Linear Equation in One Variable

Q.

What is coefficient?

Q. A man is thrice as old as his son. After $12$ years, he will be twice as old as his son at that time. Find their present ages.

Q.

A linear equation in one variable has

1. Only one solution

2. Two solutions

3. More than two solutions

4. No solution

Q. A cricket team won two more matches than they lost. If they win they get 5 points and for loss − 3 points, how many matches have they played if their total score is 50.

Q.

Explain linear equations in one variable.

Q. Fill in the blank to make the statement true.
In a bag there are 5 and 2 rupee coins. If they are equal in number and their worth is Rs. 70, then
(a) The worth of x coins of Rs. 5 each _____.
(b) The worth of x coins of Rs. 2 each _____.
(c) The equation formed is _____.
(d) There are ___5 rupee coins and __2 rupee coins.

Q.

What is the difference between a constant and a coefficient?

Q. In the last stretch of a marathon, the 5 contestants are running with Anna at the back, Yusuf in the middle, and Jim at the front. If Mary overtakes Sheila just before the finish line, in what place would Mary finish at the end of the race?

1. 2nd
2. 3rd
3. 4th
4. Cannot be determined

Q. Let $a\in (0,1]$ satisfies the equation $a^{2008}-2a+1=0$ and $S=1+a+a^2+.....+a^{2007}$. Sum of all possible value(s) of $S$, is

1. $2010$
2. $2009$
3. $2008$
4. $2$

Q. I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5 . The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

1. The number of Rs 5 coins are 30,
   number of Rs 2 coins are 70 and,
   the number of Re 1 coins are 60
2. The number of Rs 5 coins are 10,
   number of Rs 2 coins are 50 and,
   the number of Re 1 coins are 100
3. The number of Rs 5 coins are 15,
   number of Rs 2 coins are 75 and,
   the number of Re 1 coins are 70
4. The number of Rs 5 coins are 20,
   number of Rs 2 coins are 60 and,
   the number of Re 1 coins are 80

Q. Which of the following is/are not linear equation(s)?

1. $5y-7zx=29x+30$
2. $x-2x^2+3x^3=4$
3. $\frac{3x+7y}{9z+7x}=2$
4. $3x+5y-7z=2x^2$

Q. Identify which of the following is/are a linear equation(s) in two variables.

1. $x^2=5$
2. $8x=7y$
3. $x^{2}y-1=0$
4. $\frac{x}{y}-2=0$

Q. Ramesh, Suresh and Mahesh share some amount of money in the ratio of 4:6:7. If Mahesh gives Ramesh ₹2p, then each of them will have the same amount of money. How much money does Suresh have?

1. ₹2p
2. ₹8p
3. ₹4p
4. ₹p

Q. Identify the equations below, which has no solution?

1. $\frac{3}{8}(x-2)=\frac{8}{3}(x+2)$
2. $6(\frac{2}{3}x+5)=4x+5$
3. $-\frac{3}{2}(2x-8)=3x-12$
4. $4(\frac{3}{4}x+5)=3x+20$

Q. The sum of a number and its reciprocal is $17/4$. The number is ____________.

1. $4$
2. $3$
3. $6$
4. $5$

Q. Some students planted $100$ trees. Out of the $100$ trees planted, the number of non-fruit-bearing trees was one more than twice the number of fruit-bearing trees. How many fruit-bearing and non-fruit-bearing trees did they plant?

1. $33\text{and}67$
2. $34\text{and}66$
3. $35\text{and}65$
4. $32\text{and}68$

Q. The two sisters purchased eight toys. How many toys did the other sister buy if the older sister bought 5 for herself?

1. 3
2. 4
3. 5
4. 8

Q. Which of the following is/are not linear equation(s)?

1. $5y-7zx=29x+30$
2. $x-2x^2+3x^3=4$
3. $3x+5y-7z=2x^2$
4. $\frac{3x+7y}{9z+7x}=2$

Q. How many variables are present in the given equation $5x+6y=3$ ?

Q. For which of the following linear equation(s) is $x=6$ a solution?

1. $\frac{x-3}{x+3}=\frac{2}{6}$
2. $3x+5=4x-1$
3. $5x=6x+6$
4. $x-5x=6$

Q. In the last stretch of a marathon, the 5 contestants are running with Anna at the back, Yusuf in the middle, and Jim at the front. If Mary overtakes Sheila just before the finish line, in what place would Mary finish at the end of the race?

1. 2nd
2. 3rd
3. 4th
4. Cannot be determined

Q. Is this statement correct "A linear equation in one variable is an equation which can be expresses in form of ax + b = 0, where $a\ne 0$ and a, b are real numbers."

1. Yes
2. No

Q.

Which one of the following is a solution of

$\frac{0.4}{0.12x}-5=21?$

(A) x = -7.8

(B) x = -6.9

(C) x = 7.8

(D) x = 6.9

Q. Mark the correct option in the following questions:Which of the following equations is not a linear equation?

1. $5+4x=y+3$
2. $x+2y=y-x$
3. $3-x=y^2+4$
4. $x+y=0$

Q. If the sum of two consecutive natural numbers is 25, then the smaller number is .

1. $12$
2. $9$
3. $6$

Q.

State which of the following is equation conatining variable$:$

$4\times 3+9=21$

Q. $3m<13$
$2m>7$
If $m$ is an integer that satisfies the equations above, what is the value of $m$?

1. $2$
2. $3$
3. $1$
4. $4$

Q. How many solutions does the following equation have?
$6(y-8)=6y-48$

Q. For which of the following linear equation(s) is $x=6$ a solution?

1. $x-5x=6$
2. $\frac{x-3}{x+3}=\frac{2}{6}$
3. $3x+5=4x-1$
4. $5x=6x+6$