Tag: maths

Questions Related to maths

Match the column.

1. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$ (a) AA similarity criterion 
2. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \angle A=\angle P,\angle B=\angle Q$ (b) SAS similarity criterion 
3. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$$\angle A=\angle P$ (c) SSS similarity criterion 
4. In $\displaystyle \Delta ACB,DE
maths similarity relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

  1. $\displaystyle 1\rightarrow a,2\rightarrow b,3\rightarrow c,4\rightarrow d$

  2. $\displaystyle a\rightarrow d,2\rightarrow a,3\rightarrow c,4\rightarrow b$

  3. $\displaystyle 1\rightarrow b,2\rightarrow a,3\rightarrow c,4\rightarrow d$

  4. $\displaystyle 1\rightarrow c,2\rightarrow b,3\rightarrow d,4\rightarrow a$

Show answer
Correct Option: C
Explanation:

In $\triangle ABC$ and $\triangle PQR$

Option A:

If $\angle A = \angle P$      ....Given

And, $\dfrac {AB}{PQ} = \dfrac {AC}{PR}$    ...Given

$\triangle ABC \sim \triangle PQR$        ...SAS test of similarity


Option B:

If $\angle A = \angle P$      ....Given

And $\angle B = \angle Q$      ....Given

$\triangle ABC \sim \triangle PQR$        ...AA test of similarity


Option C:

If $\angle A = \angle P$      ....Given

And $\dfrac {AB}{PQ} = \dfrac {AC}{PR} = \dfrac {BC}{QR}$      ....Given

$\triangle ABC \sim \triangle PQR$        ...SS S test of similarity


Option D:

In $\triangle ACB, DE \parallel BC$

$\dfrac {AD}{BD} = \dfrac {AE}{CE} $      ....Given

This is known as basic proportionality theorem.

Say true or false:
The following is a terminating  decimal. $ 5 \div 8$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.
Here, $5$ divided by $8$ gives $0.625$.

Hence, it is a terminating decimal.

Express the following as a recurring decimal.

$\displaystyle \frac{2}{7}$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $0.\overline{28}$

  2. $0.\overline{285714}$

  3. $0.\overline{2857}$

  4. None of these

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac { 2 }{ 7 }  = 0.285714285.. = 0.\overset { \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _  }{ 285714 } $

In this division, $285714$ is a recurring decimal.

Express  the following in a recurring decimal form.

$\displaystyle \frac{3}{11}$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $0.\overline{3}$

  2. $0.\overline{29}$

  3. $0.\overline{4}$

  4. $0.\overline{27}$

Show answer
Correct Option: D
Explanation:

The value of $\displaystyle \frac { 3 }{ 11 }$ is $ 0.272727272727.. 0.\overset { \ _ \ _ \ _ \ _  }{ 27 } $

In this division $27$ is a recurring decimal.

Find, whether each of the followings is a terminating or a non-terminating decimal.

$7 \div 11$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient

Show answer
Correct Option: B
Explanation:

While expressing a fraction in the decimal form, when we perform division we get some remainder. 

If the division process does not end i.e. we do not get the remainder equal to zero; then such decimal is known as non-terminating decimal.
Here, $7$ divided by $11$ gives $0.636363636363.... $.
Therefore, this is a case of non terminating decimal.

Find whether it is a terminating or a non-terminating decimal.

$1.2 \div 0.16$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient

Show answer
Correct Option: A
Explanation:

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$1.2\div 0.16= 7.5$
Hence, terminating decimal.

Express  the following in a recurring decimal form.

$\displaystyle 2\frac{1}{6}$.

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $2.1\bar{6}$

  2. $2.1\bar{8}$

  3. $2.1\bar{4}$

  4. $2.1\bar{9}$

Show answer
Correct Option: A
Explanation:

$2\displaystyle \frac { 1 }{ 6 }  = \frac { 13 }{ 6 }  = 2.166666666.. = 2.1\overset { \ _ \ _  }{ 6 } $

In this division, $6$ is recurring. 

The decimal representation of $\dfrac {65}{455}$ will be

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. terminating

  2. non-terminating

  3. non-terminating repeating

  4. non-terminating non-repeating

Show answer
Correct Option: C
Explanation:

$\frac {65}{455}=0.\overline { 142857 } $
Therefore, the decimal representation will be non-terminating repeating.

Convert the following fraction into simple decimal recurring form.

$\displaystyle \frac{5}{6}$ = ?

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $0.4\bar 3$

  2. $0.1\bar 3$

  3. $0.\bar 4$

  4. $0.8\bar 3$

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac { 5 }{ 6 }= 0.83333333..= 0.8\overset { \ _ \ _  }{ 3 } $ 
This is a pure recurring decimal as $3$ is repeated continuously.

The non terminating non-recurring decimal cannot be represented as

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. irrational numbers

  2. rational numbers

  3. real numbers

  4. none of these

Show answer
Correct Option: B
Explanation:

Write the decimal number as a fraction $0.2020020002...... $
It is Non- terminating decimal and cannot be represented as a quotient of two integers.
Therefore, B is the correct answer.