nat

1. CIRCLE

2. 2
No.
1

3. Solve for
y.
11/3
9
A
11
B
39
C
39/1
1
D
2
No.
1

4. Solve for
y.
2
No.
1

5. 2
No.
2

6. Find the
value of x.
4
A
-4
B
5
C
-5
D
2
No.
2

7. Find the value of x.
2
No.
2

8. Write the standard
equation of the circle
with the given center
(0,0) and r = 13
x2+y2 =1
A
x2+y2 =16
B
x2+y2 =13
C
x2+y2 =169
D
No.
3

9. Write the standard equation of the circle
with the given center (0,0) and r = 13
No.
3
(x – h)2 + (y – h)2 = r2
(x – 0)2 + (y – 0)2 = 132
x 2 + y 2 = 169

10. Write the standard
equation of the circle with
the given center (5,7) and
r = 5
(x-5)2+(y-7)2
=25
A
(x-5)2+(y-7)2 =
5
B
(x-5)2+(y)2
=25
C
(x-5)2+(y)2 =5
D
No.
4

11. Write the standard equation of the circle
with the given center (5,7) and r = 5
No.
4

12. The radius of a circle is
3√5 units and its center
is at (-2, 4).
Find the equation of the
circle.
(x+2)2+y2=45
A
(x+2)2+y2=9
B
x2+y2 =45
C
(x+2)2+(y-4)2=45
D
No.
5

13. The radius of a circle is 3√5 units
and its center is at (-2, 4).
Find the equation of the circle.
No.
5

14. What is the center of a circle
given the equation (x – 7)2 + y2
= 25?
(0,7)
A
(0,-
7)
B
(-
7,0)
C
(7,0)
D
No.
6

15. What is the radius of a
circle given the equation
x2 + y2 + 10x – 4y – 11
= 0?
40
A
4 10
B
2 10
C
-2 10
D
No.
7

16. What is the radius of a circle
given the equation x2 + y2 + 10x
– 4y – 11 = 0?
No.
7
r = h2 + k2 − c
r = (−5)2 + (2)2 −(−11)
r = 25 + 4 + 11
r = 40
r = 4(10)
r = 2 10

17. Permutation

18. There are 6 flavors of ice-
cream, and 3 different cones.
How many choices?
18
A
9
B
36
C
9
D
No.
8

19. Find the numbers that can be
formed from 1 to 7
if 4 numbers are taken at a
time.
420
A
840
B
28
C
49
D
No.
9

20. Find the numbers that can be
formed from 1 to 7
if 4 numbers are taken at a time.
No.
9
7 x 6 x 5 x 4
840

21. 20
A
10
B
7
C
15
D
No.
10
How many 2 – letter code
words can be formed from
the letters of the word
RATIO?

22. No.
10
How many 2 – letter code
words can be formed from
the letters of the word
RATIO?
5 x 4
20

23. There are 7 pupils who entered
a bus with only 3 empty seats.
In how many ways can these
pupils be seated?
18
A
105
B
42
C
210
D
No.
11

24. There are 7 pupils who entered
a bus with only 3 empty seats.
In how many ways can these
pupils be seated?
No.
11
7 x 6 x 5
210

25. Find the value of 3! – 2!.
2
A
5
B
4
C
6
D
No.
12

26. Find the value of 3! – 2!.
No.
12
(3 x 2 x 1)
3! - 2! = 6
3! - 2! = - (2 x 1)
- 2
3! - 2! = 4

27. 5,04
0
A
750
B
2,520
C
285
D
No.
13
Find the value of
10!
5!
3!

28. No.
13
Find the value of
10!
5!
3!

29. Find 10P3= ?
45
A
360
B
720
C
90
D
No.
14

30. Find 10P3= ?
No.
14
nPr =
𝒏!
𝒏−𝒓 !
10P3 =
𝟏𝟎!
𝟏𝟎−𝟑 !
10P3 =
𝟏𝟎!
𝟕 !
10P3 = 720
n = 10
r = 3
10P3 =
𝟏𝟎∙𝟗∙𝟖∙𝟕!
𝟕 !
10P3 = 𝟏𝟎 ∙ 𝟗 ∙ 𝟖

31. 120
A
20
B
12
C
30
D
No.
15
In how many ways can the
letter of the word
MASAYA?

32. No.
15
In how many ways can the
letter of the word
MASAYA?
P =
P =
P =
6!
3!
6 x 5 x 4 x 3!
120
P =
n!
a!
(3!)

33. In how many ways can 7
people
be seated at a round table?
60
A
72
B
720
C
120
D
No.
16

34. In how many ways can 7
people
be seated at a round table?
No.
16
(7 – 1)!
P =
6!
P =
(n – 1)!
P =
P = 720
P = 6 x 5 x 4 x 3 x 2 x 1
7

35. There are 3 identical green flags,
three identical white flags, and two
identical red flags. Using all eight
flags, How many signals can be
made?
140
A
1020
B
560
C
280
D
No.
17

36. There are 3 identical green
flags, three identical white flags,
and two identical red flags.
Using all eight flags, How many
signals can be made?
No.
17
8!
3!3!2!
= 560

37. Combination

38. 120
A
20
B
12
C
30
D
No.
18
In how many ways can a
committee of 7 be
selected from a class of 10
students?

39. No.
18
In how many ways can a committee of 7
be selected from a class of 10 students?
nCr =
𝒏!
𝒏−𝒓 !𝒓!
10C7=
𝟏𝟎!
𝟏𝟎−𝟕 !𝟕!
10C7 =
𝟏𝟎!
𝟑!𝟕!
10C7 =
𝟏𝟎⋅𝟗∙𝟖⋅𝟕!
𝟕!∙𝟑∙𝟐∙𝟏
10C7 = 120
n = 10
r = 7
3
10C7 =
𝟏𝟎∙𝟑⋅𝟒
𝟏
4

40. In how many ways can 5
finalists be chosen from 20
contestants?
5,50
4
A
15,25
B
15,504
C
504
D
No.
19

41. No.
18
In how many ways can 5 finalists be
chosen from 20 contestants?
nCr =
𝒏!
𝒏−𝒓 !𝒓!
20C5=
𝟐𝟎!
𝟐𝟎−𝟓 !𝟓!
20C5=
𝟐𝟎!
𝟏𝟓!𝟓!
20C5 =
𝟐𝟎⋅𝟏𝟗∙𝟏𝟖⋅𝟏𝟕∙𝟏𝟔∙𝟏𝟓!
𝟏𝟓!𝟓∙𝟒∙𝟑∙𝟐∙𝟏
20C5 = 15, 504
n = 20
r = 5
20C5 =
𝟏𝟗∙𝟑∙𝟏𝟕⋅𝟏𝟔
𝟏
3

42. 6
A
4
B
12
C
20
D
No.
20
In how many ways can 2 shake
toppings be selected from 4
toppings (pearl, nata, mallows
and jelly)?