.

Example 1: Resolve the fraction \frac{x^{3}-x^{2}+x+1}{x^{2}+5} into proper fraction.

Q.35 The fraction \frac{3}{x+1} is(b) improper fraction(a) proper fraction(d) irrational fraction
Q.35 The fraction  \frac{3}{x+1}  is(b) improper fraction(a) proper fraction(d) irrational fraction

Q.35 The fraction \frac{3}{x+1} is(b) improper fraction(a) proper fraction(d) irrational fraction

Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}
Resolve into partial fractions.5.  \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}
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Resolve into partial fractions.5. \frac{3 x+7}{(x+3)\left(x^{2}+4\right)}

6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]
 6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]

6 . \[\frac{x^{2}}{(x-2)(x-1)^{2}}\]

Q.28 Partial fractions of \frac{7 x+25}{(x+3)(x+4)} is of the form(a) \frac{A}{x+3}+\frac{B x}{x+4} (b) \frac{A}{x+3}+\frac{B}{x+4} (c) \frac{A x+B}{x+3}+\frac{C}{x+4} (d) \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014
Q.28 Partial fractions of  \frac{7 x+25}{(x+3)(x+4)}  is of the form(a)  \frac{A}{x+3}+\frac{B x}{x+4} (b)  \frac{A}{x+3}+\frac{B}{x+4} (c)  \frac{A x+B}{x+3}+\frac{C}{x+4} (d)  \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014

Q.28 Partial fractions of \frac{7 x+25}{(x+3)(x+4)} is of the form(a) \frac{A}{x+3}+\frac{B x}{x+4} (b) \frac{A}{x+3}+\frac{B}{x+4} (c) \frac{A x+B}{x+3}+\frac{C}{x+4} (d) \frac{A x+B}{(x+3)(x+4)} Lahore Board 2014

Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)
Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)

Q.17 An improper fraction can be reduced to proper fraction by : (a) addition(b) subtràction (c) multiplication(d) division Lahore Board 2015; Multàn Boảrd 2004)

5. \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}
5.  \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}

5. \frac{x^{2}}{\left(x^{2}+4\right)(x+2)}

Resolve into partial fractions.5. \frac{3 x+3}{(x-1)(x+2)}
Resolve into partial fractions.5.  \frac{3 x+3}{(x-1)(x+2)}

Resolve into partial fractions.5. \frac{3 x+3}{(x-1)(x+2)}

2. Write short answers of the following questions.(ii) What is a proper fraction? .
2. Write short answers of the following questions.(ii) What is a proper fraction? .

2. Write short answers of the following questions.(ii) What is a proper fraction? .

7.\[\frac{1}{(x-1)^{2}(x+1)}\]
7.\[\frac{1}{(x-1)^{2}(x+1)}\]

7.\[\frac{1}{(x-1)^{2}(x+1)}\]

Resolve into partial fractions.5. \frac{7 x+4}{(3 x+2)(x+1)^{2}}
Resolve into partial fractions.5.  \frac{7 x+4}{(3 x+2)(x+1)^{2}}

Resolve into partial fractions.5. \frac{7 x+4}{(3 x+2)(x+1)^{2}}

Resolve into partial fractions.3. \frac{9}{(x-1)(x+2)^{2}}
Resolve into partial fractions.3.  \frac{9}{(x-1)(x+2)^{2}}

Resolve into partial fractions.3. \frac{9}{(x-1)(x+2)^{2}}

8. \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}
8.  \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}

8. \frac{1}{(x-1)^{2}\left(x^{2}+2\right)}

Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}
Resolve into partial fractions.6.  \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}

Resolve into partial fractions.6. \frac{x^{2}}{(x+2)\left(x^{2}+4\right)}

Resolve into partial fractions.4. \frac{x-5}{x^{2}+2 x-3}
Resolve into partial fractions.4.  \frac{x-5}{x^{2}+2 x-3}

Resolve into partial fractions.4. \frac{x-5}{x^{2}+2 x-3}

9. \frac{x^{4}}{1-x^{4}}
9.  \frac{x^{4}}{1-x^{4}}

9. \frac{x^{4}}{1-x^{4}}

2. Write short answers of the following questions.(iv) What are partial fractions?
2. Write short answers of the following questions.(iv) What are partial fractions?

2. Write short answers of the following questions.(iv) What are partial fractions?

2. Write short answers of the following questions.(i) Define a rational fraction.
2. Write short answers of the following questions.(i) Define a rational fraction.
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2. Write short answers of the following questions.(i) Define a rational fraction.

Q.30 Partial fractions of \frac{(x-a)(x-b)}{(x-c)(x-d)} will be of the form:(a) \frac{A}{x-c}+\frac{B}{x-d} (b) 1+\frac{A}{x-a}+\frac{B}{x-b} (c) \frac{A}{x-a}+\frac{B}{x-b} (d) 1+\frac{B}{x-c}+\frac{A}{x-d}
Q.30 Partial fractions of  \frac{(x-a)(x-b)}{(x-c)(x-d)}  will be of the form:(a)  \frac{A}{x-c}+\frac{B}{x-d} (b)  1+\frac{A}{x-a}+\frac{B}{x-b} (c)  \frac{A}{x-a}+\frac{B}{x-b} (d)  1+\frac{B}{x-c}+\frac{A}{x-d}
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Q.30 Partial fractions of \frac{(x-a)(x-b)}{(x-c)(x-d)} will be of the form:(a) \frac{A}{x-c}+\frac{B}{x-d} (b) 1+\frac{A}{x-a}+\frac{B}{x-b} (c) \frac{A}{x-a}+\frac{B}{x-b} (d) 1+\frac{B}{x-c}+\frac{A}{x-d}

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

2. Write short answers of the following questions.(viii) Resolve \frac{x}{(x-3)^{2}} into partial fractions:
2. Write short answers of the following questions.(viii) Resolve  \frac{x}{(x-3)^{2}}  into partial fractions:
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2. Write short answers of the following questions.(viii) Resolve \frac{x}{(x-3)^{2}} into partial fractions:

Q.21 The rational fraction \frac{P(x)}{Q(x)} is a proper fraction if(a) Degree of P(x)= degree of Q(x) (b) Degree of P(x)< degree of Q(x) (c) Degree of Q(x)< degree of P(x) (d) none of these
Q.21 The rational fraction  \frac{P(x)}{Q(x)}  is a proper fraction if(a) Degree of  P(x)=  degree of  Q(x) (b) Degree of  P(x)<  degree of  Q(x) (c) Degree of  Q(x)<  degree of  P(x) (d) none of these
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Q.21 The rational fraction \frac{P(x)}{Q(x)} is a proper fraction if(a) Degree of P(x)= degree of Q(x) (b) Degree of P(x)< degree of Q(x) (c) Degree of Q(x)< degree of P(x) (d) none of these

Q.6 (x-4)^{2}=x^{2}-8 x+16 is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation
Q.6  (x-4)^{2}=x^{2}-8 x+16  is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation
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Q.6 (x-4)^{2}=x^{2}-8 x+16 is(a) a transcendental equation(b) cubic equation(c) an identity(d) an equation

Q.13 The fraction \frac{x^{2}+7 x+3}{x+1} is :(a) Improper(b) Proper-(c) Equivalent(d) Identity
Q.13 The fraction  \frac{x^{2}+7 x+3}{x+1}  is :(a) Improper(b) Proper-(c) Equivalent(d) Identity
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Q.13 The fraction \frac{x^{2}+7 x+3}{x+1} is :(a) Improper(b) Proper-(c) Equivalent(d) Identity

Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation
Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation
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Q.1 A relation in which the equality is true only for a number of unknowns is called an(a) identity(b) equation(c) algebraic equation(d) algebraic relation

Resolve into partial fractions.5. \frac{x^{4}}{\left(x^{2}+2\right)^{2}}
Resolve into partial fractions.5.  \frac{x^{4}}{\left(x^{2}+2\right)^{2}}
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Resolve into partial fractions.5. \frac{x^{4}}{\left(x^{2}+2\right)^{2}}

Q.31 The partial fractions of \frac{9 x-7}{\left(x^{2}+1\right)(x+3)} are of the form:(a) \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b) \frac{A}{x^{2}+1}+\frac{B}{x+3} (c) \frac{A}{x^{2}+1} (d) \frac{B}{x+3}
Q.31 The partial fractions of  \frac{9 x-7}{\left(x^{2}+1\right)(x+3)}  are of the form:(a)  \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b)  \frac{A}{x^{2}+1}+\frac{B}{x+3} (c)  \frac{A}{x^{2}+1} (d)  \frac{B}{x+3}
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Q.31 The partial fractions of \frac{9 x-7}{\left(x^{2}+1\right)(x+3)} are of the form:(a) \frac{A x+B}{x^{2}+1}+\frac{C}{x+3} (b) \frac{A}{x^{2}+1}+\frac{B}{x+3} (c) \frac{A}{x^{2}+1} (d) \frac{B}{x+3}

(vi) (x+3)^{2}=x^{2}+6 x+9 is(a) a linear equation(b) an equation(c) an identity(d) none of these
(vi)  (x+3)^{2}=x^{2}+6 x+9  is(a) a linear equation(b) an equation(c) an identity(d) none of these
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(vi) (x+3)^{2}=x^{2}+6 x+9 is(a) a linear equation(b) an equation(c) an identity(d) none of these

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