In what interval is the function f : x -> 2x - x\(^2\) increasing?
x = 1
x < 1
x > 1
0 < x < 1
Correct answer is C
2x - x\(^2\) > 0
0 > x\(^2\) - 2x
x\(^2\) - 2x < 0
x(x - 2) < 0
x > 1
-9
-6
15
21
Correct answer is C
f(x) = x\(^3\) + px + q
f(3) 3\(^2\) + 3pf + q = 6
f\(^{1}\)(x) = 2x + p
f\(^1\)(3) = 2(3) + p = 0
p = -6
from 9 + 3p + q = 6
9 + 3(-6) + q = 6
9 - 18 + q = 6
-9 + q = 6
Q = 6 + 9
= 15
Which of the following is not an equation of a circle?
3x\(^2\) +3y\(^2\) + 5x + 7y =5
x\(^2\) + y\(^2\) + 5x + 4y = 0
5x\(^2\) + 5y\(^2\) - 16 = 0
x\(^2\) - y\(^2\) + 3x - 5y = 2
Correct answer is D
No explanation has been provided for this answer.
In how many ways can the letters of the word MEMBER be arranged?
720
360
180
90
Correct answer is C
No. of ways = \(\frac{6!}{2!2!}\)
= \(\frac{6 \times 5 \times 4 \times 3 \times 2!}{2 \times 1 \times 2!}\)
= 180 ways
0.50 square units
0.51 square units
0.53 square units
0.54 square units
Correct answer is C
Area = \(\frac{1}{2} \times 1.33 \times 0.8\)
= 0.53 square unit