e = 1
e = -1
e = -2
e = 0
Correct answer is D
Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0
What is the n-th term of the sequence 2, 6, 12, 20...?
4n - 2
2(3n - 1)
n2 + n
n2 + 3n + 2
Correct answer is C
Given that 2, 6, 12, 20...? the nth term = n\(^2\) + n
check: n = 1, u1 = 2
n = 2, u2 = 4 + 2 = 6
n = 3, u3 = 9 + 3 = 12
∴ n = 4, u4 = 16 + 4 = 20
The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles​
5x - 30
4x + 60
60 - x
3x + 61
Correct answer is C
Sum of all 4 angles of a quadrilateral = 360°
(5x-30) + (3x + 61) + (60-x) + (4x+ 60) = 360°
11x + 151 = 360°
11x = 360 - 151 = 209
x = 209/11 = 19°
Each angles is :
5x - 30 = 65°
4x+ 60 = 136°
60 - x =41°
3x + 61 = 118°
Smallest of these angles is 41°
Factorize m\(^3\) - m\(^2\) + 2m - 2
(m2 + 1)(m - 2)
(m - 1)(m + 1)(m + 2)
(m - 2)(m + 1)(m - 1)
(m2 + 2)(m - 1)
Correct answer is D
Using trial expansion of each option
(m\(^2\) + 2) (m - 1)
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x)
(x + 2)
2(x + 2)
(2x + 1)
(x2 + 4)
Correct answer is B
g(x) = x2 + 3x
When g(x + 1) = (x + 1)^2 + 3(x + 1)
= x\(^2\) + 1 + 2x + 3x + 3
= x\(^2\) + 5x + 4
g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x)
= x\(^2\) + 5x + 4 - x2 -3x
= 2x + 4 or 2(x + 4)
= 2(x + 2)