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First Year Math Number Systems Q.82 The simplified form of i^{101} is(a) -1 (b) 1(c) i (d) -i


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Q.82 The simplified form of i^{101} is(a) -1 (b) 1(c) i (d) -i

Q.64 Conjugate of -2+3 i is :(a) -2-3 i (b) 2-3 i (c) 2+3 i (d) -2+3 i Faisalabad Board 2012
Q.64 Conjugate of  -2+3 i  is :(a)  -2-3 i (b)  2-3 i (c)  2+3 i (d)  -2+3 i Faisalabad Board 2012

Q.64 Conjugate of -2+3 i is :(a) -2-3 i (b) 2-3 i (c) 2+3 i (d) -2+3 i Faisalabad Board 2012

Q.71 Modulus of 8-15 i is :(a) 8(b) -15 (c) 17(d) 8+15 i
Q.71 Modulus of  8-15 i  is :(a) 8(b)  -15 (c) 17(d)  8+15 i

Q.71 Modulus of 8-15 i is :(a) 8(b) -15 (c) 17(d) 8+15 i

Theorems: \forall z z_{1} z_{2} \in C iv) \overline{z_{1}+z_{2}}=\bar{z}_{1}+\bar{z}_{2}
Theorems:  \forall z z_{1} z_{2} \in C iv)  \overline{z_{1}+z_{2}}=\bar{z}_{1}+\bar{z}_{2}

Theorems: \forall z z_{1} z_{2} \in C iv) \overline{z_{1}+z_{2}}=\bar{z}_{1}+\bar{z}_{2}

Simplify the following:10. (03)(05)
Simplify the following:10.  (03)(05)

Simplify the following:10. (03)(05)

Q.7 Every non-repeating non-terminating decimal is(a) rational number(b) irrational number(c) integer(d) none of these
Q.7 Every non-repeating non-terminating decimal is(a) rational number(b) irrational number(c) integer(d) none of these

Q.7 Every non-repeating non-terminating decimal is(a) rational number(b) irrational number(c) integer(d) none of these

3. Name the properties used in the following inequalities:vi) a>b \Rightarrow-a<-b
3. Name the properties used in the following inequalities:vi)   a>b \Rightarrow-a<-b

3. Name the properties used in the following inequalities:vi) a>b \Rightarrow-a<-b

Q.82 The simplified form of i^{101} is(a) -1 (b) 1(c) i (d) -i
Q.82 The simplified form of  i^{101}  is(a)  -1 (b) 1(c)  i (d)  -i
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Q.82 The simplified form of i^{101} is(a) -1 (b) 1(c) i (d) -i

Q.68 The modulus of 1-i \sqrt{3} is equal to :(a) -2 (b) 2(c) -\sqrt{2} (d) \sqrt{10} Multan Board 2016 |1-| \sqrt{3} \mid=\sqrt{1^{2}+(-\sqrt{3})^{2}}=\sqrt{1+3}=\sqrt{4}=2
Q.68 The modulus of  1-i \sqrt{3}  is equal to :(a)  -2 (b) 2(c)  -\sqrt{2} (d)  \sqrt{10} Multan Board 2016 |1-| \sqrt{3} \mid=\sqrt{1^{2}+(-\sqrt{3})^{2}}=\sqrt{1+3}=\sqrt{4}=2

Q.68 The modulus of 1-i \sqrt{3} is equal to :(a) -2 (b) 2(c) -\sqrt{2} (d) \sqrt{10} Multan Board 2016 |1-| \sqrt{3} \mid=\sqrt{1^{2}+(-\sqrt{3})^{2}}=\sqrt{1+3}=\sqrt{4}=2

14. Find the multiplicative inverse of each of the following numbers:ii) (\sqrt{2}-\sqrt{5})
14. Find the multiplicative inverse of each of the following numbers:ii)  (\sqrt{2}-\sqrt{5})

14. Find the multiplicative inverse of each of the following numbers:ii) (\sqrt{2}-\sqrt{5})

Simplify the following:9. (5-4)(-3-2)
Simplify the following:9.  (5-4)(-3-2)

Simplify the following:9. (5-4)(-3-2)

15. Factorize the following:i) a^{2}+4 b^{2}
15. Factorize the following:i)  a^{2}+4 b^{2}

15. Factorize the following:i) a^{2}+4 b^{2}

Q.39 i^{10} is equal to(b) -i (a) i (c) -1 (d) none of these
Q.39  i^{10}  is equal to(b)  -i (a)  i (c)  -1 (d) none of these

Q.39 i^{10} is equal to(b) -i (a) i (c) -1 (d) none of these

4. Prove the following rules of addition: -ii) \frac{a}{b}+\frac{c}{d}=\frac{a d+b c}{b d}
4. Prove the following rules of addition: -ii)  \frac{a}{b}+\frac{c}{d}=\frac{a d+b c}{b d}

4. Prove the following rules of addition: -ii) \frac{a}{b}+\frac{c}{d}=\frac{a d+b c}{b d}

4. Prove that \bar{z}=z iff z is real
4. Prove that  \bar{z}=z  iff  z  is real

4. Prove that \bar{z}=z iff z is real

Q.19 \forall a b c \in R a<b \wedge b<c \Rightarrow a<c this property of real numbers is(a) reflexive (b) symmetric (c) transitive (d) commutativeFederal Board 2010
Q.19  \forall a b c \in R a<b \wedge b<c \Rightarrow a<c this property of real numbers is(a) reflexive (b) symmetric (c) transitive (d) commutativeFederal Board 2010

Q.19 \forall a b c \in R a<b \wedge b<c \Rightarrow a<c this property of real numbers is(a) reflexive (b) symmetric (c) transitive (d) commutativeFederal Board 2010

Q.20 Which of the following statement is correct if a and b are distinct positive real numbers?(a) 2 \sqrt{a b}=a+b (b) 2 \sqrt{a b}>a+b (c) 2 \sqrt{a b}<a+b (d) 2(a+b)=\sqrt{a b}
Q.20 Which of the following statement is correct if  a  and  b  are distinct positive real numbers?(a)  2 \sqrt{a b}=a+b (b)  2 \sqrt{a b}>a+b (c)  2 \sqrt{a b}<a+b (d)  2(a+b)=\sqrt{a b}

Q.20 Which of the following statement is correct if a and b are distinct positive real numbers?(a) 2 \sqrt{a b}=a+b (b) 2 \sqrt{a b}>a+b (c) 2 \sqrt{a b}<a+b (d) 2(a+b)=\sqrt{a b}

Simplify the following:11. (26) \div(37) .
Simplify the following:11.  (26) \div(37) .

Simplify the following:11. (26) \div(37) .

3. Simplifyiv) i^{-10}
3. Simplifyiv)  i^{-10}

3. Simplifyiv) i^{-10}

Q.38 i^{2}= (b) (01) (c) (10) (d) (-10)
Q.38  i^{2}= (b)  (01) (c)  (10) (d)  (-10)
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Q.38 i^{2}= (b) (01) (c) (10) (d) (-10)

2. Find the multiplicative inverse of each of the following numbers: -i) -3 i
2. Find the multiplicative inverse of each of the following numbers: -i)  -3 i
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2. Find the multiplicative inverse of each of the following numbers: -i) -3 i

4. Prove the following rules of addition: -i) \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}
4. Prove the following rules of addition: -i)  \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}
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4. Prove the following rules of addition: -i) \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}

Q.15 For a b \in R a>b or a=b or a<b is the(a) trichotomy property of real numbers(b) left distributive property of real numbers(c) right distributive property of real numbers(d) cancellation property of real numbers
Q.15 For  a b \in R a>b  or  a=b  or  a<b  is the(a) trichotomy property of real numbers(b) left distributive property of real numbers(c) right distributive property of real numbers(d) cancellation property of real numbers
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Q.15 For a b \in R a>b or a=b or a<b is the(a) trichotomy property of real numbers(b) left distributive property of real numbers(c) right distributive property of real numbers(d) cancellation property of real numbers

1. Graph the following numbers on the complex plane: -v) -6
1. Graph the following numbers on the complex plane: -v)  -6
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1. Graph the following numbers on the complex plane: -v) -6

5. Simplify by expressing in the form a+b i iv) \frac{3}{\sqrt{6}-\sqrt{-12}}
5. Simplify by expressing in the form  a+b i iv)  \frac{3}{\sqrt{6}-\sqrt{-12}}
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5. Simplify by expressing in the form a+b i iv) \frac{3}{\sqrt{6}-\sqrt{-12}}

Find the additive and multiplicative inverses of:\[\text { (ii) }(-35)\]
Find the additive and multiplicative inverses of:\[\text { (ii) }(-35)\]
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Find the additive and multiplicative inverses of:\[\text { (ii) }(-35)\]

Q.40 i^{22}= (a) i (b) -i (c) -1
Q.40  i^{22}= (a)  i (b)  -i (c)  -1
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Q.40 i^{22}= (a) i (b) -i (c) -1

1. Perform the indicated operations:(iii) (7-9)-(35)
1. Perform the indicated operations:(iii)  (7-9)-(35)
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1. Perform the indicated operations:(iii) (7-9)-(35)

Example 1: Find moduli of the following complex numbers:(i) 1-i \sqrt{3}
Example 1: Find moduli of the following complex numbers:(i)  1-i \sqrt{3}
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Example 1: Find moduli of the following complex numbers:(i) 1-i \sqrt{3}

4. Justify each of the following statements by citing appropriate axioms.(iv) 8.8^{-1}=1
4. Justify each of the following statements by citing appropriate axioms.(iv)  8.8^{-1}=1
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4. Justify each of the following statements by citing appropriate axioms.(iv) 8.8^{-1}=1

MDCAT/ ECAT question bank