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Chapter 13

Simple Equations — Multiple Choice Questions

Class - 6 RS Aggarwal Mathematics Solutions

Exercise 13(C) - Multiple Choice Questions

Question 1

5 less than thrice xx is

  1. 5−3x5 - 3x

  2. 3x−53x - 5

  3. 3x5\dfrac{3x}{5}

  4. 5+3x5 + 3x

Answer

Thrice x=3xx = 3x.

5 less than thrice xx means 5 is subtracted from 3x3x, i.e., 3x−53x - 5.

Hence, option 2 is the correct option.

Question 2

If 5x+8=45x + 8 = 4, then 3x3x = ?

  1. −512\dfrac{-5}{12}

  2. −1512\dfrac{-15}{12}

  3. −125\dfrac{-12}{5}

  4. 125\dfrac{12}{5}

Answer

Solving,

⇒5x+8=4 [By transposition] ⇒5x=4−8⇒5x=−4 [Dividing each side by 5] ⇒x=−45.\Rightarrow 5x + 8 = 4 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 5x = 4 - 8 \\[1em] \Rightarrow 5x = -4 \\[1em] \text{ [Dividing each side by 5] } \\[1em] \Rightarrow x = \dfrac{-4}{5}.

∴ 3x=3×−45=−1253x = 3 \times \dfrac{-4}{5} = \dfrac{-12}{5}

Hence, option 3 is the correct option.

Question 3

If 3m−8=−43m - 8 = -4, then mm = ?

  1. −34\dfrac{-3}{4}

  2. 34\dfrac{3}{4}

  3. −43\dfrac{-4}{3}

  4. 43\dfrac{4}{3}

Answer

Solving,

⇒3m−8=−4 [By transposition] ⇒3m=−4+8⇒3m=4 [Dividing each side by 3] ⇒m=43.\Rightarrow 3m - 8 = -4 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 3m = -4 + 8 \\[1em] \Rightarrow 3m = 4 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow m = \dfrac{4}{3}.

Hence, option 4 is the correct option.

Question 4

If 4x+3=154x + 3 = 15, then 2x−32x - 3 = ?

  1. 0

  2. -3

  3. 3

  4. -6

Answer

Solving,

⇒4x+3=15 [By transposition] ⇒4x=15−3⇒4x=12 [Dividing each side by 4] ⇒x=124=3.\Rightarrow 4x + 3 = 15 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 4x = 15 - 3 \\[1em] \Rightarrow 4x = 12 \\[1em] \text{ [Dividing each side by 4] } \\[1em] \Rightarrow x = \dfrac{12}{4} = 3.

∴ 2x−3=2×3−3=6−3=32x - 3 = 2 \times 3 - 3 = 6 - 3 = 3

Hence, option 3 is the correct option.

Question 5

If m3+2=5\dfrac{m}{3} + 2 = 5, then mm = ?

  1. 6

  2. 9

  3. 5

  4. 4

Answer

Solving,

⇒m3+2=5 [By transposition] ⇒m3=5−2⇒m3=3 [Multiplying each side by 3] ⇒m=3×3=9.\Rightarrow \dfrac{m}{3} + 2 = 5 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{m}{3} = 5 - 2 \\[1em] \Rightarrow \dfrac{m}{3} = 3 \\[1em] \text{ [Multiplying each side by 3] } \\[1em] \Rightarrow m = 3 \times 3 = 9.

Hence, option 2 is the correct option.

Question 6

If x2+3=5−x\dfrac{x}{2} + 3 = 5 - x, then xx = ?

  1. 43\dfrac{4}{3}

  2. 34\dfrac{3}{4}

  3. 53\dfrac{5}{3}

  4. 35\dfrac{3}{5}

Answer

Solving,

⇒x2+3=5−x [By transposition] ⇒x2+x=5−3 [Taking L.C.M.] ⇒x+2x2=2⇒3x2=2 [Multiplying each side by 2] ⇒3x=4 [Dividing each side by 3] ⇒x=43.\Rightarrow \dfrac{x}{2} + 3 = 5 - x \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{x}{2} + x = 5 - 3 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{x + 2x}{2} = 2 \\[1em] \Rightarrow \dfrac{3x}{2} = 2 \\[1em] \text{ [Multiplying each side by 2] } \\[1em] \Rightarrow 3x = 4 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{4}{3}.

Hence, option 1 is the correct option.

Question 7

If x2−5=x3−6\dfrac{x}{2} - 5 = \dfrac{x}{3} - 6, then xx = ?

  1. -5

  2. -6

  3. 3

  4. -3

Answer

Solving,

⇒x2−5=x3−6 [By transposition] ⇒x2−x3=−6+5 [Taking L.C.M.] ⇒3x−2x6=−1⇒x6=−1 [Multiplying each side by 6] ⇒x=−6.\Rightarrow \dfrac{x}{2} - 5 = \dfrac{x}{3} - 6 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{x}{2} - \dfrac{x}{3} = -6 + 5 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{3x - 2x}{6} = -1 \\[1em] \Rightarrow \dfrac{x}{6} = -1 \\[1em] \text{ [Multiplying each side by 6] } \\[1em] \Rightarrow x = -6.

Hence, option 2 is the correct option.

Question 8

If x3−x4=5\dfrac{x}{3} - \dfrac{x}{4} = 5, then xx = ?

  1. 512\dfrac{5}{12}

  2. 125\dfrac{12}{5}

  3. 6060

  4. 160\dfrac{1}{60}

Answer

Solving,

⇒x3−x4=5 [Taking L.C.M.] ⇒4x−3x12=5⇒x12=5 [Multiplying each side by 12] ⇒x=60.\Rightarrow \dfrac{x}{3} - \dfrac{x}{4} = 5 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{4x - 3x}{12} = 5 \\[1em] \Rightarrow \dfrac{x}{12} = 5 \\[1em] \text{ [Multiplying each side by 12] } \\[1em] \Rightarrow x = 60.

Hence, option 3 is the correct option.

Question 9

If 4x−1=74x - 1 = 7, then 3x−23x - 2 = ?

  1. 3

  2. 4

  3. 5

  4. 6

Answer

Solving,

⇒4x−1=7 [By transposition] ⇒4x=7+1⇒4x=8 [Dividing each side by 4] ⇒x=84=2.\Rightarrow 4x - 1 = 7 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 4x = 7 + 1 \\[1em] \Rightarrow 4x = 8 \\[1em] \text{ [Dividing each side by 4] } \\[1em] \Rightarrow x = \dfrac{8}{4} = 2.

∴ 3x−2=3×2−2=6−2=43x - 2 = 3 \times 2 - 2 = 6 - 2 = 4

Hence, option 2 is the correct option.

Question 10

If 2x2−8=2−x\dfrac{2x}{2} - 8 = 2 - x, then xx = ?

  1. 5

  2. 4

  3. 6

  4. 9

Answer

Solving,

⇒2x2−8=2−x⇒x−8=2−x [By transposition] ⇒x+x=2+8⇒2x=10 [Dividing each side by 2] ⇒x=102=5.\Rightarrow \dfrac{2x}{2} - 8 = 2 - x \\[1em] \Rightarrow x - 8 = 2 - x \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow x + x = 2 + 8 \\[1em] \Rightarrow 2x = 10 \\[1em] \text{ [Dividing each side by 2] } \\[1em] \Rightarrow x = \dfrac{10}{2} = 5.

Hence, option 1 is the correct option.

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