8th Grade > Mathematics
LINEAR EQUATIONS IN ONE VARIABLE MCQs
:
B, C, and D
An algebraic expression consists of operands (variables and numbers) and operators (+, −, ×, ÷).
When an algebraic expression is equated to another algebraic expression (which may be even 0), we get an algebraic equation.
So, 3x - 5y + 6z is not an equation, but an expression.
:
C
By substituting n = 10 in the given equation, we can find out the 10th term i.e.,
2.5x−10 = (2.5 × 10) - 10
= 25 - 10
= 15
:
B
Perimeter of swimming pool =64 (Given)
Perimeter of rectangle =2(length+breadth)
Since length and breadth are given to be in the ratio 5 : 3, we can assume them to be 5x and 3x respectively.
⇒ Length = 5x and breadth = 3x
Substituting these in the formula of perimeter, we get
64=2(5x+3x)⇒ 8x=32⇒ x=4
∴ Length of the swimming pool
=5x=5×4=20 m
:
A
37 + x = 177
x = (177)–(37) = 147 = 2
Hence, the solution of the equation 37 + x = 177 is 2.
Hence the given statement is true.
:
A
Let, the number which Anita initially thought of be x.
She subtracts 32 from x and then multiplies it by 8.
⇒(x –32)×8
According to the question, (x –32)×8=5×x8x –12=5x8x –5x=123x=12x=123x=4
Thus, the number that Anita initially thought of is 4.
:
A
Let the digit in units place be x.
Then, the digit in tens place will be 2x.
So, the number will be
(10×2x)+(1×x)=20x+x=21x
When we interchange the digits, the number will be
(10×x)+(1×2x)=10x+2x=12x
It is given that,
21x+12x=66
⇒ 33x=66
⇒ x=6633
⇒ x=2
∴The digit in units place =2
The digit in tens place =4
The original number is 42.
Verification:
Original number =42
Interchanging the digits of 42, we get 24.
Sum of the original number and the interchanged number is 42+24=66.
:
B
Let Vinay’s present age be xThen, his mother’s present age =3x
After 5 years,Vinay’s age = x+5Vinay's mother’s age = 3x+5
Sum of Vinay and Vinay's Mother's age after 5 years = 70
⇒x+5+3x+5=70⇒4x+10=70⇒4x=60⇒x=15⇒3x=45
∴Vinay’s age is 15 years and his mother’s age is 45 years.
:
A
Let the total number of students be x
According to the question,
Number of students dancing =x2
Number of students remaining =x−x2
=x2
Students playing cricket
=(34)(x2)
=3x8
Remaining students =9
⇒ (x−x2)−3x8=9⇒ x8=9⇒ x=8×9⇒ x=72
Hence, the total number of students in the class = 72
:
Let Arjun be x years old now
After 20 years, his age will be x + 20
According to question,
x + 20 = 3x or 3x = x + 20
3x - x = 20
2x = 20
x = 10
Therefore, Arjun's present age is 10 yrs.
:
C
Let the base of the triangle be x cm.
Then, the corresponding altitude of the triangle would be 3x5 cm.
If altitude is increased by 4 cm, the new altitude =3x5+4 cm
New base =x−2 cm
Area of triangle =12×base×height
Since the area remains the same, 12×x×3x5=12×(3x5+4)×(x−2)
⇒ 3x25 = 3x25+4x−6x5−8
⇒ 4x−6x5=8⇒20x−6x5=8
⇒14x=40
⇒ x=4014=207⇒ x=267 cm
Hence, base of the triangle is267 cm long.