2 3 + 3 2\sqrt{3}+\ \sqrt{3} 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> is equal to

3 3 3\sqrt{3} 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 6 2\sqrt{6} 2 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 6 4\sqrt{6} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

10 × 5 \sqrt{10}\ \times\sqrt{5} 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> × 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> is equal to

50 \sqrt{50} 5 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

15 \sqrt{15} 1 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

150 \sqrt{150} 1 5 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

What is the solution to a system of equations?

The point that the equations have in common.

The point where the two lines intersect.

The pair of equations a x + 2 y = 7 ax+2y=7 a x + 2 y = 7 a nd 3x+by=16 3 x + b y = 1 6 represent parallel lines if :

2 a − 3 b = 0 2a-3b=0 2 a − 3 b = 0

If a pair of linear equations unique solution then

a 1 a 2 ≠ b 1 b 2 \frac{a_1}{a_2}\ \ne\frac{b_1}{b_2}\ a 2 a 1  = b 2 b 1

a 1 a 2 = b 1 b 2 = c 1 c 2 \frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ =\frac{c_1}{c_2} a 2 a 1 = b 2 b 1 = c 2 c 1

a 1 a 2 = b 1 b 2 ≠ c 1 c 2 \frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2} a 2 a 1 = b 2 b 1  = c 2 c 1

a 1 a 2 ≠ b 1 b 2 ≠ c 1 c 2 \frac{a_1}{a_2}\ \ne\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2} a 2 a 1  = b 2 b 1  = c 2 c 1

In a pair of linear equations a 1 a 2 = b 1 b 2 = c 1 c 2 \frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ =\frac{c_1}{c_2} a 2 a 1 = b 2 b 1 = c 2 c 1 then they are

coincident lines, infinitely many solutions

intersecting lines, exactly one solution

In a pair of linear equations a 1 a 2 = b 1 b 2 ≠ c 1 c 2 \frac{a_1}{a_2}\ =\frac{b_1}{b_2}\ \ne\frac{c_1}{c_2} a 2 a 1 = b 2 b 1  = c 2 c 1 then they are

coincident lines, infinitely many solutions

intersecting lines, exactly one solution

a n = a + ( n − 1 ) d a_{n\ }=a\ +\left(n-1\right)d a n = a + ( n − 1 ) d

a n = d + ( n − 1 ) a a_{n\ }=d\ +\left(n-1\right)a a n = d + ( n − 1 ) a

a n = a + ( n + 1 ) d a_{n\ }=a\ +\left(n+1\right)d a n = a + ( n + 1 ) d

a n = d + ( n + 1 ) a a_{n\ }=d\ +\left(n+1\right)a a n = d + ( n + 1 ) a

The sum of the first n-term of an AP is

s = n 2 ( 2 a + ( n − 1 ) d ) s\ =\frac{n}{2}\left(2a\ +\ \left(n-1\right)d\right) s = 2 n ( 2 a + ( n − 1 ) d )

s = ( 2 a + ( n − 1 ) d ) s\ =\left(2a\ +\ \left(n-1\right)d\right) s = ( 2 a + ( n − 1 ) d )

s = n 2 ( a + ( n − 1 ) d ) s\ =\frac{n}{2}\left(a\ +\ \left(n-1\right)d\right) s = 2 n ( a + ( n − 1 ) d )

s = n 2 ( 2 a + ( n + 1 ) d ) s\ =\frac{n}{2}\left(2a\ +\ \left(n+1\right)d\right) s = 2 n ( 2 a + ( n + 1 ) d )

Which of the following is called as the section formula.

( m 1 x 2 + m 2 x 1 m 1 + m 2 , m 1 y 2 + m 2 y 1 m 1 + m 2 ) \left(\frac{m_1\ x_2\ +\ m_2\ x_1}{m_1\ +\ m_2},\ \frac{m_1\ y_2\ +\ m_2\ y_1}{m_1\ +\ m_2}\right) ( m 1 + m 2 m 1 x 2 + m 2 x 1 , m 1 + m 2 m 1 y 2 + m 2 y 1 )

( m 1 x 2 − m 2 x 1 m 1 − m 2 , m 1 y 2 − m 2 y 1 m 1 − m 2 ) \left(\frac{m_1\ x_2\ -\ m_2\ x_1}{m_1\ -\ m_2},\ \frac{m_1\ y_2\ -\ m_2\ y_1}{m_1\ -\ m_2}\right) ( m 1 − m 2 m 1 x 2 − m 2 x 1 , m 1 − m 2 m 1 y 2 − m 2 y 1 )

( m 1 x 1 + m 2 x 2 m 1 + m 2 , m 1 y 1 + m 2 y 2 m 1 + m 2 ) \left(\frac{m_1\ x_1\ +\ m_2\ x_2}{m_1\ +\ m_2},\ \frac{m_1\ y_1\ +\ m_2\ y_2}{m_1\ +\ m_2}\right) ( m 1 + m 2 m 1 x 1 + m 2 x 2 , m 1 + m 2 m 1 y 1 + m 2 y 2 )

( m 1 x 1 − m 2 x 2 m 1 − m 2 , m 1 y 1 − m 2 y 2 m 1 − m 2 ) \left(\frac{m_1\ x_1\ -\ m_2\ x_2}{m_1\ -\ m_2},\ \frac{m_1\ y_1\ -\ m_2\ y_2}{m_1\ -\ m_2}\right) ( m 1 − m 2 m 1 x 1 − m 2 x 2 , m 1 − m 2 m 1 y 1 − m 2 y 2 )

CLASS 10 MATHS (Chapter :1,2,3,4,5,7)

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CLASS 10 MATHS (Chapter :1,2,3,4,5,7)

Quiz

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Mathematics

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10th Grade

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Practice Problem

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CCSS

HSF.BF.A.2, 8.EE.C.8B, HSA.APR.B.3

+21

Standards-aligned

Jayashree Kadam

Used 9+ times

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60 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$2\sqrt{3}+\ \sqrt{3}$ is equal to

$2\sqrt{6}$

$3\sqrt{3}$

$4\sqrt{6}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\sqrt{10}\ \times\sqrt{5}$ is equal to

$\sqrt{15}$

$\sqrt{150}$

$\sqrt{50}$

$a^{-1}$ is equal to

$\frac{1}{a}$

-0.775 is a

Irrational Number

Whole Number

Integer

Rational Number

$\sqrt{3}$ is considered a...

Whole number

Integer

Irrational Number

Rational Number

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Euclid Division Lemma is used to find

HCF

LCM

Both HCF and LCM

FILL IN THE BLANK QUESTION

1 min • 1 pt

HCF of (126,156)

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