The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio.
±1
±2
±3
±4
Correct answer is B
Tn=arn−1 (Exponential sequence)
T4=ar3=2....(1)
T6=ar5=8......(2)
Divide (2) by (1),
ar5ar3=82
r2=4
r=±2
5
6
7
8
Correct answer is A
(327x)(23)=(1229)
(3×2+2×37×2+x×3)=(1229)
⟹14+3x=29
3x=29−14=15
x=5
The inverse of a function is given by f−1:x→x+14.
f:x→4x−1
f:x→4x+1
f:x→4x−14
f:x→x−12
Correct answer is A
The inverse of the inverse of a function gives the function
i.e f−1(f−1(x))=f(x)
f−1(x)=x+14
Take y = x, so
f−1(y)=y+14
Let x=f−1(y),
x=y+14⟹4x=y+1
y=f(x)=4x−1
−34
−23
45
32
Correct answer is A
92x+1=813x+2
92x+1=(92)3x+2
92x+1=96x+4
Equating powers,
2x+1=6x+4⟹−3=4x
∴
A line is perpendicular to 3x - y + 11 = 0 and passes through the point (1, -5). Find its equation.
3y - x -14 = 0
3x + y + 1 = 0
3y + x + 1 = 0
3y + x + 14 = 0
Correct answer is D
3x - y + 11 = 0 \implies y = 3x + 11
Gradient = 3
Gradient of perpendicular line = \frac{-1}{3}
\therefore \frac{y - (-5)}{x - 1} = \frac{-1}{3}
3(y + 5) = 1 - x
3y + x + 15 - 1 = 3y + x + 14 = 0