9x – ……………….. = – 21 has the solution (- 2).
Question: 9x .. = 21 has the solution (- 2). Solution: Let 9x-m= -21 has the solution (-2). Since, $x=-2$ is the solution of the equation. $\therefore$$9 \times(-2)-m=-21$ $\Rightarrow$ $-18-m=-21$ [transposing $-21$ to LHS and $-m$ to RHS] $-18+21=m$ $\Rightarrow$ $m=3$ Hence, $9 x-3=-21$ has the solution $(-2)$....
Read More →Any value of the variable,
Question: Any value of the variable, which makes both sides of an equation equal, is known as aof the equation. Solution: e.g. x + 2 = 3 = x = 3-2 = 1 [transposing 2 to RHS] Hence, x = 1 satisfies the equation and it is a solution of the equation....
Read More →The solution of the equation
Question: The solution of the equation 2y = 5y-185is. Solution: $\frac{6}{5}$ Given, $2 y=5 y-\frac{18}{5}$ $\Rightarrow$ $2 y-5 y=\frac{-18}{5}$ [transposing 5yto LHS] $\Rightarrow$ $-3 y=-\frac{18}{5}$ $\Rightarrow$ $\frac{-3 y}{-3}=\frac{-18}{-3 \times 5}$ [dividing both sides by $-3$ ] $\therefore$ $y=\frac{6}{5}$ Hence, the solution of the given equation is $\frac{6}{5}$....
Read More →The solution of the equation 3x – 4 = 1 – 2x
Question: The solution of the equation 3x 4 = 1 2x is- . Solution: 1 Given, $3 x-4=1-2 x$ $\Rightarrow$ $3 x+2 x=1+4$ [transposing $-2 x$ to LHS and $-4$ to RHS] $\Rightarrow$ $5 x=5$ $\Rightarrow$ $\frac{5 x}{5}=\frac{5}{5}$[dividing both sides by 5 ] $\therefore \quad x=1$ Hence, the solution of the given equation is 1 ....
Read More →In a linear equation, the——— power of the variable
Question: In a linear equation, the power of the variable appearing in the equation is one. Solution: highest e.g. x + 3 = O and x + 2 = 4 are the linear equations....
Read More →The sum of three consecutive multiples of 7 is 357.
Question: The sum of three consecutive multiples of 7 is 357. Find the smallest multiple. (a) 112 (b) 126 (c) 119 (d) 116 Solution: (a) Let the three consecutive multiples of 7 be $7 x,(7 x+7),(7 x+14)$ where $x$ is a natural number. According to the question, $7 x+(7 x+7)+(7 x+14)=357$ $\Rightarrow \quad 21 x+21=357$ $\Rightarrow \quad 21(x+1)=357$ $\Rightarrow \quad \frac{21(x+1)}{21}=\frac{357}{21}$ [dividing both sides by 21 ] $\Rightarrow \quad x+1=17$ $\Rightarrow \quad x=17-1 \quad$ [tran...
Read More →Arpita’s present age is thrice of Shilpa.
Question: Arpitas present age is thrice of Shilpa. If Shilpas age three years ago was x, then Arpitas present age is (a) 3 (x 3) (b)3x + 3 (c) 3x 9 (d) 3(x + 3) Solution: (d) Given, Shilpas age three years ago = x Then, Shilpas present age = (x + 3) Arpitas present age = 3 x Shilpas present age = 3 (x + 3)...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{1}{2-|x|} \geq$ $1, x \in R-\{-2,2\}$ Solution: Given: $\frac{1}{2-|x|} \geq 1, x \in \mathrm{R} .-\{-2,2\}$ Intervals of $|x|:$ $x \geq 0,|x|=x$ and $x0,|x|=-x$ Domain of $\frac{1}{2-|x|} \geq_{1}$ $\frac{1}{2-|x|} \geq 1$ is undefined at $x=-2$ and $x=2$ Therefore, Domain: $x-2$ or $x2$ Combining intervals with domain: $x-2,-2x0,0 \leq x2, x2$ For $x-2$ $\frac{1}{2-(-x)} \geq 1$ Subtrac...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: In the pie chart representing the percentages of students having interest in reading various kinds of books, the central angle of the sector representing students reading novels is 81. What is the percentage of students interested in reading novels? (a) 15% (b) 18% (c) $22 \frac{1}{2} \%$ (d) $27 \frac{1}{2} \%$ Solution: (c) $22 \frac{1}{2} \%$ Let the required percentage be $x$. Then we have : $\left(\frac{x}{100} \times 360\right)=81$ $\Rightarrow \frac{...
Read More →The digit in the ten’s place of a two-digit number
Question: The digit in the tens place of a two-digit number is 3 more than the digit in the units place. Let the digit at units place be b. Then, the number is (a) 11b+30 (b) 10b+ 30 (c) 11 b + 3 (d) 10b + 3 Solution: (a) Let digit at units place be b. Then, digit at tens place = (3 + b) Number = 10 (3 + b) + b 30 + 10b + b = 11b + 30...
Read More →prove that
Question: If 43y = 34then y is equal to (a) $-\left[\frac{3}{4}\right]^{2}$ (b) $-\left[\frac{4}{3}\right]^{2}$ (c) $\left[\frac{3}{4}\right]^{2}$ (d) $\left[\frac{4}{3}\right]^{2}$ Solution: (c) Given, $-\frac{4}{3} y=\frac{-3}{4}$ $y=\frac{-3}{4} \times \frac{-3}{4}$ [by cross-multiplication] $\Rightarrow \quad y=\left(\frac{3}{4}\right)^{2}$ Hence, the value of $y$ is $\left(\frac{3}{4}\right)^{2}$....
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: If in the pie chart representing the number of students opting for different streams of study out of a total strength of 1650 students, the central angle of the sector representing arts students is 48 then what is the number of students who opted for arts stream? (a) 220 (b) 240 (c) 275 (d) 320 Solution: (a) 220 Let the required number of students be $x$. Then we have: $\left(\frac{x}{1650} \times 360\right)=48$ $\Rightarrow \frac{360 x}{1650}=48$ $\Rightar...
Read More →The value of S in
Question: The value of $S$ in $\frac{1}{3}+S=\frac{2}{5}$ is (a) $\frac{4}{5}$ (b) $\frac{1}{15}$ (c) 10 (d) 0 Solution: (b) Given, $\frac{1}{3}+S=\frac{2}{5}$ $\Rightarrow \quad S=\frac{2}{5}-\frac{1}{3}$ $\left[\right.$ transposing $\frac{1}{3}$ to RHS $]$ $\Rightarrow \quad S=\frac{6-5}{15}$ [taking LCM in RHS] $\therefore \quad S=\frac{1}{15}$...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: If 35% of the people residing in a locality are Sikhs then the central angle of the sector representing the Sikh community in the pie chart would be (a) 108 (b) 115 (c) 126 (d) 135 Solution: (c) $126^{\circ}$ Central angle of the sector representing the sikh community $=\left(\frac{\text { value (in \%) of the sikh community }}{100} \times 360\right)^{\circ}$ $=\left(\frac{35}{100} \times 360\right)^{\circ}$ $=126^{\circ}$...
Read More →Tick (✓) the correct answer:
Question: Tick $(\checkmark$ the correct answer: A man's monthly salary is Rs 2400 and his monthly expenses on travel are Rs 250 . The central angle of the sector representing travel expenses in the pie chart would be (a) $30^{\circ}$ (b) $37 \frac{1}{2}^{\circ}$ (c) $45^{\circ}$ (d) $60^{\circ}$ Solution: (b) $37 \frac{1}{2}^{\circ}$ Central angle of the sector representing travel expenses $=\left(\frac{\text { value of expenses on travel }}{\text { monthly income }} \times 360\right)^{\circ}$ ...
Read More →The following table shows the percentages of buyers of four different brands of bathing soaps.
Question: The following table shows the percentages of buyers of four different brands of bathing soaps. Represent the above data by a pie chart. Solution: Total percentage $=100$ Central angle of each brand $=\left(\frac{\text { value (in \%) of each brand }}{100} \times 360\right)^{\circ}$ Calculation of central angles : Construction of pie chart Steps of construction: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Draw sectors whose central angles are...
Read More →Given below is the result of an annual examination of a class, showing the percentage of students in each category.
Question: Given below is the result of an annual examination of a class, showing the percentage of students in each category. Represent the above data by a pie chart. Solution: Total percentage $=100$ Central angle of each category $=\left(\frac{\text { value (in \%) of each category }}{100} \times 360\right)^{\circ}$ Calculation of central angles Construction of pie chart Steps of construction: 1. Draw a circle of any convenient radius. 2. Draw a horizontal radius of the circle. 3. Starting fro...
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{|x|-1}{|x|-2} \geq 0, x \in$ R. $-\{-2,2\}$ Solution: Given: $\frac{|x|-1}{|x|-2} \geq 0, x \in$ R. $-\{-2,2\}$ Intervals of $|x|$ : $x \geq 0,|x|=x$ and $x0,|x|=-x$ Domain of $\frac{|x|-1}{|x|-2} \geq 0$ $\frac{|x|-1}{|x|-2}$ is not defined for $x=-2$ and $x=2$ Therefore, Domain: x -2 or -2 x 2 or x 2 Combining intervals with domain: $x-2,-2x0,0 \leq x2, x2$ For $x-2$ : $\frac{|x|-1}{|x|...
Read More →A linear equation in one variable has
Question: A linear equation in one variable has (a) only one solution (b) two solutions (c) more than two solutions (d) no solution Solution: (a) A linear equation in one variable has only one solution. e.g. Solution of the linear equation $a x+b=0$ is unique, i.e. $x=\frac{-b}{a}$...
Read More →Which of the following is a linear expression?
Question: Which of the following is a linear expression? (a) $x^{2}+1$ (b) $y+y^{2}$ (c) 4 (d) $1+z$ Solution: (d) We know that, the algebraic expression in one variable having the highest power of the variable as 1, is known as the linear expression. Here, 1 + z is the only linear expression, as the power of the variable z is 1....
Read More →Linear equation in one variable has
Question: Linear equation in one variable has (a) only one variable with any power (b) only one term with a variable (c) only one variable with power 1 (d) only constant term Solution: (c) Linear equation in one variable has only one variable with power 1. e.g. 3x + 1 = 0,2y 3 = 7 and z + 9 = 2 are the linear equations in one variable....
Read More →If a and b are positive integers,
Question: If a and b are positive integers, then the solution of the equation ax = b has to be always (a) positive (b) negative (c) one (d) zero Solution: (a) If $a x=b$, then $x=\frac{b}{a}$ Since, a and b are positive integers. So, $\frac{b}{a}$ is also positive integer, Hence, the solution of the given equation has to be always positive....
Read More →The value of x,
Question: The value of x, for which the expressions 3x 4 and 2x + 1 become equal, is (a) -3 (b) 0 (c) 5 x (d) 1 Solution: (c) Given expressions 3x 4 and 2x + 1 are equal. Then, 3x-4 = 2x + 1 3x- 2x = 1 + 4 [transposing 2x to LHS and -4 to RHS] x = 5Hence, the value of x is 5....
Read More →Solve each of the following in equations and represent the solution set on
Question: Solve each of the following in equations and represent the solution set on the number line. $\frac{|x-3|}{x-3}0, x \in \mathbf{R}$ Solution: Given: $\frac{|x-3|}{x-3}0, x \in R$ $|x-3|0$ The above condition cant be true because the absolute value cannot be less than 0 Therefore There is no solution for x є R....
Read More →prove that
Question: If $\frac{5 x}{3}-4=\frac{2 x}{5}$, then the numerical value of $2 x-7$ is (a) $\frac{19}{13}$ (b) $\frac{-13}{19}$ (c) 0 (d) $\frac{13}{19}$ Solution: (b) Given,$\frac{5 x}{3}-4=\frac{2 x}{5}$ $\Rightarrow$ $\frac{5 x}{3}-\frac{2 x}{5}=4$ $\left[\right.$ transposing $\frac{2 x}{5}$ to LHS and $-4$ to RHS $]$ $\Rightarrow$ $\frac{25 x-6 x}{15}=4$ [taking LCM in LHS] $\Rightarrow$ $19 x=60$ $\Rightarrow$ $\frac{19 x}{19}=\frac{60}{19}$ [dividing both sides by 19 ] $\therefore$ $x=\frac{...
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