Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths similarity relation between perimeters of similar shapes basic proportionality theorem and its converse basic proportionality theorem

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
  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. $\displaystyle 1\rightarrow c,2\rightarrow b,3\rightarrow d,4\rightarrow a$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

Express the following as a recurring decimal.

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

  1. $0.\overline{28}$
  2. $0.\overline{285714}$
  3. $0.\overline{2857}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

Express  the following in a recurring decimal form.

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

  1. $0.\overline{3}$
  2. $0.\overline{29}$
  3. $0.\overline{4}$
  4. $0.\overline{27}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

In this division $27$ is a recurring decimal.

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

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

$7 \div 11$.

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

The non terminating non-recurring decimal cannot be represented as

  1. irrational numbers

  2. rational numbers

  3. real numbers

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.