# Math-[Diploma]-Set-1

1. What is the area of the right angled triangle whose perpendicular is 4 cm and base is 3 cm?

Area of right angled triangle = 1/2 (p×b)=1/2 (4 cm×3cm)= 1/2 (12cm²) = 6 cm².

2. What is the value of x when 4ˣ=64?

Because 4³= 4×4×4=16×4=64.

3. The mid-value of a class in a continuous series is 15. If the class interval is 10, what is the lower limit of the class?

Let the lower limit be x.
Since class interval is 10, upper limit will be x+10
Now we know that,
Mid value= (lower limit+upper limit)/ 2
or, 15 = (x+10+x)/2
or, 15= (2x+10)/2
or, 15 = x+5
or, x=15-5
∴ x=10

4. If universal set(U)= 125 and (A∪B)= 75, what is the value of complement of (A∪B)?

complement (A∪B)= U - (A∪B) =125-75=50

5. If the hypotenuse of a right angled triangle is 5 cm and base is 3 cm, what is the value of its perpendicular?

Because p= √h²-b²= √5²-3² = √25-9=√16=4

6. If a card is drawn randomly from a pack of cards, what is the probability of getting king?

In a card pack, there are 52 total cards and 4 king cards.
So probability of getting king= 4/52= 1/13

7. What is the value of x when √x-9=4?

Given, √x-9=4
Squaring on both sides, we get
(√x-9)²=4²
or, x-9=16
or, x=16+9= 25

8. If the radius of a cone is 'a' unit and slant height is 'b' unit, what will be the vertical height?

Because vertical height of a cone = √(slant height)² - (radius)²

9. What is the relation of the square and triangle standing on the same base and between the same parallel lines?

Area of triangle= 1/2 (Area of square)

10. The original value of an article is 'P'.If the value depreciates by 'R%' every year, what will be the value of the article after 'T' years?

The correct answer is P[ 1-(R/100)ᵀ ] .

11. If xᵃ. (1/xᵇ). xᵇ.(1/xᵃ)=xᶜ, what is the value of c?

xᵃ. (1/xᵇ). xᵇ.(1/xᵃ)=xᶜ
or, 1 =xᶜ
or, x⁰=xᶜ
∴c=0

12. What is the conjugate number of 2+√3?

Conjugate number means rationalising number.
For example:-
(2+√3) (2-√3)=(2)²-(√3)²= 4-3= 1.
Since we get 1 as answer which is rational number, the conjugate number of (2+√3) is (2-√3).

13. Write down the formula to find the curved surface area of a cone whose radius is 'r' and slant height is 'l'.

Curved surface area of cone = πrl

14. What is the volume of a pyramid whose base side is 'a' cm each and height is 'h' cm?

Volume of pyramid=1/3 (a²h)

15. What is the semi-perimeter of an isosceles triangle having base 'b' and equal sides 'a' each?

Semi-perimeter means half of perimeter.
So semi-perimeter of the given isosceles triangle =(2a+b)/2

16. The present population is 'P' and population increase rate is 'R%', write the formula to find total population after 'T' years.

The correct answer is P(T)=P[1+(R/100)^T ]

17. What is the formula to calculate curved surface area of a cylinder whose radius is 'r' unit and height is 'h' unit?

18. What is the formula to find the area of the triangle whose sides are 'a', 'b', 'c' and semi-perimeter is 's' ?

19. If the area of the base of a 'h' metre high cylindrical chimney is 'A' square metre, what is the volume of the chimney?